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.

The flux-switching transverse flux permanent magnet linear machine (FSTFPMLM) is proposed in this paper combining the advantages of transverse flux linear machine and flux-switching linear machine. Firstly, the structure and operating principle of FSTFPMLM is presented. Secondly, the magnetic field of a simplified FSTFPMLM is numerically computed by three-dimensional (3-D) finite element method (FEM). Thirdly, the thrust characteristics of the machine, including thrust force, cogging force and force ripple are numerically analyzed. The influence of structure parameters on the thrust characteristics has been analyzed by 3-D FEM. The law of thrust, cogging force and force ripple as the pole pitch ratio between primary and secondary and the ratio between tooth width and pole pitch of secondary variable provides the guidance to design FSTFPMLM, which aims to achieve the larger thrust, smaller cogging and force ripple using less permanent magnet materials. The thrust force capabilities of FSTFPMLM are compared with other topologies of linear machines. Finally, the prototype and experimental setup have been developed, and the calculated results and the measured results are in good agreement.

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.

The conventional production scheduling problem has mainly emphasized the time-related metrics, such as makespan, machine workload and tardiness/earliness, and so on. With the advent of the sustainable manufacturing, the green scheduling problem has been received more and more attention from scholars and researchers. In this paper, we investigate a green flexible job shop scheduling problem (GFJSP) with the consideration of environmental factors. To formulate the GFJSP problem, a mathematical model is first established to minimize the amount of total energy-consumption. To solve the model, a kind of improved African buffalo optimization (IABO) algorithm is proposed based on the characteristics of the problem. In the proposed IABO, a two-vector solution representation method is first designed, and a population initialization method is adopted to generate the initial solutions with certain quality and diversity. Based on the original ABO, several improvement strategies are introduced to enhance the performance of the algorithm, i.e., the modified individual learning mechanism and the aging-based re-initializaiton mechanism. In addition, in order to adapt our algorithm to the scheduling problem, a discrete individual updating method is developed to ensure the algorithm search directly in a discrete domain. Finally, a number of experiments have been conducted to test the performance of the proposed IABO algorithm. The simulation data demonstrate the effectiveness of the proposed IABO for the considered GFJSP.

This article proposes a competitive co-evolutionary quantum genetic algorithm for the no-wait flow shop scheduling problem with the criterion to minimize makespan, which is a renowned NP-hard combinatorial optimization problem. An innovative coding and decoding mechanism is proposed. The mechanism uses square matrix to represent the quantum individual and adapts the quantum rotation gate to update the quantum individual. In the algorithm framework, the store-with-diversity is proposed to maintain the diversity of the population. Moreover, a competitive co-evolution strategy is introduced to enhance the evolutionary pressure and accelerate the convergence. The store-with-diversity and competitive co-evolution are designed to keep a balance between exploration and exploitation. Simulations based on a benchmark set and comparisons with several existing algorithms demonstrate the effectiveness and robustness of the proposed algorithm.