Energy-Saving Distributed Flexible Job Shop Scheduling Optimization with Dual Resource Constraints Based on Integrated Q-Learning Multi-Objective Grey Wolf Optimizer

The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worker constraints.As one critical factor of production,effective utilization of worker resources can increase productivity.Meanwhile,energy consumption is a growing concern due to the increasingly serious environmental issues.Therefore,the distributed flexible job shop scheduling problem with dual resource constraints(DFJSP-DRC)for minimizing makespan and total energy consumption is studied in this paper.To solve the problem,we present a multi-objective mathematical model for DFJSP-DRC and propose a Q-learning-based multi-objective grey wolf optimizer(Q-MOGWO).In Q-MOGWO,high-quality initial solutions are generated by a hybrid initialization strategy,and an improved active decoding strategy is designed to obtain the scheduling schemes.To further enhance the local search capability and expand the solution space,two wolf predation strategies and three critical factory neighborhood structures based on Q-learning are proposed.These strategies and structures enable Q-MOGWO to explore the solution space more efficiently and thus find better Pareto solutions.The effectiveness of Q-MOGWO in addressing DFJSP-DRC is verified through comparison with four algorithms using 45 instances.The results reveal that Q-MOGWO outperforms comparison algorithms in terms of solution quality.

Improved gray wolf optimizer for distributed flexible job shop scheduling problem

The distributed flexible job shop scheduling problem(DFJSP),which is an extension of the flexible job shop scheduling problem,is a famous NP-complete combinatorial optimization problem.This problem is widespread in the manufacturing industries and comprises the following three subproblems:the assignment of jobs to factories,the scheduling of operations to machines,and the sequence of operations on machines.However,studies on DFJSP are seldom because of its difficulty.This paper proposes an effective improved gray wolf optimizer(IGWO)to solve the aforementioned problem.In this algorithm,new encoding and decoding schemes are designed to represent the three subproblems and transform the encoding into a feasible schedule,respectively.Four crossover operators are developed to expand the search space.A local search strategy with the concept of a critical factory is also proposed to improve the exploitability of IGWO.Effective schedules can be obtained by changing factory assignments and operation sequences in the critical factory.The proposed IGWO algorithm is evaluated on 69 famous benchmark instances and compared with six state-of-the-art algorithms to demonstrate its efficacy considering solution quality and computational efficiency.Experimental results show that the proposed algorithm has achieved good improvement.Particularly,the proposed IGWO updates the new upper bounds of 13 difficult benchmark instances.