Volume 51, Number 3, July-September 2017
|Page(s)||627 - 637|
|Published online||24 July 2017|
Probabilistic Tabu search with multiple neighborhoods for the Disjunctively Constrained Knapsack Problem
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
Received: 25 May 2016
Accepted: 20 June 2016
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.
Mathematics Subject Classification: 90C27 / 90C59
Key words: Probabilistic Tabu Search / knapsack problem / weighted independent set / conflict graph
© EDP Sciences, ROADEF, SMAI 2017
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