EDA based probabilistic Memetic Algorithm for distributed blocking permutation flowshop scheduling with sequence dependent setup time

Distributed permutation flowshop scheduling problem (DPFSP) is a typical NP-hard combinatorial optimization problem and represents an important area in multiple distributed production systems. In this study, both machine blocking and job sequence dependent setup time constraints are considered in DPFSP, which make the conventional model more suitable to the realistic situation. The combination with new constraints means a substantial increase in the complexity of the problem and the volatility of landscape, which sharply increase the solving difficulty. Probabilistic memetic framework (PrMF) is a novel MA framework which balances the exploration and exploitation by controlling the learning intensity of each individual. In this paper, an EDA-based PrMF algorithm, called EDAPrMF, is proposed to solve the DBPFSP with SDST, in which PrMF is modified and extended for distributed scheduling problems with two-layer encoding. Specifically, a novel solution matrix based distance matrix is defined for DBPFSP with SDST, which serves as a suitable measure between two feasible solutions and can also be connected with the probability matrix of EDA, the global search meme in PrMF. Meta-Lamarckian learning strategy is also equipped in PrMF to guide the local search direction. The experimental results and comparisons with existing algorithms show the efficiency of the proposed EDAPrMF in solving both small-scale and large-scale DBPFSP with SDSP and the effectiveness of PrMF in improve the search ability.