An estimation of distribution algorithm for solving hybrid flow-shop scheduling problem with stochastic processing time

In this paper, an effective estimation of distribution algorithm (EDA) is proposed to solve the hybrid flow-shop scheduling problem with stochastic processing time. Considering the effectiveness and robustness of a schedule, the schedule objective is to minimize the makespan of the initial scenario as well as the deviation of the makespan between all stochastic scenarios and the initial one. In the proposed EDA, a bi-objective evaluation function is employed to evaluate the individuals of the population. A probability model is presented to describe the probability distribution of the solution space. A mechanism is provided to update the probability model with the superior individuals. By sampling the probability model, new individuals can be generated among the search region with the promising solutions. Numerical testing results based on some well known benchmark instances are provided. The comparisons with the existing genetic algorithm demonstrate the effectiveness and robustness of the proposed EDA.