Using Shapley Values and Genetic Algorithms to Solve Multiobjective Optimization Problems

This paper proposes a new methodology to solve multiobjective optimization problems by invoking genetic algorithms and the concept of the Shapley values of cooperative games. It is well known that the Pareto-optimal solutions of multiobjective optimization problems can be obtained by solving the cor...

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Autor principal:	Hsien-Chung Wu
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	cooperative games genetic algorithms Pareto-optimal solutions Shapley values weighting problems Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/3fd7f708ffe648b28ec2481607dde5e8
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id	oai:doaj.org-article:3fd7f708ffe648b28ec2481607dde5e8
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spelling	oai:doaj.org-article:3fd7f708ffe648b28ec2481607dde5e82021-11-25T19:06:06ZUsing Shapley Values and Genetic Algorithms to Solve Multiobjective Optimization Problems10.3390/sym131120212073-8994https://doaj.org/article/3fd7f708ffe648b28ec2481607dde5e82021-10-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2021https://doaj.org/toc/2073-8994This paper proposes a new methodology to solve multiobjective optimization problems by invoking genetic algorithms and the concept of the Shapley values of cooperative games. It is well known that the Pareto-optimal solutions of multiobjective optimization problems can be obtained by solving the corresponding weighting problems that are formulated by assigning some suitable weights to the objective functions. In this paper, we formulated a cooperative game from the original multiobjective optimization problem by regarding the objective functions as the corresponding players. The payoff function of this formulated cooperative game involves the symmetric concept, which means that the payoff function only depends on the number of players in a coalition and is independent of the role of players in this coalition. In this case, we can reasonably set up the weights as the corresponding Shapley values of this formulated cooperative game. Under these settings, we can obtain the so-called Shapley–Pareto-optimal solution. In order to choose the best Shapley–Pareto-optimal solution, we used genetic algorithms by setting a reasonable fitness function.Hsien-Chung WuMDPI AGarticlecooperative gamesgenetic algorithmsPareto-optimal solutionsShapley valuesweighting problemsMathematicsQA1-939ENSymmetry, Vol 13, Iss 2021, p 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	cooperative games genetic algorithms Pareto-optimal solutions Shapley values weighting problems Mathematics QA1-939
spellingShingle	cooperative games genetic algorithms Pareto-optimal solutions Shapley values weighting problems Mathematics QA1-939 Hsien-Chung Wu Using Shapley Values and Genetic Algorithms to Solve Multiobjective Optimization Problems
description	This paper proposes a new methodology to solve multiobjective optimization problems by invoking genetic algorithms and the concept of the Shapley values of cooperative games. It is well known that the Pareto-optimal solutions of multiobjective optimization problems can be obtained by solving the corresponding weighting problems that are formulated by assigning some suitable weights to the objective functions. In this paper, we formulated a cooperative game from the original multiobjective optimization problem by regarding the objective functions as the corresponding players. The payoff function of this formulated cooperative game involves the symmetric concept, which means that the payoff function only depends on the number of players in a coalition and is independent of the role of players in this coalition. In this case, we can reasonably set up the weights as the corresponding Shapley values of this formulated cooperative game. Under these settings, we can obtain the so-called Shapley–Pareto-optimal solution. In order to choose the best Shapley–Pareto-optimal solution, we used genetic algorithms by setting a reasonable fitness function.
format	article
author	Hsien-Chung Wu
author_facet	Hsien-Chung Wu
author_sort	Hsien-Chung Wu
title	Using Shapley Values and Genetic Algorithms to Solve Multiobjective Optimization Problems
title_short	Using Shapley Values and Genetic Algorithms to Solve Multiobjective Optimization Problems
title_full	Using Shapley Values and Genetic Algorithms to Solve Multiobjective Optimization Problems
title_fullStr	Using Shapley Values and Genetic Algorithms to Solve Multiobjective Optimization Problems
title_full_unstemmed	Using Shapley Values and Genetic Algorithms to Solve Multiobjective Optimization Problems
title_sort	using shapley values and genetic algorithms to solve multiobjective optimization problems
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/3fd7f708ffe648b28ec2481607dde5e8
work_keys_str_mv	AT hsienchungwu usingshapleyvaluesandgeneticalgorithmstosolvemultiobjectiveoptimizationproblems
_version_	1718410272825147392

Using Shapley Values and Genetic Algorithms to Solve Multiobjective Optimization Problems

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