A multi-objective migrating birds optimization algorithm based on game theory for dynamic flexible job shop scheduling problem

The occurrence of dynamic events such as machine breakdown during workshop production can make the original scheduling scheme infeasible. Therefore, this paper establishes a mathematical model for a multi-objective dynamic flexible job shop scheduling problem with machine breakdown, and proposes a multi-objective migrating birds optimization algorithm based on game theory. Firstly, in order to solve the problem of difficult to determine the weight in weighted multi-objective optimization, this paper introduces game theory to balance the Pareto optimality and fairness between the two objectives of production efficiency and stability. When solving the solution of the game model, there may be no perfect Nash equilibrium solution, so a solution method that approximates the Nash equilibrium solution is designed. In the improved migrating algorithm, neighborhood operators based on path relinking and machine age are designed to improve the search ability. Based on the attributes of multi-objective problems, a multiple similarity measure method is designed to select and replace solutions. The experiment part proves the effectiveness of the game strategy in multi-objective optimality and fairness, and concludes that the algorithm has good performance by comparing with the advanced algorithms in recent years.