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 algorithm’s convergence, and all terms on the algorithm were strictly defined in mathematical language, and seven theorems related to the algorithm’s convergence were completely proved in the probability space. One of the theorems found the sufficient and necessary conditions for the algorithm’s 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.

Concerning the defects of Genetic Algorithm (GA) in the deficiency of keeping population diversity, prematurity, low success rate and so on, the crossover operation in GA was redesigned by Latin hypercube sampling. Combined with immune mechanism, chromosome concentration was defined and selection strategy was designed, thus an improved genetic algorithm was given based on Latin hypercube sampling and immune mechanism. The Traveling Salesman Problem (TSP) and the Maximum Clique Problem (MCP) were used to verify the new algorithm. The results show, in terms of solution quality, convergence speed, and other indicators, the new algorithm is better than the classical genetic algorithm and good-point-set genetic algorithm.