Probabilistic Tabu search with multiple neighborhoods for the Disjunctively Constrained Knapsack Problem
Ben Salem, Mariem1 ; Hanafi, Saïd2 ; Taktak, Raouia3 ; Ben Abdallah, Hanêne4
1 FSEGS/MIRACL, Université de Sfax, Tunisia
2 Université de Valenciennes, LAMIH – UMR CNRS 8201, France
3 ISIMS/CRNS, Université de Sfax, Tunisia
4 King Abdulaziz University, Jeddah, Saudi Arabia
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 3, pp. 627-637.

Given a set of items, each with a profit and a weight and a conflict graph describing incompatibilities between items, the Disjunctively Constrained Knapsack Problem is to select the maximum profit set of compatible items while satisfying the knapsack capacity constraint. We develop a probabilistic tabu search heuristic with multiple neighborhood structures. The proposed algorithm is evaluated on a total of 50 benchmark instances from the literature up to 1000 items. Computational results disclose that the proposed tabu search method outperforms recent state-of-the-art approaches. In particular, our approach is able to reach 46 best known solutions and discover 8 new best known solutions out of 50 benchmark instances.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2016049
Classification : 90C27, 90C59
Mots-clés : Probabilistic Tabu Search, knapsack problem, weighted independent set, conflict graph
Ben Salem, Mariem 1 ; Hanafi, Saïd 2 ; Taktak, Raouia 3 ; Ben Abdallah, Hanêne 4

1 FSEGS/MIRACL, Université de Sfax, Tunisia
2 Université de Valenciennes, LAMIH – UMR CNRS 8201, France
3 ISIMS/CRNS, Université de Sfax, Tunisia
4 King Abdulaziz University, Jeddah, Saudi Arabia 
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     title = {Probabilistic {Tabu} search with multiple neighborhoods for the {Disjunctively} {Constrained} {Knapsack} {Problem}},
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Ben Salem, Mariem; Hanafi, Saïd; Taktak, Raouia; Ben Abdallah, Hanêne. Probabilistic Tabu search with multiple neighborhoods for the Disjunctively Constrained Knapsack Problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 3, pp. 627-637. doi : 10.1051/ro/2016049. http://www.numdam.org/articles/10.1051/ro/2016049/

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