A discrete electromagnetism-like mechanism for single machine total weighted tardiness problem with sequence-dependent setup times

Abstract

Electromagnetism-like mechanism (EM) is a novel meta-heuristic, inspired by the attraction–repulsion mechanism of electromagnetic theory. There are very few applications of EM in scheduling problems. This paper presents a discrete EM (DEM) algorithm for minimizing the total weighted tardiness in a single-machine scheduling problem with sequence-dependent setup times. Unlike other discrete EM algorithms that use a random key method to deal with the discreteness, the proposed DEM algorithm employs a completely different approach, with an attraction–repulsion mechanism involving crossover and mutation operators. The proposed algorithm not only accomplishes the intention of an EM algorithm but also can be applied in other combinatorial optimization problems. To verify the algorithm, it is compared with a discrete differential evolution (DDE) algorithm, which is the best meta-heuristic for the considered problem. Computational experiments show that the performance of the proposed DEM algorithm is better than that of the DDE algorithm in most benchmark problem instances. Specifically, 30 out of 120 aggregated best-known solutions in the literature are further improved by the DEM algorithm, while other another 70 instances are solved to an equivalent degree.