The max-min algorithm for maximizing the spread of pareto fronts applied to multiobjective structural optimization

Abstract

This paper introduces an algorithm for the maximization of the spreading factor of Pareto fronts. A set of synthetic functions is used to contrast the spreading of our approach against the one produced by NSGA-II and SPEA-2. A bi-objective structural optimization design problem with constraints is also solved with the proposed technique. The goal is to minimize weight and displacements in the structure, subject to three physical constraints: Von Misses Stress (subject to a maximum permissible), small holes, and the number of pieces used to build the structure. The finite element method is used to evaluate the potential solutions elaborated by the search algorithm in the discrete space of the structural problem. Since we approach bi-criterion optimization problems, a selection mechanism based on Pareto dominance determines the best potential solutions. However, the number of potential solutions in this kind of problems is large and the size of the Pareto set is limited to a target number. Thus, the goal of this paper is to introduce an algorithm that picks as many potential solutions as the target number while keeping the maximum spreading of the Pareto front.