Heuristics for Non-dominated Sets of Two-Agent Scheduling on a Single Parallel-Batching Machine

Abstract

Abstract. We study a bi-objective problem of scheduling the jobs from two agents on a single parallel-batching machine with the objective of minimizing the makespans of the both agents. All jobs have an equal processing time and non-identical job sizes. We define a boundary of Pareto-optimal set and then present two metrics to evaluate the quality of a non-dominated set. Based on two different strategies, two heuristics are proposed to generate non-dominated sets. Furthermore, we compare the performance of the heuristics with the widely used non-dominated sorting genetic algorithm (NSGA-II), and evaluate the quality of the obtained non-dominated set based on the proposed metrics. The results show that the proposed heuristics outperform NSGA-II, and the obtained nondominated set is very close to the Pareto-optimal set.