Local branching-based algorithms for the disjunctively constrained knapsack problem

Authors:
Hakim Akeb;Mhand Hifi;Mohamed Elhafedh Ould Ahmed Mounir
Affiliations:
ISC Paris School of Management, 22 Boulevard du Fort de Vaux, 75017 Paris, France;Université de Picardie Jules Verne, Equipe ROAD-MIS, 5 rue du Moulin Neuf, 80000 Amiens, France;Université de Picardie Jules Verne, Equipe ROAD-MIS, 5 rue du Moulin Neuf, 80000 Amiens, France
Venue:
Computers and Industrial Engineering
Year:
2011

Citing 7
Cited 0

A new algorithm for the 0-1 knapsack problem

Management Science
A local branching heuristic for mixed-integer programs with 2-level variables, with an application to a telecommunication network design problem

Networks
Reduction strategies and exact algorithms for the disjunctively constrained knapsack problem

Computers and Operations Research
Using Decomposition Techniques and Constraint Programming for Solving the Two-Dimensional Bin-Packing Problem

INFORMS Journal on Computing
An Exact Approach for the Vehicle Routing Problem with Two-Dimensional Loading Constraints

Transportation Science
A column generation method for the multiple-choice multi-dimensional knapsack problem

Computational Optimization and Applications
The Multidimensional Knapsack Problem: Structure and Algorithms

INFORMS Journal on Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

The disjunctively constrained knapsack problem (DCKP) is a variant of the well-known single constrained knapsack problem with special disjunctive constraints. This paper investigates the use of the local branching techniques for solving large-scale DCKP. Three versions of the algorithm are considered. The first version is based on the standard local branching which uses a starting solution provided by a specialized rounding solution procedure. The second version applies a two-phase solution procedure embedded in the local branching. For each subtree, the procedure serves to construct the set of objects containing the assigned variables and a second set including the free variables. The first set provides a partial local solution to the DCKP, whereas, for the second set, a truncated exact tree-search is applied for completing the partial local feasible solution. Finally, a diversification strategy is considered constituting the third version of the algorithm. All versions of the proposed algorithm are computationally analyzed on a set of benchmark instances of the literature and the obtained solutions are compared to those provided by existing algorithms. Encouraging results have been obtained.