Hybrid Particle Swarm Optimization with Sine Cosine Algorithm and Nelder–Mead Simplex for Solving Engineering Design Problems

Abstract

This paper introduces a novel hybrid evolutionary algorithm that combines particle swarm optimization (PSO) algorithm with sine–cosine algorithm (SCA) and Nelder–Mead simplex (NMS) optimization technique. However, the algorithm of PSO has some drawbacks like locating local minima rather than global minima, low converge rate and low balance between exploration and exploitation. In this paper, the combination of PSO algorithm with update positions mathematical equation in SCA and NMS technique is presented in order to solve these problems. So a new hybrid strategy called PSOSCANMS is introduced. The SCA algorithm is based on the behavior of sine and cosine functions in the mathematical formula used for solutions. However, the NMS mathematical formulations attempt to replace the worst vertex with a new point, which depends on the worst point and the center of the best vertices. The combined effect of both mathematical formulations of PSO ensures a consistency of exploitation and exploration that makes the search in the search space more effective. Further, it escapes into the local minimum issue and resolves the low converge rate problem. In order to test PSOSCANMS’s performance, a set of 23 well-known unimodal and multimodal functions have been benchmarked. Experimental results showed that PSOSCANMS is more successful than PSO and outperforms the other state-of-the-art compared algorithms over the tested optimization problems. Moreover, an engineering design problem such as spring compression, welded beam is also considered. The result of the problems in engineering design and application problems shows that the algorithm proposed is relevant in difficult cases involving unknown search areas.