Solving the 0-1 Multidimensional Knapsack Problem with Resolution Search

Sylvain Boussier (1) , Michel Vasquez (2, 3) , Yannick Vimont (2) , Said Hanafi (4) , Philippe Michelon (1)

1 LIA - Laboratoire Informatique d'Avignon
2 LGI2P - Laboratoire de Génie Informatique et Ingénierie de Production
3 IMT - MINES ALES - IMT - MINES ALES
4 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201

We propose an exact method which combines the resolution search and branch & bound algorithms for solving the 0–1 Multidimensional Knapsack Problem. This algorithm is able to prove large–scale strong correlated instances. The optimal values of the 10 constraint, 500 variable instances of the OR-Library are exposed. These values were previously unknown.

Mots clés: 0–1 Multidimensional Knapsack Problem; Resolution Search; Branch & Bound

Domaines: Mathématique discrète [cs.DM]

Sylvain Boussier, Michel Vasquez, Yannick Vimont, Said Hanafi, Philippe Michelon. Solving the 0-1 Multidimensional Knapsack Problem with Resolution Search. VI ALIO/EURO Workshop on Applied Combinatorial Optimization, Dec 2008, Buenos Aires, Argentina. ⟨hal-00381898⟩