Solution of multiobjective optimization problems: coevolutionary algorithm based on evolutionary game theory |
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Authors: | Email author" target="_blank">Kwee-Bo?SimEmail author Ji-Yoon?Kim |
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Affiliation: | (1) School of Electrical and Electronic Engineering, Chung-Ang University, 221 Huksuk-Dong, 156-756 Dongjak-Ku, Seoul, Korea |
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Abstract: | When attempting to solve multiobjective optimization problems (MOPs) using evolutionary algorithms, the Pareto genetic algorithm
(GA) has now become a standard of sorts. After its introduction, this approach was further developed and led to many applications.
All of these approaches are based on Pareto ranking and use the fitness sharing function to keep diversity. On the other hand,
the scheme for solving MOPs presented by Nash introduced the notion of Nash equilibrium and aimed at solving MOPs that originated
from evolutionary game theory and economics. Since the concept of Nash Equilibrium was introduced, game theorists have attempted
to formalize aspects of the evolutionary equilibrium. Nash genetic algorithm (Nash GA) is the idea to bring together genetic
algorithms and Nash strategy. The aim of this algorithm is to find the Nash equilibrium through the genetic process. Another
central achievement of evolutionary game theory is the introduction of a method by which agents can play optimal strategies
in the absence of rationality. Through the process of Darwinian selection, a population of agents can evolve to an evolutionary
stable strategy (ESS). In this article, we find the ESS as a solution of MOPs using a coevolutionary algorithm based on evolutionary
game theory. By applying newly designed coevolutionary algorithms to several MOPs, we can confirm that evolutionary game theory
can be embodied by the coevolutionary algorithm and this coevolutionary algorithm can find optimal equilibrium points as solutions
for an MOP. We also show the optimization performance of the co-evolutionary algorithm based on evolutionary game theory by
applying this model to several MOPs and comparing the solutions with those of previous evolutionary optimization models.
This work was presented, in part, at the 8th International Symposium on Artificial Life and Robotics, Oita, Japan, January
24#x2013;26, 2003. |
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Keywords: | Multiobjective optimization problems (MOPs) Pareto optimal set Game theory Nash genetic algorithm Evolutionary stable strategy (ESS) Coevolutionary algorithm |
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