An efficient algorithm for multi-objective structural optimization problems using an improved pbest-based differential evolution algorithm

Abstract

Multi-objective optimization (MOO) for structural design is addressed. A new MOO algorithm, named MOEA/D-EpDE, which combines the advantages of a recently developed pbest-based differential evolution method (EpDE) and the multi-objective evolutionary algorithm based on decomposition with dynamical resource allocation (MOEA/D_DRA), is proposed to solve such challenging MOO problems effectively. In MOEA/D-EpDE, a decomposition approach is performed using MOEA/D_DRA to convert a problem of approximation of the Pareto front (PF) into many scalar optimization problems, in which a dynamic computational resource allocation strategy is used to optimize the computational efforts. The EpDE algorithm, a robust single objective optimization (SOO) algorithm, is improved for MOO to solve the scalar optimization problems effectively. A simple technique for integrating an external archive to MOEA/D-EpDE is also developed to save good Pareto optimal solutions during the optimization process. The performance of MOEA/D-EpDE is first evaluated through 5 bi-objectives (ZDT1–4 and ZDT6) and 7 tri-objectives unconstrained benchmark functions. Numerical results revealed that the proposed method outperformed several MOO algorithms given the inverted generational distance (IGD) indicator. In the end, MOEA/D-EpDE is applied to solve three real-world design problems, including a welded-beam and two nonlinear inelastic truss structures. The effectiveness of the proposed algorithm is confirmed through comparison with some recently developed algorithms regarding several indicators: generational distance (GD), GD+, IGD, IGD+, and Hypervolume (HV).