Multiscale Quantum Harmonic Oscillator Algorithm With Multi-Harmonic Oscillators for Numerical Optimization

Abstract

The multiscale quantum harmonic oscillator algorithm (MQHOA) is inspired by the physical meaning of quantum wavefunction. Particles have no efficient interaction and share a wavefunction during the evolution process. In this paper, a multi-harmonic oscillator strategy is introduced, which employs multiple wavefunctions to generate new particles. The external population information can be utilized in the process of evolution. The proposed method enhances the cooperation and interaction for particles by a local collaborative operation. Moreover, an adaptive weight operator is employed in the proposed algorithm, which makes a fine-tune of solutions to keep the diversity of particles. The proposed algorithm is verified on standard benchmark functions. Wilcoxon rank sum test is adopted to ascertain the superiority of the proposed algorithm. The experiments have been conducted with several renowned heuristic algorithms. The numerical results reveal that the proposed algorithm outperforms the comparison algorithms for numerical optimization. INDEX TERMS Multiscale quantum harmonic oscillator algorithm, multi-harmonic oscillators, wavefunction, quantum-inspired algorithm, cooperation and interaction.

A review of recent advances in quantum-inspired metaheuristics

“…So, we conduct a comparison between some of the algorithms. The algorithms is this comparison are Entanglement-Enhanced Quantum-inspired Tabu Search Algorithm (Entanglement-QTS) [ 98 ], Multi-scale Quantum Harmonic Oscillator Algorithm (MQHOA) [ 104 ], Multiscale Quantum Harmonic Oscillator Algorithm With Multi-Harmonic Oscillators (MHO-MQHOA) [ 110 ], Quantum Salp Swarm Algorithm (QSSA) [ 89 ], Half Significant Bit QEA (HSBQEA) [ 25 ], Stepwise Real QEA [ 25 ], enhanced Quantum behaved Particle Swarm Optimization (e-QPSO) [ 77 ], Quantum-Inspired Acromyrmex Evolutionary Algorithm (QIAEA), and Quantum Enhanced Colliding Bodies Optimization (QECBO) [ 108 ]. Six well-known benchmark functions are selected for this comparison.…”