LWMEO: An efficient equilibrium optimizer for complex functions and engineering design problems

Abstract

Optimization algorithm is an important method to solve complex extremum function and engineering design constraint problems, and the improvement of algorithm optimization performance is inseparable from efficient strategies and mechanisms. Equilibrium optimizer (EO) is a novel intelligent optimization algorithm with simple mechanism and easy implementation. It has a good solution effect on some optimization problems. However, when solving complex multimodal problems and engineering design problems, EO has some disadvantages, such as easy to fall into local optimal, low searching accuracy and slow convergence speed. In order to solve complex function extremum and engineering design optimization problems more effectively, improve the optimization performance and application ability of the equilibrium optimizer, and further expand the application field and space of the algorithm, an adaptive equilibrium optimizer (LWMEO) with three efficient optimization strategies is proposed. Based on the basic update strategy of the equilibrium optimizer, the random walk strategy of preferred area based on Lévy flight is introduced to expand the algorithm’s search range and enhances its exploration capability; by adding the whale optimization algorithm’s spiral encirclement mechanism enables the individuals in the population to perform a spiral search near the best solution and improves the algorithm’s exploitation capability; the introduction of the adaptive proportional mutation strategy strengthens the algorithm’s ability to jump out of the local optimal solutions, while accelerating its convergence speed. Time complexity analysis proves that the LWMEO algorithm has the same time complexity as the equilibrium optimizer. Using the Markov chain process, it is theoretically proven that the LWMEO has convergence and can converge to the global optimum. LWMEO and 6 representative comparison algorithms with superior performance are used to solve CEC2014 test function suite and several classical multimodal test functions with different optimization characteristics. Each algorithm is run independently for 50 times in the same environment, and the best value, average value and standard deviation obtained by LWMEO were generally superior to the other six comparison algorithms. The convergence curve drops faster and the line body is smoother. These experimental data and convergence curves show that the LWMEO’s optimization ability, convergence speed and solution stability are obviously superior to the comparison algorithm. Meanwhile, the p-value of Wilcoxon’s rank-sum test are less than 0.05, indicating that LWMEO has significant differences over comparison algorithm. Finally, the LWMEO is applied to 8 different engineering design optimization problems, and the best value, average value and standard deviation obtained from 50 optimization designs are also significantly better than other comparison algorithms, which verifies the applicability, stability and efficiency of LWMEO in solving engineering design constrained optimization problems.