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To our knowledge, this paper investigates the first application of meta-heuristic algorithms to tackle the parallel machines scheduling problem with weighted late work criterion and common due date (   \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$P|{{d}_{j}}=d|{{Y}_{w}}$$\end{document}P  |    d  j    =  d  |    Y  w). Late work criterion is one of the performance measures of scheduling problems which considers the length of late parts of particular jobs when evaluating the quality of scheduling. Since this problem is known to be NP-hard, three meta-heuristic algorithms, namely ant colony system, genetic algorithm, and simulated annealing are designed and implemented, respectively. We also propose a novel algorithm named LDF (largest density first) which is improved from LPT (longest processing time first). The computational experiments compared these meta-heuristic algorithms with LDF, LPT and LS (list scheduling), and the experimental results show that SA performs the best in most cases. However, LDF is better than SA in some conditions, moreover, the running time of LDF is much shorter than SA.

Meta-heuristic algorithms for parallel identical machines scheduling problem with weighted late work criterion and common due date