COLMA: a chaos-based mayfly algorithm with opposition-based learning and Levy flight for numerical optimization and engineering design

The Mayfly Algorithm (MA) is a widely used metaheuristic algorithm characterized by a simple structure with simple parameters. However, MA may have problems such as poor global search ability and tend to fall into local optima. To overcome these limitations, this paper presents a chaos-based mayfly algorithm with opposition-based learning and Levy flight (COLMA) to boost the global search and local exploitation performance. In COLMA, we first introduced tent chaos to optimize the initialization process of the mayfly population, as random initialization processes may result in low diversity of the mayfly population. In addition, the gravity coefficient has been replaced with an adaptive gravity coefficient to balance the global search ability and local exploitation ability during the iterative process of the algorithm. In the process of updating the position of the male mayfly population, an opposition-based learning strategy based on an iterative chaotic map with infinite collapses is adopted to prevent the male mayfly population from falling into local optima. At the same time, in order to solve the problem of small search range of female mayfly population, Levy flight strategy was introduced to replace random walk strategy. Finally, an offspring optimization strategy was proposed to increase the probability of the offspring mayfly population approaching the optimal solution. To verify the effectiveness and superiority of COLMA and the adopted strategy, experiments were conducted on the classical benchmark functions, CEC 2017 benchmark suite and CEC 2020 real-world constraint optimization problems, and the results were statistically tested using the Wilcoxon signed rank test and Friedman test. The analysis results show that the proposed COLMA has statistical validity and reliability and has great advantages compared with MA, variant MA in terms of optimization accuracy, stability and convergence speed.