An exact algorithm for the 0---1 linear knapsack problem with a single continuous variable

Authors:
Geng Lin;Wenxing Zhu;M. M. Ali
Affiliations:
Center for Discrete Mathematics and Theoretical Computer Science, Fuzhou University, Fuzhou, China 350108 and Department of Mathematics, Minjiang University, Fuzhou, China 350108;Center for Discrete Mathematics and Theoretical Computer Science, Fuzhou University, Fuzhou, China 350108;School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa
Venue:
Journal of Global Optimization
Year:
2011

Citing 8
Cited 0

A lift-and-project cutting plane algorithm for mixed 0-1 programs

Mathematical Programming: Series A and B
Mixed 0-1 programming by lift-and-project in a branch-and-cut framework

Management Science
On the complexity of integer programming

Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem

Management Science
Aggregation and Mixed Integer Rounding to Solve MIPs

Operations Research
A Major Appliance Manufacturer Rethinks Its Inventory Policies for Service Vehicles

Interfaces
Strengthening Chvátal-Gomory cuts and Gomory fractional cuts

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

The 0---1 linear knapsack problem with a single continuous variable (KPC) is an extension of the binary knapsack problem (KP). It is an NP-hard problem. In this paper, we show that KPC can be reduced to KP and a pseudo-knapsack problem (PKP), which is similar to the traditional knapsack problem except that the profits of items may be non-positive, and the weight sum has two sided limits on capacity. We use the Dynamic Programming algorithm COMBO (Martello et al., Manag Sci 45(3):414---424, 1999) to solve KP, and modify the branch and bound method EXPKNAP (Pisinger, Eur J Oper Res 87:175---187, 1995) for KP to solve the PKP. Numerical experiments show the efficiency of our method.