Multi-objective discrete water wave optimization algorithm for solving the energy-saving job shop scheduling problem with variable processing speeds

For the job shop with variable processing speeds, the aim of energy saving and consumption reduction is implemented from the perspective of production scheduling. By analyzing the characteristics of the workshop, a multi-objective mathematical model is established with the objective of reducing the total energy consumption and shortening the makespan. A multi-objective discrete water wave optimization (MODWWO) algorithm is proposed for solving the problem. Firstly, a two-vector encoding method is adopted to divided the scheduling solution into two parts, which represent speed selection and operation permutation in the scheduling solution, respectively. Secondly, some dispatching rules are used to initialize the population and obtain the initial scheduling solutions. Then, three operators of the basic water wave optimization algorithm are redesigned to make the algorithm adaptive for the multi-objective discrete scheduling problem under study. A new propagation operator is presented with the ability of balancing global exploration and local exploitation based on individual rank and neighborhood structures. A novel refraction operator is designed based on crossover operation, by which each individual can learn from the current best individual to absorb better information. And a breaking operator is modified based on the local search strategy to enhance the exploitation ability. Finally, extensive simulation experiments demonstrate that the proposed MODWWO algorithm is effective for solving the considered energy-saving scheduling problem.