Modified Multiobjective Evolutionary Algorithm based on Decomposition for Low-Carbon Scheduling of Distributed Permutation Flow-Shop

Low-carbon scheduling has raised great interest during recent years under the background of green economy. In this paper, a modified multiobjective evolutionary algorithm based on decomposition (MOEA/D-M) is proposed to solve the distributed permutation flow-shop low-carbon scheduling problem (DPFLCSP) with the criteria of minimizing the makespan and carbon emission. Under the framework of basic MOEA/D, an operator-selection strategy is designed to enhance the exploration ability. This strategy is based on the relative position between solutions and reference point in the normalized objective space. Meanwhile, a local intensification component based on angles of solutions in the normalized objective space is incorporated in the algorithm to improve the quality of the explored solutions. This local intensification consists of some operators specially designed according to the properties of the problem. To balance the convergence and diversity, two different neighborhoods named mating neighborhood and replacement neighborhood are used. Besides, the critical path based carbon saving method is also used. Computational comparisons demonstrate the effectiveness of the operator-selection strategy and the superior quality of the MOEA/D-M to other algorithms.