A Discrete Grey Wolf Optimization Algorithm for Minimizing Penalties on a Single Machine Scheduling Problem

Abstract

AbstractThis paper proposes a new penalty function for scheduling problems that aims to minimize tardiness penalties on a single machine in which each job has its own due date. The problem asks for finding a complete schedule of all jobs, minimizing the total penalties for tardiness jobs. According to this performance measure, a tardiness penalty will be applied to the job if it is finished after its due date. This problem is NP-hard problem. The problem has many real life applications especially in industries such as production systems and acceptance orders. A discrete grey wolf optimization algorithm (DGWO) is proposed for solving this problem. The problem under consideration is a discrete optimization problem. Therefore, we modified and improved the original grey wolf optimization algorithm (GWO) to adapt it with the problem. To ensure that the proposed DGWO is effective and efficient, the average and maximum relative errors between DGWO and optimal solutions are computed. According to our results, the proposed DGWO outputs near optimal solutions in most problem instances size.KeywordsScheduling problemsTardiness penaltiesPenalty functionProduction systemsGrey Wolf Optimization Algorithm