Multi-Scale Quantum Harmonic Oscillator Algorithm With Centroid Motion for Global Numerical Optimization Problems

Xinggui Ye,Peng Wang

doi:10.1109/access.2019.2927044

Abstract

This paper proposes a new approach for function optimization using a new variant of multi-scale quantum harmonic optimization algorithm (MQHOA). The new approach introduces a centroid motion to improve the convergence efficiency, which is called MQHOA with centroid motion (CM-MQHOA). Instead of replacing the worst particle by the current best individual in the quantum harmonic oscillator process in MQHOA, the weakest player is replaced by a current centroid position in the proposed algorithm. Simple mechanisms are added to maintain the diversity of the population and help achieve the global optima in difficult unimodal and multimodal search spaces. The benefits of the proposed algorithm are improved performance in terms of effectiveness, reliability, accuracy, and efficiency. The approach appears to be able to efficiently deal with several unimodal and multimodal benchmark functions. A variety of standard benchmark functions are used to illustrate the proposed approach. The experimental results are compared with several state-of-the-art optimization algorithms. The comparative results indicate the competitiveness of the proposed algorithm and suggest a viable and attractive addition to the portfolio of computational intelligence techniques.

Highlights

Global optimization problems universally exist in the realworld scenarios, such as maximization of benefit or minimization of cost in science, engineering and business
Several well-defined benchmark functions are utilized to compare the performances of CM-multi-scale quantum harmonic optimization algorithm (MQHOA) with the original MQHOA
The tracing of convergence path reveals the significant improvement of convergence performance in CMMQHOA compared with the original MQHOA

Summary

INTRODUCTION

Global optimization problems universally exist in the realworld scenarios, such as maximization of benefit or minimization of cost in science, engineering and business. Inspired by quantum theory [34], [35] and quantum annealing method [36], the main idea of MQHOA is that the process of solving an optimization problem f (x) can be regarded as particles in quantum system transferring from high energy levels to the ground state under a potential well V (x) [29]. The smaller the σ is, the narrower the search space will be It can be seen in (3) and (4), from high energy levels to the ground state, the wavefunction of quantum harmonic oscillator changes from n scattered and intertwined Gaussian functions in (3) to an overlapped Gaussian function in (4). We introduce an improved MQHOA with centroid motion (CM-MQHOA) to enhance the diversification of the particles and reduce the total iteration time

MAIN IDEA

WAVEFUNCTION

CONVERGENCE OF CM-MQHOA

EXPERIMENTAL RESULTS AND DISCUSSION

CONCLUSION