Success history based adaptive multi-objective differential evolution variants with an interval scheme for solving simultaneous topology, shape and sizing truss reliability optimisation

Abstract

A general approach based on the most probable point (MPP) method for solving reliability truss optimisation with simultaneous topology, shape and sizing (TSS) design variables is developed. The design problems are solved using double loop optimisation where the inner loop is for reliability index and the probability of failure approximation is solved by Harris Hawk Optimisation (HHO). The outer loop, the main TSS truss optimisation loop, is solved by two newly developed algorithms, namely interval success history based adaptive multi-objective differential evolution (iSHAMODE) and its hybrid variant with the whale optimisation algorithm (iSHAMODE-WO). Six TSS truss optimisation problems are evaluated. The results from the proposed method for reliability approximation and First Order Second Moment (FOSM) are compared and validated with Monte Carlo Simulation (MCS). The proposed method shows more consistent and accurate results compared to FOSM. Furthermore, the efficiency of the proposed optimisation algorithms (iSHAMODE and iSHAMODE-WO) is proved; they can outperform their predecessors and several state-of-the-art algorithms including multi-objective multi-verse optimisation algorithm (MOMVO), multi-objective grasshopper optimisation algorithm (MOGOA), multi-objective dragonfly optimisation (MODA), multi-objective salp swarm algorithm (MSSA), hybridisation of real-code population-based incremental learning and differential evolution (RPBILDE), and multi-objective meta-heuristic with iterative parameter distribution estimation (MMIPDE).