An effective multi-objective whale swarm algorithm for energy-efficient scheduling of distributed welding flow shop

Distributed welding flow shop scheduling problem is an extension of distributed permutation flow shop scheduling problem, which possesses a set of identical factories of welding flow shop. On account of several machines can process one job simultaneously in welding shop, increasing the amount of machines can short the processing time of operation while waste more energy consumption at the same time. Thus, energy-efficient is of great significance to take total energy consumption into account in scheduling. A multi-objective mixed integer programming model for energy-efficient scheduling of distributed welding flow shop is presented based on three sub-problems with allocating jobs among factories, scheduling the jobs in each factory and determining the amount of machines upon each job. A multi-objective whale swarm algorithm is proposed to optimize the total energy consumption and makespan simultaneously. In the proposed algorithm, a new initialization method is designed to improve the quality of the initial solution. And various update operators, as well as local search, are designed according to the feature of the problem. To conduct the experiment, diversified indicators are applied to evaluate the proposed algorithm and other MOEAs performance. And the experiment results demonstrate the effectiveness of the proposed method. The proposed algorithm is applied in the real-life case with great performance compared with other MOEAs.