Lévy flight and chaos theory-based gravitational search algorithm for mechanical and structural engineering design optimization

Abstract The main aim of this article is to explore the real-life problem-solving potential of the proposed Lévy flight-based chaotic gravitational search algorithm (LCGSA) for the minimization of engineering design variables of speed reducer design (SRD), three bar truss design (TBTD), and hydrodynamic thrust bearing design (HTBD) problems. In LCGSA, the diversification of the search space is carried out by Lévy flight distribution. Simultaneously, chaotic maps have been utilized for the intensification of the candidate solutions towards the global optimum. Moreover, the penalty function method has been used to deal with the non-linear and fractional design constraints. The investigation of experimental outcomes has been performed through various performance metrics like statistical measures, run time analysis, convergence rate, and box plot analysis. Moreover, statistical verification of experimental results is carried out using a signed Wilcoxon rank-sum test. Furthermore, eleven heuristic algorithms were employed for comparative analysis of the simulation results. The simulation outcomes clearly show that LCGSA provides better values for TBTD and HTBD benchmarks than standard GSA and most of the competing algorithms. Besides, all the participating algorithms, including LCGSA, have the same results for the SRD problem. On the qualitative side, LCGSA has successfully resolved entrapment in local minima and convergence issues of standard GSA.