VNS/TS for a parallel machine scheduling problem
Résumé
The goal of this work is to develop an efficient metaheuristic to solve the parallel machine scheduling problem where the objective function is to minimize the weighted number of late jobs. This problem appears in several real-life applications and particularly in finance and production management. The weighted number of late jobs can also be seen as an indicator of the quality of a solution or as a minor objective in multi-objective optimisation. To our knowledge, only a limited number of methods have been developed to solve this problem. The best-performing method to date is based on constraint propagation techniques and does not succeed in optimally solving instances of fifty jobs with more than sixty percent success rate. One of the aims of this research is to provide an efficient method to solve problems with up to 100 jobs at least. A problem-specific representation is used to represent solutions. It consists of a priority list of late jobs and a list of early and sequenced jobs for each machine. This representation is well-suited for this objective and easy to manipulate with any computer language. Based on this representation, a set of neighbourhoods is used in a VNS strategy. To obtain good results a tabu search procedure is embedded as the local search mechanism. Numerical experiments are conducted on a set of instances of 50 jobs and compared with an exact procedure. Results prove that the proposed method can indeed be used to find solutions of large instances.
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