Game Theory Based Evolutionary Algorithms: A Review with Nash Applications in Structural Engineering Optimization Problems

A general review of game-theory based evolutionary algorithms (EAs) is presented in this study. Nash equilibrium, Stackelberg game and Pareto optimality are considered, as game-theoretical basis of the evolutionary algorithm design, and also, as problems solved by evolutionary computation. Applicati...

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Bibliographic Details
Published in:Archives of computational methods in engineering Vol. 24; no. 4; pp. 703 - 750
Main Authors: Greiner, David, Periaux, Jacques, Emperador, Jose M., Galván, Blas, Winter, Gabriel
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.11.2017
Springer Nature B.V
Subjects:
Domain decomposition methods
Engineering
Evolutionary algorithms
Evolutionary design method
Game theory
Genetic algorithms
Inverse problems
Mathematical analysis
Mathematical and Computational Engineering
Matrix methods
Optimization
Original Paper
Pareto optimum
Stiffness matrix
Structural engineering
Evolutionary Algorithm
Domain Decomposition
Nash Equilibrium
Multiobjective Optimization
Nash
ISSN:1134-3060, 1886-1784
Online Access:Get full text
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Summary:A general review of game-theory based evolutionary algorithms (EAs) is presented in this study. Nash equilibrium, Stackelberg game and Pareto optimality are considered, as game-theoretical basis of the evolutionary algorithm design, and also, as problems solved by evolutionary computation. Applications of game-theory based EAs in computational engineering are listed, with special emphasis in structural optimization and, particularly, in skeletal structures. Additionally, a set of three problems are solved: reconstruction inverse problem, fully stressed design problem and minimum constrained weight, for discrete sizing of frame skeletal structures. We compare panmictic EAs, Nash EAs using 4 different static domain decompositions, including also a new dynamic domain decomposition. Two frame structural test cases of 55 member size and 105 member size are evaluated with the linear stiffness matrix method. Numerical experiments show the efficiency of the Nash EAs approach, confirmed with statistical significance analysis of results, and enhanced with the dynamic domain decomposition.
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ISSN:1134-3060
1886-1784
DOI:10.1007/s11831-016-9187-y