Résumé : In this work, a new branch-and-price-and-cut algorithm is proposed to solve the one-dimensional bin packing problem (1D-BPP). The 1D-BPP is one of the most fundamental problems in combinatorial optimization and has been extensively studied for decades. Recently, Delorme et al. (2016) proposed 500 new test instances for the 1D-BPP; the best exact algorithm proposed in the literature can optimally solve 167 of these new instances, with a time limit of one hour imposed to each execution of the algorithm. The exact algorithm proposed in this paper is based on the classical set-partitioning model for the 1D-BPP and the subset-row inequalities proposed by Jepsen et al. (2008). We describe an ad-hoc label-setting algorithm to solve the pricing problem, dominance and fathoming rules to speedup its computation and a new primal heuristic. The exact algorithm can easily handle some practical constraints, like the incompatibility between the items, and therefore we also apply it to solve the 1D-BPP with conflicts (1D-BPPC). The proposed method is tested on a large family of 1D-BPP and 1D-BPPC classes of instances. For the 1D-BPP, the proposed method can optimally solve 237 instances of the new set of difficult instances; the largest instance involves 1003 items and bins of capacity 80,000. For the 1D-BPPC, the experiments show that the method is highly competitive with state-of-the-art methods, and successfully closed several open 1D-BPPC instances.

Dernière modification : Thursday 21 November 2024

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