Peng Fuming

Convergence analysis of general evolutionary algorithms

Traditional Evolutionary Algorithm(EA) convergence research focuses on specific algorithm;consequently the conclusion is only suitable for some specific algorithm.In order to study the convergence of all EAs,this paper presented a general EA including EAs of all operator types.A probability space was set up for the purpose of studying the algorithms convergence,and all terms on the algorithm were strictly defined in mathematical language,and seven theorems related to the algorithms convergence were completely proved in the probability space.One of the theorems found the sufficient and necessary conditions for the algorithms convergence in probability.More importantly,these theorems are suitable to all types of EAs.A system composed of these theorems was established,which could be used to guide the EA design and judge the correctness of an EA theoretically.