Iron and steel industry is a significant basic industry of national economy. Steelmaking-Refining-Continuous Casting (SRCC) is one of the bottlenecks of the iron and steel production process. SRCC scheduling problems are world-wide and NP-hard problems. SRCC scheduling problems considering energy saving are named Energy-Efficient SRCC (EESRCC) scheduling problems. Effective EESRCC scheduling algorithms would not only help to enhance the production efficiency, but also help to reduce the energy saving. This paper proposed a Discrete Growth Optimizer (DGO) to solve the EESRCC scheduling problems. Differ from the traditional GO, the proposed DGO is enhanced by incorporating five strategies. More specifically, a population initialization heuristic is designed to generate a relatively ‘good’ initial population. The control based local search is devised to enhance the intensification and diversification abilities of the proposed DGO. The restricted local search is designed to further improve the three best solutions found so far. The enhanced learning phase is devised to learn from the three best solutions found so far and elite solutions in the population. The multi-type reflection phase is developed to further enhance the solutions in the population. The effectiveness of the DGO has been verified by the experiments.

This paper investigated Integrated Hybrid Flowshop Scheduling with Sequence-Dependent Setup Times and Vehicle Routing Problems Considering Customer Priority (IHFSS-VRPC). The IHFSS-VRPC are joint optimization problems, which integrate the Hybrid Flowshop Scheduling with Sequence-Dependent Setup Times (HFSP-SDST) with the Vehicle Routing Problems (VRP) Considering Customer Priority and maximum driving distance constraint. The problems are different from the Integrated Hybrid Flowshop Scheduling Problems (HFSP) and VRP. To deal with the IHFSS-VRPC effectively, this paper proposed a Hybrid Fireworks Algorithm (HFWA). In the proposed HFWA, six key components, i.e., Two stage decoding, Population initialization, Variable Neighbourhood Search (VNS) based local search, Explosion amplitude calculation, Mutation operator and Selection strategy, were elaborately to enhance the search abilities. More specifically, the Two stage decoding was presented to compile effective schedules, the Population initialization, Explosion amplitude calculation and Selection strategy were devised to balance the exploitation and exploration capacities. The VNS based local search was developed to improve the exploitation capacities, while the Mutation operator was devised to enhance the exploration capacities. The performance of the proposed HFWA has been demonstrated by conducting comparison experiments on a set of instances.

Job shop scheduling problem (JSSP) is a typical scheduling problem in manufacturing. Traditional scheduling methods fail to guarantee both efficiency and quality in complex and changeable production environments. This paper proposes an end-to-end deep reinforcement learning (DRL) method to address the JSSP. In order to improve the quality of solutions, a network model based on transformer and attention mechanism is constructed as the actor to enable a DRL agent to search in its solution space. The Proximal policy optimization (PPO) algorithm is utilized to train the network model to learn optimal scheduling policies. The trained model generates sequential decision actions as the scheduling solution. Numerical experiment results demonstrate the superiority and generality of the proposed method compared with other three classic heuristic rules.

This paper investigates an energy-efficient hybrid flowshop scheduling problem with the consideration of machines with different energy usage ratios, sequence-dependent setups, and machine-to-machine transportation operations. To minimize the makespan and total energy consumption simultaneously, a mixed-integer linear programming (MILP) model is developed. To solve this problem, a three-stage multiobjective approach based on decomposition (TMOA/D) is suggested, in which each solution is bound with a main weight vector and a set of its neighbors. Accordingly, a variable direction strategy is developed to ensure each solution along its main direction is thoroughly exploited and can jump to the neighboring directions using a proximity principle. To ensure an active schedule of arranging jobs to machines, a two-level solution representation is employed. In the first phase, each solution attempts to improve itself along its current weight vector through a developed neighborhood-based local search. In the second phase, the promising solutions are selected through the technique for order preference by similarity to an ideal solution. Then, they attempt to update themselves with a proposed global replacement strategy via incorporation with their closing solutions. In the third phase, a solution conducts a large perturbation when it goes through all its assigned weight vectors. Extensive experiments are conducted to test the performance of TMOA/D, and the results demonstrate that TMOA/D has a very competitive performance.