Estimation of Distribution Algorithms with Fuzzy Sampling for Stochastic Programming Problems

Generating practical methods for simulation-based optimization has attracted a great deal of attention recently. In this paper, the estimation of distribution algorithms are used to solve nonlinear continuous optimization problems that contain noise. One common approach to dealing with these problem...

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Published in:	Applied sciences Vol. 10; no. 19; p. 6937
Main Authors:	Hedar, Abdel-Rahman, Allam, Amira A., Fahim, Alaa
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01.10.2020
Subjects:	Algorithms Approximation Design Distribution management software estimation of distribution algorithms Fuzzy algorithms Fuzzy logic fuzzy sampling Fuzzy sets Fuzzy systems Genetic algorithms Mathematical functions Measurement Methods Mutation Noise Normal distribution Optimization Probability distribution Random variables Sample size Sampling techniques Simulation simulation-based optimization Stochastic programming variable sample path Saudi Arabia
ISSN:	2076-3417, 2076-3417
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Abstract	Generating practical methods for simulation-based optimization has attracted a great deal of attention recently. In this paper, the estimation of distribution algorithms are used to solve nonlinear continuous optimization problems that contain noise. One common approach to dealing with these problems is to combine sampling methods with optimal search methods. Sampling techniques have a serious problem when the sample size is small, so estimating the objective function values with noise is not accurate in this case. In this research, a new sampling technique is proposed based on fuzzy logic to deal with small sample sizes. Then, simulation-based optimization methods are designed by combining the estimation of distribution algorithms with the proposed sampling technique and other sampling techniques to solve the stochastic programming problems. Moreover, additive versions of the proposed methods are developed to optimize functions without noise in order to evaluate different efficiency levels of the proposed methods. In order to test the performance of the proposed methods, different numerical experiments were carried out using several benchmark test functions. Finally, three real-world applications are considered to assess the performance of the proposed methods.
AbstractList	Generating practical methods for simulation-based optimization has attracted a great deal of attention recently. In this paper, the estimation of distribution algorithms are used to solve nonlinear continuous optimization problems that contain noise. One common approach to dealing with these problems is to combine sampling methods with optimal search methods. Sampling techniques have a serious problem when the sample size is small, so estimating the objective function values with noise is not accurate in this case. In this research, a new sampling technique is proposed based on fuzzy logic to deal with small sample sizes. Then, simulation-based optimization methods are designed by combining the estimation of distribution algorithms with the proposed sampling technique and other sampling techniques to solve the stochastic programming problems. Moreover, additive versions of the proposed methods are developed to optimize functions without noise in order to evaluate different efficiency levels of the proposed methods. In order to test the performance of the proposed methods, different numerical experiments were carried out using several benchmark test functions. Finally, three real-world applications are considered to assess the performance of the proposed methods. Generating practical methods for simulation-based optimization has attracted a great deal of attention recently. In this paper, the estimation of distribution algorithms are used to solve nonlinear continuous optimization problems that contain noise. One common approach to dealing with these problems is to combine sampling methods with optimal search methods. Sampling techniques have a serious problem when the sample size is small, so estimating the objective function values with noise is not accurate in this case. In this research, a new sampling technique is proposed based on fuzzy logic to deal with small sample sizes. Then, simulation-based optimization methods are designed by combining the estimation of distribution algorithms with the proposed sampling technique and other sampling techniques to solve the stochastic programming problems. Moreover, additive versions of the proposed methods are developed to optimize functions without noise in order to evaluate different efficiency levels of the proposed methods. In order to test the performance of the proposed methods, different numerical experiments were carried out using several benchmark test functions. Finally, three real-world applications are considered to assess the performance of the proposed methods. Keywords: estimation of distribution algorithms; stochastic programming; simulation-based optimization; fuzzy sampling; variable sample path
Audience	Academic
Author	Allam, Amira A. Hedar, Abdel-Rahman Fahim, Alaa
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SubjectTerms	Algorithms Approximation Design Distribution management software estimation of distribution algorithms Fuzzy algorithms Fuzzy logic fuzzy sampling Fuzzy sets Fuzzy systems Genetic algorithms Mathematical functions Measurement Methods Mutation Noise Normal distribution Optimization Probability distribution Random variables Sample size Sampling techniques Simulation simulation-based optimization Stochastic programming variable sample path
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Title	Estimation of Distribution Algorithms with Fuzzy Sampling for Stochastic Programming Problems
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