Game theory based evolutionary algorithms: a review with nash applications in structural engineering optimization problems

Abstract

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.