A Simple and Comprehensive Method Based on Measure Comparison for Global Convergence Analysis in Evolutionary Computation

In problem-independent theoretical studies of evolutionary computation (EC) algorithms, convergence is one of the most frequently mentioned properties of an algorithm’s search capability. However, we have observed that the term convergence represents different, and sometimes even contradictory, properties in different researches. This paper briefly reviews and summarizes some key works in these two directions and subsequently demonstrates that some results from stable convergence and global convergence are mutually exclusive properties. The mutual exclusivity between these two convergences inspires us to propose a scope and domain measure comparison-based (SDMC) method, by comparing the measures of the population’s search scope and the problem’s feasible domain. The SDMC method is simple yet complete for analyzing the global convergence of EC algorithms instead of modeling the algorithms as homogeneous Markov chains. The linear decreasing inertia weight particle swarm optimization (LDIW-PSO) is taken as an example to show how to analysis the global convergence with the proposed SDMC method.