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Primal Heuristics for Branch-and-Price: the assets of diving methods

Ruslan Sadykov 1 François Vanderbeck 1, 2 Artur Pessoa 3 Issam Tahiri 1, 2 Eduardo Uchoa 3
1 Realopt - Reformulations based algorithms for Combinatorial Optimization
LaBRI - Laboratoire Bordelais de Recherche en Informatique, IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : Primal heuristics have become an essential component in mixed integer programming (MIP) solvers. Extending MIP based heuristics, our study outlines generic procedures to build primal solutions in the context of a branch-and-price approach and reports on their performance. Our heuristic decisions carry on variables of the Dantzig-Wolfe reformulation, the motivation being to take advantage of a tighter linear programming relaxation than that of the original compact formulation and to benefit from the combinatorial structure embedded in these variables. We focus on the so-called diving methods that use re-optimization after each LP rounding. We explore combinations with diversification- intensification paradigms such as limited discrepancy search , sub-MIPing, local branching, and strong branching. The dynamic generation of variables inherent to a column generation approach requires specific adaptation of heuristic paradigms. We manage to use simple strategies to get around these technical issues. Our numerical results on generalized assignment, cutting stock, and vertex coloring problems sets new benchmarks, highlighting the performance of diving heuristics as generic procedures in a column generation context and producing better solutions than state-of-the-art specialized heuristics in some cases.
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Submitted on : Thursday, April 13, 2017 - 4:28:18 PM
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Ruslan Sadykov, François Vanderbeck, Artur Pessoa, Issam Tahiri, Eduardo Uchoa. Primal Heuristics for Branch-and-Price: the assets of diving methods. INFORMS Journal on Computing, Institute for Operations Research and the Management Sciences (INFORMS), 2019, 31 (2), pp.251-267. ⟨10.1287/ijoc.2018.0822⟩. ⟨hal-01237204v3⟩



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