A copula-based hybrid estimation of distribution algorithm for m-machine reentrant permutation flow-shop scheduling problem

Aiming at the m-machine reentrant permutation flow-shop scheduling problem (MRPFSSP), a copula-based hybrid estimation of distribution algorithm (CHEDA) is presented to minimize the makespan criterion. Firstly, we establish both the operation-based model and the graph model for MRPFSSP, and then several inherent properties about critical path and blocks are proposed and analyzed. Secondly, the copula theory is utilized to build CHEDA's probability model (i.e., the joint distribution function, JDF) to efficiently extract the useful information from the excellent individuals. Thirdly, the global search based on the JDF model and a new population sampling method is designed to find the promising sub-regions in the total solution space. Fourthly, a problem-dependent local search based on the critical path and blocks is embedded into CHEDA to enhance the local exploitation ability. Finally, simulation experiments and comparisons demonstrate the effectiveness of the proposed CHEDA.