Solving the Multidimensional Multiple-choice Knapsack Problem by constructing convex hulls

Authors:
Md Mostofa Akbar;M. Sohel Rahman;M. Kaykobad;E. G. Manning;G. C. Shoja
Affiliations:
Department of CSC, PANDA Lab, University of Victoria, Victoria, BC, Canada, USA and Department of CSE, BUET, Dhaka, Bangladesh;Department of CSE, BUET, Dhaka, Bangladesh;Department of CSE, BUET, Dhaka, Bangladesh;Department of CSC, PANDA Lab, University of Victoria, Victoria, BC, Canada, USA;Department of CSC, PANDA Lab, University of Victoria, Victoria, BC, Canada, USA
Venue:
Computers and Operations Research
Year:
2006

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Abstract

This paper presents a heuristic to solve the Multidimensional Multiple-choice Knapsack Problem (MMKP), a variant of the classical 0-1 Knapsack Problem. We apply a transformation technique to map the multidimensional resource consumption to single dimension. Convex hulls are constructed to reduce the search space to find the near-optimal solution of the MMKP. We present the computational complexity of solving the MMKP using this approach. A comparative analysis of different heuristics for solving the MMKP has been presented based on the experimental results.