A hybrid differential evolution algorithm for flexible job shop scheduling with outsourcing operations and job priority constraints

• A flexible job shop scheduling problem with outsourcing and job priority is studied. • Resources that have different processing times to handle one operation are studied. • A sequence-based mathematical model which minimizes the overdue days is proposed. • A hybrid self-adaptive differential evolution algorithm (HSDE) is proposed. • Experiments are carried out to verify the effectiveness of the model and algorithm. Owing to the increasing complexity of products and the specialization of enterprises, production outsourcing has become a common practice in industrial manufacturing. Moreover, different jobs feature various priorities in actual production. The previous research that aims to minimize the makespan may not be applicable in real scenarios. Therefore, this study investigates a flexible job shop scheduling problem with outsourcing operations and job priority constraints. We propose a sequence-based mathematical model aiming at minimizing weighted overdue days, which considers the outsourcing constraints and different overdue weights of jobs with different priorities. An efficient hybrid self-adaptive differential evolution algorithm with heuristic strategies (HSDE) is proposed to address this problem. In HSDE, a well-designed chromosome encoding and decoding method is presented. To eliminate individuals that do not satisfy the outsourcing constraints, we add a penalty term to improve the objective function. By considering heuristic strategies for initial chromosome generation, the proposed approach is able to achieve a high-quality initial population. Crossover and mutation operators with self-adaptive control of the parameters are established to enlarge the search range and accelerate the convergence speed. Finally, several experiments are conducted to verify the effectiveness of the proposed model and algorithm. Experimental results confirm that the proposed algorithm outperforms other algorithms both in efficiency and accuracy.