Energy-Conscious Scheduling Problem in a Flexible Job Shop Using a Discrete Water Wave Optimization Algorithm

As more and more attention is paid to green manufacturing, production scheduling has been proved to be an efficient method for the reduction of environmental pollution. It is well-known that the flexible job shop scheduling problem (FJSP) is a very complex combinatorial optimization problem with strong theoretical and background for application. However, the problem has been extensively investigated and historically concerned with some indicators related to time, e.g., flow time, makespan, and workload. In this study, an energy-conscious FJSP is investigated with the consideration of the energy consumption. First, a mathematical model of the energy-conscious FJSP is built with the objective of optimizing the sum of the energy consumption cost and the completion-time cost. Due to the fact that the basic water wave optimization (WWO) was developed for various continuous problems, a discrete water wave optimization (DWWO) algorithm is proposed to solve the model. In our DWWO algorithm, a three-string encoding approach is first adopted to represent each individual wave. To make the algorithm adapt for the considered scheduling problem, three discrete evolutionary operations are redesigned according to the characteristics of the problem, i.e., propagation, refraction, and breaking. Finally, extensive experimental simulations are conducted to test the proposed DWWO algorithm. The comparison results demonstrate that the proposed DWWO algorithm is efficient for the energy-conscious FJSP.