Optimal solutions for unrelated parallel machines scheduling problems using convex quadratic reformulations |
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Authors: | M-C Plateau YA Rios-Solis |
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Institution: | 1. CEDRIC – CNAM, 292 Rue Saint Martin, 75003 Paris, France;2. LIP6 – University Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France |
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Abstract: | In this work, we take advantage of the powerful quadratic programming theory to obtain optimal solutions of scheduling problems. We apply a methodology that starts, in contrast to more classical approaches, by formulating three unrelated parallel machine scheduling problems as 0–1 quadratic programs under linear constraints. By construction, these quadratic programs are non-convex. Therefore, before submitting them to a branch-and-bound procedure, we reformulate them in such a way that we can ensure convexity and a high-quality continuous lower bound. Experimental results show that this methodology is interesting by obtaining the best results in literature for two of the three studied scheduling problems. |
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Keywords: | Scheduling Quadratic programming Convex reformulations Parallel machines |
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