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Flexible job shop scheduling problem (FJSP) is a typical discrete combinatorial optimization problem, which can be viewed as an extended version of the classical job shop scheduling problem. In previous researches, the scheduling problem has historically emphasized the production efficiency. Recently, scheduling problems with green criterion have been paid great attention by researchers. In this paper, the mathematical model of the low-carbon flexible job shop scheduling problem is established with the objective of minimizing the sum of the energy consumption cost and the earliness/tardiness cost. For solving the model, a kind of bi-population based discrete cat swarm optimization algorithm (BDCSO) is presented to obtain the optimal scheduling scheme in the workshop. In the framework of the BDCSO, two sub-populations are used to adjust the machine assignment and operation sequence respectively. At the initialization stage, a two-component discrete encoding mechanism is first employed to represent each individual, and then a heuristic method is adopted to generate the initial solutions with good quality and diversity. By considering the discrete characteristics of the scheduling problem, the modified updating methods are developed for the seeking and tracing modes to ensure the algorithm work directly in a discrete domain. To coordinate the global and local search in each sub-population, six adjustment curves are used to change the number of cats in the seeking and tracing modes, based on which six algorithms are developed, i.e., LBDCSO, SinBDCSO, CosBDCSO, TanBDCSO, LnBDCSO, and SquareBDCSO. In addition, the information exchanging strategy is introduced to implement the cooperation of the two sub-populations. Finally, extensive simulation based on random instances and benchmark instances is carried out. The comparisons results demonstrate the effectiveness of the proposed algorithms in solving the FJSP under study.

Optimizing the Low-Carbon Flexible Job Shop Scheduling Problem Considering Energy Consumption