A hybrid estimation of distribution algorithm for distributed permutation flowshop scheduling with flowline eligibility

This paper studies a new extension of distributed permutation flow shop scheduling problem (DPFSP) referred to as the DPFSP with flowline eligibility. Under this extension, the problem contains two stages. At the first assignment stage, a set N of n jobs is distributed among F factories with flowline eligibility constraint, i.e., not all the factories are available for every job. Then each factory can be regarded as a regular permutation flow shop scheduling problem (PFSP) in which jobs assigned to each factory have to be processed on m machines according to the given permutation. The objective is to minimize the maximum completion time or makespan of all the factories. The flowline eligibility constraint adds asymmetry and complexity to the regular DPFSP. In the proposed hybrid estimation of distribution algorithm (hybrid EDA), a heuristic of Framinan and Leisten (FLH) based solution-generate method (FLHSGM), two novel factory-based operators are proposed, and an effective local search based on variable neighborhood search (VNS) is employed and incorporated into EDA. Numerical simulations with comprehensive computational and statistical analysis are carried out. The experimental results and comparisons with existing algorithms show that the FLHSGM and the VNS-based local search enhances the search ability of EDA and the effectiveness of the hybrid EDA in solving both small-scale and large-scale DPFSP with flowline eligibility.