摘要
针对一些智能优化算法缺乏完备数学物理理论基础的现状,利用优化问题和量子物理在概率意义上的相似性,建立优化问题的薛定谔方程,将优化问题转化为以目标函数为约束条件的基态波函数问题,同时利用波函数定义了算法的能量、隧道效应和熵,实现了以波函数为中心的优化问题量子模型.这一纲要利用了量子物理完备的理论框架,建立起了优化问题与量子理论广泛的内在联系.从量子物理的角度回答了优化问题解的概率描述,邻域采样函数的选择,算法演化的过程设计,多尺度过程的必要性等问题.智能优化算法的量子理论纲要可以作为研究与构造算法的理论工具,其有效性已得到初步验证.
Many metaheuristics,which are based on the metaphor of natural phenomena,are lacking the support of a complete mathematical or physical theory.In this paper,the Schrödinger equation of optimization problems is proposed based on the basic probabilistic similarities between an optimization problem and a quantum system.It transforms the optimization problem into a quantum physics problem with the objective function as the constrained conditions.Meanwhile,the algorithm energy,quantum tunnel effect,and entropy are defined based on the probabilistic interpretation of the wave function.This wave function based quantum physical model establishes a comprehensive internal relationship between optimization problems and quantum theory,and theoretically answers the following questions:probabilistic description of solution of optimization problems,selection of neighborhood function,evolutionary process of optimization,necessity of multi-scale process,etc.Those quantum theories of intelligent optimization algorithm can be used as a theoretical means for the analysis of optimization systems.Its effectiveness has been preliminarily verified.
作者
王鹏
辛罡
WANG Peng;XIN Gang(School of Computer Science and Technology,Southwest Minzu University,Chengdu 610225;Chengdu Institute of Computer Application,Chinese Academy of Sciences,Chengdu 610041;University of Chinese Academy of Sciences,Beijing 100049)
出处
《自动化学报》
EI
CAS
CSCD
北大核心
2023年第11期2396-2408,共13页
Acta Automatica Sinica
基金
西南民族大学中央高校基本科研业务费专项资金项目(2020NYB18)资助。
关键词
优化问题
优化算法
量子理论
波函数
基态
Optimization problem
optimization algorithm
quantum theory
wave function
ground state
