Mathematical modeling and hybrid evolutionary algorithm to schedule flexible job shop with discrete operation sequence flexibility

Abstract

In actual industrial production, several operations of a job may not have precedence relationships and can be placed at any point in the process route. However, traditional flexible job shop scheduling problems (FJSP) often assume that all operations of each job must be processed in strict linear order. Therefore, this research addresses the FJSP with discrete operation sequence flexibility (FJSPDS) with the objective of minimizing the makespan. Based on existing models, two novel mixed-integer linear programming (MILP) models are formulated by improving the description methods of variables and constraints, significantly enhancing the models’ performance. Additionally, a hybrid evolutionary algorithm (HEA) is proposed to solve large-scale instances through the following three aspects. An improved encoding method is proposed, which makes the search space of the HEA and solution space of the problem more compatible and reduces the possibility of optimal solutions being missed. A special neighborhood structure is designed according to the characters of sequence-free operations, and an iterative local search method is introduced to improve the quality of the solution. A knowledge-driven reinitialization operator is developed, which generates new individuals based on the features of the historical elite population, guiding the evolution of populations, avoiding premature convergence while also avoiding falling into local optima. Finally, a total of 110 benchmark problem instances are utilized to verify the superior effectiveness of the MILP models and the HEA in solving FJSPDS.