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 ( ${C_{\max }} $Cmax) 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.