Multi-objective optimum design of truss structures using differential evolution algorithms

Abstract

Multi-objective structural optimization problems (MOSOPs) with two objectives are widely discussed in the literature. Most MOSOPs that refer to trusses are formulated to minimize the weight and the maximum nodal displacement. This paper formulates MOSOPs with several objective functions combined with various formulations. The objective functions are the weight, the natural frequencies of vibration, the maximum nodal displacement, and the critical load factor concerning the structure’s global stability. The design variables are the cross-sectional areas of the bars, the nodal coordinates, and the presence or absence of bars in the final optimized structure. The third evolution step of generalized differential evolution (GDE3), the success history–based adaptive multi-objective differential evolution (SHAMODE) and the success history–based adaptive multi-objective differential evolution with whale optimization (SHAMODE-WO), and the multi-objective meta-heuristic with iterative parameter distribution estimation (MM-IPDE) are the differential evolution algorithms used in this paper. The experiments refer to the 10-, 25-, 56-, 72-, 120-, and 582-bar trusses and a 33-bar ground-structure system. Multi-criteria decision-making (MCDM) is adopted to extract solutions from the Pareto front according to preferences of the decision-maker (DM) used in the ground-structure system. The complete data for each extracted solution are provided, including its optimized topology.