A memetic algorithm for minimizing the total weighted completion time on a single machine under step-deterioration |
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| Authors: | Jalil Layegh Fariborz Jolai Mohsen Sadegh Amalnik |
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| Affiliation: | 1. State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China;2. School of Chemistry and Chemical Engineering, Shenyang Normal University, Shenyang 110034, China;3. University of Chinese Academy of Sciences, Beijing 100049, China;1. School of Economics and Management, Southeast University, Nanjing, Jiangsu, 210096, China;2. DeGroote School of Business, McMaster University, Hamilton, Ontario, L8S4M4, Canada;3. School of Sciences, East China Institute of Technology, Nanchang, Jiangxi, 330000, China;1. Department of Physics, M.L. Sukhadia University, Udaipur 313001, Rajasthan, India;2. Department of Pure & Applied Physics, University of Kota, Kota 324007, Rajasthan, India |
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| Abstract: | In this paper, we consider minimizing total weighted completion time criteria on a single machine. Jobs processing times are step function of its starting time and all jobs have a common due date. First, we present some new lemmas and dominance properties for this NP-hard problem, and then a memetic algorithm using these properties is developed. We compare the solutions of the memetic algorithm with optimal solutions obtained from complete enumeration. The results show that the average percentage error of the proposed algorithm from optimal solutions is about 2% and as the variance of processing time increase, the percentage errors decrease. |
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