Green Job Shop Scheduling Problem With Discrete Whale Optimization Algorithm

In the last few decades, production scheduling problems have been studied for optimizing production efficiency involving the time-related indicators, such as completion time, earliness/tardiness time, or flow time. Currently, with the consideration of sustainable development, the green scheduling problem has been paid more and more attention. Here, a green job shop scheduling problem is considered to minimize the sum of energy-consumption cost and completion-time cost in the workshop. In this paper, a mathematical model is first established with the consideration of multi-speed machines. A discrete whale optimization algorithm (DWOA) is then proposed for solving the model. In the proposed algorithm, a two-string encoding is adopted to represent the two sub-problems: job permutation and speed selection. Then, a heuristic method is used to initialize the population to enhance the quality of initial solutions. By considering the discrete characteristics of the problem, the individual updating operators are redesigned to ensure the algorithm work directly in a discrete scheduling domain. In addition, a variable neighborhood search strategy is embedded to further improve the search ability. The extensive experiments have been performed to test the DWOA. The computational data reveal the promising advantages of the DWOA on the considered problem.