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The flexible job shop scheduling problem (FJSP) is a difficult discrete combinatorial optimization problem, which has been widely studied due to its theoretical and practical significance. However, previous researchers mostly emphasized on the production efficiency criteria such as completion time, workload, flow time, etc. Recently, with considerations of sustainable development, low-carbon scheduling problems have received more and more attention. In this paper, a low-carbon FJSP model is proposed to minimize the sum of completion time cost and energy consumption cost in the workshop. A new bio-inspired metaheuristic algorithm called discrete whale optimization algorithm (DWOA) is developed to solve the problem efficiently. In the proposed DWOA, an innovative encoding mechanism is employed to represent two sub-problems: Machine assignment and job sequencing. Then, a hybrid variable neighborhood search method is adapted to generate a high quality and diverse population. According to the discrete characteristics of the problem, the modified updating approaches based on the crossover operator are applied to replace the original updating method in the exploration and exploitation phase. Simultaneously, in order to balance the ability of exploration and exploitation in the process of evolution, six adjustment curves of a are used to adjust the transition between exploration and exploitation of the algorithm. Finally, some well-known benchmark instances are tested to verify the effectiveness of the proposed algorithms for the low-carbon FJSP. [ABSTRACT FROM AUTHOR]

In this paper, a novel improved whale optimization algorithm (IWOA), based on the integrated approach, is presented for solving the flexible job shop scheduling problem (FJSP) with the objective of minimizing makespan. First of all, to make the whale optimization algorithm (WOA) adaptive to the FJSP, the conversion method between the whale individual position vector and the scheduling solution is firstly proposed. Secondly, a resultful initialization scheme with certain quality is obtained using chaotic reverse learning (CRL) strategies. Thirdly, a nonlinear convergence factor (NFC) and an adaptive weight (AW) are introduced to balance the abilities of exploitation and exploration of the algorithm. Furthermore, a variable neighborhood search (VNS) operation is performed on the current optimal individual to enhance the accuracy and effectiveness of the local exploration. Experimental results on various benchmark instances show that the proposed IWOA can obtain competitive results compared to the existing algorithms in a short time. [ABSTRACT FROM AUTHOR]