A multi-neighborhood-based multi-objective memetic algorithm for the energy-efficient distributed flexible flow shop scheduling problem

This paper focuses on an energy-efficient distributed flexible flow shop scheduling problem (EEDFFSP) with variable machine speed. The EEDFFSP needs to solve four sub-problems: factory assignment, determination of the job sequence at each stage, machine selection, and the speed selection for each job on a machine. A multi-neighborhood-based multi-objective memetic algorithm (MMMA) is proposed to optimize total weighted tardiness and energy consumption. The MMMA employs a two-level encoding scheme including a job permutation and a speed matrix. A highly-efficient decoding strategy is utilized to reduce the search space of the sub-problems. In the initial phase, a weighted NEH (Nawaz-Enscore-Ham) based-initial method is developed to generate an initial population. Two genetic global search operators are designed to perform exploration evolution. Then, several multiple neighborhoods including several permutation adjustment operations within or between factories, an energy-saving strategy, and a speed adjustment strategy are integrated to enhance exploitation ability. The comprehensive experiments on extensive instances are performed to test the contribution of the main components and the performance of the MMMA. The average values of Hypervolume and Unary Epsilon indicators obtained by the variants of the MMMA without the initialization method, genetic global search, local search, and energy-saving strategy are worse than the complete MMMA, which demonstrates a significant contribution of these components to the MMMA. The MMMA obtains the best values of indicators among all the compared algorithms within a limited run time, which demonstrates the MMMA is an effective and efficient algorithm for solving the EEDFFSP.

Automated summary

This paper proposes a multi-objective memetic algorithm with a two-level encoding scheme to solve the energy-efficient distributed flexible flow shop scheduling problem. Through comprehensive experiments, the effectiveness of the algorithm in optimizing total weighted tardiness and energy consumption is verified.