Multiobjective Optimum Design of Structures with Genetic Algorithm and Game Theory: Application to Life-Cycle Cost Design

Abstract

This chapter focuses on genetic algorithm and game theory, as well as a life-cycle cost model for a innovative design methodology. A design methodology needs to be developed using multiobjective and multilevel optimization techniques to balance the initial cost of structure with expected losses from potential earthquake-induced structural damage. Genetic algorithms (GAs) have the characteristic of maintaining a population of solutions, and can search in a parallel manner for many nondominated solutions, which coincide with the requirement of a Pareto optimal set in a multiobjective optimization problem. In the GA, to avoid missing Pareto optimal points during evolutionary processes, a new concept called Pareto-set filter is adopted in which the points of rank 1 are put into the filter and then, undergo a nondominated check. In addition, a niche technique is provided to prevent a genetic drift in population evolution. This technique sets a replacement rule for reproduction procedures. A revised penalty function method is introduced to transfer a constrained problem into a nonconstrained one. The transferred function of a point contains information on a point's status (feasible or infeasible), position in a search region, and distance to the Pareto optimal set.