混合优化算法的全局收敛性分析

Global Convergence Analysis of Hybrid Optimization Algorithms

目前混合优化算法主要是基于实验的经验分析,有关其全局收敛性的理论分析较少.基于单调有界序列的极限定理,从统一性角度提出并证明了混合优化算法全局收敛的多个充分条件,进而得到混合优化算法设计和分析的基本准则:采用独立运行的全局收敛子算法的混合优化算法是全局收敛的;采用周期性重启动或引入随机个体的策略在参与比较和保留精英的条件下可以保证改进型算法的全局收敛性;高效实用的混合优化算法应采用搜索效率较高的算法作为主体而以其他算法作为辅助策略.

Currently,hybrid optimization algorithms are mainly based on empirical analysis of the experiment while the global convergence analysis of hybrid algorithm has less been studied in theory.In this work,with the aid of limit theorem of monotone bounded sequence,several sufficient conditions of global convergence about hybrid algorithms are proposed and proved from the perspective of unity.Further,a few of the basic criteria in hybrid algorithm design and analysis are obtained as follows.Hybrid algorithm using independently running global convergent sub-algorithm is global convergent;the global convergence of improved algorithm is guaranteed if the strategy like periodic restart or random individuals is in use under the conditions of participating in comparison and elite reservation;and an efficient hybrid algorithm should take the high-efficient searching algorithm as the main body while assisted by other algorithms as auxiliary strategies.