A bi-objective scheduling problem on batch machines via a Pareto-based ant colony system

This research aims to minimize the bi-criteria of makespan and maximum tardiness on a set of identical batch-processing machines arranged in parallel. Each machine can process multiple jobs simultaneously as long as the machine capacity is not exceeded. Each job is defined by its processing time, ready time, due date, and size. The processing time and ready time of a batch are represented by the largest processing time and release time among all jobs in the batch, respectively. For this problem, a scheduling algorithm based on the framework of a multi-objective ant colony optimization (MOACO) approach called a Pareto-based ant colony system (PACS) was developed. Based on the constructive characteristics of PACS, a new mechanism of solution construction was introduced so that the proposed algorithm had the ability to explore the entire solution space. Moreover, corresponding to the new construction mechanism, a candidate list strategy and a form of dynamic heuristic information were developed to reduce the search space and direct the search toward the promising regions, respectively. Through extensive computational experiments with various problem instances, the effectiveness of the proposed algorithm was evaluated by measuring the computational efficiency and solution quality. The experiment results demonstrated that PACS had a superior performance compared to other benchmark algorithms, especially for large job instances.