A Parallel Machine Scheduling Problem Minimizing the Total Weighted Earliness and Total Weighted Tardiness by a Multi-Objective Scatter Search Method

The parallel machine scheduling problem is an important and difficult problem to be considered in the real-world situations. Traditionally, this problem consists of the scheduling of a set of independent jobs on parallel machines with the aim of minimizing the maximum job completion. In today's manufacturing systems, in which both early and tardy finishing of job processing are undesired, the objectives related to earliness and tardiness penalties have become increasingly popular. In this paper, two major goals are considered as follows: (1) total weighted earliness; (2) total weighted tardiness. Due to the complexity of such a hard problem, a new multi-objective meta-heuristic method, i.e. multi-objective scatter search (MOSS), is proposed to obtain the locally Pareto-optimal frontier where the simultaneous minimization of the above-mentioned objectives is desired. In order to validate the performance of the proposed MOSS method, in terms of solution quality and diversity level, various test problems are considered and the reliability of this method, based on different comparison metrics, is compared with the Elite Tabu Search (ETS) devised in this paper. The computational results show the high capability of the proposed MOSS method.