An effective estimation of distribution algorithm for solving uniform parallel machine scheduling problem with precedence constraints

In this paper, an effective estimation of distributed algorithm (eEDA) is proposed to solve the uniform parallel machine scheduling problem with precedence constraints (prec-UFPMSP). In the eEDA, the permutation-based encoding scheme is adopted and the earliest finish time (EFT) method is used to decode the solutions to the detail schedules. A new effective probability model is designed to describe the relative positions of the jobs. Based on such a model, an incremental learning based updating method is developed and a sampling mechanism is proposed to generate feasible solutions with good diversity. In addition, the Taguchi method of design-of-experiment (DOE) method is used to investigate the effect of key parameters on the performance of the eEDA. Finally, numerical tests are carried out to demonstrate the superiority of the probability model, and the comparative results show that the eEDA outperforms the existing algorithm for most cases.