This paper presents an efficient scheme to locate multiple peaks on multi-modal optimization problems by
using genetic algorithms (GAs). The premature convergence problem shows due to the loss of diversity,
the multi-population technique can be applied to maintain the diversity in the population and the
convergence capacity of GAs. The proposed scheme is the combination of multi-population with adaptive
mutation operator, which determines two different mutation probabilities for different sites of the
solutions. The probabilities are updated by the fitness and distribution of solutions in the search space
during the evolution process. The experimental results demonstrate the performance of the proposed
algorithm based on a set of benchmark problems in comparison with relevant algorithms.
A Genetic Algorithm on Optimization Test FunctionsIJMERJOURNAL
ABSTRACT: Genetic Algorithms (GAs) have become increasingly useful over the years for solving combinatorial problems. Though they are generally accepted to be good performers among metaheuristic algorithms, most works have concentrated on the application of the GAs rather than the theoretical justifications. In this paper, we examine and justify the suitability of Genetic Algorithms in solving complex, multi-variable and multi-modal optimization problems. To achieve this, a simple Genetic Algorithm was used to solve four standard complicated optimization test functions, namely Rosenbrock, Schwefel, Rastrigin and Shubert functions. These functions are benchmarks to test the quality of an optimization procedure towards a global optimum. We show that the method has a quicker convergence to the global optima and that the optimal values for the Rosenbrock, Rastrigin, Schwefel and Shubert functions are zero (0), zero (0), -418.9829 and -14.5080 respectively
A Non-Revisiting Genetic Algorithm for Optimizing Numeric Multi-Dimensional F...ijcsa
Genetic Algorithm (GA) is a robust and popular stochastic optimization algorithm for large and complex search spaces. The major shortcomings of Genetic Algorithms are premature convergence and revisits to individual solutions in the search space. In other words, Genetic algorithm is a revisiting algorithm that escorts to duplicate function evaluations which is a clear wastage of time and computational resources. In this paper, a non-revisiting genetic algorithm with adaptive mutation is proposed for the domain of MultiDimensional numeric function optimization. In this algorithm whenever a revisit occurs, the underlined search point is replaced with a mutated version of the best/random (chosen probabilistically) individual from the GA population. Furthermore, the recommended approach is not using any extra memory resources to avoid revisits. To analyze the influence of the method, the proposed non-revisiting algorithm is evaluated using nine benchmarks functions with two and four dimensions. The performance of the proposed genetic algorithm is superior as contrasted to simple genetic algorithm as confirmed by the experimental results.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Engineering Research Publication
Best International Journals, High Impact Journals,
International Journal of Engineering & Technical Research
ISSN : 2321-0869 (O) 2454-4698 (P)
www.erpublication.org
An Heterogeneous Population-Based Genetic Algorithm for Data Clusteringijeei-iaes
As a primary data mining method for knowledge discovery, clustering is a technique of classifying a dataset into groups of similar objects. The most popular method for data clustering K-means suffers from the drawbacks of requiring the number of clusters and their initial centers, which should be provided by the user. In the literature, several methods have proposed in a form of k-means variants, genetic algorithms, or combinations between them for calculating the number of clusters and finding proper clusters centers. However, none of these solutions has provided satisfactory results and determining the number of clusters and the initial centers are still the main challenge in clustering processes. In this paper we present an approach to automatically generate such parameters to achieve optimal clusters using a modified genetic algorithm operating on varied individual structures and using a new crossover operator. Experimental results show that our modified genetic algorithm is a better efficient alternative to the existing approaches.
A Genetic Algorithm on Optimization Test FunctionsIJMERJOURNAL
ABSTRACT: Genetic Algorithms (GAs) have become increasingly useful over the years for solving combinatorial problems. Though they are generally accepted to be good performers among metaheuristic algorithms, most works have concentrated on the application of the GAs rather than the theoretical justifications. In this paper, we examine and justify the suitability of Genetic Algorithms in solving complex, multi-variable and multi-modal optimization problems. To achieve this, a simple Genetic Algorithm was used to solve four standard complicated optimization test functions, namely Rosenbrock, Schwefel, Rastrigin and Shubert functions. These functions are benchmarks to test the quality of an optimization procedure towards a global optimum. We show that the method has a quicker convergence to the global optima and that the optimal values for the Rosenbrock, Rastrigin, Schwefel and Shubert functions are zero (0), zero (0), -418.9829 and -14.5080 respectively
A Non-Revisiting Genetic Algorithm for Optimizing Numeric Multi-Dimensional F...ijcsa
Genetic Algorithm (GA) is a robust and popular stochastic optimization algorithm for large and complex search spaces. The major shortcomings of Genetic Algorithms are premature convergence and revisits to individual solutions in the search space. In other words, Genetic algorithm is a revisiting algorithm that escorts to duplicate function evaluations which is a clear wastage of time and computational resources. In this paper, a non-revisiting genetic algorithm with adaptive mutation is proposed for the domain of MultiDimensional numeric function optimization. In this algorithm whenever a revisit occurs, the underlined search point is replaced with a mutated version of the best/random (chosen probabilistically) individual from the GA population. Furthermore, the recommended approach is not using any extra memory resources to avoid revisits. To analyze the influence of the method, the proposed non-revisiting algorithm is evaluated using nine benchmarks functions with two and four dimensions. The performance of the proposed genetic algorithm is superior as contrasted to simple genetic algorithm as confirmed by the experimental results.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Engineering Research Publication
Best International Journals, High Impact Journals,
International Journal of Engineering & Technical Research
ISSN : 2321-0869 (O) 2454-4698 (P)
www.erpublication.org
An Heterogeneous Population-Based Genetic Algorithm for Data Clusteringijeei-iaes
As a primary data mining method for knowledge discovery, clustering is a technique of classifying a dataset into groups of similar objects. The most popular method for data clustering K-means suffers from the drawbacks of requiring the number of clusters and their initial centers, which should be provided by the user. In the literature, several methods have proposed in a form of k-means variants, genetic algorithms, or combinations between them for calculating the number of clusters and finding proper clusters centers. However, none of these solutions has provided satisfactory results and determining the number of clusters and the initial centers are still the main challenge in clustering processes. In this paper we present an approach to automatically generate such parameters to achieve optimal clusters using a modified genetic algorithm operating on varied individual structures and using a new crossover operator. Experimental results show that our modified genetic algorithm is a better efficient alternative to the existing approaches.
Classification accuracy analyses using Shannon’s EntropyIJERA Editor
There are many methods for determining the Classification Accuracy. In this paper significance of Entropy of
training signatures in Classification has been shown. Entropy of training signatures of the raw digital image
represents the heterogeneity of the brightness values of the pixels in different bands. This implies that an image
comprising a homogeneous lu/lc category will be associated with nearly the same reflectance values that would
result in the occurrence of a very low entropy value. On the other hand an image characterized by the
occurrence of diverse lu/lc categories will consist of largely differing reflectance values due to which the
entropy of such image would be relatively high. This concept leads to analyses of classification accuracy.
Although Entropy has been used many times in RS and GIS but its use in determination of classification
accuracy is new approach.
Particle Swarm Optimization based K-Prototype Clustering Algorithm iosrjce
IOSR Journal of Computer Engineering (IOSR-JCE) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of computer engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in computer technology. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Application of the analytic hierarchy process (AHP) for selection of forecast...Gurdal Ertek
In this paper, we described an application of the Analytic Hierarchy Process (AHP) for the ranking and selection of forecasting software. AHP is a multi-criteria decision making (MCDM) approach, which is based on the pair-wise comparison
of elements of a given set with respect to multiple criteria. Even though there are applications of the AHP to software selection problems, we have not encountered a study that involves forecasting software. We started our analysis by filtering
among forecasting software that were found on the Internet by undergraduate students as a part of a course project. Then we processed a second filtering step, where we reduced the number of software to be examined even further. Finally we
constructed the comparison matrices based upon the evaluations of three “semiexperts”, and obtained a ranking of forecasting software of the selected software using the Expert Choice software. We report our findings and our insights, together with the results of a sensitivity analysis.
http://research.sabanciuniv.edu.
Software Cost Estimation Using Clustering and Ranking SchemeEditor IJMTER
Software cost estimation is an important task in the software design and development process.
Planning and budgeting tasks are carried out with reference to the software cost values. A variety of
software properties are used in the cost estimation process. Hardware, products, technology and
methodology factors are used in the cost estimation process. The software cost estimation quality is
measured with reference to the accuracy levels.
Software cost estimation is carried out using three types of techniques. They are regression based
model, anology based model and machine learning model. Each model has a set of technique for the
software cost estimation process. 11 cost estimation techniques fewer than 3 different categories are
used in the system. The Attribute Relational File Format (ARFF) is used maintain the software product
property values. The ARFF file is used as the main input for the system.
The proposed system is designed to perform the clustering and ranking of software cost
estimation methods. Non overlapped clustering technique is enhanced with optimal centroid estimation
mechanism. The system improves the clustering and ranking process accuracy. The system produces
efficient ranking results on software cost estimation methods.
Several approaches are proposed to solve global numerical optimization problems. Most of researchers have experimented the robustness of their algorithms by generating the result based on minimization aspect. In this paper, we focus on maximization problems by using several hybrid chemical reaction optimization algorithms including orthogonal chemical reaction optimization (OCRO), hybrid algorithm based on particle swarm and chemical reaction optimization (HP-CRO), real-coded chemical reaction optimization (RCCRO) and hybrid mutation chemical reaction optimization algorithm (MCRO), which showed success in minimization. The aim of this paper is to demonstrate that the approaches inspired by chemical reaction optimization are not only limited to minimization, but also are suitable for maximization. Moreover, experiment comparison related to other maximization algorithms is presented and discussed.
Predicting an Applicant Status Using Principal Component, Discriminant and Lo...inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
One of the obstacles that hinder the usage of mutation testing is its impracticality, two main contributors of this are a large number of mutants and a large number of test cases involves in the process. Researcher usually tries to address this problem by optimizing the mutants and the test case separately. In this research, we try to tackle both of optimizing mutant and optimizing test-case simultaneousl y using a coevolution optimization method. The coevolution optimization method is chosen for the mutation testing problem because the method works by optimizing multiple collections (population) of a solution. This research found that coevolution is better suited for multiproblem optimization than other single population methods (i.e. Genetic Algorithm), we also propose new indicator to determine the optimal coevolution cycle. The experiment is done to the artificial case, laboratory, and also a real case.
Methodology of thesis 'research barriers in the implementation of reverse log...Irfan iftekhar
These are the barriers in the implementation of reverse logistics due to lack of interest and knowledge of top decision makers of the organizations. Besides when an entity's organizational capabilities are strong, it can progress smoothly, but when they are weak it can find it difficult to get the job done, making errors due to underestimating the problems. An organization's capability is its ability which can win over the barriers in the implementation of RL practices. This consists of the strategy of a company, its strategic plans, its commitment, employees' hiring and skills development, a working system of performance appraisal and supporting programs.
Patterns that only occur in objects belonging to a
single class are called Jumping Emerging Patterns (JEP). JEP
based Classifiers are considered one of the successful classification
systems. Due to its comprehensibility, simplicity and strong
differentiating abilities JEPs have captured significant recognition.
However, discovery of JEPs in a large pattern space is normally a
time consuming and challenging task because of their exponential
behaviour. In this work a novel method based on genetic
algorithm (GA) is proposed to discover JEPs in large pattern
space. Since the complexity of GA is lower than other algorithms,
so we have combined the power of JEPs and GA to find high
quality JEPs from datasets to improve performance of
classification system. Our proposed method explores a set of high
quality JEPs from pattern search space unlike other methods in
literature that compute complete set of JEPs, Large numbers of
duplicate and redundant JEPs are filtered out during their
discovery process. Experimental results show that our proposed
Genetic-JEPs are effective and accurate for classification of a
variety of data sets and in general achieve higher accuracy than
other standard classifiers.
A BENCHMARK MODEL FOR INTERNAL ASSESSMENT OF INDUSTRY USING FUZZY TOPSIS APPR...ijmech
Internal assessment is one of the most important factor of an industry, needs appropriate improvement
planning between the departments with development of Benchmark model among them. The proposed study
applies Fuzzy Technique for Order Preference by Similarity to Ideal Solution to rank different alternatives.
The preliminary results indicate that the proposed model is capable of determining appropriate
competition between departments which are Human Resource, Finance, Production, Quality Assurance. To
remove the subjectivity, the linguistic data about the attributes is converted into a crisp score by using
fuzzy numbers and then the different alternatives are evaluated based on attributes by TOPSIS approach to
find the best alternative according to the industry’s requirement. Thus the endeavor has been made by the
authors to give a simple model for the evaluation of internal assessment of an industry
Selection of Equipment by Using Saw and Vikor Methods IJERA Editor
Now a days, Lean manufacturing becomes a key strategy for global competition. In this environment the most important process is the selection of the equipment. Equipment selection is a very important issue for effective manufacturing companies due to the fact that improperly selected machines can negatively affect the overall performance of manufacturing system. The availability of large number of equipments are more hence, the selection of suitable equipment for certain operation/ product becomes difficult. On the other hand selecting the best equipment among many alternatives is a Multi-criteria decision making ( MCDM ) Problems. In this Paper an approach which employs SAW, VIKOR Methods proposed for the equipment selection problem. The SAW and VIKOR is used to analyze the structure of the equipment selection problem and to determine weights of criteria and to obtain Final Ranking
Applying the big bang-big crunch metaheuristic to large-sized operational pro...IJECEIAES
In this study, we present an investigation of comparing the capability of a big bang-big crunch metaheuristic (BBBC) for managing operational problems including combinatorial optimization problems. The BBBC is a product of the evolution theory of the universe in physics and astronomy. Two main phases of BBBC are the big bang and the big crunch. The big bang phase involves the creation of a population of random initial solutions, while in the big crunch phase these solutions are shrunk into one elite solution exhibited by a mass center. This study looks into the BBBC’s effectiveness in assignment and scheduling problems. Where it was enhanced by incorporating an elite pool of diverse and high quality solutions; a simple descent heuristic as a local search method; implicit recombination; Euclidean distance; dynamic population size; and elitism strategies. Those strategies provide a balanced search of diverse and good quality population. The investigation is conducted by comparing the proposed BBBC with similar metaheuristics. The BBBC is tested on three different classes of combinatorial optimization problems; namely, quadratic assignment, bin packing, and job shop scheduling problems. Where the incorporated strategies have a greater impact on the BBBC's performance. Experiments showed that the BBBC maintains a good balance between diversity and quality which produces high-quality solutions, and outperforms other identical metaheuristics (e.g. swarm intelligence and evolutionary algorithms) reported in the literature.
Issues in Query Processing and OptimizationEditor IJMTER
The paper identifies the various issues in query processing and optimization while
choosing the best database plan. It is unlike preceding query optimization techniques that uses only a
single approach for identifying best query plan by extracting data from database. Our approach takes
into account various phases of query processing and optimization, heuristic estimation techniques
and cost function for identifying the best execution plan. A review report on various phases of query
processing, goals of optimizer, various rules for heuristic optimization and cost components involved
are presented in this paper.
4313ijmvsc02A FUZZY AHP APPROACH FOR SUPPLIER SELECTION PROBLEM: A CASE STUDY...ijmvsc
Supplier selection is one of the most important functions of a purchasing department. Since by deciding the best supplier, companies can save material costs and increase competitive advantage. However this decision becomes complicated in case of multiple suppliers, multiple conflicting criteria, and imprecise parameters. In addition the uncertainty and vagueness of the experts’ opinion is the prominent characteristic of the problem. Therefore an extensively used multi criteria decision making tool Fuzzy AHP can be utilized as an approach for supplier selection problem. This paper reveals the application of Fuzzy AHP in a gear motor company determining the best supplier with respect to selected criteria. The contribution of this study is not only the application of the Fuzzy AHP methodology for supplier selection problem, but also releasing a comprehensive literature review of multi criteria decision making problems. In addition by stating the steps of Fuzzy AHP clearly and numerically, this study can be a guide of the methodology to be implemented to other multiple criteria decision making problems.
Classification accuracy analyses using Shannon’s EntropyIJERA Editor
There are many methods for determining the Classification Accuracy. In this paper significance of Entropy of
training signatures in Classification has been shown. Entropy of training signatures of the raw digital image
represents the heterogeneity of the brightness values of the pixels in different bands. This implies that an image
comprising a homogeneous lu/lc category will be associated with nearly the same reflectance values that would
result in the occurrence of a very low entropy value. On the other hand an image characterized by the
occurrence of diverse lu/lc categories will consist of largely differing reflectance values due to which the
entropy of such image would be relatively high. This concept leads to analyses of classification accuracy.
Although Entropy has been used many times in RS and GIS but its use in determination of classification
accuracy is new approach.
Particle Swarm Optimization based K-Prototype Clustering Algorithm iosrjce
IOSR Journal of Computer Engineering (IOSR-JCE) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of computer engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in computer technology. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Application of the analytic hierarchy process (AHP) for selection of forecast...Gurdal Ertek
In this paper, we described an application of the Analytic Hierarchy Process (AHP) for the ranking and selection of forecasting software. AHP is a multi-criteria decision making (MCDM) approach, which is based on the pair-wise comparison
of elements of a given set with respect to multiple criteria. Even though there are applications of the AHP to software selection problems, we have not encountered a study that involves forecasting software. We started our analysis by filtering
among forecasting software that were found on the Internet by undergraduate students as a part of a course project. Then we processed a second filtering step, where we reduced the number of software to be examined even further. Finally we
constructed the comparison matrices based upon the evaluations of three “semiexperts”, and obtained a ranking of forecasting software of the selected software using the Expert Choice software. We report our findings and our insights, together with the results of a sensitivity analysis.
http://research.sabanciuniv.edu.
Software Cost Estimation Using Clustering and Ranking SchemeEditor IJMTER
Software cost estimation is an important task in the software design and development process.
Planning and budgeting tasks are carried out with reference to the software cost values. A variety of
software properties are used in the cost estimation process. Hardware, products, technology and
methodology factors are used in the cost estimation process. The software cost estimation quality is
measured with reference to the accuracy levels.
Software cost estimation is carried out using three types of techniques. They are regression based
model, anology based model and machine learning model. Each model has a set of technique for the
software cost estimation process. 11 cost estimation techniques fewer than 3 different categories are
used in the system. The Attribute Relational File Format (ARFF) is used maintain the software product
property values. The ARFF file is used as the main input for the system.
The proposed system is designed to perform the clustering and ranking of software cost
estimation methods. Non overlapped clustering technique is enhanced with optimal centroid estimation
mechanism. The system improves the clustering and ranking process accuracy. The system produces
efficient ranking results on software cost estimation methods.
Several approaches are proposed to solve global numerical optimization problems. Most of researchers have experimented the robustness of their algorithms by generating the result based on minimization aspect. In this paper, we focus on maximization problems by using several hybrid chemical reaction optimization algorithms including orthogonal chemical reaction optimization (OCRO), hybrid algorithm based on particle swarm and chemical reaction optimization (HP-CRO), real-coded chemical reaction optimization (RCCRO) and hybrid mutation chemical reaction optimization algorithm (MCRO), which showed success in minimization. The aim of this paper is to demonstrate that the approaches inspired by chemical reaction optimization are not only limited to minimization, but also are suitable for maximization. Moreover, experiment comparison related to other maximization algorithms is presented and discussed.
Predicting an Applicant Status Using Principal Component, Discriminant and Lo...inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
One of the obstacles that hinder the usage of mutation testing is its impracticality, two main contributors of this are a large number of mutants and a large number of test cases involves in the process. Researcher usually tries to address this problem by optimizing the mutants and the test case separately. In this research, we try to tackle both of optimizing mutant and optimizing test-case simultaneousl y using a coevolution optimization method. The coevolution optimization method is chosen for the mutation testing problem because the method works by optimizing multiple collections (population) of a solution. This research found that coevolution is better suited for multiproblem optimization than other single population methods (i.e. Genetic Algorithm), we also propose new indicator to determine the optimal coevolution cycle. The experiment is done to the artificial case, laboratory, and also a real case.
Methodology of thesis 'research barriers in the implementation of reverse log...Irfan iftekhar
These are the barriers in the implementation of reverse logistics due to lack of interest and knowledge of top decision makers of the organizations. Besides when an entity's organizational capabilities are strong, it can progress smoothly, but when they are weak it can find it difficult to get the job done, making errors due to underestimating the problems. An organization's capability is its ability which can win over the barriers in the implementation of RL practices. This consists of the strategy of a company, its strategic plans, its commitment, employees' hiring and skills development, a working system of performance appraisal and supporting programs.
Patterns that only occur in objects belonging to a
single class are called Jumping Emerging Patterns (JEP). JEP
based Classifiers are considered one of the successful classification
systems. Due to its comprehensibility, simplicity and strong
differentiating abilities JEPs have captured significant recognition.
However, discovery of JEPs in a large pattern space is normally a
time consuming and challenging task because of their exponential
behaviour. In this work a novel method based on genetic
algorithm (GA) is proposed to discover JEPs in large pattern
space. Since the complexity of GA is lower than other algorithms,
so we have combined the power of JEPs and GA to find high
quality JEPs from datasets to improve performance of
classification system. Our proposed method explores a set of high
quality JEPs from pattern search space unlike other methods in
literature that compute complete set of JEPs, Large numbers of
duplicate and redundant JEPs are filtered out during their
discovery process. Experimental results show that our proposed
Genetic-JEPs are effective and accurate for classification of a
variety of data sets and in general achieve higher accuracy than
other standard classifiers.
A BENCHMARK MODEL FOR INTERNAL ASSESSMENT OF INDUSTRY USING FUZZY TOPSIS APPR...ijmech
Internal assessment is one of the most important factor of an industry, needs appropriate improvement
planning between the departments with development of Benchmark model among them. The proposed study
applies Fuzzy Technique for Order Preference by Similarity to Ideal Solution to rank different alternatives.
The preliminary results indicate that the proposed model is capable of determining appropriate
competition between departments which are Human Resource, Finance, Production, Quality Assurance. To
remove the subjectivity, the linguistic data about the attributes is converted into a crisp score by using
fuzzy numbers and then the different alternatives are evaluated based on attributes by TOPSIS approach to
find the best alternative according to the industry’s requirement. Thus the endeavor has been made by the
authors to give a simple model for the evaluation of internal assessment of an industry
Selection of Equipment by Using Saw and Vikor Methods IJERA Editor
Now a days, Lean manufacturing becomes a key strategy for global competition. In this environment the most important process is the selection of the equipment. Equipment selection is a very important issue for effective manufacturing companies due to the fact that improperly selected machines can negatively affect the overall performance of manufacturing system. The availability of large number of equipments are more hence, the selection of suitable equipment for certain operation/ product becomes difficult. On the other hand selecting the best equipment among many alternatives is a Multi-criteria decision making ( MCDM ) Problems. In this Paper an approach which employs SAW, VIKOR Methods proposed for the equipment selection problem. The SAW and VIKOR is used to analyze the structure of the equipment selection problem and to determine weights of criteria and to obtain Final Ranking
Applying the big bang-big crunch metaheuristic to large-sized operational pro...IJECEIAES
In this study, we present an investigation of comparing the capability of a big bang-big crunch metaheuristic (BBBC) for managing operational problems including combinatorial optimization problems. The BBBC is a product of the evolution theory of the universe in physics and astronomy. Two main phases of BBBC are the big bang and the big crunch. The big bang phase involves the creation of a population of random initial solutions, while in the big crunch phase these solutions are shrunk into one elite solution exhibited by a mass center. This study looks into the BBBC’s effectiveness in assignment and scheduling problems. Where it was enhanced by incorporating an elite pool of diverse and high quality solutions; a simple descent heuristic as a local search method; implicit recombination; Euclidean distance; dynamic population size; and elitism strategies. Those strategies provide a balanced search of diverse and good quality population. The investigation is conducted by comparing the proposed BBBC with similar metaheuristics. The BBBC is tested on three different classes of combinatorial optimization problems; namely, quadratic assignment, bin packing, and job shop scheduling problems. Where the incorporated strategies have a greater impact on the BBBC's performance. Experiments showed that the BBBC maintains a good balance between diversity and quality which produces high-quality solutions, and outperforms other identical metaheuristics (e.g. swarm intelligence and evolutionary algorithms) reported in the literature.
Issues in Query Processing and OptimizationEditor IJMTER
The paper identifies the various issues in query processing and optimization while
choosing the best database plan. It is unlike preceding query optimization techniques that uses only a
single approach for identifying best query plan by extracting data from database. Our approach takes
into account various phases of query processing and optimization, heuristic estimation techniques
and cost function for identifying the best execution plan. A review report on various phases of query
processing, goals of optimizer, various rules for heuristic optimization and cost components involved
are presented in this paper.
4313ijmvsc02A FUZZY AHP APPROACH FOR SUPPLIER SELECTION PROBLEM: A CASE STUDY...ijmvsc
Supplier selection is one of the most important functions of a purchasing department. Since by deciding the best supplier, companies can save material costs and increase competitive advantage. However this decision becomes complicated in case of multiple suppliers, multiple conflicting criteria, and imprecise parameters. In addition the uncertainty and vagueness of the experts’ opinion is the prominent characteristic of the problem. Therefore an extensively used multi criteria decision making tool Fuzzy AHP can be utilized as an approach for supplier selection problem. This paper reveals the application of Fuzzy AHP in a gear motor company determining the best supplier with respect to selected criteria. The contribution of this study is not only the application of the Fuzzy AHP methodology for supplier selection problem, but also releasing a comprehensive literature review of multi criteria decision making problems. In addition by stating the steps of Fuzzy AHP clearly and numerically, this study can be a guide of the methodology to be implemented to other multiple criteria decision making problems.
This paper presents a set of methods that uses a genetic algorithm for automatic test-data generation in
software testing. For several years researchers have proposed several methods for generating test data
which had different drawbacks. In this paper, we have presented various Genetic Algorithm (GA) based test
methods which will be having different parameters to automate the structural-oriented test data generation
on the basis of internal program structure. The factors discovered are used in evaluating the fitness
function of Genetic algorithm for selecting the best possible Test method. These methods take the test
populations as an input and then evaluate the test cases for that program. This integration will help in
improving the overall performance of genetic algorithm in search space exploration and exploitation fields
with better convergence rate.
COMPARISON BETWEEN THE GENETIC ALGORITHMS OPTIMIZATION AND PARTICLE SWARM OPT...IAEME Publication
Close range photogrammetry network design is referred to the process of placing a set of
cameras in order to achieve photogrammetric tasks. The main objective of this paper is tried to find
the best location of two/three camera stations. The genetic algorithm optimization and Particle
Swarm Optimization are developed to determine the optimal camera stations for computing the three
dimensional coordinates. In this research, a mathematical model representing the genetic algorithm
optimization and Particle Swarm Optimization for the close range photogrammetry network is
developed. This paper gives also the sequence of the field operations and computational steps for this
task. A test field is included to reinforce the theoretical aspects.
In recent years, consumers and legislation have been pushing companies to optimize their activities in such a way as to reduce negative environmental and social impacts more and more. In the other side, companies
must keep their total supply chain costs as low as possible to remain competitive.This work aims to develop a model to traveling salesman problem including environmental impacts and to identify, as far as possible, the contribution of genetic operator’s tuning and setting in the success and
efficiency of genetic algorithms for solving this problem with consideration of CO2 emission due to transport. This efficiency is calculated in terms of CPU time consumption and convergence of the solution. The best transportation policy is determined by finding a balance between financial and environmental
criteria.Empirically, we have demonstrated that the performance of the genetic algorithm undergo relevant
improvements during some combinations of parameters and operators which we present in our results part.
Dynamic Radius Species Conserving Genetic Algorithm for Test Generation for S...ijseajournal
This paper critically examined nine different software models for modeling / developing multi-agent based
systems. The study revealed that the different models examined have their various advantages /
disadvantages and uniqueness in terms of practical development/deployment of the multi-agent based
information system in question. The agentology model is one methodology that can be easily adopted or
adapted for the development of any multi-agent based software prototype because it was inspired by the
best practices and good ideas contained in other agent oriented methodologies like CoMoMas, MASE,
GAIA, Prometheus, HIM, MASim and Tropos.
Performance Analysis of Genetic Algorithm as a Stochastic Optimization Tool i...paperpublications3
Abstract: Engineering design problems are complex by nature because of their critical objective functions involving many variables and Constraints. Engineers have to ensure the compatibility with the imposed specifications keeping the manufacturing costs low. Moreover, the methodology may vary according to the design problem.
The main issue is to choose the proper tool for optimization. In the earlier days, a design problem was optimized by some of the conventional optimization techniques like gradient Search, evolutionary optimization, random search etc. These are known as classical methods.
The method is to be properly Chosen depending on the nature of the problem- an incorrect choice may sometimes fail to give the optimal solution. So the methods are less robust.
Now-a-days soft-computing techniques are being widely used for optimizing a function. These are more robust. Genetic algorithm is one such method. It is an effective tool in the realm of stochastic optimization (non-classical). The algorithm produces many strings and generation to reach the optimal point.
The main objective of the paper is to optimize engineering design problems using Genetic Algorithm and to analyze how the algorithm reaches the optima effectively and closely. We choose a mathematical expression for the objective function in terms of the design variables and optimize the same under given constraints using GA.
BINARY SINE COSINE ALGORITHMS FOR FEATURE SELECTION FROM MEDICAL DATAijejournal
A well-constructed classification model highly depends on input feature subsets from a dataset, which may contain redundant, irrelevant, or noisy features. This challenge can be worse while dealing with medical datasets. The main aim of feature selection as a pre-processing task is to eliminate these features and select the most effective ones. In the literature, metaheuristic algorithms show a successful performance to find optimal feature subsets. In this paper, two binary metaheuristic algorithms named S-shaped binary Sine Cosine Algorithm (SBSCA) and V-shaped binary Sine Cosine Algorithm (VBSCA) are proposed for feature selection from the medical data. In these algorithms, the search space remains continuous, while a binary position vector is generated by two transfer functions S-shaped and V-shaped for each solution. The proposed algorithms are compared with four latest binary optimization algorithms over five medical datasets from the UCI repository. The experimental results confirm that using both bSCA variants enhance the accuracy of classification on these medical datasets compared to four other algorithms.
BINARY SINE COSINE ALGORITHMS FOR FEATURE SELECTION FROM MEDICAL DATAacijjournal
A well-constructed classification model highly depends on input feature subsets from a dataset, which may contain redundant, irrelevant, or noisy features. This challenge can be worse while dealing with medical datasets. The main aim of feature selection as a pre-processing task is to eliminate these features and select the most effective ones. In the literature, metaheuristic algorithms show a successful performance to find optimal feature subsets. In this paper, two binary metaheuristic algorithms named S-shaped binary Sine Cosine Algorithm (SBSCA) and V-shaped binary Sine Cosine Algorithm (VBSCA) are proposed for feature selection from the medical data. In these algorithms, the search space remains continuous, while a binary position vector is generated by two transfer functions S-shaped and V-shaped for each solution. The proposed algorithms are compared with four latest binary optimization algorithms over five medical datasets from the UCI repository. The experimental results confirm that using both bSCA variants enhance the accuracy of classification on these medical datasets compared to four other algorithms.
Improving the effectiveness of information retrieval system using adaptive ge...ijcsit
Traditional Genetic Algorithm which is used in previous studies depends on fixed control parameters
especially crossover and mutation probabilities, but in this research we tried to use adaptive genetic
algorithm.
Genetic algorithm started to be applied in information retrieval system in order to optimize the query by
genetic algorithm, a good query is a set of terms that express accurately the information need while being
usable within collection corpus, the last part of this specification is critical for the matching process to be
efficient, that is why most research efforts are actually put toward the query improvement.
We investigated the use of adaptive genetic algorithm (AGA) under vector space model, Extended Boolean
model, and Language model in information retrieval (IR), the algorithm used crossover and mutation
operators with variable probability, where a traditional genetic algorithm (GA) uses fixed values of those,
and remain unchanged during execution. GA is developed to support adaptive adjustment of mutation and
crossover probability; this allows faster attainment of better solutions. The paper has been tested using
242 Arabic abstracts collected from the proceedings of the Saudi Arabian National conference.
The potential role of ai in the minimisation and mitigation of project delayPieter Rautenbach
Artificial intelligence (AI) can have wide reaching application within the construction
industry, however, the actual application of this set of technologies is currently under exploited. This
paper considers the role that the application of AI can take in optimising the efficiencies of project
execution and how this can potentially reduce project duration and minimise and mitigate delay on
projects.
A MULTI-POPULATION BASED FROG-MEMETIC ALGORITHM FOR JOB SHOP SCHEDULING PROBLEMacijjournal
The Job Shop Scheduling Problem (JSSP) is a well known practical planning problem in the
manufacturing sector. We have considered the JSSP with an objective of minimizing makespan. In this
paper, we develop a three-stage hybrid approach called JSFMA to solve the JSSP. In JSFMA,
considering a method similar to Shuffled Frog Leaping algorithm we divide the population in several sub
populations and then solve the problem using a Memetic algorithm. The proposed approach have been
compared with other algorithms for the Job Shop Scheduling and evaluated with satisfactory results on a
set of the JSSP instances derived from classical Job Shop Scheduling benchmarks. We have solved 20
benchmark problems from Lawrence’s datasets and compared the results obtained with the results of the
algorithms established in the literature. The experimental results show that JSFMA could gain the best
known makespan in 17 out of 20 problems.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
List the problems that can be efficiently solved by Evolutionary P.pdfinfomalad
List the problems that can be efficiently solved by Evolutionary Programming?
List the problems that can be efficiently solved by Evolutionary Programming?
Solution
Evolutionary Programming is a Global Optimization algorithm and is an instance of an
Evolutionary Algorithm from the field of Evolutionary Computation. The approach is a sibling
of other Evolutionary Algorithms such as the Genetic Algorithm, and Learning Classifier
Systems. It is sometimes confused with Genetic Programming given the similarity in name, and
more recently it shows a strong functional similarity to Evolution Strategies.
Inspiration
Evolutionary Programming is inspired by the theory of evolution by means of natural selection.
Specifically, the technique is inspired by macro-level or the species-level process of evolution
(phenotype, hereditary, variation) and is not concerned with the genetic mechanisms of evolution
(genome, chromosomes, genes, alleles).
Metaphor
A population of a species reproduce, creating progeny with small phenotypical variation. The
progeny and the parents compete based on their suitability to the environment, where the
generally more fit members constitute the subsequent generation and are provided with the
opportunity to reproduce themselves. This process repeats, improving the adaptive fit between
the species and the environment.
Strategy
The objective of the Evolutionary Programming algorithm is to maximize the suitability of a
collection of candidate solutions in the context of an objective function from the domain. This
objective is pursued by using an adaptive model with surrogates for the processes of evolution,
specifically hereditary (reproduction with variation) under competition. The representation used
for candidate solutions is directly assessable by a cost or objective function from the domain.
Problems for evolutionary algorithms
Evolutionary programming are useful for problems for which no mechanistic method is available
– or when unreasonable assumptions need to be made. Problems for which you cannot calculate
or derive a solution. Problems for which you have to find a solution.
Aspects of problems that lend them to Evolutionary Programming solution include:
Assignment of individuals into groups, wherever simple ranking and truncation will not work.
This usually involves interactions, whereby whether an individual should be in a group depends
on what other individuals will be in that group. Example: developing multiplex groupings for
genotyping.
Problems where thresholds are involved, for example when the value of a solution depends on
whether certain thresholds have been passed, or the fate of an individual depends on passing one
or more thresholds. Example: Supply chain optimizing to target multiple product end-points
and/or turnoff dates.
Combinatorially tedious problems, where many combinations of components can exist. Example:
The setting up of animal matings. Below are the few applications:
Learning classifier systems, or .
Similar to Multi-Population Methods with Adaptive Mutation for Multi-Modal Optimization Problems (20)
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
Here is something new! In our next Connector Corner webinar, we will demonstrate how you can use a single workflow to:
Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
But there’s more:
In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
And...
Speakers:
Akshay Agnihotri, Product Manager
Charlie Greenberg, Host
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
Smart TV Buyer Insights Survey 2024 by 91mobiles.pdf91mobiles
91mobiles recently conducted a Smart TV Buyer Insights Survey in which we asked over 3,000 respondents about the TV they own, aspects they look at on a new TV, and their TV buying preferences.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024
Multi-Population Methods with Adaptive Mutation for Multi-Modal Optimization Problems
1. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
DOI : 10.5121/ijscai.2013.2201 1
Multi-Population Methods with Adaptive
Mutation for Multi-Modal Optimization Problems
Imtiaz Korejo1
, Shengxiang Yang2
(IEEE Member), Kamran Brohi3
, Z.U.A.
Khuhro4
1
Institute of Mathematics & Computer Science, University of Sindh, Jamshoro,
Pakistan
cskorejo@gmail.com
2
School of Computer Science and Informatics, De Montfort University, Leicester,
United Kingdom
syang@dmu.ac.uk
ABSTRACT
This paper presents an efficient scheme to locate multiple peaks on multi-modal optimization problems by
using genetic algorithms (GAs). The premature convergence problem shows due to the loss of diversity,
the multi-population technique can be applied to maintain the diversity in the population and the
convergence capacity of GAs. The proposed scheme is the combination of multi-population with adaptive
mutation operator, which determines two different mutation probabilities for different sites of the
solutions. The probabilities are updated by the fitness and distribution of solutions in the search space
during the evolution process. The experimental results demonstrate the performance of the proposed
algorithm based on a set of benchmark problems in comparison with relevant algorithms.
KEYWORDS
Multi-population approaches, adaptive mutation operator, multi-modal function optimization, genetic
algorithms.
1. INTRODUCTION
Genetic algorithms (GAs) are adaptive heuristic search techniques inspired by genetic
inheritance and natural evolution of species. Over the years, GAs have been successfully used
for solving many optimization problems due to the properties of easy-to-use and robustness for
determining candidate solution for ambitious problems. There are a lot of applications of GAs in
different areas of real world problems, such as science, engineering, business, and social
science. The interested reader may wish to consult [11]. The basic concept of GAs was
introduced by John Holland in the 1960s in the USA. There are different components of GAs,
such as the encoding scheme, the population size, the selection approaches, the crossover and
mutation operators; the performance of GAs depends on good choice of operators and relevant
parameters. However, it is difficult to choose proper operators and relevant parameters for the
optimal performance. A limited amount of research has been done on GAs to find multiple
optima for multi-modal optimization problems. However, the implicit parallism of GAs is able
to find several optima (or multiple optima including global and local optima) in the search space
instead of just a single solution. Recently, researchers have shown a great interest in optimizing
multimodal functions with GAs. Several GA techniques have been proposed to optimize multi-
modal problems.
In recent years, various techniques have been suggested into standard evolutionary
algorithms (EAs) to divide the population proposed to optimize multi-modal problems. In recent
years, various techniques have been suggested into standard evolutionary algorithms (EAs) to
divide the population into different sub-populations, including k-means clustering algorithm
[16], self-organizing scouts (SOS) [5], multinational GAs [38], clustering scheme [27], niching
2. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
2
method [28], and a hierarchical clustering [46]. These techniques have considered sub-
populations as a means of increasing the diversity of GAs. The main motivation behind these
schemes is to maintain multiple populations on different peaks, the highest peak in the search
space is the global optimum and other peaks with a lower height than the global optimum are
local optima.
There are different schemes for controlling the values of relevant parameters and
genetic operators of an EA. Parameter control or adaptive adaptation techniques can be
classified into three categories: deterministic adaptation, adaptive adaptation, and self-adaptive
adaptation approaches. Deterministic adaptation adjusts the values of parameter according to
some deterministic rule without using any feedback information from the search space. The
strategy variables are modified by using the feedback information from the search space. This is
called adaptive adaptation. The best example of this type of adaptive adaptations is
Rechenberg’s “success rule” in evolutionary strategies (ESs) [31] (p. 110). In the case of self-
adaptive adaptation, parameters are altered by EAs themselves. Strategy parameters to be
altered are encoded into chromosomes and undergo variation with the rest of the chromosome.
The self-adaptive adaptation was proposed by Back and Schlutz [3] into GAs.
In this paper, a new multi-population with adaptive mutation operator is proposed for
GAs. Two different multi-population approaches are considered in this study, one is species
with adaptive mutation (SWAM) and another is basin with adaptive mutation (BWAM). The
proposed technique can maintain the exploration and exploitation in the evolution process,
which can be considered into the category of adaptive adaptation EAs. This paper gives the
comparison of several adaptive mutation operators, including adaptive GA, self-adaptive GA,
and site-specific rate GA with our proposed technique. The experimental results demonstrate,
the proposed algorithm exhibits better performance in terms of the quality of candidate solutions
found on the benchmark problems.
The rest of this paper is outlined as follows. Section 2 explains related work, the
classification of adaptation in EAs, and some sub-population approaches. Section 3 presents the
SWAM and BWAM adaptive mutation operators in detail. Section 4 describes the experimental
study of comparing our proposed techniques with other algorithms. Finally, conclusion and
discussions on further directions of research are stated in Section 5.
2. RELATED RESEARCH
Generally speaking, a lot of research has been done on selecting appropriate genetic
operators and relevant parameters for GAs to find optimal or near-optimal solutions. Usually,
these genetic operators and relevant parameters are fixed before the execution of GAs. For
example, some constant mutation probabilities are derived from experience or by trial-and-error.
It is very difficult, if not impossible, to find suitable parameter setting for the optimal
performance of GAs. Different values of parameters and operators might be optimal at different
levels of the evolutionary process. Due to this reason, researchers are turning to adaptive
operators and parameters for GAs to find the optimal results.
2.1. Adaptation in GAs
The main motivation of adapting a GA is to adjust genetic operators and relevant
parameters in order to find better solutions of a problem. Adaptation in GAs is one of the most
important and promising research areas. The efficiency of GAs is dependent on not only the
algorithms, representation, and operators for the problem, but the set of the parameter values for
GAs to find a good solution. There are different methods for controlling the values of various
parameters and genetic operators of GAs. Generally, there are two classification schemes [1],
[8], [9]. The classification of adaptation based on these two distinct schemes are explained as
follows:
1) Type of adaptation: the type of adaptation means how a parameter is modified.
3. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
3
2) Level of adaptation: the level of adaptation means where changes occur.
The above classification schemes were first introduced by Angeline in [1]. According to
Angeline, the type of adaptation is further divided into absolute update rules and empirical
update rules. The level of adaptation is also further classified into three levels, i.e., population
level, individual level, and component level. In [8], [9], the authors extended the classification
schemes and broadened the idea introduced by Angeline in [1]. They further classified the type
of adaptation in two subfields: parameter tuning and parameter control. This is bases on the
technique of adaptation applied in the process. It is explained as follows
1) Parameter Tuning or Static Adaptation: Parameter tuning (or static adaptation) means
to set the suitable parameters before the run of EAs and they remain constant during the
execution of EAs. In other words, no change in the parameters occurs. Static adaptation is done
by an external process (e.g., a person or a program) for selecting appropriate values. Many
researchers have suggested different static appropriate values for key parameters of GAs. These
values are derived from experiences or by trial-and-error methods. In [18], De Jong proposed
static single-point crossover and mutation probabilities for finding a good solution for problems
using a traditional GA. Some other researchers also suggested well known heuristics with other
static parameters for finding a good solution for problems [2], [11], [30], [25], [23], [24]. The
different values of parameters and operators might be optimal at different levels of the
evolutionary process. Due to this reason, static adaptation (parameter tuning) is gradually
discouraged in the EA community. So, there is no common optimal parameter setting that can
be found a prior (consult to No Free Lunch Theorem [42]). According to this problem,
researchers diverted their attention towards adaptive adaptation (parameter control) methods.
2) Parameter Control or Adaptive Adaptation: Strategy parameters are adjusted on the
basis of various methods during the execution of EAs. This class of adaptation can be further
divided into three classes, described as deterministic adaptation, adaptive adaptation, and self-
adaptive adaptation. Deterministic adaptation adjusts the values of parameter according to some
deterministic rule without using any feedback information from the search space. Adaptive
adaptation modifies strategy variables by using feedback information from the search space.
The best example of adaptive adaptations is Rechenberg’s “1/5 success rule” in ESs [31] (p.
110). In the case of self-adaptive adaptation, the parameters are altered by EAs themselves.
Strategy parameters to be altered are encoded into chromosomes and undergo variation with the
rest of the chromosome. The self-adaptive adaptation was first proposed by Schwefel [32] into
ESs.
There are three distinct levels at which adaptation can take place in adaptive EAs [34].
For the population-level adaptation, strategy parameters are modified globally for the whole
population. Various examples are available for population-level adaptation in ESs and GAs
[43], [44]. For the individual level adaptation, an EA modifies the strategy parameters of an
individual and these modifications occur independently with each individual. In [41], the
crossover probability in a GA is changed at the individual level. For the component level
adaptation, parameters are changed for some genes of an individual in the population. Self-
adaptation is a well-known example of component-level adaptation.
Fogarty [10] proposed a dynamic mutation rate control scheme for GAs, in which the
mutation rate decreases exponentially over the number of generations. In papers [6], [7], Devis
proposed an effective algorithm that updates operator probabilities according to the performance
of the operators. This scheme specifies for the modification of operator rates in associated to the
fitness of solutions generated by the operators. It has been introduced for the steady state GA.
Srinivas and Patnaik [37] suggested an adaptive GA that uses an adaptive crossover and
mutation probability scheme. The rates of crossover and mutation are modified according to the
fitness of the solution. Uyar el al. proposed an asymmetric gene based adaptive mutation
(GBAM) technique [39]. In GBAM, each gene locus has two different mutation probabilities:
is used for those loci that have the value of “1” and is used for those loci that have
the value of “0”. The probabilities of and are automatically updated based on the
4. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
4
feedback information from the search space, according to the relative success or failure of those
chromosomes having a “1” or “0” at that locus for each generation. Yang and Uyar [45]
suggested another gene based adaptive mutation with fitness and allele distribution correlation
(GBAM FAD). The mutation rates of each gene locus are adaptively modified based on the
correlated feedback information from the search process, according to the relative success or
failure of solutions.
A dynamic mutation GA (DMGA) was proposed by [15]. This approach simultaneously
uses four mutation operators in solving optimization problems. These mutation operators are
adaptively applied in the GA. In [19], the authors introduced an adaptive mutation technique,
which is closely related to Hong’s method, simultaneously applying multiple mutation operators
in GAs [15]. The authors proposed a directed mutation (DM) operator for real coded GAs [17],
which is to explore the promising area in the search space by using the feedback information
from the current population.
This is an altered version of the standard mutation. In the DM scheme, solution moving
is not only based on the feedback information of average fitness of intervals, but also on the
population distribution. By taking into account the information of population distribution, DM
avoids the premature convergence problem.an adaptive mutation technique, which is closely
related to Hong’s method, simultaneously applying multiple mutation operators in GAs [15].
The authors proposed a directed mutation (DM) operator for real coded GAs [17], which is to
explore the promising area in the search space by using the feedback information from the
current population. This is an altered version of the standard mutation. In the DM scheme,
solution moving is not only based on the feedback information of average fitness of intervals,
but also on the population distribution. By taking into account the information of population
distribution, DM avoids the premature convergence problem.
2.2. Multi-population Approaches
Several researchers have considered multi-population schemes for locating multiple
peaks in a multi-modal fitness landscape. These approaches can be applied to cover solutions on
different peaks with different multi-populations. In this paper, we focus on more than one peak
in the fitness landscape. A global optimum is the best peak in the fitness landscape and local
optima are referred to the rest of the lower height peaks. Some other techniques have been
proposed to maintain the diversity of the population. These approaches work just like multi-
population schemes, which are crowding [21], fitness sharing [12], island and parallel GAs [13],
[4]. Multi-population techniques can improve the diversity in the GA and avoid the premature
convergence problem.
Branke et al. [5] introduced a self-organizing scout (SOS) algorithm, which has shown
promising results on evaluated problems. In this scheme, the population consists of a parent
population that explores through the whole search space and child populations that locate
previously detected optima. The parent population is continuously examined. If the condition is
satisfied, then a child population is split off from the parent population. The size of each child
population is updated regularly, although the total number of solutions are fixed and no new
solutions are proposed.
Ursem [38] proposed a multi-population scheme referred to as the multinational GA,
which employs a multinational GA technique to find multiple peaks of multi-modal problems in
dynamic environments. Each nation corresponds to the policy and best representatives. In
multinational GAs, a “hill-valley detection” approach is applied to sample points on a line
marked between policies. This procedure uses migration of solutions from one nation to
another, to merge nations, and to create a new nation in a newly located region.
A clustering approach for multi-modal functions was proposed in [27]. This approach
determines the number of clusters within the k-means particle swarm optimization (PSO)
algorithm. It has been applied for the optimization of a criterion function in a probabilistic
mixture-model framework. In this algorithm, particles are supposed to be generated by a mix of
5. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
5
several probabilistic distributions. Each different cluster is associated to a different distribution.
Then, locating the optimum number k is equivalent to adapting the model with the determined
data while optimizing some criterion.
The niching method [28] and the species conserving GA (SCGA) [20] have been used
for multi-modal optimization problems. Both the clearing (niching) procedure and SCGA
adapted a scheme for splitting population according to the nation of species, which is
incorporated under the evolution process of a standard GA. The two methods have shown to
provide best results on evaluated multi-modal problems.
Yang and Li [46] developed a hierarchical clustering based PSO algorithm which is
specially introduced for finding and tracking multiple optima in dynamic environments. This
approach can distribute particles in separate promising subregions and the main contribution of
this approach is adaptively modifying the number of sub-swarms required, and automatically
compute the search region for each sub-swarm. A fast local search method is incorporated in
this approach , which specifies the optimal solutions in promising subregion detected by the
clustering scheme.
3. MULTI-POPULATION SCHEMES WITH ADAPTIVE
MUTATION OPERATOR
3.1 Motivation
In order to explain the problem of premature convergence is due to the loss of diversity,
the multi-population approach can be applied to maintain the diversity and retain the
convergence capacity of GAs. The suggested technique is composed of multi-population with
adaptive mutation operator, which identifies two different mutation rate vectors for each
subpopulation. These vectors are updated by using the fitness and distribution of individuals in
the fitness landscape. Each site of solution having two different mutation rates. This approach
can be able to improve the performance of the algorithm and to avoid the premature
convergence to multi-modal optimization problems.
3.2 Multi-population Schemes
1) Species Based Multi-population approach: A species can be a collection of
individuals sharing with common characteristic regarding to the similarity of the individuals.
The measurement of two individuals similarity is calculated by the hamming distance. The
smaller hamming distance between two individuals, the more similar they are. Species-based
particle swarm optimization(SPSO) scheme was proposed by Parrot and Li [26].
2) An Other Multi-population approach: In this paper [40], the authors has recently
proposed a partitioned technique, which divides the current population into different
subpopulation according to the fitness and distribution of individuals in the landscape. Each
subpopulation can be able to ideally incorporate the basins of attraction of similar optima. The
basic idea of proposed partition scheme is to distribute best individuals away from each
other(according to the distance measure) under the different peak in the search space.
3.3 Adaptive Mutation Operator with Multi-population approaches
Traditionally, mutation operator considered as a background operator, it affects the
alteration of the value of each bit of individual with small mutation probability ∈ [0,1].
The main motivation of the mutation in the GAs has been that of insurance policy against
permanent loss or unexplore genetic material in the population to avoid the premature
convergence of the GAs to local optima.
The adaptive techniques are used to accelerate the convergence speed and preserving
GAs from being trapped into local optima. The important contribution of adaptive mutation
operator to improve the performance of GAs. All above explained adaptive schemes are used to
6. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
6
a single population in the process of evolution, either using steady state GA or generational
GAs.
In this paper, multi-population with adaptive mutation scheme is proposed. Basically
adaptive mutation operator is combining with two different multi-population approaches, one is
species based multi-population and the other one is basin (fitness of solution and distribution of
individual in the search space) based approach. BWAM and SWAM represents basin with
adaptive mutation and species with adaptive mutation respectively. GAs has two properties
exploration and exploitation but the problem is that how to balance these properties during the
evolution. In order to address this problem, the researchers have been used separately multi-
population approaches and adaptive probabilities of genetic operators to increase the diversity
during the evolution. Our proposed scheme is going to combine both of them for finding the
better solution in the multi-modal problems. This technique is applied to maintain the balance of
explorative and exploitative properties of genetic operator.
The framework of the multi-population GAs with the adaptive mutation scheme is
represented in Algorithm 1. This algorithm starts from randomly generated population which is
called p population. Then, sub-populations are created either using BWGA or SWGA scheme.
When sub-populations have been generated then, calculate mutation probability, apply mutation
and selection approaches on them. At the end, overlapping and convergence techniques are
applied on each sub-population before starts the next generation. Some of the task in this
algorithm are similar to the classical SGA but here we are going to focus on the main operations
of this approach, including partition, Statistics, Mutation, overlapping and convergence
methods. These methods determine the general theme of technique. The detail description of the
these functions are given in the following:
Algorithm 1: Multi-population scheme with adaptive mutation operator
1: Randomly create an initial population ;
2: Evalute the fitness of each solution of ;
3: 0;
4 partition( );
5: while ( < max gen) do
6: for ( to ) do
7: Statistics( );
8: Mutation( );
9: Selection( );
10: end for
11: Overlapping( );
12: Convergence( );
13: if (p < MinInds) then
14: regeneratep:=Re-initialization(removedSols);
15: := partition( );
16: Merge and into
17: end if
18: + 1;
19: end while
1) partition(pt):There are several techniques available in the literature to generate multi-
population, two approaches are considered in this paper, detail explanation of these techniques
are mentioned in the section 3.2. represents the current population, which is passed to the
partition function as a parameter. The functionality of this method is to divide the current
population into different subpopulation. The different sub-population have different position in
7. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
7
the fitness landscape. The multi-population scheme can be applied to maintain the diversity
according to the convergence. This approach can be helpful towards getting the better results on
multi-modal problems. Each sub-population has assigned and update probabilities separately. In
the following section will compute the probability of each site of individual of each sub-
population.
2)Statistics: In the statistics method, the mutation rates are computed by using the
feedback information of current sub-population. Each sub-population has defined two different
probability vectors, where and are the mutation rates and of subpopulation at
generation . Each vector contains set of element, which is associating to the probabilities of
keeping a particular allele at each site. Initially each element of vector is set to an initial value
within its determined boundaries. These vectors are generated real-valued probabilities of the
each sub-population, which determines high quality sub-population with high probability. For
each generation vectors are updated based on the fitness and distribution of solutions in the
specified sub-population, it means that each sub-population has altered own vectors
independently. The two different mutation rates are specified for each site of solution
of each sub-population. The estimation of both vectors are updated on the explication shown in
equation 2 and 3.
( , + 1) =
( , ) + ,
1
>
( , ) − ,
(1)
( , + 1) =
( , ) − ,
1
>
( , ) + ,
(2)
where is the updated value of mutation probabilities of the vectors, is the average fitness
with allele “1“ of those individuals which are contained in subpopulation for site at
generation , and is the average fitness of the subpopulation at iteration .
3) Mutation : This function is performed mutation on each sub-population at every
iteration. It is distinctly employed on each subpopulation using the associated vectors. Suppose,
an offspring ( ́ = { ́ , … … ́ })generated by mutation of parent ( = { , … … })
according to corresponding vectors, which is the member of subpopulation. The mutation is
performed on whole solution site by site, which is mentioned in the Algorithm 2, where Rnd is
the uniform random number, which is generated within the interval(0,1).
Algorithm 2 Mutated each Individual by using adaptive mutation
1: (j 0 to 1 )
2: ( [ ] == 0)
3: Rand(0,1) < M [j]
4: ́[ ] = 1;
5:
6: else
7: Rand(0,1) < M [j]
8: ́[ ] = 0;
9: end if
10: end if
11: end for
8. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
8
The proposed mutation scheme is applied with two different partition approaches (See
Section 3.2). The contribution of the adaptive mutation with multiple population is summarized
in the following distinct characteristics:
1) It describes the two different vectors for each subpopulation.
2) Each site of subpopulation having two different mutation rates and different mutation
probabilities for the different locus of the encoded individual.
3) The rate of each locus are updated iteration-by-iteration to modify the current state of the
evolution.
4) This is the one of the important property of this approach, which investigates the undetected
regions around the search space.
5) The suggested method is focused on the locating multiple optima of the multi-modal
optimization problems.
3.4 Overlapping and Convergence of sub-populations
After mutation and selection operations, all the subpopulations are checked regarding
overlapping and convergence. Normally, the overlapping check between two subpopulations
can determined by comparing the distance of the best solutions of the sub-populations. If the
search radius of best individuals of sup-populations is less than threshold value , than
delete the sub-population, which is related to less fitness best solution and keep the total
individuals, which are associated to the removed sub-population. Algorithms 3 is shown the
overlapping search of sub-populations.
Algorithm 3: The algorithm for overlapping search
1: while ( . () > 0) ( < . ()) do
2: 1 ( );
3: 0;
4: + 1;
5: while ( . () > 0) ( < . ()) do
6: if ( ( 1, 2) < ) then
7: if ( 1 < 2) then
8: + ( ). ();
9: ( );
10: else
11: + ( ). ();
12: ( );
13: end if
14: end if
15: end while
16: end while
After overlapping search, all sub-populations will undergo the convergence process, which is
determined to see weather sub-population has converged. If the total similar solutions of
associated sub-population is greater than threshold value _ , the value of threshold
(0.95*size of subpopulation) is fixed in this paper. If sub-population is converged on one of the
available peaks then sub-population is removed from , which is converged. Convergence
of subpopulation is given in the algorithm 4.
Algorithm 4 Algorithm for determine convergence of subpopulation
1: for _ ∈ do
2: if ( > (0.95 ∗ . ())) then
9. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
9
3: + . ();
4: ;
5: end if
6: end for
4. EXPERIMENTAL STUDY
In this section, there are three different group of experiments were conducted on well-known
decision problems, which has been evaluated in the popular area of maximum satisfiability
(MAX-SAT) problems. Boolean satisfiability problem involves finding an assignment of
variables that maximizes the number of satisfied clauses of a given constraints. The general
form of these constraints are presented in conjunctive normal form (CNF) or product-of-sum
form. MAX-SAT is also well known NP-hard optimization problems. In addition, Boolean
satisfiability expression has applied to introduced a approach for generating problems with
controllable degree of ”multimodality” and ”epistasis”.
In the rest of this section, first introduce the mapping between GAs to MAX-SAT
problems, spear [36] for generating constraints with controllable degree of multi-modality and
epistasis and then investigate the result of experiments.
4.1 Boolean Satisfiability and Genetic Algorithms
In order to employ GAs to any particular problem, that problem consider two critical
components: 1) specify the appropriate representation for the solution space (search space) and
2) define an external evolution function which determines utility of individuals (fitness of
individuals). MAX-SAT has a simple string representation which is highly compatible to the
GAs. Each individual shows binary strings of length in which bit determines the truth value
of the boolean variable of the boolean variables shown in the boolean expression.
Any candidate solution is evaluated by the fitness function, which delegates fitness
value 1 to that individual (string) boolean values of that string by which the boolean expression
is evaluated to 1 and 0 to other solutions.
Spear proposed another scheme [36] that has been assigned fitness to individual
subexpressions in the original expression and aggregate them in some way to produce a
complete individual fitness value. According to this context the general and natural way is to
specify the value of TRUE to be 1 and the value of FALSE to be 0 by Smith [35].
4.3 Comparison of proposed scheme with other approaches
The performance of proposed algorithm is compared with some existing GAs
techniques, which are chosen from the GAs literature. According to the performance, these
algorithms were tested on different multi-modal boolean satisfiability problems, which are
widely applied in the literature. Initially our scheme has been compared to standard GAs with
random fixed mutation and crossover probabilities. In addition, the proposed technique
compared with some other parameter control approaches such as adaptive [37], self-adaptive [3]
and SSRGA [40] schemes. These all comparable approaches are considered, which briefly
described as follows:
The simple genetic algorithm (SGA) is collection of individuals, these solutions of SGA
are represented as a bit string of length , mutation and crossover operators are used in the SGA
as a variation operator. The probabilities of these variation operators are initially assigned by
random values (0,1) in our experiments. The initial values are fixed during the whole evolution
process.
Srinivas and Patnaik introduced a adaptive genetic algorithm (AGA) [37] which is
efficient adaptive algorithm for multimodal optimization problems. The main motivation of this
approach is to maintain the diversity in the population and retain the convergence capacity of
10. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
10
the GA by using adaptive probabilities of crossover and mutation. The rate of mutation and
crossover are updated depending on the fitness values of the solutions. In order to address the
convergence property, to determines and for each solution to protect highly-fit solutions
from high disruption. The mutation and crossover rates are updated applying following
equations.
=
( − ) ( −⁄ ), ≥
,
(3)
=
( − ) ( −⁄ ), ≥
,
(4)
where and represents the maximum fitness and average fitness of the population,
′
is
the larger of the fitness values of the individual to be crossed and is the fitness of solution
which is being mutated. 1, 2, 3, 4 ∈ [0,1] are predefined constants. These predefined
constant values are taken from [37], same values are considered for our experiments.
Self-adaptive genetic algorithm (SAGA) was developed by Back and Schutz [3]. which
uses single mutation rate separately per solution. For example an individual composes of a bit
binary string of length and associated mutation rate μ ∈ [0, 1]. The new mutation probability is
adjusted according to the following equation.
́ = 1 +
1 −
exp (0,1) (5)
where = 0.22 is the learning rate and N(0, 1) is the uniform distributed value with mean 0.0
and standard deviation 1.0. The new solution is specified through bit wise mutation of l bits
applying the mutated mutation rate value ́. The mutation rate is not less than 1/ .
Vafaee and Peter recently proposed a site-specific rate genetic algorithm (SSRGA) [40]
scheme. Which introduced mutation scheme to determines different mutation rate for different
sites of the individuals. The main motivation of this approach to face both explorative and
exploitative responsibilities of variation operators. This scheme starts from partitions of
population into number of sub-populations is defined based on fitness and distribution of
solutions contained in the search space. Then, in order to identify the representative individual
associating to each sub-population. Finally, the result of this procedure is a probability vector
(SSR vector) with elements associating to the rate of possessing a specific allele at each locus of
every solution included in a sub-population.
4.4 Experimental setting
In order to investigate our proposed scheme with other four approaches on problems
with different level of difficulty, the difficulty of the problem means to modify the length of
individuals and population size . Generally, the problem becomes more difficult if the length
of individuals would be increase. To avoid the premature convergence due to increase
population size and may also be the algorithms have a ability to find a better solutions during
the evolution process. We have been considered different levels of problem difficulty by using
the parameter pairs ( , ) with (20,30), (30,50), (50,50) and (60,70). These parameter setting is
used to multimodal landscape with different degree of multi-modality by assigning number of
peaks 1,5,10. Each peak is shown by a randomly created solution of length , which identifies
the specific position of peak in the search space. The default setting of parameters applied in the
experiments of this paper can be observed in the original papers [37], [3], [40]. To compare the
performance of multi-population with adaptive approach with other described above algorithms
in section 4.3. All algorithms were allowed same population size, length of individual, stop
criteria and maximum number of generations for each run.
11. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
11
4.4.1. Analysis of Parameter Sensitivity
The performance of included approaches depends on the operator and parameters applied. In
this paper, the key parameters are considered for the sensitivity analysis such as population size,
individual length
and radius( ). To locate the multiple optima by using the small population size, it is not
always good idea. Increasing the population size, however, to reduce the probability of being
trapped into local optimum and increasing the probability of locating better solution during the
evolution process. Solution is consist of length of bit binary string, if length of string
increases the problem become more challenging since the state space is exponentially expended
according to the length of solution increases.
Table 1
Parameter setting for all compared algorithms
Parameter Setting
l 20 30 50 60
n 30 50 50 70
r 0.5 0.6 0.7
Peaks 01 05 10
r( ) is used to determine the species and species seed in the SPSO [26] and to identify
the representative individual from population [40]. The radius (r) is the key parameter to both
approaches. If the radius is too small, there is potential problem that few isolated solutions
species may tarp into local optimum due to very small size of radius. In this context, the loss of
diversity then the algorithms can’t contribute further more during the process. If radius is too
large, there may be more than one optimum within the radius. It is very difficult to choose the
suitable value of radius. In this paper, we have considered different values of radius to
investigate the performance of algorithms. The different parameters and their settings of
different level of multi-modality problems applied in our experiments can be seen in Table 1. In
order to determine that which parameter setting gives the great performance among the
compared algorithms.
4.4.2 Experimental Results and Analysis
In order to investigate that multi-population with adaptive mutation schemes can
improve the performance of GAs on solution quality and convergence rate for multi-modality
problems. All algorithms were run independently 50 times on the different degree of multi-
modality problems. From the Table 2, It can be determined that the same value of r is
considered for first three algorithms because which is related to these approaches; the r is
applied with distinctly in different algorithms, first one is used a r as threshold (minimum
distance between two solutions), value in BWAM, another one is determined as a radius of the
each species SWAM and last one is considered of r values with same meaning as in first one.
The experimental results are shown in Table 2, which gives detail result of average and
standard deviation of the best-found fitness values during the evolution. Both values are
computed when the maximum number of iteration is completed or the global optimum is found.
The algorithm determine better results among the other algorithms which presents bold average
best fitness. In addition, those average best fitness values are underlined which is associated
with smallest standard deviation among the other approaches. The effect of smaller standard
deviation determine to produced reliable solutions.
1) Effect of varying the length of solution and population size: The algorithms have
been investigated on different problems with different level of difficulty. The difficulty means
to change the length of individual and population size. The problem would become more
difficult if increasing the length of solution. The size of population is increasing, however, less
probability of premature convergence to local optimum and increase probability to locate the
13. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
13
2) Effect of varying the peaks: The performance of BWAM and SWAM is equal on
specific setting of( , ) on the different number of peaks, but efficiency of SSRGA sightly
declines as number of peaks increases. However, the rest of the compared algorithms are
reversed.
3) Effect of varying the ( / ): Niche radius(r) is a very important role
regarding the performance of both approaches (BWAM and SWAM), which is determine
subpopulations. The many species could be generated if the value of r is very small. it is a big
problem due to this reason few isolated solutions of sup-population trap into local optimum very
quickly. Setting r to a too large will cause more than one optimum could be contained within the
circle (r). The experiments determine the effect of the different values on the performance of
those algorithms which are associated with the r in this paper.
The statistical results of comparing algorithms is investigated applying two-tailed t-test
with a 98 degree of freedom at 0.05 level of significance. Table 3 presents t-test results of
comparing pair of algorithms, where the result is determined as “s+” ,“s-”, “+”, “-”, and “ _ ” if
the first algorithm in pairs is significantly better than, significantly worse than the
insignificantly better than, insignificantly worse than or equivalent to the second algorithm,
respectively. The t-test result of comparing algorithms shows on peak 10 and is
chosen 0.6 * with different level of problem settings. From Table 3 it can be observed that the
BWAM and SWAM both approaches are statistically better than other comparing schemes to
locating the optimum value in the fitness landscape. Here we presents only statistical results
of compared techniques with different level of difficulty of different problems on peak 10.
According to the parameter setting of different level of multi-modality problems are
divided into three categories such as simple problems, bit harder problems, and difficult
problems. The performance of all algorithms varies on different categories. From Fig.1 it can be
determined that the convergence speed of involved algorithms, which were tested on different
level of difficulty in simple multi-modal problems. In Fig.1 BWAM, SWAM, and SSRGA have
a higher convergence rate than self-adaptive GA, adaptive GA, and Standard GA on simple
problems. The overall the convergence speed of BWAM and SWAM is initially better than
SSRGA on simple problems but with time going the performance of all three algorithms are
same except last two rows in Fig.1.
Table 3
t-test values of comparing algorithms on different problems with different level of difficulty
Problems (20,30) (30,50) (50,50) (60,70)
BWAM-SWAM ~ ~ ~ ~
BWAM-SSRGA ~ ~ s+ s+
BWAM-SAGA s+ s+ s+ s+
BWAM-AGA s+ s+ s+ s+
BWAM-SGA s+ s+ s+ s+
SWAM-SSRGA ~ ~ s+ s+
SWAM-SAGA s+ s+ s+ s+
SWAM-AGA s+ s+ s+ s+
SWAM-SGA s+ s+ s+ s+
SSRGA-SAGA s+ s+ s+ s+
SSRGA-AGA s+ s+ s+ s+
SSRGA-SGA s+ s+ s+ s+
SAGA-AGA s+ s- s+ s-
SAGA-SGA s+ s+ s- s-
AGA-SGA s+ s+ - -
14. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
14
Fig 2. presents the results of the evolutionary process of compared algorithms on bit harder
problems. It can be clearly noticed that the convergence speed of BWAM and SWAM are
quicker than other approaches but it is interesting to observe that different scheme have different
15. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
15
Fig 1. Evolutionary process of the comparison algorithms on simple problems
Fig. 2. Evolutionary process of comparison algorithms on bit harder problems.
convergence rate on different (bit harder) problems with different peaks. On few problems, the
BWAM is initially better than SWAM regarding convergence speed.
From Fig3. it can be seen that the convergence rate of BWAM initially is faster than
SWAM from beginning to 50 generations on first column, afterwards the both schemes have
same convergence curve. In this figure, the convergence curves are quiet clear among the
compared algorithms.
Analyzing the convergence rate of six comparing schemes. The very interesting things
is that the convergence speed of both (BWAM, SWAM) approaches is initially quick
convergence rate than compared techniques even on simple problems where SSRGA is going to
compete to the BWAM and SWAM. It can also be seen two properties of proposed approach
from above figures. The first one is the quick convergence rate against with other comparable
algorithms except simple problems. BWAM and SWAM have quick convergence speed than
other compared approaches on different levels of problem difficulty by setting the parameters.
Another goal of suggested scheme is the ability to explore the prominent area by avoiding the
premature convergence in the fitness landscape on multimodality problems. The proposed
technique reduce the less probability of trapping into local optima and increase the probability
of locating the better results than the other algorithms.
16. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
16
5. CONCLUSION AND FUTURE WORK
From the beginning, community of evolutionary algorithm has been done lot of work regarding
to increase the performance and locating multiple optima in multi-modal optimization problems
of GAs. The exploration and exploitation are becoming two main characteristic in the case of
performance. The researchers have applied multi-population scheme to increase the efficiency
of GAs in this context.
This paper proposed a new mutation approach, which is the combination of multi-
population and adaptive mutation genetic operator. It is determine two different probability
Fig. 3. Evolutionary process of comparison algorithms on difficult problems.
vectors for each sub-population. Each vector contains elements associating to the probabilities
of possessing a specific allele at each site. These vectors are updated during the evolution
process. The suggested mutation scheme has been considered two different multi-population
techniques in this paper.
In order to analysis the performance of the our proposed algorithms, experimental
results were conducted on different benchmark problems and to compare the results to standard
GA, and some other approaches which belongs to parameter control approaches. From the
experiments, it can be seen that suggested scheme is greatly improve the performance of GA
regarding to the locating and tracking the multiple optima in the fitness landscape by using the
multi-population with adaptive mutation operator.
In the future, we will use proposed mutation scheme to large and complex real-world
problems because GAs have a lot of applications in different area of real-world problems such
as science, engineering, business and social science, the interested reader may wish to refer [11]
p. 125. In addition, it would be interesting to combine clustering partition technique with
adaptive mutation operator to improve the performance of GAs. Finally, we will conduct further
experiments on epistatic [36] and deceptive[11] benchmark problems, which are similar to the
multi-modal problems.
17. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
17
REFERENCES
[1] P.J. Angeline, (1995) “Adaptive and Self-adaptive evolutionary computations,” In M. Palaniswami
and Y. Attikiouzel, editors, Computational Intelligence: A dynamic system perspective, pp. 152-
163. IEEE Press.
[2] T. B¨ack, (1992) “Self-Adaptation in Genetic Algorithms,” In Proc. of the 1st European Conf. on
Artificial Life, pp. 263-271.
[3] T. Back and M. Sch¨utz, (1996) “Intelligent mutation rate control in canonical genetic algorithms,”
In Foundation of Intellignet Systems, Springer, pp. 158-167.
[4] M. Bessaou, A. Paetrowski, and P. Siarry (2000) “Island model cooperating with speciation for
multimodal optimization,” In Proc. of the 6th Int.Conf. on Parallel Problem Solving from Nature,
pp. 16-20.
[5] J. Branke, T. Kaubler, C. Schmidt, and H. Schmeck, (2000) “A multi-population approach to
dynamic optimization problems,” In Proc. of the 4th Int. Conf. on Adaptive Comput. Des Manuf,
pp. 299-308.
[6] L. Davis, (1989) “Adapting operator probabilities in genetic algorithms,” Proc. of the 3rd Int.
Conf. on Genetic Algorithms, pp. 61-69.
[7] L. Davis, (1991) “Hankbook of Genetic Algorithms,” Van Nostrand Reinhold.
[8] A.E Eiben, R. Hinterding, and Z. Michalewicz, (1999) “Parameter Control in Evolutionary
Algorithms,” IEEE Trans. on Evol. Comput., 3(2): pp. 124- 141.
[9] A.E. Eiben, Z. Michalewicz, M. Schoenauer, and J.E. Smith. (2007) Parameter Control in
Evolutionary Algorithms, Parameter setting in Evolutionary Algorithms, Chapter 2, Springer
Verlag, pp. 19-46.
[10] T.C. Fogarty, (1989) “Varing the probability of mutation in genetic algorithms,” In Proc. of the
3rd Int. Conf. on Genetic Algorithms, pp. 104-109.
[11] D. E. Goldberg, (1989) Genetic Algorithms in Search, Optimization, and Machine Learning, New
York: Addison-Wesley.
[12] D. E. Goldberg, and J. Richardson, (1987) “Genetic algorithms with sharing for multimodal
function optimization,” In Proc. of the 2nd Int. Conf.on Genetic Algorithms, pp. 41-49.
[13] V.S. Gordon, D. Whitley, and A. Bohn, (1992) “Dataflow parallelism in genetic algorithms,” In
parallel Problem Solving from Nature, pp. 533-542.
[14] J. J. Greffenstette, (1986) “Optimization of Control Parameters for Genetic Algorithms,” IEEE
Trans. on Sys. Man and Cyber., 16(1): pp. 122-128.
[15] T. P. Hong, H. S. Wang, and W. C. Chen. (2000) “Simultaneously applying multiple mutation
operators in genetic algorithms,” Journal of Heuristics, 6: pp. 439-455.
[16] J. Kennedy. (2000) “Stereotyping: Improving particle swarm performance with cluster analysis,”
In Proc. 2000 IEEE Congr. Evol. Comput, pp. 1507- 1512.
[17] I. Korejo, S. Yang and C. Li, (2010) “A Directed Mutation Operator for Real Coded Genetic
Algorithms,” EvoApplications 2010, Part I, LNCS 6024,pp. 491-500.
[18] K. A. De Jong, (1975) “An Analysis of the Behavior of a Class of Genetic Adaptive Systems,”
PhD Thesis, Department of Computer and Communication Science, University of Michigan, Ann
Abor.
[19] C. Li, S. Yang, and I. Korejo, (2008) “An Adaptive Mutation Operator for particle swarm
optimization,” In Proc. of the 2008 UK Workshop on Computational Intelligence, pp. 165-170.
[20] J. P. Li, M. E. Balazs, G. Parks, and P. J. Clarkson, (2002) “A species Conserving genetic
algorithm for multimodal function optimization,” Evol. Comput., vol. 10, no. 3, pp. 207-234.
18. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
18
[21] S. W. Mahfound, (1992) “Crowding and preselection revisited,” In Proc. of the 2nd Int. Conf. on
Parallel Problem Solving from Nature, vol 2, pp. 27-36.
[22] H. M¨uhlenbein, (1992) “How Genetic Algorithms Really Work I. Mutation and Hillclimbing,”
In Proc. of the 2nd Int. Conf. on Parallel Problem Solving from Nature, pp. 15-29.
[23] G. Ochoa, (2002) “Setting the mutation rate: Scope and limitations of the 1/l heuristics,” Proc. of
the 2002 Genetic and Evol. Comput. Conf.,pp. 315-322.
[24] G. Ochoa, (2006) “Error thresholds in genetic algorithms,” Evol. Comput.,vol. 14, no. 2, pp. 157-
182.
[25] G. Ochoa, (1999) “Error thresholds and their relation to optimal mutation rates,” Springer-Verlag,
Berlin, Germany.
[26] D. Parrott and X. Li, (2006) “Locating and tracking multiple dynamic optima by a particle swarm
model using speciation,” IEEE Trans. Evol. Comput., vol. 10, no. 4, pp. 440-458, Aug.
[27] A. Passaro and A. Starita, (2008) “Particle swarm opotimization for multimodal functions: A
clustering approach,” J. Artif. Evol. Appl., vol. 2008, pp. 1-15.
[28] A. Petrowski, (1996) “A clearing procedure as a niching method for gentic algorithms,” In Proc.
1996 IEEE Int. Conf. Evol. Comput., pp. 798-803.
[29] R. Rechenberg, (1996) Evolutionary Algorithms in Theory and Practice. New York: Oxford
University, Press.
[30] J. D. Schaffer, R. A. Caruana, L. J. Eshelman, and R. Das, (1989) “A Study of Control Paramters
Affecting Online Performance of Genetic Algorithms for Function Optimization,” Proc. of the 3rd
Int. Conf. on Genetic Algorithms, pp. 51-60.
[31] H. P. Schwefel, (1995) Evolution and Optimum Seeking, Chichester, UK: John Wiley.
[32] H. P. Schwefel, (1981) “Numerical optimization computer models,” Chichester,Wiley.
[33] J.E. Smith and T.C. Fogarty, (1996) “Self-adaptation of mutation rates in a steady state genetic
algorithm,” In Proc. of the 3rd IEEE Conf. on Evol. Comput., pp. 318-323.
[34] J.E. Smith and T.C. Fogarty, (1997) “Operator and parameter Adaptation in genetic algorithms,”
Soft Comput., vol. 1, no. 2, pp. 81-87.
[35] G. Smith, (1979) “Adaptive genetic algorithms and boolean satisfiability problem,” Technical
Report, University of Pittsburgh, Pittsburgh.
[36] W. M. Spears, (2000) Evolutionary algorithms, the role of mutation and recombination, Natural
Computing, Speringer-Verlag, Berlin, Germany.
[37] M. Srinivas and L.M. Patnaik, (1994) “Adaptive probabilities of crossover and mutation in genetic
algorithms,” IEEE Trans. on System, Man and Cybern., vol. 24, no. 4, pp. 656-666.
[38] R. K. Ursem, (2000) “Multinational GAs: Multimodal Optimizaiton Techniques in Dynamic
Enviroments,” In Proc. 2nd Genetic Evol. Comput. Conf., pp. 19-26.
[39] S. Uyar, S. Sariel, and G. Eryigit, (2004) “A gene based adaptive mutation strategy for genetic
algorithms,” Proc. of the 2004 Genetic and Evol. Comput. Conf., pp. 271-281.
[40] F. Vafee and P. C. Nelson (2010) “An Explorative and Exploitative Mutation Scheme,” Proc.
2010 IEEE World Congr. on Comput. Intell., pp. 18-23.
[41] T. White and F. Oppacher, (1994) “Adaptive crossover using automata”, Proc. of the 3rd Conf. on
PPSN, pp. 229-238.
[42] D. H. Wolpert and W. G. Macready, (1997) “No free lunch theorems for optimization,” IEEE
Trans. on Evol. Comput., vol. 1, no. 1, pp. 67- 82.
[43] S. Yang, (2002) “Adaptive non-uniform crossover based on statistics for genetic algorithms,” Proc.
of the 2002 Genetic and Evol. Comput. Conf., pp. 650-657.
19. International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013
19
[44] S. Yang, (2003) “Adaptive mutation using statistics mechansim for genetic algorithms,” In F.
Coenen, A. Preece, and A. Macintosh (editors), Research and Devlelopment in Intelligent System
XX, pp. 19-32.
[45] S. Yang and S. Uyar, (2006) “Adaptive mutation with fitness and allele distribution correlation for
genetic algorithms,” Proc. of the 21st ACM Symp. on Applied Computing, pp. 940-944.
[46] S. Yang and C. Li, (2010) “A clustering particle swarm opotimizer for locating and tracking
multiple optima in dynamic environments,” IEEE Trans. on Evol. Comput. vol. 14, no. 6, pp. 959-
974, December.
Authors
Imtiaz Ali Korejo received his B.Sc.(Hons) and M.Sc.(Hons) in Computer Science
from University of Sindh, Jamshoro, Pakistan, in 1999, and 2000, respectively. He
worked as a research associate in the Institute of Mathematics and Computer
Science, University of Sindh, Jamshoro, Pakistan from 2001 to April 2003, as a
Lecturer in the same institute from April 2003 to 2012; He is currently working in
the same institute as an Assistant Professor since April 2012. He received his Ph.D.
from the Department of Computer Science, University of Leicester, United
Kingdom in 2012.
His research interests are evolutionary algorithms, genetic algorithms and adaptive approaches.
Shengxiang Yang received the B.Sc. and M.Sc. degrees in automatic control and
the Ph.D. degree in systems engineering from Northeastern University, China in
1993, 1996, and 1999, respectively. From October 1999 to June 2012, he worked
as a Postdoctoral Research Associate in the Department of Computer Science,
King's College London, U.K., a Lecturer in the Department of Computer Science,
University of Leicester, U.K., and a Senior Lecturer in the Department of
Information Systems and Computing, Brunel University, U.K., respectively. Since
July 2012, he has been appointed as a Professor at the Center for Computational
Intelligence, School of Computer Science and Informatics, De Montfort University, U.K.
His major research interests include evolutionary and genetic algorithms, swarm intelligence,
computational intelligence in dynamic and uncertain environments, artificial neural networks for
scheduling and relevant real-world applications. He has over 150 publications. He has given invited
keynote speeches in several international conferences and co-organized several symposiums, workshops
and special sessions in conferences. He serves as the area editor, associate editor or editorial board
member for four international journals. He has co-edited several books and conference proceedings and
co-guest-edited several journal special issues. He is the chair of the Task Force on Evolutionary
Computation in Dynamic and Uncertain Environments, Evolutionary Computation Technical Committee,
IEEE Computational Intelligence Society, and the founding chair of the Task Force on Intelligent
Network Systems, Intelligent Systems Applications Technical Committee, IEEE Computational
Intelligence Society.