Global Convergence Analysis of Hybrid Optimization Algorithms

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.