A multi-objective artificial bee colony algorithm for single machine scheduling with family setup under TOU tariffs

Time-of-use (TOU) electricity tariffs have been widely implemented in the manufacturing industry in many countries. This paper investigates a single machine scheduling problem involving incompatible job families with sequence-dependent setup times to minimise total electricity cost and total tardiness simultaneously. To tackle this problem, we propose a multi-objective artificial bee colony (MABC) algorithm. Utilising the dominance properties of the problem, we develop tailored heuristics aimed at improving the quality of initial food sources, and design multi-directional neighbourhood structures to explore desirable neighbour solutions along each objective direction. We construct a novel fitness function that not only considers Pareto rank but also incorporates the hypervolume contribution indicator to identify the promising solution space. Moreover, local integer programming is embedded into the MABC algorithm to intensify the search towards Pareto solutions. The experimental results indicate that the MABC algorithm performs significantly better than NSGA-II, SPEA2, and MOEA/D algorithms.