Potential Well Analysis of Multi Scale Quantum Harmonic Oscillator Algorithms

Abstract

Abstract The multiscale quantum harmonic-oscillator algorithm is an intelligent optimization algorithm based on quantum harmonic wave functions. Although it is effective for many optimization problems, an analysis for its performance is still lacking. This paper discusses the harmonic-oscillator potential well, delta-function potential well, and infinite-square potential well in terms of their application in evolutionary algorithms. Of the three, the harmonic-oscillator potential well is considered to give the most precise approximation for complex objective functions. When combined with the harmonic-oscillator potential well, the multiscale quantum harmonic-oscillator algorithm exhibits good adaptability in terms of the convergence of the wave function. To verify its global optimization performance, experiments are conducted using a double-well function to analyze the convergence of the multiscale quantum harmonic-oscillator algorithm and a suite of benchmark functions to compare the performance of different potential wells. The experimental results indicate that the multiscale quantum harmonic-oscillator algorithm with the harmonic-oscillator potential well is a better practical choice than the other two potential well models, and show that the multiscale quantum harmonic-oscillator algorithm is a potential quantum heuristic algorithm for optimization.KeywordsMulti-scale quantum harmonic oscillator algorithmHeuristic algorithmGlobal optimizationPotential well