Problem reduction heuristic for the 0-1 multidimensional knapsack problem

Authors:
Raymond R. Hill;Yong Kun Cho;James T. Moore
Affiliations:
Air Force Institute of Technology, Department of Operational Sciences, 2950 Hobson Way, Wright-Patterson AFB, OH 45433, USA;22 Itaewan-Ro, Yongsan-GU, Ministry of National Defense, Seoul, South Korea;Air Force Institute of Technology, Department of Operational Sciences, 2950 Hobson Way, Wright-Patterson AFB, OH 45433, USA
Venue:
Computers and Operations Research
Year:
2012

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Abstract

This paper introduces new problem-size reduction heuristics for the multidimensional knapsack problem. These heuristics are based on solving a relaxed version of the problem, using the dual variables to formulate a Lagrangian relaxation of the original problem, and then solving an estimated core problem to achieve a heuristic solution to the original problem. We demonstrate the performance of these heuristics as compared to legacy heuristics and two other problem reduction heuristics for the multi-dimensional knapsack problem. We discuss problems with existing test problems and discuss the use of an improved test problem generation approach. We use a competitive test to highlight the performance of our heuristics versus the legacy heuristic approaches. We also introduce the concept of computational versus competitive problem test data sets as a means to focus the empirical analysis of heuristic performance.