Application of EM algorithm to hybrid flow shop scheduling problems with a special blocking

In this paper, we consider hybrid flow shop (HFS) scheduling problem with a special blocking constraint. Objective function is makespan minimization. HFS and RCb blocking constraint are firstly presented. Then, an integer linear model is presented to find the optimal solution and a lower bound is proposed for high size problems. In order to faster obtain a solution, especially for big size problems, an electromagnetism-like (EM) algorithm is proposed and some mechanisms are introduced to adapt EM-algorithm to HFS scheduling problems. Its performances are compared with optimal solutions when they have been obtained and lower bound for more complex problems. Opportunity to develop and adapt such a meta-heuristic is clearly demonstrated with presented solutions accuracy and time.