Alternating control tree search for knapsack/covering problems

The Multidimensional Knapsack/Covering Problem (KCP) is a 0–1 Integer Programming Problem containing both knapsack and weighted covering constraints, subsuming the well-known Multidimensional Knapsack Problem (MKP) and the Generalized (weighted) Covering Problem . We propose an Alternating Control T...

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Bibliographic Details
Published in:Journal of heuristics Vol. 16; no. 3; pp. 239 - 258
Main Authors: Hvattum, Lars Magnus, Arntzen, Halvard, Løkketangen, Arne, Glover, Fred
Format: Journal Article
Language:English
Published: Boston Springer US 01.06.2010
Springer Science + Business Media
Springer Nature B.V
Subjects:
Artificial Intelligence
Calculus of Variations and Optimal Control; Optimization
Capital budgeting
Heuristic
Integer programming
Knapsack problem
Management Science
Mathematics
Mathematics and Statistics
Methods
Operations Research
Operations Research/Decision Theory
Studies
Covering
Knapsack
Tree search
Heuristic
ISSN:1381-1231, 1572-9397
Online Access:Get full text
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Summary:The Multidimensional Knapsack/Covering Problem (KCP) is a 0–1 Integer Programming Problem containing both knapsack and weighted covering constraints, subsuming the well-known Multidimensional Knapsack Problem (MKP) and the Generalized (weighted) Covering Problem . We propose an Alternating Control Tree Search (ACT) method for these problems that iteratively transfers control between the following three components: (1) ACT-1, a process that solves an LP relaxation of the current form of the KCP. (2) ACT-2, a method that partitions the variables according to 0, 1, and fractional values to create sub-problems that can be solved with relatively high efficiency. (3) ACT-3, an updating procedure that adjoins inequalities to produce successively more constrained versions of KCP, and in conjunction with the solution processes of ACT-1 and ACT-2, ensures finite convergence to optimality. The ACT method can also be used as a heuristic approach using early termination rules. Computational results show that the ACT-framework successfully enhances the performance of three widely different heuristics for the KCP. Our ACT-method involving scatter search performs better than any other known method on a large set of KCP-instances from the literature. The ACT-based methods are also found to be highly effective on the MKP.
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ISSN:1381-1231
1572-9397
DOI:10.1007/s10732-008-9100-4