Enhanced Multi-Scale Quantum Harmonic Oscillator Algorithm with Opposition-based Learning

Multi-scale Quantum Harmonic Oscillator Algorith-m (MQHOA) is a recently proposed metaheuristic algorithm (MA), which simulates the photoelectron moves from high energy level down to the ground energy level. It requires few parameters, yet verified effective and efficient to solve numerical problems. However, it is easy to get trapped into local optima and suffer from premature convergence. This work proposes an enhanced MQHOA with opposition-based learning (OMQHOA) to balance the exploration and exploitation. An adaptive scaling strategy and a jumping rate scheme are proposed to enhance the diversity of the particles. The performance of the proposed algorithm is validated by evaluating on several benchmark problems with different dimensions, including the success rate of finding the global optimum over multiple independent trials, trajectory of convergence, and Wilcoxon rank-sum tests. The empirical results are compared with MQHOA, recent variants of MQHOA, and some state-of-the-art MAs, which show the superiority or at least competitiveness of the proposed approach.