Abstract:

Multi-scale quantum harmonic oscillator algorithm is an intelligent optimization algorithm based on quantum theory. The energy level stabilization process is one of the core iterative processes of the algorithm, and the energy level stability criterion is the condition for judging whether the algorithm reaches metastable state. Through the analysis of the physical model of the algorithm, it was considered that each iteration of the algorithm in the initial sampling stage is a process of energy level descent, so that the algorithm without energy level stability criterion was also able to realize the evolution from high energy state to metastable state until ground state. The results of the algorithm without energy level stability criterion on six standard test functions show the excellent performance of the algorithm in terms of solution accuracy, success rate and number of iterations. The wave function of the algorithm shows that the algorithm without energy level stability criterion can still converge from the high-energy state to the ground state, and is simpler in structure, easier to use and less difficult to implement. Multi-scale quantum oscillator algorithm without energy level stability criterion can be applied in a more concise and efficient way.

Key words: multi-scale quantum harmonic oscillator algorithm, optimization algorithm, energy level stability, quantum model, success rate, wave function

摘要：

多尺度量子谐振子算法是一种基于量子理论构建的智能优化算法。能级稳定过程是该算法的核心迭代过程之一，能级稳定判据是判断算法是否达到暂稳态的条件。通过对算法物理模型的分析，可知算法在初始采样阶段每一次迭代操作都是能级下降的过程，所以取消能级稳定判据，也可实现算法从高能态过渡到暂稳态直至基态的进化过程。无能级稳定判据的算法在6个标准测试函数上的结果显示其在求解精度、成功率、迭代次数上均表现出了优异的性能，算法的波函数显示无能级稳定判据的算法仍然可以完成从高能态到基态的收敛，且算法在结构上更加简洁，易用性更高，实现难度更低。无能级稳定判据的多尺度量子谐振子算法能够以更加简洁且有效的方式进行应用。

关键词: 多尺度量子谐振子算法, 优化算法, 能级稳定, 量子模型, 成功率, 波函数