Under the current environmental pressure, many manufacturing enterprises are urged or forced to adopt effective energy-saving measures. However, environmental metrics, such as energy consumption and CO2 emission, are seldom considered in the traditional production scheduling problems. Recently, the energy-related scheduling problem has been paid increasingly more attention by researchers. In this paper, an energy-efficient job shop scheduling problem (EJSP) is investigated with the objective of minimizing the sum of the energy consumption cost and the completion-time cost. As the classical JSP is well known as a non-deterministic polynomial-time hard (NP-hard) problem, an improved whale optimization algorithm (IWOA) is presented to solve the energy-efficient scheduling problem. The improvement is performed using dispatching rules (DR), a nonlinear convergence factor (NCF), and a mutation operation (MO). The DR is used to enhance the initial solution quality and overcome the drawbacks of the random population. The NCF is adopted to balance the abilities of exploration and exploitation of the algorithm. The MO is employed to reduce the possibility of falling into local optimum to avoid the premature convergence. To validate the effectiveness of the proposed algorithm, extensive simulations have been performed in the experiment section. The computational data demonstrate the promising advantages of the proposed IWOA for the energy-efficient job shop scheduling problem.

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Workshop scheduling has mainly focused on the performances involving the production efficiency, such as times and quality, etc. In recent years, environmental metrics have attracted the attention of many researchers. In this study, an energy-efficient job shop scheduling problem is considered, and a grey wolf optimization algorithm with double-searching mode (DMGWO) is proposed with the objective of minimizing the total cost of energy-consumption and tardiness. Firstly, the algorithm starts with a discrete encoding mechanism, and then a heuristic algorithm and the random rule are employed to implement the population initialization. Secondly, a new framework with double-searching mode is developed for the GWO algorithm. In the proposed DMGWO algorithm, besides of the searching mode of the original GWO, a random seeking mode is added to enhance the global search ability. Furthermore, an adaptive selection operator of the two searching modes is also presented to coordinate the exploration and exploitation. In each searching mode, a discrete updating method of individuals is designed by considering the discrete characteristics of the scheduling solution, which can make the algorithm directly work in a discrete domain. In order to further improve the solution quality, a local search strategy is embedded into the algorithm. Finally, extensive simulations demonstrate the effectiveness of the proposed DMGWO algorithm for solving the energy-efficient job shop scheduling problem based on 43 benchmarks.

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