An operator-inspired framework for metaheuristics and its applications on job-shop scheduling problems

Abstract

The job-shop scheduling problem (JSP) is a well-known combinatorial optimization problem in manufacturing systems. For the past two decades, real-number metaheuristics have been widely used to solve the JSP using the real-number transform methods. A limitation of the real-number metaheuristics is the premature convergence due to the stochasticity of the transform methods. To eliminate this limitation, a novel operator framework has been designed, building the bridge between the discrete optimization problem (JSP) and real-number metaheuristics (also called continuous metaheuristics). Specifically, this paper captures the core operators of the real-number metaheuristics, namely, addition, subtraction, and multiplication. Firstly, three new operators are reconstructed according to several simple neighborhood structures to solve the JSP robustly and effectively. The properties of the arithmetic (symmetry) are taken into account in the reconstruction of the proposed operators to avoid excessive redundant searches. Secondly, a positional similarity-based population diversity is presented for the JSP to demonstrate the intrinsic distinctions between the proposed operators and the transform methods during the evolutionary process. Finally, the results of five widely used benchmark test suites (185 instances) show that the proposed operators can achieve a better balance between exploration and exploitation than the current real-number transform methods.