Convergence Analysis of the New Hybrid Genetic Algorithm for the Job Shop Scheduling Problem

In our recent paper [10], we proposed a new hybrid genetic algorithm (NHGA) for the job shop scheduling problems. The method of encoding we used is Natural coding instead of traditional binary coding. This manner of coding has a lot of advantages but its convergence is still an open issue for years. In genetic algorithms (GAs), the population evolves continuously through different generations. At each the generation, the population is characterized by a value of the objective function. Considering this value as a state of the generation, the evolutionary process of the population can be supposed a Markov chain. Therefore, this paper analyzes the convergence property of the NHGA by applying properties of Markov chains. Based on the Markov chain analysis of genetic algorithm, we find out the proposed method leads to the convergence to the global optimum in the case of Natural coding.