A matrix-cube-based estimation of distribution algorithm for blocking flow-shop scheduling problem with sequence-dependent setup times

Abstract

The blocking flow-shop scheduling problem with sequence-dependent setup times (BFSP_SDST) is a strong NP-hard problem that exists widely in practice. However, research on this issue is still quite limited. Hence, this paper presents a novel matrix-cube-based estimation of distribution algorithm (MCEDA) to minimize the makespan criterion of the BFSP_SDST. In MCEDA's global search, a matrix cube is devised to reasonably learn the promising patterns in excellent solutions or individuals, and then a matrix-cube-based probabilistic model is developed to quickly guide global search toward the potential promising regions in solution space. A diversity controlling mechanism is also added to avoid the stagnation of global search. In MCEDA's local search, an iterated multi-neighborhood local search controlled by the probabilistic model in global search is designed to execute deeper exploitation from those promising regions. Additionally, two constructive heuristics for generating high-quality initial individuals and one fast Insert-based neighbor evaluation method for accelerating the efficiency of local search are presented based on an analysis of the problem's features. MCEDA's efficacy and superiority in solving the BFSP SDST are demonstrated through comprehensive comparisons with 22 state-of-the-art algorithms.