A cooperative memetic algorithm with feedback for the energy-aware distributed flow-shops with flexible assembly scheduling

Abstract

With economic globalization and increasingly concerned sustainable manufacturing, energy-aware distributed scheduling and flexible assembly are significant to optimize global supply chains. Considering the setup and transportation times, this paper addresses the energy-aware distributed flow-shop with flexible assembly scheduling problem (EADFFASP), which contains four strongly coupled sub-problems at both production and assembly stages, i.e., factory assignment of all jobs and sequence of jobs in each factory as well as assembly machine assignment of all products and sequence of products. To minimize total tardiness and energy consumption simultaneously, a mathematical formulation is presented and a cooperative memetic algorithm with feedback (CMAF) is proposed. First, two problem-specific heuristics are designed to initialize population collaboratively with certain quality and diversity. Second, a cooperative search with a feedback mechanism is proposed via utilizing the history information. Third, a local intensification with multiple problem-specific operators is designed to enhance the exploitation. Fourth, multiple selection strategies are utilized cooperatively to balance the exploration and exploitation. Besides, an energy-saving strategy is employed to further reduce energy consumption. The effect of parameter setting is investigated and extensive numerical comparisons are carried out. The results demonstrate the effectiveness of both the feedback mechanism and local intensification, and the comparisons also show that the CMAF outperforms the existing algorithms in solving the EADFFASP.