Damping vibration-based IGMM optimization algorithm: fast and significant

Abstract

The ideal gas molecular movement (IGMM) algorithm has been introduced by the authors recently. Detailed studies on its behaviors uncover the fact that the gas molecules also experience a local self-vibration as they move. A comprehensive study was carried out here to introduce the molecular vibration thoroughly as a damping phenomenon supporting convergence rationally with a hindering behavior as molecules travel toward the global best. Thus, a new algorithm containing a molecular operand on vibrational effect (MOVE) was introduced and three different functions were employed to simulate molecular vibrations and pursue investigation. They include simple harmonic, driven harmonic and damped harmonic motions. A number of optimization problems were attempted including a set of unconstrained problems, 23 benchmark functions consisting of unimodal, multimodal and multimodal functions with fix dimensions, and also three well-known constrained engineering problems. Moreover, in a statistically significant way, Wilcoxon’s rank-sum nonparametric statistical test was carried out at the 5% significance level. Overall, the damped harmonic motion function as a molecular vibration simulator supported the optimization procedure best among the other two vibrational functions and other algorithms involved in the research. It showed a relatively better act, causing a faster escalation in the convergence throughout the optimization process. The results intensely show that the MOVE operand significantly boosts the performance of the IGMM and one could certify the significance of VIGMM, proposed in the present study, over some other metaheuristic optimization algorithms.