Bi-Population Based Discrete Bat Algorithm for the Low-Carbon Job Shop Scheduling Problem

Job shop scheduling problem (JSP) is a combinatorial optimization problem, which has been widely studied due to its strong theoretical and background for application. However, in previous studies on the traditional JSP, the optimization objective is mainly relative to time, such as makespan, flow time, tardiness, earliness, and workload. With the advent of green manufacturing, energy consumption should be considered in the JSP. Therefore, a low-carbon JSP is studied in this paper. Due to the NP-hard nature, a meta-heuristic algorithm, bat algorithm (BA), is considered in this paper. According to the characteristics of the problem, a kind of bi-population-based discrete BA (BDBA) is proposed to minimize the sum of the energy consumption cost and the completion-time cost. A parallel searching mechanism is first introduced to the algorithm, by which the population is divided into two sub-populations to, respectively, adjust the job permutation and the processing speed of each machine. Three communication strategies are used to implement the cooperation between the sub-populations. In addition, due to the fact that the original BA was developed to deal with the continuous problems, a modified discrete updating approach is proposed to make the BA algorithm directly work in a discrete domain. Finally, extensive simulations have been conducted to test the effectiveness of the proposed BDBA algorithm. The experimental data demonstrate that the proposed BDBA is effective in solving the low-carbon JSP under study.