An effective multi-objective discrete virus optimization algorithm for flexible job-shop scheduling problem with controllable processing times

- A multi-objective model for FJSP with controllable processing times is constructed.
- A new multi-objective discrete virus optimizer is proposed to solve this problem.
- A new exploitation scheme is designed to improve the performance of the algorithm.
- The proposed method outperforms other methods on most instances.
- The proposed method is successfully used to address a real-world case.

The scheduling problems with controllable processing times (CPT) are commonly encountered in some manufacturing industries. CPT means the processing times of operations can be controlled by allocating additional resources. However the flexible job-shop scheduling problem (FJSP) with CPT is seldom explored due to its essential complexity. In addition, FJSP usually involves several conflicting objectives in the practical production. Therefore, the multi-objective FJSP with CPT (MOFJSP-CPT) is highly important in terms of theoretical research and practical application. Thus, this paper focuses on the MOFJSP-CPT. Firstly, this study formulates a mathematical model with the objectives of minimizing both the makespan and the total additional resource consumption. Then, to solve this problem, we propose a new multi-objective discrete virus optimization algorithm (MODVOA) with a three-part representation for each virus, an improved method for yielding the initial population, and an ensemble of operators for updating each virus. To further improve the exploitation, a problem-specific exploitation mechanism is implemented in the later stage of the search process. Finally, to evaluate the effectiveness of the MODVOA, the MODVOA is compared with other well-known multi-objective evolutionary algorithms including NSGA-II and SPEA2. Experimental results on randomly generated instances and a real-world case demonstrate that the proposed MODVOA can achieve a better performance than other algorithms for solving the MOFJSP-CPT.