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.