Improving computational mechanics optimum design using helper objectives: An application in frame bar structures

Abstract

Considering evolutionary multiobjective algorithms for improving single objective optimization problems is focused in this work on introducing the concept of helper objectives in a computational mechanics problem: the constrained mass minimization in real discrete frame bar structures optimum design. The number of different cross-section types of the structure is proposed as a helper objective. It provides a discrete functional landscape where the non-dominated frontier is constituted. of a low number of discrete isolated points. Therefore, the population diversity treatment becomes a key point in the multiobjective approach performance. Two different-sized test cases, four mutation rates and two codifications (binary and gray) are considered in the performance analysis of four algorithms: single-objective elitist evolutionary algorithm, NSGAII, SPEA2 and DENSEA. Results show how an appropriate multiobjective approach that nnakes use of the proposed helper objective outperforms the single objective optimization in terms of average final solutions and enhanced robustness related to mutation rate variations.