Facing increasingly serious ecological problems, sustainable development and green manufacturing have attracted much attention. Meanwhile, with the development of globalization, distributed manufacturing is becoming widespread. This paper addresses an energy-efficient scheduling of the distributed permutation flow-shop (EEDPFSP) with the criteria of minimizing both makespan and total energy consumption. Considering the distributed and multiobjective optimization complexity, a knowledge-based cooperative algorithm (KCA) is proposed to solve the EEDPFSP. First, a cooperative initialization scheme is presented with both extended energy-efficient Nawaz-Enscore-Ham heuristic and slowest allowable speed rule that are specially designed to produce good initial solutions with certain diversity. Second, several properties of the nondominated solutions are investigated based on the characteristics of the bi-objective problem, which are used to develop the knowledge-based search operators. Third, a cooperative search strategy of multiple operators is designed for the solutions with different characteristics to tradeoff two objectives. Fourth, a knowledge-based local intensification is used for exploiting better nondominated solutions sufficiently. Moreover, an energy saving method based on the critical path is used to further improve the performance. The effect of parameter setting on the KCA is investigated with the Taguchi method of design-of-experiment. Extensive computational tests and comparisons are carried out, which verify the effectiveness of the special designs of the KCA in solving the EEDPFSP.

With increasing environmental awareness and energy requirement, sustainable manufacturing has attracted growing attention. Meanwhile, distributed manufacturing systems have become emerging due to the development of globalization. This article addresses the energy-aware distributed hybrid flow-shop scheduling (EADHFSP) with minimization of makespan and energy consumption simultaneously. We present a mixed-integer linear programming model and propose a cooperative memetic algorithm (CMA) with a reinforcement learning (RL)-based policy agent. First, an encoding scheme and a reasonable decoding method are designed, considering the tradeoff between two conflicting objectives. Second, two problem-specific heuristics are presented for hybrid initialization to generate diverse solutions. Third, solutions are refined with appropriate improvement operator selected by the RL-based policy agent. Meanwhile, an effective solution selection method based on the decomposition strategy is utilized to balance the convergence and diversity. Fourth, an intensification search with multiple problem-specific operators is incorporated to further enhance the exploitation capability. Moreover, two energy-saving strategies are designed for improving the nondominated solutions. The effect of parameter setting is investigated and extensive numerical tests are carried out. The comparative results demonstrate that the special designs are effective and the CMA is superior to the existing algorithms in solving the EADHFSP.

In the context of globalization and decentralized economies, the distributed manufacturing and scheduling systems have become emerging in large enterprises. This article addresses the distributed hybrid flow-shop scheduling problem (DHFSP) with heterogeneous factories to minimize makespan. Different from single-factory scheduling problem, DHFSP contains several strongly coupled sub-problems, i.e., factory assignment of jobs and the job sequencing in each hybrid flow-shop. In this article, we present a mixed integer linear programming model for the DHFSP and make a first attempt to propose a bi-population cooperative memetic algorithm (BCMA) for solving such a strongly NP-hard problem. The proposed optimization framework comprises collaborative initialization, bi-population cooperation and local intensification. To generate diverse solutions with small makespan, two knowledge-based heuristics are designed for collaborative initialization by utilizing the lower bound of the problem and the historic information of elite solutions during search process. To balance exploration and exploitation, two populations are evolved in a cooperative way. To further enhance the optimization capability, intensification search with multiple problem-specific operators is incorporated. The effect of parameter setting is investigated and extensive computational tests are carried out. The comparative results show that the BCMA is more effective than both the Math solver Gurobi and the existing iterated greedy algorithm, and the effectiveness of each specific design is also verified in solving DHFSP.

As a new analogy paradigm of human learning process, reinforcement learning (RL) has become an emerging topic in computational intelligence (CI). The synergy between the RL and CI is an emerging way to develop efficient solution algorithms for solving complex combinatorial optimization (CO) problems like machine scheduling problem. In this paper, we proposed an efficient optimization algorithm based on Deep RL for solving permutation flow-shop scheduling problem (PFSP) to minimize the maximum completion time. Firstly, a new deep neural network (PFSPNet) is designed for the PFSP to achieve the end-to-end output without limitation of problem sizes. Secondly, an actor-critic method of RL is used to train the PFSPNet without depending on the collection of high-quality labelled data. Thirdly, an improvement strategy is designed to refine the solution provided by the PFSPNet. Simulation results and statistical comparison show that the proposed optimization algorithm based on deep RL can obtain better results than the existing heuristics in similar computational time for solving the PFSP.

With the rise of globalization and environmental concerns, distributed scheduling and energy-efficient scheduling have become crucial topics in the informational manufacturing system. Additionally, the growing consideration about realistic constraints, such as transportation time and finite transportation resources, has made the scheduling problem increasingly complex. Facing these challenges, special mechanisms are required to improve the efficiency of solving algorithms. In this article, a bi-learning evolutionary algorithm (BLEA) is proposed to solve the distributed energy-efficient flexible job shop problem with transportation constraints (DEFJSP-T). First, we integrate statistical learning (SL) and evolutionary learning (EL) in the framework, while decomposition and Pareto dominance methods are employed in different stages to handle conflicting objectives. During the SL stage, probability models are established to statistically search for advantageous substructures on each weight vector, and an update mechanism is devised to improve the exploration. In the EL stage, the genetic operators are introduced and an improved local search that takes into account the problem properties is proposed to realize sufficient exploitation. Finally, according to the performance of the SL, a novel switching mechanism between SL and EL is designed to ensure the rational allocation of computing resources. Extensive experiments are conducted to test the performances of the BLEA. The statistical comparison shows that the BLEA is superior in solving the DEFJSP-T in terms of efficiency and effectiveness.