Multi-objective SHADE with manta ray foraging optimizer for structural design problems

Abstract

This paper presents a hybrid multi-objective success history-based parameter adaptive differential evolution (SHADE) with manta ray foraging optimizer (MRFO) for structural design problems, called MO-SHADE-MRFO. In the proposed algorithm, the updating rules of SHADE, a variant of differential evolution with great performance, are combined with the operators from MRFO, a recent swarm-based metaheuristic algorithm inspired from the manta ray with cyclone, chain and somersault foraging behaviors, which can balance the exploration and exploitation of the algorithm for structural design problems. Furthermore, MO-SHADE-MRFO utilizes the external archive to save and update the obtained Pareto fronts during the optimization process. The proposed algorithm is verified by multi-objective truss optimization problems with two objectives of minimizing the structural weight and the compliance, including 10-bar, 25-bar, 37-bar, 120-bar, 200-bar and 942-bar truss problems. Moreover, 9 different multi-objective metaheuristic algorithms are implemented to compare with the proposed algorithm, where three metrics are used to measure the performance of the algorithms, including hypervolume (HV), inverted generational distance (IGD), and spacing-to-extent (STE). According to the experimental results, MO-SHADE-MRFO can provide the best statistical values of HV, IGD and STE in most cases, ranking the first among the compared algorithms. Besides, the proposed algorithm also gives well-distributed Pareto solutions for the tested problems, illustrating the effectiveness of the hybrid updating rules of SHADE and MRFO.