Multiscale quantum harmonic oscillator optimization algorithm with multiple quantum perturbations for numerical optimization

摘要

Multi-scale quantum harmonic oscillator algorithm (MQHOA) is a recent proposed intelligent algorithm, in which the optimization process can be regarded as the multi-scale quantum annealing process with respect to the constraint of the harmonic oscillator potential well. It has been proved effective and efficient to deal with unimodal and multimodal numerical optimization problems. However, it takes a long time for the particles system to reach the ground-state equilibrium at each annealing scale. Motivated by this situation, a diffusion Monte Carlo method based dynamic sampling regulation strategy is proposed to enhances the sampling efficiency by dynamically adjusting the sampling frequency. Moreover, the particles with different kinetic energies are introduced into the optimization system as quantum perturbations, which reduces the probability of the algorithm falling into a local optimum by keeping the different searching scales simultaneously. The theoretical derivations of this method are presented. The effectiveness of the algorithm is studied by comparing it with previous versions of the MQHOA and several famous intelligent algorithms on uniand multimodal benchmark functions. The experimental results illustrate that the proposed method has a comparable performance for numerical optimization problems.