An order-based estimation of distribution algorithm for stochastic hybrid flow-shop scheduling problem

Abstract

In view of the stochastic nature of the data in real-world manufacturing systems, it is crucial to develop effective algorithms to solve the scheduling problems with uncertainty. In this paper, an order-based estimation of distribution algorithm (OEDA) is proposed to solve the hybrid flow-shop scheduling problem (HFSP) with stochastic processing times. Considering the effectiveness and robustness of a schedule, it aims to minimise the makespan of the initial scenario as well as the deviation of all results of the stochastic scenarios and the initial one. To be specific, a bi-objective function is used to evaluate the individuals of the population, and a probability model is designed to describe the probability distribution of the solution space. Meanwhile, optimal computing budget allocation (OCBA) technique is employed to provide a reliable identification to the good solutions among the population. A mechanism is also presented to update the probability model with the superior individuals that are identified by the OCBA. The new individuals are generated by sampling the probability model to track the area with promising solutions. In addition, the influence of parameter setting is investigated based on Taguchi method of design-of-experiment (DOE), and a suitable parameter setting is suggested. Extensive numerical testing results and comparisons with the existing algorithm are provided, which demonstrate the effectiveness of the proposed OEDA.