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
As the complexity of choosing optimised and task specific steps and ML models is often beyond non-experts, the rapid growth of machine learning applications has created a demand for off-the-shelf machine learning methods that can be used easily and without expert knowledge. We call the resulting research area that targets progressive automation of machine learning AutoML.
Although it focuses on end users without expert knowledge, AutoML also offers new tools to machine learning experts, for example to:
1. Perform architecture search over deep representations
2. Analyse the importance of hyperparameters.
Genetic Algorithm (GA) is a search-based optimization technique based on the principles of Genetics and Natural Selection. It is frequently used to find optimal or near-optimal solutions to difficult problems which otherwise would take a lifetime to solve. It is frequently used to solve optimization problems, in research, and in machine learning.
Large Language Models, No-Code, and Responsible AI - Trends in Applied NLP in...David Talby
An April 2023 presentation to the AMIA working group on natural language processing. The talk focuses on three current trends in NLP and how they apply in healthcare: Large language models, No-code, and Responsible AI.
And then there were ... Large Language ModelsLeon Dohmen
It is not often even in the ICT world that one witnesses a revolution. The rise of the Personal Computer, the rise of mobile telephony and, of course, the rise of the Internet are some of those revolutions. So what is ChatGPT really? Is ChatGPT also such a revolution? And like any revolution, does ChatGPT have its winners and losers? And who are they? How do we ensure that ChatGPT contributes to a positive impulse for "Smart Humanity?".
During a key note om April 3 and 13 2023 Piek Vossen explained the impact of Large Language Models like ChatGPT.
Prof. PhD. Piek Th.J.M. Vossen, is Full professor of Computational Lexicology at the Faculty of Humanities, Department of Language, Literature and Communication (LCC) at VU Amsterdam:
What is ChatGPT? What technology and thought processes underlie it? What are its consequences? What choices are being made? In the presentation, Piek will elaborate on the basic principles behind Large Language Models and how they are used as a basis for Deep Learning in which they are fine-tuned for specific tasks. He will also discuss a specific variant GPT that underlies ChatGPT. It covers what ChatGPT can and cannot do, what it is good for and what the risks are.
As the complexity of choosing optimised and task specific steps and ML models is often beyond non-experts, the rapid growth of machine learning applications has created a demand for off-the-shelf machine learning methods that can be used easily and without expert knowledge. We call the resulting research area that targets progressive automation of machine learning AutoML.
Although it focuses on end users without expert knowledge, AutoML also offers new tools to machine learning experts, for example to:
1. Perform architecture search over deep representations
2. Analyse the importance of hyperparameters.
Genetic Algorithm (GA) is a search-based optimization technique based on the principles of Genetics and Natural Selection. It is frequently used to find optimal or near-optimal solutions to difficult problems which otherwise would take a lifetime to solve. It is frequently used to solve optimization problems, in research, and in machine learning.
Large Language Models, No-Code, and Responsible AI - Trends in Applied NLP in...David Talby
An April 2023 presentation to the AMIA working group on natural language processing. The talk focuses on three current trends in NLP and how they apply in healthcare: Large language models, No-code, and Responsible AI.
And then there were ... Large Language ModelsLeon Dohmen
It is not often even in the ICT world that one witnesses a revolution. The rise of the Personal Computer, the rise of mobile telephony and, of course, the rise of the Internet are some of those revolutions. So what is ChatGPT really? Is ChatGPT also such a revolution? And like any revolution, does ChatGPT have its winners and losers? And who are they? How do we ensure that ChatGPT contributes to a positive impulse for "Smart Humanity?".
During a key note om April 3 and 13 2023 Piek Vossen explained the impact of Large Language Models like ChatGPT.
Prof. PhD. Piek Th.J.M. Vossen, is Full professor of Computational Lexicology at the Faculty of Humanities, Department of Language, Literature and Communication (LCC) at VU Amsterdam:
What is ChatGPT? What technology and thought processes underlie it? What are its consequences? What choices are being made? In the presentation, Piek will elaborate on the basic principles behind Large Language Models and how they are used as a basis for Deep Learning in which they are fine-tuned for specific tasks. He will also discuss a specific variant GPT that underlies ChatGPT. It covers what ChatGPT can and cannot do, what it is good for and what the risks are.
YouTube Link: https://youtu.be/guVvtZ7ZClw
***Machine Learning Course: https://www.edureka.co/masters-program/machine-learning-engineer-training ***
This PPT on "apriori Algorithm explained" provides you with a detailed and comprehensive knowledge of the Apriori Algorithm and Market Basket Analysis that Companies use to sell more products and gain profits. Topics covered in this PPT are as follows:
Market Basket Analysis
Association Rule Mining
Apriori Algorithm
Python DEMO
Follow us to never miss an update in the future.
YouTube: https://www.youtube.com/user/edurekaIN
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Facebook: https://www.facebook.com/edurekaIN/
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Castbox: https://castbox.fm/networks/505?country=in
Slides for a talk about Graph Neural Networks architectures, overview taken from very good paper by Zonghan Wu et al. (https://arxiv.org/pdf/1901.00596.pdf)
BERT: Bidirectional Encoder Representations from TransformersLiangqun Lu
BERT was developed by Google AI Language and came out Oct. 2018. It has achieved the best performance in many NLP tasks. So if you are interested in NLP, studying BERT is a good way to go.
A non-technical overview of Large Language Models, exploring their potential, limitations, and customization for specific challenges. While this deck is tailored for an audience from the financial industry in mind, its content remains broadly applicable.
(Note: Discover a slightly updated version of this deck at slideshare.net/LoicMerckel/introduction-to-llms.)
Sentiment Analysis Using Hybrid Structure of Machine Learning AlgorithmsSangeeth Nagarajan
Sentiment Analysis is the process used to determine the attitude/ opinion/ emotion expressed by a person about a particular topic. The presentation dealt with general approach and different machine learning based classification alogorithms. The slides is based on the work "Sentiment analysis using Neuro-Fuzzy and Hidden Markov models of text" by Rustamov S , Mustafayev E and Clements M A.
How to Win Machine Learning Competitions ? HackerEarth
This presentation was given by Marios Michailidis (a.k.a Kazanova), Current Kaggle Rank #3 to help community learn machine learning better. It comprises of useful ML tips and techniques to perform better in machine learning competitions. Read the full blog: http://blog.hackerearth.com/winning-tips-machine-learning-competitions-kazanova-current-kaggle-3
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.
YouTube Link: https://youtu.be/guVvtZ7ZClw
***Machine Learning Course: https://www.edureka.co/masters-program/machine-learning-engineer-training ***
This PPT on "apriori Algorithm explained" provides you with a detailed and comprehensive knowledge of the Apriori Algorithm and Market Basket Analysis that Companies use to sell more products and gain profits. Topics covered in this PPT are as follows:
Market Basket Analysis
Association Rule Mining
Apriori Algorithm
Python DEMO
Follow us to never miss an update in the future.
YouTube: https://www.youtube.com/user/edurekaIN
Instagram: https://www.instagram.com/edureka_learning/
Facebook: https://www.facebook.com/edurekaIN/
Twitter: https://twitter.com/edurekain
LinkedIn: https://www.linkedin.com/company/edureka
Castbox: https://castbox.fm/networks/505?country=in
Slides for a talk about Graph Neural Networks architectures, overview taken from very good paper by Zonghan Wu et al. (https://arxiv.org/pdf/1901.00596.pdf)
BERT: Bidirectional Encoder Representations from TransformersLiangqun Lu
BERT was developed by Google AI Language and came out Oct. 2018. It has achieved the best performance in many NLP tasks. So if you are interested in NLP, studying BERT is a good way to go.
A non-technical overview of Large Language Models, exploring their potential, limitations, and customization for specific challenges. While this deck is tailored for an audience from the financial industry in mind, its content remains broadly applicable.
(Note: Discover a slightly updated version of this deck at slideshare.net/LoicMerckel/introduction-to-llms.)
Sentiment Analysis Using Hybrid Structure of Machine Learning AlgorithmsSangeeth Nagarajan
Sentiment Analysis is the process used to determine the attitude/ opinion/ emotion expressed by a person about a particular topic. The presentation dealt with general approach and different machine learning based classification alogorithms. The slides is based on the work "Sentiment analysis using Neuro-Fuzzy and Hidden Markov models of text" by Rustamov S , Mustafayev E and Clements M A.
How to Win Machine Learning Competitions ? HackerEarth
This presentation was given by Marios Michailidis (a.k.a Kazanova), Current Kaggle Rank #3 to help community learn machine learning better. It comprises of useful ML tips and techniques to perform better in machine learning competitions. Read the full blog: http://blog.hackerearth.com/winning-tips-machine-learning-competitions-kazanova-current-kaggle-3
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.
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 Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
In real world applications, most of the optimization problems involve more than one objective to
be optimized. The objectives in most of engineering problems are often conflicting, i.e., maximize
performance, minimize cost, maximize reliability, etc. In the case, one extreme solution would not satisfy
both objective functions and the optimal solution of one objective will not necessary be the best solution
for other objective(s). Therefore different solutions will produce trade-offs between different objectives
and a set of solutions is required to represent the optimal solutions of all objectives. Multi-objective
formulations are realistic models for many complex engineering optimization problems. Customized
genetic algorithms have been demonstrated to be particularly effective to determine excellent solutions to
these problems. A reasonable solution to a multi-objective problem is to investigate a set of solutions, each
of which satisfies the objectives at an acceptable level without being dominated by any other solution. In
this paper, an overview is presented describing various multi objective genetic algorithms developed to
handle different problems with multiple objectives.
Multi-Population Methods with Adaptive Mutation for Multi-Modal Optimization ...ijscai
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.
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.
Using particle swarm optimization to solve test functions problemsriyaniaes
In this paper the benchmarking functions are used to evaluate and check the particle swarm optimization (PSO) algorithm. However, the functions utilized have two dimension but they selected with different difficulty and with different models. In order to prove capability of PSO, it is compared with genetic algorithm (GA). Hence, the two algorithms are compared in terms of objective functions and the standard deviation. Different runs have been taken to get convincing results and the parameters are chosen properly where the Matlab software is used. Where the suggested algorithm can solve different engineering problems with different dimension and outperform the others in term of accuracy and speed of convergence.
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.
Convergence tendency of genetic algorithms and artificial immune system in so...ijcsity
By the advances in the Evolution Algorithms (EAs) and the intelligent optimization metho
ds we witness the
big revolutions in solving the optimization problems. The application of the evolution algorithms are not
only not limited to the combined optimization problems, but also are vast in domain to the continuous
optimization problems. In this
paper we analyze and study the Genetic Algorithm (GA) and the Artificial
Immune System (AIS)
algorithm
which are capable in escaping the local optimization and also fastening
reaching the global optimization and to show the efficiency of the GA and AIS th
e application of them in
Solving Continuous Optimization Functions (SCOFs) are studied. Because of the multi variables and the
multi
-
dimensional spaces in SCOFs the use of the classic optimization methods, is generally non
-
efficient
and high cost. In other
words the use of the classic optimization methods for SCOFs generally leads to a
local optimized solution. A possible solution for SCOFs is to use the EAs which are high in probability of
succeeding reaching the local optimized solution. The results in pa
per show that GA is more efficient than
AIS in reaching the optimized solution in SCOFs.
Similar to A Genetic Algorithm on Optimization Test Functions (20)
Modeling And Simulation Swash Plate Pump Response Characteristics in Load Sen...IJMERJOURNAL
ABSTRACT: Fluid Power is widely employed in applications required high loads such as tractors, cranes, and airplanes. In load sensing hydraulic systems, loads are controlled by adjusting a pump-valve arrangement. In this paper, the swash plate pump hydraulic characteristics will be determined, the pump and its fluid gains will be derived to obtain the pump overall transfer function. Firstly, the swash plate pump mechanism is analyzed and its dynamic model is constructed; the pump pressure and flow rate are plotted and the possible improvement is introduced. The load sensing unit parameters such as orifice width, orifice area, maximum passage area, and piston area at X and Y will be examined to identify their influence on the pump characteristics; and the optimum parameters will be introduced. All results are developed and simulated numerically.
Generation of Electricity Through A Non-Municipal Solid Waste Heat From An In...IJMERJOURNAL
ABSTRACT: Energy production, waste disposal, and pollution minimization are key problems that must be addressed for sustainable cities of the environment. Waste management has become a major concern worldwide, and incineration is now being used increasingly to treat waste that cannot be recycled economically. The total heat content of non- municipal waste varies from countries to countries. The tonnage of generation in Nigeria is expected to soar over the next few years and the exploitation of this renewable energy locked up in urban solid municipal waste into grid energy can be taken advantage off.The heat generated from this incinerated plant can be used to generate electricity which will reduce overdependence on fossil fuel and the use of generator which in turn reduces pollution disposal of this waste is incinerated plant for the production of electricity. Hence, this paper intends to review the nonmunicipal waste potential in Nigeria, evaluate its environment and economic cost, and energy content of municipal solid waste deposits in Nigeria.
A New Two-Dimensional Analytical Model of Small Geometry GaAs MESFETIJMERJOURNAL
ABSTRACT : In this paper, a simple and exact analytical model for Small Geometry GaAs MESFET is developed to determine the potential distribution along the channel of the device. The model is based on the exact solution of two-dimensional Poisson’s equation in the depletion region under the gate. Then the obtained model is used to study the channel potential and threshold voltage of the device. Using the analytical model, the effect of the device parameter and bias conditions on performance of the device is investigated. The obtained results are graphically exhibited and discussed. In order to verification of the analytical results, TCAD device simulator is used and good accordance is observed.
Design a WSN Control System for Filter Backwashing ProcessIJMERJOURNAL
ABSTRACT: Day by day, there is a higher rate of need for accurate automation system to be used in industries and environment monitoring and control. In water treatment plants during the filtration phase, there is a process called backwashing, which particles suspended in the filter basin are removed. in this process the water are forcedly pumped through the filter in upward direction at enough speed to expand the filter media. Therefore, various types of valves used, which are opened and closed in a time sequencing manner. The paper proposed an automation control system for the backwashing process to be initiated and completed automatically using PLC, level sensors and valves installed inside the filter basin. Practically, a control system has been applied which all valves are opened and closed according to wireless signals coming from PLCs on its suitable time. In summary, the control in the process demonstrated that the proposed system is efficient, effective, and able to be reliable. Besides, the results increase the productivity at a low-cost mode.
Application of Customer Relationship Management (Crm) Dimensions: A Critical ...IJMERJOURNAL
ABSTRACT”: Customer relationship management is crucial due to the competitive environment. For this reason, it has become a widely implemented strategy across the hotel industry in retaining customers and maintaining good relationships with them. It also promotes customer satisfaction and loyalty which lead to the achievement of competitive business performance. However, due to the ever-increasing competition and the continuous changing customers’ needs in the hotel industry, the ability to achieve customer satisfaction is becoming a major challenge. Using 40 respondents from 20 hotels, this paper, therefore, explores the managers’ perspective into how the application of CRM dimensions impact on the performance of hotels and also examines the relationships between them since studies evaluating their relationships are limited. It studies CRM from the hotels’ perceptive as Guest Services Managers and Marketing Managers were the respondents. This study employed an exploratory research design and quantitative technique. The survey was conducted in New Delhi and simple random sampling was the sampling technique used to select respondents. With the study’s objectives in mind, the developed research hypotheses constructed were tested using multiple regression analysis as the statistical tool. Through the results, it has been revealed that CRM dimensions are positively related to the performance of hotels. Finally, CRM dimensions are highly recommended as a competitive strategic tool to enhance competitiveness.
Comparisons of Shallow Foundations in Different Soil ConditionIJMERJOURNAL
ABSTRACT: Soil is considered by the engineer as a complex material produced by weathering of the solid rock. Footings are structural elements that transmit column or wall loads to the underlying soil below the structure. Footings are designed to transmit these loads to the soil without exceeding its safe bearing capacity. Each building demands the need to solve a problem of foundation on different types of soil. The main aim of this project is to design the appropriate foundation as per size and shape on cohesive, non-cohesive and rocky soil. In this paper different foundation are studied for a middle side and corner column of a building with different bearing capacities. Based on the study and judicial judgment the type of foundation is decided as per depth, quantity of steel and quantity of concrete and try to find which shape of the foundation is more stable, economical and ways to reduce the ease of construction of the building
Place of Power Sector in Public-Private Partnership: A Veritable Tool to Prom...IJMERJOURNAL
ABSTRACT: Public Private Partnership involves private sector engagement in infrastructural development. Though in the past, the country infrastructure had been experiencing a decline in the system, this is because, government had been the sole contributor to infrastructural finance and had often taken responsibility for implementation, operations and maintenance as well. This decline in the system is caused by escalating population growth depending on available infrastructure, decaying of existing power infrastructure, political instability and corruption in the system. The ongoing reform is about bringing the system to a lime light. Hence, Public Private Partnership participation in the infrastructural development in Nigeria, will create favorable environment for an investors, provide job opportunities, long time policy, decision making and efficient use of the available resources. This paper therefore dwells on overview of the public private partnership with regards to energy and other infrastructural development of Nigeria. Challenges of the partnership and possible solutions towards subduing the problems are proffered.
Study of Part Feeding System for Optimization in Fms & Force Analysis Using M...IJMERJOURNAL
ABSTRACT: This paper describes the development of a flexible and vibratory bowl feeding system which is suitable for use in a flexible manufacturing system. The vibratory bowl feeder for automatic assembly, presents a geometric model of the feeder, and develops force analysis, leading to dynamical modeling of the vibratory feeder. Based on the leaf-spring modeling of the three legs of the symmetrically arranged bowl of the feeder, and equating the vibratory feeder to a three-legged parallel mechanism, the paper reveals the geometric property of the feeder. The effects of the leaf-spring legs are transformed to forces and moments acting on the base and bowl of the feeder. Resultant forces are obtained based upon the coordinate transformation, and the moment analysis is produced based upon the orthogonality of the orientation matrix. This reveals the characteristics of the feeder, that the resultant force is along the z-axis and the resultant moment is about the z direction and further generates the closed-form motion equation.
Investigating The Performance of A Steam Power PlantIJMERJOURNAL
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Study of Time Reduction in Manufacturing of Screws Used in Twin Screw PumpIJMERJOURNAL
ABSTRACT: This paper gives the characteristics of Time reduction in manufacturing of screws for Twin screw pumps. Screws are playing a vital role in the performance of pumps, because pumps give the fluids transfer rate with the help of screws. There is a gap in screws which shows its positiveness. This indicates that we are studying about positive displacements pumps. Positive displacements pumps having no point of contact between screws, because of that there will be no any friction formation. Automation is best for development of product to reduce time in manufacturing of any product. In this paper we also tried to explain this feature of Automation to help reduction of time to manufacture of product to increase productivity.
Mitigation of Voltage Imbalance in A Two Feeder Distribution System Using IupqcIJMERJOURNAL
ABSTRACT: Proliferation of electronic equipment in commercial and industrial processes has resulted in increasingly sensitive electrical loads to be fed from power distribution system which introduce contamination to voltage and current waveforms at the point of common coupling of industrial loads. The unified power quality conditioner (UPQC) is connected between two different feeders (lines), hence this method of connection of the UPQC is called as Interline UPQC (IUPQC).This paper proposes a new connection for a UPQC to improve the power quality of two feeders in a distribution system. Interline Unified Power Quality Conditioner (IUPQC), specifically aims at the integration of series VSC and Shunt VSC to provide high quality power supply by means of voltage sag/swell compensation, harmonic elimination in a power distribution network, so that improved power quality can be made available at the point of common coupling. The structure, control and capability of the IUPQC are discussed in this paper. The efficiency of the proposed configuration has been verified through simulation using MATLAB/ SIMULINK.
Adsorption of Methylene Blue From Aqueous Solution with Vermicompost Produced...IJMERJOURNAL
ABSTRACT: The removal of Methylene blue as a synthetic dye from aquatic system was investigated by using vermicompost. The dye concentration, contact time and pH of the solution carried out in the adsorption studies. Batch adsorption experimental data were suitable for the Langmuir isotherm and a very good fit to the second order kinetic model (pH=10). The maximum adsorption capacity calculated 256.66 mg g-1 . Vermicompost and the dye loaded vermicompost were characterized by SEM and FTIR. It was found that the vermicompost is stable without losing their activity.
Analytical Solutions of simultaneous Linear Differential Equations in Chemica...IJMERJOURNAL
ABSTRACT: Analytical method for solving homogeneous linear differential equations in chemical kinetics and pharmacokinetics using homotopy perturbation method has been proposed. The mathematical model that depicts the pharmacokinetics is solved. Herein, we report the closed form of an analytical expression for concentrations species for all values of kinetic parameters. These results are compared with numerical results and are found to be in satisfactory agreement. The obtained results are valid for the whole solution domain.
Experimental Investigation of the Effect of Injection of OxyHydrogen Gas on t...IJMERJOURNAL
ABSTRAC: Oxy-Hydrogen gas, H2O2, is a mixture of hydrogen and oxygen produced by water electrolysis. In this work, an experimental exploration was carried out in order to study the effect of the addition of oxy-hydrogen gas into inlet air manifold on speed performance characteristics of a diesel engine at different operating conditions. The experimental work was performed on a test rig comprising a four stroke 5.67 liters water-cooled diesel engine and a Heenan hydraulic dynamometer. Instrumentation included devices for measuring engine speed, load, fuel consumption and inlet air flow rate. The measurements were conducted at 1000, 1500, 2000 and 2500 rpm. At each speed, the engine load was adjusted to 20%, 40% and 80% from the engine full load which corresponds to engine brake mean effective pressures of 1.55, 3.11, and 6.22 bar, respectively, for Oxy-hydrogen generator supplied Currents of 26A and electrolyte concentration of 25 %. The fuel saving percentage and so the brake thermal efficiency for the H2O2 enriched CI engine is more evidently seen at low loads and high-speed conditions. the volumetric efficiency drop was about 5 % at small speeds and reaches to about 2% at higher engine speed.
Hybrid Methods of Some Evolutionary Computations AndKalman Filter on Option P...IJMERJOURNAL
ABSTRACT: The search for a better option price continues within the financial institution. In pricing a put option, holders of the underlying stock always want to make the best decision by maximizing profit. We present an optimal hybrid model among the following combinations: Kalman Filter-Genetic Programming(KF-GP), Kalman Filter-Evolutionary Strategy(KF-ES) and Evolutionary Strategy -Genetic Programming(ES- GP). Our results indicate that the hybrid method involving Kalman Filter-Evolutionary Strategy(KF-ES) is the best model for any investor. Sensitivity analysis was conducted on the model parameters to ascertain the rigidity of the model.
An Efficient Methodology To Develop A Secured E-Learning System Using Cloud C...IJMERJOURNAL
ABSTRACT: Now-a-days, each and every action involved in our life becomes computerized in order to reduce the time, complexity and manual power. The education systems are also being computerized, to train the students in a much efficient way. This system is termed as E-Learning. E-Learning is an Internet-based learning process, in which the Internet technology is used to design, implement, manage and extend learning, which will improve the efficiency of learning. Learning, Teaching and Training are intensely connected components, which are all included in the development of E-Learning system. Cloud Computing provides an efficient platform to support the E-Learning systems, as it can be dramatically changes over time .In this paper, an overview on the new emerging E-Learning system , utilization of the SAAS (Software as a Service) and the methodology to test the efficiency of the person in a secured way are described.
Nigerian Economy and the Impact of Alternative Energy.IJMERJOURNAL
ABSTRACT: Nigeria is endowed with natural resources which are aim at developing the country.The need for alternative energy resources to drive the nation economy cannot be over-emphasized. The incessant power failure has grossly affected the economy, seriously slowing down development in rural and sub-rural settlement. A robust solution must be found to end the crises. Alternative energy source has the potential of solving power problem in Nigeria as well as providing safer and cleaner environment than the fossil fuel. This paper also examines the socio–economic benefits of the alternative energy (solar, wind, biomass, hydro and geothermal) to the nation economy and the utilization of the resources to meet human needs and the generation yet unborn and to provide sustainable development, thereby improve the standard of living and mitigating climate change.
ABSTRACT: Many writers describe empowerment as a process as opposed to a condition or state of being which is being a key feature of empowerment emphasized by many researchers. As a process empowerment becomes difficult to be measured by standard tools available to social scientists. As case study helps in bringing us to understand a complex issue or object and can extend experience or add strength to what is already known through previous research. Case studies also emphasized on detailed contextual analysis of a limited number of events or conditions and their relationships. Researcher had made use of this qualitative research method to examine contemporary real-life situations.
Validation of Maintenance Policy of Steel Plant Machine Shop By Analytic Hier...IJMERJOURNAL
ABSTRACT: In this paper the maintenance activities of the Machine shop of Steel plant have been considered. As maintenance is a routine activity to keep a machine at its normal operating condition so that it can deliver its expected performance without causing any loose of time on account of accidental damage or breakdown and maintenance is a recurring activity. So for reduction of maintenance cost and safety of the operator as well as the residents of nearby area it is better to decide which machines should go for which type of maintenance. For this decision AHP is used and the Expert choice software is used for that calculations and this paper is for the validation of results.
li-fi: the future of wireless communicationIJMERJOURNAL
ABSTRACT: Nowadays people and their electronic devices access wireless internet. But, clogged airwaves are going to make it increasingly difficult to latch onto a reliable signal. So, Radio waves are just one part of the spectrum that can carry our data. We can use “Data through Illumination”. In this process, the data is sent through an LED source that varies in intensity faster than the human eye could follow. The future can be envisioned where the data for laptops, smart phones and all other smart applications is transmitted through the light in our living room. And security would be a snap—if you can’t see the light, you can’t access the data.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
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A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
A Genetic Algorithm on Optimization Test Functions
1. International
OPEN ACCESS Journal
Of Modern Engineering Research (IJMER)
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 7 | Iss. 3 | Mar. 2017 | 1 |
A Genetic Algorithm on Optimization Test Functions
Emmanuel S. Adabor1*
, Joseph Ackora-Prah2
1
School of Technology, Ghana Institute of Management and Public Administration, Accra, Ghana
2
Department of Mathematics, Kwame Nkrumah University of Science and Technology, PMB, Kumasi, Ghana
*Corresponding Author: emmanuelsadabor@gmail.com
I. INTRODUCTION
Global optimization techniques have been applied to real life problems such as determining the best
solution from a set of possible solutions. Algorithms for such purpose are deterministic if there is a clear relation
between the characteristics of the possible solution and the fitness for a given problem. On the other hand,
probabilistic algorithms solve problems where the relation between a solution and fitness is complicated and the
dimensionality of the search space is very high. Such algorithms employ heuristic approaches: Monte Carlo
class of search algorithms. Several approaches that can determine the maximum or minimum of optimization
problems exist. An extremely basic approach is the random search approach that randomly explores the search
space by randomly selecting any solution and testing with other solutions [1,2,3]. Although this allows a good
number of solutions to be tested, it does not guarantee global optima. However, it is successfully applied when
employed in other algorithms [1].
The gradient based methods can be used to solve optimization problems in which the objective
functions are smooth [1]. These employ local search by finding a gradient vector or Hessian matrix for
generating better minima of solutions to a problem. Although these methods are tractable and search in shorter
times, they are only applied to functions which are smooth.
Furthermore, there are greedy algorithms for problems where objective functions are not continuous [4].
These methods explore only neighbouring solutions to the current solution for optimal solution. This property
makes them unreliable since they could be trapped on local optima. However, repeating the greedy algorithms
with different starting solutions have been found to produce better results [1].
In the Simulated Annealing search method, a solution is accepted to be better than the current solution
if it improves the objective function [5,6,7]. If a solution does not improve the objective function, then it is
accepted with a probability. Even though the Simulated Annealing method produces very good results, Genetic
Algorithms (GAs) have been found to be better because they test populations of solutions instead of a single
solution or point in the Simulated Annealing method [8,9].
Recently, GAs have become dynamic and easy to use due to further research. For instance, Naoki et al.,
(2001) utilized the thermo-dynamical genetic algorithms (TDGA), a genetic algorithm which maintains the
diversity of the population by evaluating its entropy, for the problem of adaptation to changing environments
[10]. A modification of genetic algorithm is used in the problem of wavelength selection in the case of a
multivariate calibration performed by Partial Least Squares (PLS). The Genetic Algorithm sets weights to
balance the components out to solve the problem by an automated approach [11].
Wiendahl and Garlichs presented a graphical-oriented decision support system for the decentralized
production scheduling of assembly systems using a Genetic Algorithm as the scheduling algorithm [12]. In the
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 meta-
heuristic 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.
Keywords: Genetic Algorithms, Combinatorial problems, multimodal optimization problems, meta-
heuristic algorithms
2. A Genetic Algorithm On Optimization Test Functions
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 7 | Iss. 3 | Mar. 2017 | 2 |
past, GAs have been applied to solve resource constrained project scheduling problem (RCPSP) to minimize
make-span subject to precedence constraints and resources availability [13]. In these approaches, resources are
considered renewable as well as single mode of conducting every activity. A new permutation of encoding
scheme was designed in the GA to inherit all the advantages of both the new permutation-based encoding
scheme and the priority-based encoding schemes which were introduced [13].
In Biological Sciences, GAs have been applied to medical optimal control problem in immunology [14].
The author of such application provided the main strands of GA theory. Dynamic programming methods have
been applied to solve Multiple Sequence Alignment in Molecular Biology leading to exponential time
complexity. This has necessitated the use of GAs to solve the Multiple Sequence Alignment problem resulting in
improved results over the dynamic programming methods [15]. The determination of the risk factors of the
Alzheimer's disease provides insights into the disease. Although statistical approaches have been used for this
purpose, GAs have been more useful and efficient for identifying these factors since they are able to search
combinations of variables when search space is large [16].
Recent developments in design of experiments in Statistics have found GAs to be effective tools for
optimum designs. In particular, desirable experimental designs that exploit the intrinsic capabilities of GAs have
been produced. See Lin et al. (2015) for instances [17]. GAs have also been applied to optimizing pipe networks
[18], Resource Economics problem [19], hydrological model (GASAKe) [20], surface electromyography signal
[21], IIR digital filters [22] and Bayesian Networks [23].
The justifications for applying GAs are not well understood even with the numerous applications.
Therefore, in this paper, we show the suitability of GAs for solving complex problems involving more than one
variable with multiple modes and their ability to escape from being trapped in local optimal solutions. These are
shown in the examination of the performance of GAs on special optimization test functions. The test functions
are Rosenbrock function, Schwefel function, Rastrigin function and Shubert function.
II. METHOD
2.1 Simple Genetic Algorithm (GA)
The GA handles a population of possible solutions represented by a set of chromosomes. It proceeds by
coding all the possible solutions into chromosomes before determining reproduction operators. They are applied
directly on the chromosomes, and are used to perform mutations and recombination. Each chromosome has an
associated value that corresponds to the fitness of the solution [1].
Figure 1. Overview of Genetic Algorithm
2.1.1 Encoding and Selection
Encoding is representing individual genes using bits, numbers, trees, arrays, lists or any other objects.
The binary string uses bit string made up of zero (0) and one (1). Fig. 2 is an example of a binary string
encoding. Every bit string is a solution but not necessarily the best solution.
3. A Genetic Algorithm On Optimization Test Functions
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Figure 2. A Population of four chromosomes
Selection involves choosing individuals in the population for the next generation. It also determines
number of offspring that will be created by each. The purpose of the selection is to derive fitter individuals in
order to improve solution. The level of the fitness function determines the chances of an individual to be
selected.
In order to select fitter chromosomes for the mating pool, the proportional fitness (roulette wheel)
selection method which selects parent by probabilities were applied. This means that the probability of selecting
an individual is directly proportional to its fitness. This is a linear search through a roulette wheel with the slots
in the wheel weighted in proportion to the individual's fitness values. The population is explored until a target
value is reached. The roulette wheel constructs the relative fitness and cumulative fitness of chromosomes in its
first stage. The relative fitness of each chromosome for a maximization problem is
n
=k
k
i
i
f
f
=w
1
(1)
where
f k is the fitness of the k-th chromosome, and n is population size while the expression for a
minimization problem is:
n
k
k
i
i
F
F
=w
1
(2)
and
1+ff=F imaxi (3)
where maxf is the maximum fitness of all chromosomes and kF is the reverse magnitude fitness.
The cumulative fitness (cj) of the j-th chromosome is given by Equation (4):
j
=i
ij w=c
1
(4)
In the second stage, a random number, rj, is chosen and if rj > cj then the j-th chromosome is selected.
2.1.2. Crossover
Crossover is taking two parent solutions and producing children solution from them. Better offspring
are created by applying crossover to the mating pool to enable the GA to converge. This involves randomly
choosing some crossover points, copying every element before this point from the first parent and copying every
element after the crossover point from the other parent. In particular, we choose two crossover points and the
contents between these points are exchanged between two mated parents. The two points crossover enhance the
performance of the GA by maintaining the building blocks while exploring the search space. The power of
crossover operation to thoroughly explore the search space diminishes as the GA approaches convergence.
A crossover probability of 1 implies all offspring must be made by crossover. If it is 0, then a whole
new generation is to be generated from exact copies of chromosomes from old population. The new
4. A Genetic Algorithm On Optimization Test Functions
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 7 | Iss. 3 | Mar. 2017 | 4 |
chromosomes are intended to bear the good parts of old chromosomes so that the new chromosomes are
better/fitter individuals. This informed the choice of 80% crossover probability in this research.
2.1.3. Mutation
Mutation maintains genetic diversity in the population generated from crossover. This enables the
algorithm to escape from being trapped on local optimal solutions. The binary representation of the solutions
suffices that a simple mutation of each gene with a small probability would be needed. A Bit flipping mutation
was adopted in implementing the algorithm. This involves changing 0 to 1 and 1 to 0 based on a mutation
chromosome generated. As illustrated in Fig. 3, a parent is considered and a mutation chromosome is randomly
generated. For a 1 in mutation chromosome, the corresponding bit in parent chromosome is flipped (0 to 1 and 1
to 0) and child chromosome is produced.
Figure 3. Mutation flipping
The mutations to existing parents or chromosomes are performed with a mutation probability. If
mutation probability is 100%, the entire chromosome is changed, if it is 0%, nothing is changed. Thus, offspring
are generated immediately after crossover in case the mutation probability is zero. However, if mutation is
performed, one or more parts of a chromosome are changed. The mutation probability used to examine the
simple GA in this work is 0.2 permitting diversity in the population of solutions.
2.1.4. Replacement
Once offspring are produced, the parent population is assessed with the offspring for possible
replacement to form new set of solutions. The weaker parents are replaced in a weak replacement procedure to
ensure optimum performance of the GA. This involves replacing a weaker parent by a strong child. For instance
given two parents and two offspring, only the fittest two of the four individuals, parent or child form part of the
new population. Replacing the weak parents with fitter children improves the fitness of the candidate population
solution.
2.1.5. Termination of Search
The algorithm converges after a specified number of generations, a fixed time and a zero change in the
fitness value over a specified number of consecutive generations.
2.2 Test Functions
Test functions enable the evaluation of optimization algorithms with respect to their convergence rate,
robustness and precision. These functions belong to the class of multi-modal and multidimensional functions
with large number of extrema. Examples of such functions are the Rosenbrock function [24], the Rastrigin
function [25,26], the Schwefel function and the Shubert function [27].
2.2.1. Rosenbrock Function
The Rosenbrock function (Fig. 4) given by Equation (5), has a global optimum that lies inside a long,
narrow, parabolic-shaped flat valley.
82.048,2.041001
222
yx,,xy+x=yx,f (5)
The convergence to the global optimum by search algorithms is difficult and hence this problem has
been frequently used to test the performance of optimization algorithms. The minimum point causes a lot of
problems for search algorithms such as the method of steepest descents which will quickly find the entrance to
the valley and then spend several times searching from one side to the other. Such algorithms converge very
slowly toward the minimum.
5. A Genetic Algorithm On Optimization Test Functions
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 7 | Iss. 3 | Mar. 2017 | 5 |
Figure 4. Overview of Rosenbrock function
2.2.2. Rastrigin Function
This function is highly multi-modal as illustrated in Fig. 5. Nevertheless, the locations of local minima
are regularly distributed across the plot of the function.
Figure 5. Overview of Rastrigin function
The Rastrigin function is given by Equation (6).
.5.12,5.12210cos10
1
2
i
n
=i
ii x,πxx+n=xf (6)
2.2.3. Schwefel Function
The Schwefel function is given by Equation (7). It is highly deceptive in that the global minimum is
geometrically distant over the parameter space. That is the consecutive best local minima are distant from one
another (See Fig. 6). This makes search algorithms falter in converging to the direction of the global minimum
of the function.
500,500sin
1
i
n
=i
ii x,xx=xf (7)
6. A Genetic Algorithm On Optimization Test Functions
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Figure 6. Overview of Schwefel function
2.2.4. Shubert Function
The Shubert function is a multi-variable function with multiple modes making it difficult for several algorithms
to easily obtain the optimal solution. The complex nature of the function is illustrated in Fig. 7. The Shubert
function can be written as a function of two variables shown in Equation (8).
.5.12,5.1211cos11cos
5
1
5
1
yx,,+y+ii+x+ii=yx,f
=i=i
(8)
Figure 7. Overview of Shubert function
III. RESULTS
3.1. Performance Indicators of Algorithms
The performance of the simple GA is measured by the values of the optimal solutions. The manual
implementation of the GA is infeasible due to the huge population size that is generated at each stage of the
algorithm. Therefore, the minima of the test functions were solved with MATLAB codes (MathWorks Inc., 2006)
and the results were examined to ascertain the performance of the algorithm. For optimum performance of the
algorithm, the initial population size was limited to 50. This ensures an effective exploration of search space and
quick convergence.
Furthermore, a maximum of 100 generations was specified since the generations hereafter do not produce
7. A Genetic Algorithm On Optimization Test Functions
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significant difference in the optimal values for each function. Nevertheless, the algorithm stops when there are
no improvements in the optimal value after 50 consecutive generations. This accounts for the limit on the stall
generations. It must, however, be stated that there is no perfect way for setting parameters except by
experimental training which have been conducted [28]. Therefore, the choice of these parameters and the others
are well justified.
3.2. Performance on Test Functions
The minima of the Rosenbrock function, Rastrigin function, Schwefel function and Shubert function
are presented in Table 1. The minima of all the functions were reached at the end of 51 generations and at a
point where the average change in fitness values were less than the tolerance,
-6
101 .
Table 1. Results of Mimina of functions
Function Number of decision
Variables
Optimal solution Optimal value
Rosenbrock 2 1.0070, 1.0140 0.0000
Rastrigin 1 0.0000 0.0000
Rastrigin 5 0.0125, 0, -0.0*, 0.001, -
0.0*
0.0309
Schwefel 1 420.9618 -418.9829
Schwefel 10
V114
10 114
107620.4
Shubert 1 -0.2001 -14.5080
Shubert 3 -0.1887, -0.2017, -0.2258 3
103.0246
Vector, V = (-0.0*,0.0*,-0.0*,-0.0*,-0.0*,0.0*,-0.0*,-4.9300,-0.0*,0)
* value is not zero
The simulations of the search for best fitness values were investigated. In search for best fitness values
from the initial values, it was revealed that though the fitness values for the population differed greatly, the GA
was able to identify the best value at each stage of the search. For instance, the search for the minimum of the
Rosenbrock function identified a mean fitness value of 30 though the optimal value was about zero (0) in the
first generation. Details of similar observations at each stage of the search are presented in Fig. 8.
Figure 8. A simple Genetic Algorithm search for optimal value of the Rosenbrock function. The best fitness
value overall the generations was approximately zero (0) and the mean fitness value over all generations was
68.3697.
Although the simple Genetic Algorithm began with a poor initial randomly generated population of
solutions having achieved a mean fitness value of 9.6 for the Rastrigin function, it achieved the expected
optimal value from the beginning of the search over 51 generations. Details of these observations and the
thorough search through the regularly distributed modes of the Rastrigin function are presented in Fig. 9.
8. A Genetic Algorithm On Optimization Test Functions
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Figure 9. The blue plot is mean fitness for generation and the black plot is the best fitness for
generation. A simple Genetic Algorithm search for optimal value of the Rastrigin function.
The nature of the simple GA search for the optimal value of the Schwefel function was also
investigated. It was revealed that though an optimal value of -418.9829 was achieved after 51 generations, the
best initial value at the first stage of the search was about zero which coincided with the mean fitness value. The
progress of the search for the minimum of the Schwefel function from the initial optimal value to the final
optimal value at the end of 51 generations are presented in Fig. 10.
Figure 10. A simple Genetic Algorithm search for optimal value of the Schwefel function. The blue plot is mean
fitness for generation and the black plot is the best fitness for generation.
Besides these exploratory abilities shown by the GA, it was able to identify the optimal value of the
Shubert function. In particular, after 38 generations, the mean fitness value of population coincides with the
optimal value at subsequent generations. Fig. 11 presents details of the search for the best minimum of the
Shubert function.
9. A Genetic Algorithm On Optimization Test Functions
| IJMER | ISSN: 2249–6645 | www.ijmer.com | Vol. 7 | Iss. 3 | Mar. 2017 | 9 |
Figure 11. A simple Genetic Algorithm search for optimal value of the Shubert function. The blue plot is mean
fitness for generation and the black plot is the best fitness for generation.
IV. DISCUSSION
The Rosenbrock function had the optimal value of zero which occurred at the point (1.0070, 1.0140).
The results of the Rosenbrock function confirms results in the literature that it has a minimum value of zero
occurring at (1, 1) [27]. The simple GA obtained this optimal value at the 51st generation in 2.35 seconds. This
implies that though the Rosenbrock function has an optimal value difficult to achieve by classical optimization
techniques, the precision of GA is proved by the optimal value it achieved. In addition, the simple GA has quick
convergence rate. This is justified by the time the GA used to achieve the optimal value of zero. Thus, GA
performs a thorough search to find near optimal value of the Rosenbrock function within a shorter time escaping
most possible traps of local minima.
The exploratory nature of the GA search for best minima of the Rosenbrock function is described in Fig.
8. Though the minimum of the function is found in a valley, the average mean fitness values depict that the
algorithm proved robust during the search as it had to choose from high and low fitness values at consecutive
generations. For instance, after 21 generations, the mean fitness was zero but it increased to about 171 after the
47th generation. The algorithm proved robust achieving the optimal value at the end of 51 generations. These
varying mean fitness values of the Rosenbrock function indicate that the function is complex.
The global minimum for an n-dimensional Rastrigin function has been found to be zero (0) at 0ix
for i =1, 2, …, n [27]. The Simple GA found the minimum value of the single-variable Rastrigin function to be
zero and it occurred at zero. The optimal value of the Rastrigin function of five variables was zero. These values
are indications of the accuracy of the GA to achieve optimal values within shorter time limits.
The robustness of the GA was proved by the nature of its exploration over search space whose minima
are regularly distributed across the Rastrigin function (See Fig. 9). Although the algorithm started with a poor
mean fitness value due to the nature of the function, it converged in subsequent generations until the 51st
generation where it achieved the optimal value of the Rastrigin function (See Fig. 9). Thus, precision of the near
optimal values make GAs robust and highly recommended for solving complex optimization problems.
The accuracy of GA was proved when it located the minimum of a single-variable Schwefel function at
420.9618 with an optimal value of -418.9829 in 23.02 Seconds. In the literature, the global minimum for an n-
dimensional Schwefel function is -418.9829n at xi = 420.9618 for i = 1, 2,…,n [27]. The GA further revealed the
minimum of the Schwefel function of 10 variables which are presented in Table 1.
Despite the deceptive nature of the Schwefel function having consecutive best local minima distant
from one another (See Fig. 6), the GA was able to produce the best minimum value as in the literature. These
suggest that GAs are robust, efficient and do not compromise on time of search. In Fig. 10, it is shown that
though the search was unstable in the initial generations of the search, it stabilizes at the end of the 20th
generation. It converged to the optimal value from the 25th generation to the 51st generation. These prove the
suitability of the GA to solve problems of such nature. These results provide enough justifications for the use of
10. A Genetic Algorithm On Optimization Test Functions
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GA for optimizing complex and multi-variable problems.
The simple GA found the minimum of a Shubert function to be -14.5080 at -0.2001. This value was
reached at the 51st generation when the stopping criterion was satisfied. In general, the global minimum for an
n-dimensional Shubert function is multiple of -14.5080 [27]. Further results with n = 3 is presented in Table 1.
The robustness of the GA was proved further by the search for the optimal value of complex Shubert
function (Fig. 7). Though the simple GA started with a poor mean fitness value due to the nature of the function,
it was able to keep the best fitness throughout other generations until a better value was found. This resulted in
repeated optimal values from the 15th generation to 44th generation. This is due to the selection criteria that
were implemented by the algorithm. These results indicate the ability of the GA to exhaustively search for the
near optimal value of a single variable shubert function. Thus, based on the performance of the GA on the
Shubert function, they show they are robust and accurate while maintaining good search over short time.
The results answer skepticism of Wang (1991) and others as to the efficiency and robustness of GAs
[29,30]. Furthermore, the results prove that GAs easily escape from millions of local optima and reliably
converge to a single value close to the optimum which was suggested in [31].
V. CONCLUSION
The simple GA has provided good solutions to the test functions. Except for some randomization of the
initial population especially when set distant from a local optimum, the time taken by the algorithm to complete
each search is small. GAs are therefore robust, works with precision and has quick convergence to the direction
of the global optimum making them more desirable for complex search problems.
REFERENCES
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