0-1 QUADRATIC KNAPSACK PROBLEMS: AN EXACT APPROACH BASED ON A t-LINEARIZATION *

Abstract : This paper presents an exact solution method based on a new linearization scheme for the 0-1 quadratic knapsack problem, which consists of maximizing a quadratic pseudo-Boolean function with nonnegative coefficients subject to a linear capacity constraint. Contrasting with traditional linearization schemes, our approach adds only one extra variable. The suggested linearization framework provides a tight upper bound, which is used in a branch-and-bound scheme. This upper bound is numerically compared with that of [A. Billionnet, A. Faye, and E. Soutif, European J. Oper. Res., 112 (1999), pp. 664–672], and our branch-and-bound scheme with the exact algorithm of [W. D. Pisinger, A. B. Rasmussen, and R. Sandvik, INFORMS J. Comput., 19 (2007), pp. 280–290]. The experiments show that our upper bound is quite competitive (less than 1% from the optimum). In addition, the proposed branch-and-bound clearly outperforms the algorithm developed by Pisinger et al. for low density instances (25%) for all instances up to 400 variables.
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Submitted on : Monday, May 23, 2016 - 2:47:48 PM
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Diego Carlos Rodrigues, D Quadri, P Michelon, S Gueye. 0-1 QUADRATIC KNAPSACK PROBLEMS: AN EXACT APPROACH BASED ON A t-LINEARIZATION *. SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2012, ⟨10.1137/110820762⟩. ⟨hal-01320143⟩

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