In this paper, a hybrid method for solving multi-objective problem has been provided. The proposed
method is combining the ε-Constraint and the Cuckoo algorithm. First the multi objective problem
transfers into a single-objective problem using ε-Constraint, then the Cuckoo optimization algorithm will
optimize the problem in each task. At last the optimized Pareto frontier will be drawn. The advantage of
this method is the high accuracy and the dispersion of its Pareto frontier. In order to testing the efficiency
of the suggested method, a lot of test problems have been solved using this method. Comparing the results
of this method with the results of other similar methods shows that the Cuckoo algorithm is more suitable
for solving the multi-objective problems.
A Comparison between FPPSO and B&B Algorithm for Solving Integer Programming ...Editor IJCATR
Branch and Bound technique (B&B) is commonly used for intelligent search in finding a set of integer solutions within a space of interest. The corresponding binary tree structure provides a natural parallelism allowing concurrent evaluation of sub-problems using parallel computing technology. Flower pollination Algorithm is a recently-developed method in the field of computational intelligence. In this paper is presented an improved version of Flower pollination Meta-heuristic Algorithm, (FPPSO), for solving integer programming problems. The proposed algorithm combines the standard flower pollination algorithm (FP) with the particle swarm optimization (PSO) algorithm to improve the searching accuracy. Numerical results show that the FPPSO is able to obtain the optimal results in comparison to traditional methods (branch and bound) and other harmony search algorithms. However, the benefits of this proposed algorithm is in its ability to obtain the optimal solution within less computation, which save time in comparison with the branch and bound algorithm.Branch and bound, flower pollination Algorithm; meta-heuristics; optimization; the particle swarm optimization; integer programming.
A HYBRID COA-DEA METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMS ijcsa
The Cuckoo optimization algorithm (COA) is developed for solving single-objective problems and it cannot be used for solving multi-objective problems. So the multi-objective cuckoo optimization algorithm based on data envelopment analysis (DEA) is developed in this paper and it can gain the efficient Pareto frontiers. This algorithm is presented by the CCR model of DEA and the output-oriented approach of it.The selection criterion is higher efficiency for next iteration of the proposed hybrid method. So the profit function of the COA is replaced by the efficiency value that is obtained from DEA. This algorithm is
compared with other methods using some test problems. The results shows using COA and DEA approach for solving multi-objective problems increases the speed and the accuracy of the generated solutions.
THE NEW HYBRID COAW METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMSijfcstjournal
In this article using Cuckoo Optimization Algorithm and simple additive weighting method the hybrid COAW algorithm is presented to solve multi-objective problems. Cuckoo algorithm is an efficient and structured method for solving nonlinear continuous problems. The created Pareto frontiers of the COAW proposed algorithm are exact and have good dispersion. This method has a high speed in finding the
Pareto frontiers and identifies the beginning and end points of Pareto frontiers properly. In order to validation the proposed algorithm, several experimental problems were analyzed. The results of which indicate the proper effectiveness of COAW algorithm for solving multi-objective problems.
The New Hybrid COAW Method for Solving Multi-Objective Problemsijfcstjournal
In this article using Cuckoo Optimization Algorithm and simple additive weighting method the hybrid COAW algorithm is presented to solve multi-objective problems. Cuckoo algorithm is an efficient and structured method for solving nonlinear continuous problems. The created Pareto frontiers of the COAW proposed algorithm are exact and have good dispersion. This method has a high speed in finding the Pareto frontiers and identifies the beginning and end points of Pareto frontiers properly. In order to validation the proposed algorithm, several experimental problems were analyzed. The results of which indicate the proper effectiveness of COAW algorithm for solving multi-objective problems
Multi objective predictive control a solution using metaheuristicsijcsit
The application of multi objective model predictive control approaches is significantly limited with
computation time associated with optimization algorithms. Metaheuristics are general purpose heuristics
that have been successfully used in solving difficult optimization problems in a reasonable computation
time. In this work , we use and compare two multi objective metaheuristics, Multi-Objective Particle
swarm Optimization, MOPSO, and Multi-Objective Gravitational Search Algorithm, MOGSA, to generate
a set of approximately Pareto-optimal solutions in a single run. Two examples are studied, a nonlinear
system consisting of two mobile robots tracking trajectories and avoiding obstacles and a linear multi
variable system. The computation times and the quality of the solution in terms of the smoothness of the
control signals and precision of tracking show that MOPSO can be an alternative for real time
applications.
A Comparison between FPPSO and B&B Algorithm for Solving Integer Programming ...Editor IJCATR
Branch and Bound technique (B&B) is commonly used for intelligent search in finding a set of integer solutions within a space of interest. The corresponding binary tree structure provides a natural parallelism allowing concurrent evaluation of sub-problems using parallel computing technology. Flower pollination Algorithm is a recently-developed method in the field of computational intelligence. In this paper is presented an improved version of Flower pollination Meta-heuristic Algorithm, (FPPSO), for solving integer programming problems. The proposed algorithm combines the standard flower pollination algorithm (FP) with the particle swarm optimization (PSO) algorithm to improve the searching accuracy. Numerical results show that the FPPSO is able to obtain the optimal results in comparison to traditional methods (branch and bound) and other harmony search algorithms. However, the benefits of this proposed algorithm is in its ability to obtain the optimal solution within less computation, which save time in comparison with the branch and bound algorithm.Branch and bound, flower pollination Algorithm; meta-heuristics; optimization; the particle swarm optimization; integer programming.
A HYBRID COA-DEA METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMS ijcsa
The Cuckoo optimization algorithm (COA) is developed for solving single-objective problems and it cannot be used for solving multi-objective problems. So the multi-objective cuckoo optimization algorithm based on data envelopment analysis (DEA) is developed in this paper and it can gain the efficient Pareto frontiers. This algorithm is presented by the CCR model of DEA and the output-oriented approach of it.The selection criterion is higher efficiency for next iteration of the proposed hybrid method. So the profit function of the COA is replaced by the efficiency value that is obtained from DEA. This algorithm is
compared with other methods using some test problems. The results shows using COA and DEA approach for solving multi-objective problems increases the speed and the accuracy of the generated solutions.
THE NEW HYBRID COAW METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMSijfcstjournal
In this article using Cuckoo Optimization Algorithm and simple additive weighting method the hybrid COAW algorithm is presented to solve multi-objective problems. Cuckoo algorithm is an efficient and structured method for solving nonlinear continuous problems. The created Pareto frontiers of the COAW proposed algorithm are exact and have good dispersion. This method has a high speed in finding the
Pareto frontiers and identifies the beginning and end points of Pareto frontiers properly. In order to validation the proposed algorithm, several experimental problems were analyzed. The results of which indicate the proper effectiveness of COAW algorithm for solving multi-objective problems.
The New Hybrid COAW Method for Solving Multi-Objective Problemsijfcstjournal
In this article using Cuckoo Optimization Algorithm and simple additive weighting method the hybrid COAW algorithm is presented to solve multi-objective problems. Cuckoo algorithm is an efficient and structured method for solving nonlinear continuous problems. The created Pareto frontiers of the COAW proposed algorithm are exact and have good dispersion. This method has a high speed in finding the Pareto frontiers and identifies the beginning and end points of Pareto frontiers properly. In order to validation the proposed algorithm, several experimental problems were analyzed. The results of which indicate the proper effectiveness of COAW algorithm for solving multi-objective problems
Multi objective predictive control a solution using metaheuristicsijcsit
The application of multi objective model predictive control approaches is significantly limited with
computation time associated with optimization algorithms. Metaheuristics are general purpose heuristics
that have been successfully used in solving difficult optimization problems in a reasonable computation
time. In this work , we use and compare two multi objective metaheuristics, Multi-Objective Particle
swarm Optimization, MOPSO, and Multi-Objective Gravitational Search Algorithm, MOGSA, to generate
a set of approximately Pareto-optimal solutions in a single run. Two examples are studied, a nonlinear
system consisting of two mobile robots tracking trajectories and avoiding obstacles and a linear multi
variable system. The computation times and the quality of the solution in terms of the smoothness of the
control signals and precision of tracking show that MOPSO can be an alternative for real time
applications.
MULTIPROCESSOR SCHEDULING AND PERFORMANCE EVALUATION USING ELITIST NON DOMINA...ijcsa
Task scheduling plays an important part in the improvement of parallel and distributed systems. The problem of task scheduling has been shown to be NP hard. The time consuming is more to solve the problem in deterministic techniques. There are algorithms developed to schedule tasks for distributed environment, which focus on single objective. The problem becomes more complex, while considering biobjective.This paper presents bi-objective independent task scheduling algorithm using elitist Nondominated
sorting genetic algorithm (NSGA-II) to minimize the makespan and flowtime. This algorithm generates pareto global optimal solutions for this bi-objective task scheduling problem. NSGA-II is implemented by using the set of benchmark instances. The experimental result shows NSGA-II generates efficient optimal schedules.
Optimization of Mechanical Design Problems Using Improved Differential Evolut...IDES Editor
Differential Evolution (DE) is a novel evolutionary
approach capable of handling non-differentiable, non-linear
and multi-modal objective functions. DE has been consistently
ranked as one of the best search algorithm for solving global
optimization problems in several case studies. This paper
presents an Improved Constraint Differential Evolution
(ICDE) algorithm for solving constrained optimization
problems. The proposed ICDE algorithm differs from
unconstrained DE algorithm only in the place of initialization,
selection of particles to the next generation and sorting the
final results. Also we implemented the new idea to five versions
of DE algorithm. The performance of ICDE algorithm is
validated on four mechanical engineering problems. The
experimental results show that the performance of ICDE
algorithm in terms of final objective function value, number
of function evaluations and convergence time.
Optimization of Mechanical Design Problems Using Improved Differential Evolut...IDES Editor
Differential Evolution (DE) is a novel evolutionary
approach capable of handling non-differentiable, non-linear
and multi-modal objective functions. DE has been consistently
ranked as one of the best search algorithm for solving global
optimization problems in several case studies. This paper
presents an Improved Constraint Differential Evolution
(ICDE) algorithm for solving constrained optimization
problems. The proposed ICDE algorithm differs from
unconstrained DE algorithm only in the place of initialization,
selection of particles to the next generation and sorting the
final results. Also we implemented the new idea to five versions
of DE algorithm. The performance of ICDE algorithm is
validated on four mechanical engineering problems. The
experimental results show that the performance of ICDE
algorithm in terms of final objective function value, number
of function evaluations and convergence time.
This work considers the multi-objective optimization problem constrained by a system of bipolar fuzzy relational equations with max-product composition. An integer optimization based technique for order of preference by similarity to the ideal solution is proposed for solving such a problem. Some critical features associated with the feasible domain and optimal solutions of the bipolar max-Tp equation constrained optimization problem are studied. An illustrative example verifying the idea of this paper is included. This is the first attempt to study the bipolar max-T equation constrained multi-objective optimization problems from an integer programming viewpoint.
This work considers the multi-objective optimization problem constrained by a system of bipolar fuzzy relational equations with max-product composition. An integer optimization based technique for order of preference by similarity to the ideal solution is proposed for solving such a problem. Some critical features associated with the feasible domain and optimal solutions of the bipolar max-Tp equation constrained optimization problem are studied. An illustrative example verifying the idea of this paper is included. This
is the first attempt to study the bipolar max-T equation constrained multi-objective optimization problems
from an integer programming viewpoint.
Manager’s Preferences Modeling within Multi-Criteria Flowshop Scheduling Prob...Waqas Tariq
This paper proposes a metaheuristic to solve the permutation flow shop scheduling problem where several criteria are to be considered, such as: the makespan, total flowtime and total tardiness of jobs. The proposed metaheuristic is based on tabu search algorithm. The Compromise Programming model and the concept of satisfaction functions are utilized to integrate explicitly the Manager’s preferences. The proposed approach has been tested through a computational experiment. This approach can be useful for large scale scheduling problems and the Manager can consider additional scheduling criteria.
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.
Duality Theory in Multi Objective Linear Programming Problemstheijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Theoretical work submitted to the Journal should be original in its motivation or modeling structure. Empirical analysis should be based on a theoretical framework and should be capable of replication. It is expected that all materials required for replication (including computer programs and data sets) should be available upon request to the authors.
The International Journal of Engineering & Science would take much care in making your article published without much delay with your kind cooperation
A NEW APPROACH IN DYNAMIC TRAVELING SALESMAN PROBLEM: A HYBRID OF ANT COLONY ...ijmpict
Nowadays swarm intelligence-based algorithms are being used widely to optimize the dynamic traveling salesman problem (DTSP). In this paper, we have used mixed method of Ant Colony Optimization (AOC) and gradient descent to optimize DTSP which differs with ACO algorithm in evaporation rate and innovative data. This approach prevents premature convergence and scape from local optimum spots and also makes it possible to find better solutions for algorithm. In this paper, we’re going to offer gradient descent and ACO algorithm which in comparison to some former methods it shows that algorithm has significantly improved routes optimization.
The assignment problem is a special type of linear programming problem and it is sub class of transportation problem. Assignment problems are defined with two sets of inputs i.e. set of resources and set of demands. Hungarian algorithm is able to solve assignment problems with precisely defined demands and resources.Nowadays, many organizations and competition companies consider markets of their products. They use many salespersons to improve their organizations marketing. Salespersons travel form one city to another city for their markets. There are some problems in travelling which salespeople should go which city in minimum cost. So, travelling assignment problem is a main process for many business functions. Mie Mie Aung | Yin Yin Cho | Khin Htay | Khin Soe Myint "Minimization of Assignment Problems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26712.pdfPaper URL: https://www.ijtsrd.com/computer-science/other/26712/minimization-of-assignment-problems/mie-mie-aung
A BI-OBJECTIVE MODEL FOR SVM WITH AN INTERACTIVE PROCEDURE TO IDENTIFY THE BE...gerogepatton
A support vector machine (SVM) learns the decision surface from two different classes of the input points, there are misclassifications in some of the input points in several applications. In this paper a bi-objective quadratic programming model is utilized and different feature quality measures are optimized simultaneously using the weighting method for solving our bi-objective quadratic programming problem. An important contribution will be added for the proposed bi-objective quadratic programming model by getting different efficient support vectors due to changing the weighting values. The numerical examples, give evidence of the effectiveness of the weighting parameters on reducing the misclassification between two classes of the input points. An interactive procedure will be added to identify the best compromise solution from the generated efficient solutions.
A BI-OBJECTIVE MODEL FOR SVM WITH AN INTERACTIVE PROCEDURE TO IDENTIFY THE BE...ijaia
A support vector machine (SVM) learns the decision surface from two different classes of the input points, there are misclassifications in some of the input points in several applications. In this paper a bi-objective quadratic programming model is utilized and different feature quality measures are optimized simultaneously using the weighting method for solving our bi-objective quadratic programming problem. An important contribution will be added for the proposed bi-objective quadratic programming model by getting different efficient support vectors due to changing the weighting values. The numerical examples, give evidence of the effectiveness of the weighting parameters on reducing the misclassification between two classes of the input points. An interactive procedure will be added to identify the best compromise solution from the generated efficient solutions.
Nonlinear Programming: Theories and Algorithms of Some Unconstrained Optimiza...Dr. Amarjeet Singh
Nonlinear programming problem (NPP) had become an important branch of operations research, and it was the mathematical programming with the objective function or constraints being nonlinear functions. There were a variety of traditional methods to solve nonlinear programming problems such as bisection method, gradient projection method, the penalty function method, feasible direction method, the multiplier method. But these methods had their specific scope and limitations, the objective function and constraint conditions generally had continuous and differentiable request. The traditional optimization methods were difficult to adopt as the optimized object being more complicated. However, in this paper, mathematical programming techniques that are commonly used to extremize nonlinear functions of single and multiple (n) design variables subject to no constraints are been used to overcome the above challenge. Although most structural optimization problems involve constraints that bound the design space, study of the methods of unconstrained optimization is important for several reasons. Steepest Descent and Newton’s methods are employed in this paper to solve an optimization problem.
ENHANCING ENGLISH WRITING SKILLS THROUGH INTERNET-PLUS TOOLS IN THE PERSPECTI...ijfcstjournal
This investigation delves into incorporating a hybridized memetic strategy within the framework of English
composition pedagogy, leveraging Internet Plus resources. The study aims to provide an in-depth analysis
of how this method influences students’ writing competence, their perceptions of writing, and their
enthusiasm for English acquisition. Employing an explanatory research design that combines qualitative
and quantitative methods, the study collects data through surveys, interviews, and observations of students’
writing performance before and after the intervention. Findings demonstrate a beneficial impact of
integrating the memetic approach alongside Internet Plus tools on the writing aptitude of English as a
Foreign Language (EFL) learners. Students reported increased engagement with writing, attributing it to
the use of Internet plus tools. They also expressed that the memetic approach facilitated a deeper
understanding of cultural and social contexts in writing. Furthermore, the findings highlight a significant
improvement in students’ writing skills following the intervention. This study provides significant insights
into the practical implementation of the memetic approach within English writing education, highlighting
the beneficial contribution of Internet Plus tools in enriching students' learning journeys.
A SURVEY TO REAL-TIME MESSAGE-ROUTING NETWORK SYSTEM WITH KLA MODELLINGijfcstjournal
Messages routing over a network is one of the most fundamental concept in communication which requires
simultaneous transmission of messages from a source to a destination. In terms of Real-Time Routing, it
refers to the addition of a timing constraint in which messages should be received within a specified time
delay. This study involves Scheduling, Algorithm Design and Graph Theory which are essential parts of
the Computer Science (CS) discipline. Our goal is to investigate an innovative and efficient way to present
these concepts in the context of CS Education. In this paper, we will explore the fundamental modelling of
routing real-time messages on networks. We study whether it is possible to have an optimal on-line
algorithm for the Arbitrary Directed Graph network topology. In addition, we will examine the message
routing’s algorithmic complexity by breaking down the complex mathematical proofs into concrete, visual
examples. Next, we explore the Unidirectional Ring topology in finding the transmission’s
“makespan”.Lastly, we propose the same network modelling through the technique of Kinesthetic Learning
Activity (KLA). We will analyse the data collected and present the results in a case study to evaluate the
effectiveness of the KLA approach compared to the traditional teaching method.
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and multi-modal objective functions. DE has been consistently
ranked as one of the best search algorithm for solving global
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presents an Improved Constraint Differential Evolution
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Differential Evolution (DE) is a novel evolutionary
approach capable of handling non-differentiable, non-linear
and multi-modal objective functions. DE has been consistently
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presents an Improved Constraint Differential Evolution
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This work considers the multi-objective optimization problem constrained by a system of bipolar fuzzy relational equations with max-product composition. An integer optimization based technique for order of preference by similarity to the ideal solution is proposed for solving such a problem. Some critical features associated with the feasible domain and optimal solutions of the bipolar max-Tp equation constrained optimization problem are studied. An illustrative example verifying the idea of this paper is included. This is the first attempt to study the bipolar max-T equation constrained multi-objective optimization problems from an integer programming viewpoint.
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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
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The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Theoretical work submitted to the Journal should be original in its motivation or modeling structure. Empirical analysis should be based on a theoretical framework and should be capable of replication. It is expected that all materials required for replication (including computer programs and data sets) should be available upon request to the authors.
The International Journal of Engineering & Science would take much care in making your article published without much delay with your kind cooperation
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The assignment problem is a special type of linear programming problem and it is sub class of transportation problem. Assignment problems are defined with two sets of inputs i.e. set of resources and set of demands. Hungarian algorithm is able to solve assignment problems with precisely defined demands and resources.Nowadays, many organizations and competition companies consider markets of their products. They use many salespersons to improve their organizations marketing. Salespersons travel form one city to another city for their markets. There are some problems in travelling which salespeople should go which city in minimum cost. So, travelling assignment problem is a main process for many business functions. Mie Mie Aung | Yin Yin Cho | Khin Htay | Khin Soe Myint "Minimization of Assignment Problems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26712.pdfPaper URL: https://www.ijtsrd.com/computer-science/other/26712/minimization-of-assignment-problems/mie-mie-aung
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enthusiasm for English acquisition. Employing an explanatory research design that combines qualitative
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integrating the memetic approach alongside Internet Plus tools on the writing aptitude of English as a
Foreign Language (EFL) learners. Students reported increased engagement with writing, attributing it to
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improvement in students’ writing skills following the intervention. This study provides significant insights
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simultaneous transmission of messages from a source to a destination. In terms of Real-Time Routing, it
refers to the addition of a timing constraint in which messages should be received within a specified time
delay. This study involves Scheduling, Algorithm Design and Graph Theory which are essential parts of
the Computer Science (CS) discipline. Our goal is to investigate an innovative and efficient way to present
these concepts in the context of CS Education. In this paper, we will explore the fundamental modelling of
routing real-time messages on networks. We study whether it is possible to have an optimal on-line
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architecture styles, possible components, integration methods (connectors) and the exact application of
each style.
The objective of this research work was a comparative analysis of software architecture styles by its
weakness and benefits in order to select by the programmer during their design time. Finally, in this study,
the researcher has been identified architectural styles, weakness, and Strength and application areas with
its component, connector and Interface for the selected architectural styles.
SYSTEM ANALYSIS AND DESIGN FOR A BUSINESS DEVELOPMENT MANAGEMENT SYSTEM BASED...ijfcstjournal
A design of a sales system for professional services requires a comprehensive understanding of the
dynamics of sale cycles and how key knowledge for completing sales is managed. This research describes
a design model of a business development (sales) system for professional service firms based on the Saudi
Arabian commercial market, which takes into account the new advances in technology while preserving
unique or cultural practices that are an important part of the Saudi Arabian commercial market. The
design model has combined a number of key technologies, such as cloud computing and mobility, as an
integral part of the proposed system. An adaptive development process has also been used in implementing
the proposed design model.
AN ALGORITHM FOR SOLVING LINEAR OPTIMIZATION PROBLEMS SUBJECTED TO THE INTERS...ijfcstjournal
Frank t-norms are parametric family of continuous Archimedean t-norms whose members are also strict
functions. Very often, this family of t-norms is also called the family of fundamental t-norms because of the
role it plays in several applications. In this paper, optimization of a linear objective function with fuzzy
relational inequality constraints is investigated. The feasible region is formed as the intersection of two
inequality fuzzy systems defined by frank family of t-norms is considered as fuzzy composition. First, the
resolution of the feasible solutions set is studied where the two fuzzy inequality systems are defined with
max-Frank composition. Second, some related basic and theoretical properties are derived. Then, a
necessary and sufficient condition and three other necessary conditions are presented to conceptualize the
feasibility of the problem. Subsequently, it is shown that a lower bound is always attainable for the optimal
objective value. Also, it is proved that the optimal solution of the problem is always resulted from the
unique maximum solution and a minimal solution of the feasible region. Finally, an algorithm is presented
to solve the problem and an example is described to illustrate the algorithm. Additionally, a method is
proposed to generate random feasible max-Frank fuzzy relational inequalities. By this method, we can
easily generate a feasible test problem and employ our algorithm to it.
LBRP: A RESILIENT ENERGY HARVESTING NOISE AWARE ROUTING PROTOCOL FOR UNDER WA...ijfcstjournal
Underwater detector network is one amongst the foremost difficult and fascinating analysis arenas that
open the door of pleasing plenty of researchers during this field of study. In several under water based
sensor applications, nodes are square measured and through this the energy is affected. Thus, the mobility
of each sensor nodes are measured through the water atmosphere from the water flow for sensor based
protocol formations. Researchers have developed many routing protocols. However, those lost their charm
with the time. This can be the demand of the age to supply associate degree upon energy-efficient and
ascendable strong routing protocol for under water actuator networks. During this work, the authors tend
to propose a customary routing protocol named level primarily based routing protocol (LBRP), reaching to
offer strong, ascendable and energy economical routing. LBRP conjointly guarantees the most effective use
of total energy consumption and ensures packet transmission which redirects as an additional reliability in
compare to different routing protocols. In this work, the authors have used the level of forwarding node,
residual energy and distance from the forwarding node to the causing node as a proof in multicasting
technique comparisons. Throughout this work, the authors have got a recognition result concerning about
86.35% on the average in node multicasting performances. Simulation has been experienced each in a
wheezy and quiet atmosphere which represents the endorsement of higher performance for the planned
protocol.
STRUCTURAL DYNAMICS AND EVOLUTION OF CAPSULE ENDOSCOPY (PILL CAMERA) TECHNOLO...ijfcstjournal
This research paper examined and re-evaluates the technological innovation, theory, structural dynamics
and evolution of Pill Camera(Capsule Endoscopy) technology in redirecting the response manner of small
bowel (intestine) examination in human. The Pill Camera (Endoscopy Capsule) is made up of sealed
biocompatible material to withstand acid, enzymes and other antibody chemicals in the stomach is a
technology that helps the medical practitioners especially the general physicians and the
gastroenterologists to examine and re-examine the intestine for possible bleeding or infection. Before the
advent of the Pill camera (Endoscopy Capsule) the colonoscopy was the local method used but research
showed that some parts (bowel) of the intestine can’t be reach by mere traditional method hence the need
for Pill Camera. Countless number of deaths from stomach disease such as polyps, inflammatory bowel
(Crohn”s diseases), Cancers, Ulcer, anaemia and tumours of small intestines which ordinary would have
been detected by sophisticated technology like Pill Camera has become norm in the developing nations.
Nevertheless, not only will this paper examine and re-evaluate the Pill Camera Innovation, theory,
Structural dynamics and evolution it unravelled and aimed to create awareness for both medical
practitioners and the public.
AN OPTIMIZED HYBRID APPROACH FOR PATH FINDINGijfcstjournal
Path finding algorithm addresses problem of finding shortest path from source to destination avoiding
obstacles. There exist various search algorithms namely A*, Dijkstra's and ant colony optimization. Unlike
most path finding algorithms which require destination co-ordinates to compute path, the proposed
algorithm comprises of a new method which finds path using backtracking without requiring destination
co-ordinates. Moreover, in existing path finding algorithm, the number of iterations required to find path is
large. Hence, to overcome this, an algorithm is proposed which reduces number of iterations required to
traverse the path. The proposed algorithm is hybrid of backtracking and a new technique(modified 8-
neighbor approach). The proposed algorithm can become essential part in location based, network, gaming
applications. grid traversal, navigation, gaming applications, mobile robot and Artificial Intelligence.
EAGRO CROP MARKETING FOR FARMING COMMUNITYijfcstjournal
The Major Occupation in India is the Agriculture; the people involved in the Agriculture belong to the poor
class and category. The people of the farming community are unaware of the new techniques and Agromachines, which would direct the world to greater heights in the field of agriculture. Though the farmers
work hard, they are cheated by agents in today’s market. This serves as a opportunity to solve
all the problems that farmers face in the current world. The eAgro crop marketing will serve as a better
way for the farmers to sell their products within the country with some mediocre knowledge about using
the website. This would provide information to the farmers about current market rate of agro-products,
their sale history and profits earned in a sale. This site will also help the farmers to know about the market
information and to view agricultural schemes of the Government provided to farmers.
EDGE-TENACITY IN CYCLES AND COMPLETE GRAPHSijfcstjournal
It is well known that the tenacity is a proper measure for studying vulnerability and reliability in graphs.
Here, a modified edge-tenacity of a graph is introduced based on the classical definition of tenacity.
Properties and bounds for this measure are introduced; meanwhile edge-tenacity is calculated for cycle
graphs and also for complete graphs.
COMPARATIVE STUDY OF DIFFERENT ALGORITHMS TO SOLVE N QUEENS PROBLEMijfcstjournal
This Paper provides a brief description of the Genetic Algorithm (GA), the Simulated Annealing (SA)
Algorithm, the Backtracking (BT) Algorithm and the Brute Force (BF) Search Algorithm and attempts to
explain the way as how the Proposed Genetic Algorithm (GA), the Proposed Simulated Annealing (SA)
Algorithm using GA, the Backtracking (BT) Algorithm and the Brute Force (BF) Search Algorithm can be
employed in finding the best solution of N Queens Problem and also, makes a comparison between these
four algorithms. It is entirely a review based work. The four algorithms were written as well as
implemented. From the Results, it was found that, the Proposed Genetic Algorithm (GA) performed better
than the Proposed Simulated Annealing (SA) Algorithm using GA, the Backtracking (BT) Algorithm and
the Brute Force (BF) Search Algorithm and it also provided better fitness value (solution) than the
Proposed Simulated Annealing Algorithm (SA) using GA, the Backtracking (BT) Algorithm and the Brute
Force (BF) Search Algorithm, for different N values. Also, it was noticed that, the Proposed GA took more
time to provide result than the Proposed SA using GA.
PSTECEQL: A NOVEL EVENT QUERY LANGUAGE FOR VANET’S UNCERTAIN EVENT STREAMSijfcstjournal
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and spatial event streams. However, we usually cannot get the accurate data because the device sensing
accuracy limitations of the system. We only can get the uncertain data from the complex and limited
environment of the VANET. Because the VANET’s event streams are consist of the uncertain data, so they
are also uncertain. How effective to express and process these uncertain event streams has become the core
issue for the VANET system. To solve this problem, we propose a novel complex event query language
PSTeCEQL (probabilistic spatio-temporal constraint event query language). Firstly, we give the definition
of the possible world model of VANET’s uncertain event streams. Secondly, we propose an event query
language PSTeCEQL and give the syntax and the operational semantics of the language. Finally, we
illustrate the validity of the PSTeCEQL by an example.
CLUSTBIGFIM-FREQUENT ITEMSET MINING OF BIG DATA USING PRE-PROCESSING BASED ON...ijfcstjournal
Now a day enormous amount of data is getting explored through Internet of Things (IoT) as technologies
are advancing and people uses these technologies in day to day activities, this data is termed as Big Data
having its characteristics and challenges. Frequent Itemset Mining algorithms are aimed to disclose
frequent itemsets from transactional database but as the dataset size increases, it cannot be handled by
traditional frequent itemset mining. MapReduce programming model solves the problem of large datasets
but it has large communication cost which reduces execution efficiency. This proposed new pre-processed
k-means technique applied on BigFIM algorithm. ClustBigFIM uses hybrid approach, clustering using kmeans algorithm to generate Clusters from huge datasets and Apriori and Eclat to mine frequent itemsets
from generated clusters using MapReduce programming model. Results shown that execution efficiency of
ClustBigFIM algorithm is increased by applying k-means clustering algorithm before BigFIM algorithm as
one of the pre-processing technique.
A MUTATION TESTING ANALYSIS AND REGRESSION TESTINGijfcstjournal
Software testing is a testing which conducted a test to provide information to client about the quality of the
product under test. Software testing can also provide an objective, independent view of the software to
allow the business to appreciate and understand the risks of software implementation. In this paper we
focused on two main software testing –mutation testing and mutation testing. Mutation testing is a
procedural testing method, i.e. we use the structure of the code to guide the test program, A mutation is a
little change in a program. Such changes are applied to model low level defects that obtain in the process
of coding systems. Ideally mutations should model low-level defect creation. Mutation testing is a process
of testing in which code is modified then mutated code is tested against test suites. The mutations used in
source code are planned to include in common programming errors. A good unit test typically detects the
program mutations and fails automatically. Mutation testing is used on many different platforms, including
Java, C++, C# and Ruby. Regression testing is a type of software testing that seeks to uncover
new software bugs, or regressions, in existing functional and non-functional areas of a system after
changes such as enhancements, patches or configuration changes, have been made to them. When defects
are found during testing, the defect got fixed and that part of the software started working as needed. But
there may be a case that the defects that fixed have introduced or uncovered a different defect in the
software. The way to detect these unexpected bugs and to fix them used regression testing. The main focus
of regression testing is to verify that changes in the software or program have not made any adverse side
effects and that the software still meets its need. Regression tests are done when there are any changes
made on software, because of modified functions.
GREEN WSN- OPTIMIZATION OF ENERGY USE THROUGH REDUCTION IN COMMUNICATION WORK...ijfcstjournal
Advances in micro fabrication and communication techniques have led to unimaginable proliferation of
WSN applications. Research is focussed on reduction of setup operational energy costs. Bulk of operational
energy costs are linked to communication activities of WSN. Any progress towards energy efficiency has a
potential of huge savings globally. Therefore, every energy efficient step is an endeavour to cut costs and
‘Go Green’. In this paper, we have proposed a framework to reduce communication workload through: Innetwork compression and multiple query synthesis at the base-station and modification of query syntax
through introduction of Static Variables. These approaches are general approaches which can be used in
any WSN irrespective of application.
A NEW MODEL FOR SOFTWARE COSTESTIMATION USING HARMONY SEARCHijfcstjournal
Accurate and realistic estimation is always considered to be a great challenge in software industry.
Software Cost Estimation (SCE) is the standard application used to manage software projects. Determining
the amount of estimation in the initial stages of the project depends on planning other activities of the
project. In fact, the estimation is confronted with a number of uncertainties and barriers’, yet assessing the
previous projects is essential to solve this problem. Several models have been developed for the analysis of
software projects. But the classical reference method is the COCOMO model, there are other methods
which are also applied such as Function Point (FP), Line of Code(LOC); meanwhile, the expert`s opinions
matter in this regard. In recent years, the growth and the combination of meta-heuristic algorithms with
high accuracy have brought about a great achievement in software engineering. Meta-heuristic algorithms
which can analyze data from multiple dimensions and identify the optimum solution between them are
analytical tools for the analysis of data. In this paper, we have used the Harmony Search (HS)algorithm for
SCE. The proposed model which is a collection of 60 standard projects from Dataset NASA60 has been
assessed.The experimental results show that HS algorithm is a good way for determining the weight
similarity measures factors of software effort, and reducing the error of MRE.
AGENT ENABLED MINING OF DISTRIBUTED PROTEIN DATA BANKSijfcstjournal
Mining biological data is an emergent area at the intersection between bioinformatics and data mining
(DM). The intelligent agent based model is a popular approach in constructing Distributed Data Mining
(DDM) systems to address scalable mining over large scale distributed data. The nature of associations
between different amino acids in proteins has also been a subject of great anxiety. There is a strong need to
develop new models and exploit and analyze the available distributed biological data sources. In this study,
we have designed and implemented a multi-agent system (MAS) called Agent enriched Quantitative
Association Rules Mining for Amino Acids in distributed Protein Data Banks (AeQARM-AAPDB). Such
globally strong association rules enhance understanding of protein composition and are desirable for
synthesis of artificial proteins. A real protein data bank is used to validate the system.
International Journal on Foundations of Computer Science & Technology (IJFCST)ijfcstjournal
International Journal on Foundations of Computer Science & Technology (IJFCST) is a Bi-monthly peer-reviewed and refereed open access journal that publishes articles which contribute new results in all areas of the Foundations of Computer Science & Technology. Over the last decade, there has been an explosion in the field of computer science to solve various problems from mathematics to engineering. This journal aims to provide a platform for exchanging ideas in new emerging trends that needs more focus and exposure and will attempt to publish proposals that strengthen our goals. Topics of interest include, but are not limited to the following:
Because the technology is used largely in the last decades; cybercrimes have become a significant
international issue as a result of the huge damage that it causes to the business and even to the ordinary
users of technology. The main aims of this paper is to shed light on digital crimes and gives overview about
what a person who is related to computer science has to know about this new type of crimes. The paper has
three sections: Introduction to Digital Crime which gives fundamental information about digital crimes,
Digital Crime Investigation which presents different investigation models and the third section is about
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DISTRIBUTION OF MAXIMAL CLIQUE SIZE UNDER THE WATTS-STROGATZ MODEL OF EVOLUTI...ijfcstjournal
In this paper, we analyze the evolution of a small-world network and its subsequent transformation to a
random network using the idea of link rewiring under the well-known Watts-Strogatz model for complex
networks. Every link u-v in the regular network is considered for rewiring with a certain probability and if
chosen for rewiring, the link u-v is removed from the network and the node u is connected to a randomly
chosen node w (other than nodes u and v). Our objective in this paper is to analyze the distribution of the
maximal clique size per node by varying the probability of link rewiring and the degree per node (number
of links incident on a node) in the initial regular network. For a given probability of rewiring and initial
number of links per node, we observe the distribution of the maximal clique per node to follow a Poisson
distribution. We also observe the maximal clique size per node in the small-world network to be very close
to that of the average value and close to that of the maximal clique size in a regular network. There is no
appreciable decrease in the maximal clique size per node when the network transforms from a regular
network to a small-world network. On the other hand, when the network transforms from a small-world
network to a random network, the average maximal clique size value decreases significantly
Explore our comprehensive data analysis project presentation on predicting product ad campaign performance. Learn how data-driven insights can optimize your marketing strategies and enhance campaign effectiveness. Perfect for professionals and students looking to understand the power of data analysis in advertising. for more details visit: https://bostoninstituteofanalytics.org/data-science-and-artificial-intelligence/
Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...John Andrews
SlideShare Description for "Chatty Kathy - UNC Bootcamp Final Project Presentation"
Title: Chatty Kathy: Enhancing Physical Activity Among Older Adults
Description:
Discover how Chatty Kathy, an innovative project developed at the UNC Bootcamp, aims to tackle the challenge of low physical activity among older adults. Our AI-driven solution uses peer interaction to boost and sustain exercise levels, significantly improving health outcomes. This presentation covers our problem statement, the rationale behind Chatty Kathy, synthetic data and persona creation, model performance metrics, a visual demonstration of the project, and potential future developments. Join us for an insightful Q&A session to explore the potential of this groundbreaking project.
Project Team: Jay Requarth, Jana Avery, John Andrews, Dr. Dick Davis II, Nee Buntoum, Nam Yeongjin & Mat Nicholas
Techniques to optimize the pagerank algorithm usually fall in two categories. One is to try reducing the work per iteration, and the other is to try reducing the number of iterations. These goals are often at odds with one another. Skipping computation on vertices which have already converged has the potential to save iteration time. Skipping in-identical vertices, with the same in-links, helps reduce duplicate computations and thus could help reduce iteration time. Road networks often have chains which can be short-circuited before pagerank computation to improve performance. Final ranks of chain nodes can be easily calculated. This could reduce both the iteration time, and the number of iterations. If a graph has no dangling nodes, pagerank of each strongly connected component can be computed in topological order. This could help reduce the iteration time, no. of iterations, and also enable multi-iteration concurrency in pagerank computation. The combination of all of the above methods is the STICD algorithm. [sticd] For dynamic graphs, unchanged components whose ranks are unaffected can be skipped altogether.
Levelwise PageRank with Loop-Based Dead End Handling Strategy : SHORT REPORT ...Subhajit Sahu
Abstract — Levelwise PageRank is an alternative method of PageRank computation which decomposes the input graph into a directed acyclic block-graph of strongly connected components, and processes them in topological order, one level at a time. This enables calculation for ranks in a distributed fashion without per-iteration communication, unlike the standard method where all vertices are processed in each iteration. It however comes with a precondition of the absence of dead ends in the input graph. Here, the native non-distributed performance of Levelwise PageRank was compared against Monolithic PageRank on a CPU as well as a GPU. To ensure a fair comparison, Monolithic PageRank was also performed on a graph where vertices were split by components. Results indicate that Levelwise PageRank is about as fast as Monolithic PageRank on the CPU, but quite a bit slower on the GPU. Slowdown on the GPU is likely caused by a large submission of small workloads, and expected to be non-issue when the computation is performed on massive graphs.
A HYBRID COA/ε-CONSTRAINT METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMS
1. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.5, No.5, September 2015
DOI:10.5121/ijfcst.2015.5503 27
A HYBRID COA/ε-CONSTRAINT METHOD FOR
SOLVING MULTI-OBJECTIVE PROBLEMS
Mahdi parvizi, Elham Shadkam and Niloofar jahani
Department of Industrial Engineering, Faculty of Eng.; Khayyam University, Mashhad,
Iran
ABSTRACT
In this paper, a hybrid method for solving multi-objective problem has been provided. The proposed
method is combining the ε-Constraint and the Cuckoo algorithm. First the multi objective problem
transfers into a single-objective problem using ε-Constraint, then the Cuckoo optimization algorithm will
optimize the problem in each task. At last the optimized Pareto frontier will be drawn. The advantage of
this method is the high accuracy and the dispersion of its Pareto frontier. In order to testing the efficiency
of the suggested method, a lot of test problems have been solved using this method. Comparing the results
of this method with the results of other similar methods shows that the Cuckoo algorithm is more suitable
for solving the multi-objective problems.
KEYWORDS
Cuckoo optimization algorithm (COA), ε-Constraint, Pareto frontier, MODM (Multi-objective decision
making), Optimization.
1. INTRODUCTION
In the single-objective optimization it is assumed that the decision makers connect to a single
purpose Such as maximizing the profit, minimizing the costs, minimizing the waste, maximizing
the market share etc. But in the real world, the decision maker checks more than a single
objective. For example in order to study the production level in a company, if only the profit
would be examined and all other objectives such as customer satisfaction, staff satisfaction, the
production diversity, market share etc would be rejected, the results won't be reliable. So using
the multi-objective decision making (MODM) is necessary. Finding an optimized answer that
covers all of the restrictions together is impossible in multi-objective problems. So using the
Pareto frontier, reliable answers for a multi-objective problem will be obtained. There are many
different ways for solving multi-objective problems. These ways divide in two groups. Combined
methods (all of the objectives acts as a single one) and the limited methods (one of the objective
function will be kept and other ones would be act as the restriction).
Ehrgott and Gandibleux studied on the approximate and the accurate problems related to the
combination method of multi-objective problems [1]. Hannan and Klein submitted an algorithm
for solving multi-objective integer linear programming. This algorithm use to eliminate the extra
known dominant solutions [2]. Leumanns et al. submitted a meta-heuristic algorithm in order to
find approximate effective solutions of multi-objective integer programming, using the ε-
Constraint [3]. Sylva and Crema submitted a solution for finding the set of non-dominant vectors
in multi-objective integer linear programming [4]. Arakaw et al. combined the GDEA and the GA
methods to generate the efficient frontier in multi-objective optimization problems. [5] Deb used
the evolutionary algorithms for solving the multi-objective algorithms [6]. Nakayama drew the
2. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.5, No.5, September 2015
28
Pareto frontier of the multi-objective optimization algorithms using DEA (Data Envelopment
Analysis) [7]. Agarwal drew the Pareto frontier of the multi-objective optimization algorithms
using GA (Genetic Algorithm) [8]. Vincova used the DEA in order to find the Pareto frontier [9].
Reyes-Sierra investigated the solution of multi-objective optimization algorithm using the particle
swarm algorithm [10]. Seiford and Tone helped the multi-objective optimization algorithm using
DEA and publishing related software [11]. Pham solved the multi-objective optimization
algorithm using the Bee Algorithm [12]. Durillo and Garc'ıa-Nieto investigated a new solution for
multi-objective optimization algorithm based on the particle swarm algorithm [13]. Yun studied
the solution of multi-objective optimization algorithm using the GA and DEA. Also he found the
Pareto frontiers of efficient points using this method [14]. Yang used the Cuckoo optimization
algorithm in order to find the Pareto frontiers [15]. Gorjestani et al. proposed a COA multi
objective algorithm using DEA method [16].
This article submits a hybrid algorithm that uses the advantages of both the Cuckoo algorithm and
the ε-Constraint method simultaneously. The submitted algorithm solves the multi-objective
problems for allowable εs using the Cuckoo algorithm and the Matlab software. At last for each
iteration, it finds a Pareto answer and linking these answers draw the Pareto frontier. This method
draws a better Pareto frontier than other similar methods. In the second section, the Cuckoo
algorithm will be introduced. The third section explains the multi-objective algorithm and the ε-
Constraint method. In the fourth section, the suggested hybrid algorithm of this article will be
investigated in details. Test problems and their solution with similar algorithms compares in the
fifth section then in the last section, the conclusion and the future offers will be submitted.
2. THE CUCKOO ALGORITHM INTRODUCTION
The cuckoo search was expanded by Xin-She Yang and Suash Deb in 2009. After that the
Cuckoo optimization algorithm was submitted by Ramin Rajabioun in 2011 [17]. This algorithm
applied in several researches such as production planning problem [18](Akbarzadeh and
Shadkam, 2015), portfolio selection problem [19](Shadkam et al., 2015), evaluation of
organization efficiency [20](Shadkam and Bijari, 2015), evaluation of COA [21](Shadkam and
Bijari, 2014) and so on
Flowchart of the Cuckoo algorithm is given in the figure 1
3. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.5, No.5, September 2015
Figure1: the Cuckoo algorithm flowchart
For more information refer to [17
3. THE MULTI-OBJECTIVE ALGORITHM
General form of a multi-objective opt
Max (Min)=
Max (Min)=
⋮
Max(Min)=
s.t.
, 1, 2 …
0, 1,2, … . ,
In the multi-objective problems, we face some objectives in contrast of single
algorithms that has just one objective. In this model, k is the number of objective functions that
can be either max or min and m is the number of restrictions and n is the number problem's
variables.
In the multi-objective optimization problems there is
objective functions simultaneously. For this reason, the Pareto optimal
International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.5, No.5, September 2015
Figure1: the Cuckoo algorithm flowchart
7].
OBJECTIVE ALGORITHM AND THE ε-CONSTRAINT METHOD
objective optimization problem is as (1):
objective problems, we face some objectives in contrast of single
algorithms that has just one objective. In this model, k is the number of objective functions that
min and m is the number of restrictions and n is the number problem's
objective optimization problems there is not a certain answer that optimizes
objective functions simultaneously. For this reason, the Pareto optimal concept is introduced.
International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.5, No.5, September 2015
29
ONSTRAINT METHOD:
(1)
objective problems, we face some objectives in contrast of single-objective
algorithms that has just one objective. In this model, k is the number of objective functions that
min and m is the number of restrictions and n is the number problem's
not a certain answer that optimizes all of the
concept is introduced.
4. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.5, No.5, September 2015
30
The Pareto optimal concept explanation is that x∗ x ... ,x , x! is an optimal pareto. If for
each allowablex
"and i={1,2,..k}, we have (for minimizing problem): ∀ %& ̅∗ ≤ ̅
Then x∗ will be the optimal Pareto that n is the number of decision making variables and k is the
number of objective functions. In other words, x∗ is an optimal Pareto if there is no other x
"vector
that doesn’t make at least one objective function worse in order to improve some of the objective
functions.
4. ε-CONSTRAINT METHOD
In this method, one of the different objective functions will be selected and other objective
functions will act as the restrictions considering a specific constraint and the problem changes
into a single-objective problem. Using different εs results optimal pareto answers.
General form of this method is given as (2).
Min F(X)={ , … , )(x)}
*. +.
( ) <=>b
≥ 0
Min F(X)= ( )
s.t.
( ) <=>b
( ) ≤ ε , ≠ , = 1,..,n
≥ 0
(2)
If the objective function is max, the constraint is f/(x) ≥ ε/. Selecting the ε is the most important
thing in this method because the answers are so sensitive to this parameter. So the selected ε must
be in range of f/
01!
≤ ε/ ≤ f/
023
for each objective function.
5. THE COA/ ε-CONSTRAINT HYBRID ALGORITHM
Step 1: first according to the objective function of main problem, the mathematical model will be
written based on the ε-Constraint method and the problem is converted from multi-objective to
single-objective problem.
Step 2: the obtained function from the ε-Constraint method will be described as the meta-heuristic
Cuckoo algorithm function.
Step 3: the iterations including the εs for solving the main problem is formed for the Cuckoo
algorithm, and this loop will be iterate until the Cuckoo algorithm ends.
Step 4: according to the first laying time and the initial number of cuckoos, a matrix will be
formed from the habitats in the beginning of implementing the Cuckoo algorithm.
Step 5: the obtained function from step 2 gets the habitats matrix as its input data and finds the
objective problem magnitude according to the new restrictions for each habitat.
Step 6: the Cuckoo algorithm sorts the habitats according to their quantity and objective functions
as usual and the rest of the tasks will be the same as it is described in references number [17].
Step 7: in each iteration of the loop, the habitat that earns the most quantity of the objective
function called best cuckoo and will be saved in a different matrix.
Step 8: after exiting the formed loop, the functionsf and f calculate for each saved points.
5. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.5, No.5, September 2015
31
Step 9: a plot of the f and f functions quantity will be drawn that is the Pareto frontier of the
main multi-objective optimization problem.
6. SOLVING TEST PROBLEMS
A number of test functions have been provided that can help to validate the suggested approach in
table 4.
Table 4. Test problems
According to high importance of the input parameters of meta-heuristic algorithm and its effect
on the final answer, the parameters of the Cuckoo algorithm for solving any problems are given
below:
Number of initial population=5, minimum number of eggs for each=2, maximum number of eggs
for each cuckoo= 4, number of clusters=1.
constraints
Objective function
, ≥ 0
4≤ ( − 2) + ( − 2)
=
=
1
( − 1)5
+ ≤ 0
, ≥ 0
= 2 −
= −
2
− −3 5
≥ 0
≥ −1, ≤ 2
=
=
3
, ≥ 0
( ) + ( − 5) ≥ 25
= 4 + 4
= ( − 5) + ( − 5)
4
−5 ≤ ≤5, i=1,2,3
= ( : −10exp (
=
− 0.2> + ? )
= ∑ [| |C.D
5
= + 5 Sin( 5
)]
5
Cos(16arctan(
GH
GI
)) ≥ 0-1- 0.1 +
( − 0.5) + ( − 0.5) ≥ −0.5
≥ 0, ≥ π
=
=
6
−4 ≤ x1 ≤4, i = 1,2
min f = 1 − exp(− :(x1 −
1
√n
)
!
1=
)
min f = 1 − exp(−:(x1 +
1
√n
)
!
1=
)
7
∈ [0.1,1N, ∈ [0,5N
9 + ≥ 6
9 + ≥ 1
=
=
(1 + )
8
3 − ≥ −10
∈ [−20,20N, ∈ [−20,20N
( ) + ( ) ≥ 225
= ( − 2) +( − 1) + 2
( − 1) - = 9
9
6. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.5, No.5, September 2015
32
Test problem 1: [22,17]
For solving the example using the ε-Constraint method, one of the objective functions will be
kept and the other one will be added to the constraints as it mentioned before. For this test
function, we keep f in the objective function and add f to the constraint and the problem will be
as the equation (3):
=
s.t.
( − 2) + ( − 2) ≥ 4
≥ ε
0
(3)
In order to find the allowable range of ε, f will be solved once with min function and once with
max function. The allowable range will be the 0 ≤ε≤ 4.
For finding allowable εs with the pace of 0.01, the problem will be solved using the Cuckoo
algorithm and the Matlab software for 400 iterations. The Pareto frontier is shown in figure 2.
Also the results of finding the Pareto frontier using the similar methods are shown in this figure
too.
Figure 2. Comparing the suggested method with other methods
Ranking Method
DEA Method
COA/ε–Constraint Method
7. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.5, No.5, September 2015
33
Test problem 2: [22,17]
The converted problem is as the equation (4)
= 2 −
s.t.
+( − 1)5 ≤ 0
− ≥ ε
0
(4)
The allowable range of ε will be the −1 ≤ε≤ 0and the pace is 0.0025. The Pareto frontier after
400 iterations is shown in figure 3.
Figure 3. Comparing the suggested method with other methods
Test problem 3: [22,17]
The allowable range of ε will be the −2 ≤ε≤ 2 and the pace is 0.01and the Pareto frontier after
400 iterations is shown in figure 4.
Ranking Method
DEA Method
COA/ε–Constraint Method
8. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.5, No.5, September 2015
34
Figure 4. Comparing the suggested method with other methods
Test problem 4:[23,18]
The allowable range of ε will be the 0 ≤ε≤ 50 and the pace is 0. 125. The Pareto frontier after
400 iterations is shown in figure 5.
Ranking Method
DEA Method
COA/ε–Constraint Method
COA/ε–Constraint Method
9. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.5, No.5, September 2015
35
Figure 5. Comparing the suggested method with other methods
Test problem 5:[24,19]
The allowable range of ε will be the −11 ≤ε≤ 20 and the pace is 0. 0775. The Pareto frontier
after 400 iterations is shown in figure 6.
Figure 6. Comparing the suggested method with other methods
Ranking Method
GDEA Method
SPEA Method
NSGA-II Method
COA/ε–Constraint Method
10. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.5, No.5, September 2015
36
Test problem 6:[24,19]
The allowable range of ε will be the 0 ≤ε≤ 1.2 and the pace is 0. 008. The Pareto frontier after
400 iterations is shown in figure 7.
Figure 7. Comparing the suggested method with other methods
Test problem 7: [24,19]
The allowable range of ε will be the −25 ≤ε≤ 1 and the pace is 0. 065. The Pareto frontier after
400 iterations is shown in figure 8.
Ray–Tai–Seow’s Method
NSGA-II Method
COA/ε–Constraint Method
11. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.5, No.5, September 2015
37
Figure 8. Comparing the suggested method with other methods
Test problem 8: [24,19]
The allowable range of ε will be the 1 ≤ε≤ 9 and the pace is 0.02. The Pareto frontier after 400
iterations is shown in figure 9.
Ranking Method
GDEA Method
COA/ε–Constraint Method
COA/ε–Constraint Method
12. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.5, No.5, September 2015
38
Figure 9. Comparing the suggested method with other methods
Test problem 9:[24,19]
The allowable range of ε will be the −196 ≤ε≤ 72 and the pace is 2.68. The Pareto frontier after
400 iterations is shown in figure 10.
Figure 10. Comparing the suggested method with other methods
NSGA-II_Method
Ray–Tai–Seow’s Method
Ray–Tai–Seow’s Method
NSGA-II Method
COA/ε–Constraint Method
13. International Journal in Foundations of Computer Science & Technology (IJFCST) Vol.5, No.5, September 2015
39
According to the Pareto frontier resulted from different functions, it is evident that the suggested
method provides uniform and exact frontiers in fewer iterations than other similar methods.
7. CONCLUSION
In this paper, we presented a hybrid method for solving multi-objective problems using the
Cuckoo algorithm and the ε-Constraint method. According to the obtained results from the
proposed method and comparing the obtained Pareto frontiers with the results of similar methods
such as GDEA/GA, DEA/GA, RANKING, NSGA-II, Ray–Tai–Seow’s and SPEA, we concluded
that not only the Cuckoo algorithm finds better Pareto frontiers but also, it needs shortest time to
give the Pareto frontier. Pareto frontier of proposed method has more dispersion than the other
similar algorithms. So the COA/ε-Constraint method is a suitable and reliable method for solving
multi-objective optimization problems. In the future, solving the problems with more objectives,
multi-objective allocation problem and multi-objective problems of project controlling with
minimizing the time and cost target would be in order.
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