An improved multi-objective firefly algorithm for energy-efficient hybrid flowshop rescheduling problem

Hybrid flowshop scheduling problem is a hot research topic, and is widely applied for production shop or line in chemical industry, metallurgical industry, semiconductor manufacturing and other industries. However, on the one hand, the uncertain events are inevitable in actual production, which will disrupt the production plan. On the other hand, nowadays the energy problem becomes more and more serious, and attracts much attention in the manufacturing industry. Therefore, an energy-efficient hybrid flowshop rescheduling problem under the machine breakdown is addressed in this paper. Firstly, the mathematical model for the problem is established, and an energy saving strategy based on problem model is designed, which can ensure the reduction of energy consumption without affecting the production efficiency. Then, an improved multi-objective firefly algorithm is proposed to optimize the production efficiency, energy consumption and production stability. To express the problem characteristics, a two-level encoding mechanism is used to describe the individual, and a corresponding decoding mechanism is presented to generate the scheduling scheme. By simulating the location updating law of the fireflies, the population updating rule is designed, in which the variable neighborhood search is employed to avoid the local optimal. To ensure the quality of the solution set, the fast non-dominated sorting method and elite individual reserving strategy are introduced to the population evolution. Finally, the numerical experimental results indicate that the designed energy saving strategy is effective, and the proposed algorithm obtains better Pareto frontier and performs the better convergence and diversity comparing with MOEA/D and NSGA-II, the common algorithms to solve complex multi-objective optimization problem.