A matrix cube-based estimation of distribution algorithm for the energy-efficient distributed assembly permutation flow-shop scheduling problem

•The sequence model of energy-efficient DAPFSP is first established.•A heuristic and a hybrid method are presented to generate initial solutions.•A multidimensional probabilistic model is designed to learn the promising patterns.•A critical path-based local search is used to improve the quality of solutions.•Two speed adjustment strategies are proposed to enhance the performance of MCEDA.