Abstract: Multi-scale quantum harmonic oscillator optimization algorithm (MQHOA) is a novel algorithm inspired by the physical model of harmonic oscillator and the probability interpretation of quantum harmonic oscillator’s wave function. This paper demonstrates the uncertainty relationship between global searching accuracy and local searching accuracy, and defines the wave function of MQHOA according to quantum model. Quantum harmonic oscillator convergence and multi-scale convergence are nested, and are the basic convergence processes of MQHOA to gradually approach the global optimal solution. The comparison experiments with quantum-behaved particle swarm optimization (QPSO) and simulated annealing (SA) on 15 benchmark functions show that MQHOA has good performance in adaptability, stability and accuracy when tackling with function global optimization algorithm.

Key words: multi-scale quantum harmonic oscillator optimization algorithm (MQHOA), optimization algorithm, uncertainty relationship, Gauss random number

摘要： 依据谐振子物理模型及量子谐振子波函数的概率解释构造了一种新的全局优化算法——多尺度量子谐振子优化算法（multi-scale quantum harmonic oscillator optimization algorithm，MQHOA）。定义了算法的波函数，并利用算符方法证明了全局搜索精度和局部搜索精度之间的测不准关系, 指出算法必须包含量子谐振子收敛和多尺度收敛两个嵌套的基本收敛过程，才能实现对全局最优解的逐步逼近。通过与量子粒子群算法和模拟退火算法对15种标准测试函数进行实验比对，证明了MQHOA在求解函数全局优化问题时具有更好的适应性、稳定性和精确性。

关键词: 多尺度量子谐振子优化算法（MQHOA）, 优化算法, 测不准关系, 高斯随机数