Energy-efficient scheduling for multi-objective two-stage flow shop using a hybrid ant colony optimisation algorithm

Reducing energy costs has become an important concern for sustainable manufacturing systems, owing to concern for the environment. We present a multi-objective hybrid ant colony optimisation (MHACO) algorithm for a real-world two-stage blocking permutation flow shop scheduling problem to address the trade-off between total energy costs (TEC) and makespan () as measures of the service level with the time-of-use (TOU) electricity price. We explore the energy-saving potential of the manufacturing industry in consideration of the differential energy costs generated by variable-speed machines. A mixed integer programming model is developed to formulate this problem. In the MHACO algorithms, the max-min pheromone restriction rules and the local search rules avoid the localisation trap and enhance neighbourhood search capabilities, respectively. The Taguchi method and small-scale pilot experiments are employed to determine the appropriate experimental parameters. Based on three well-known multi-objective optimisation algorithms, viz., NSGAII, SPEA2, and MODEA, six algorithms with different batch-sorting methods are adopted as a comparison in small-, moderate-, and large-scale instances. A four-dimensional performance evaluation system is established to evaluate the obtained Pareto frontier approximations. The computational results show that the proposed MHACO-Johnson algorithm outperforms other algorithms in terms of solution quality, quantity, and distribution, although it is time consuming when dealing with moderate- to large-scale instances.