A Fast Algorithm for Knapsack Problem with Conflict Graph

Jiaxin Li (), Yan Lan (), Feng Chen (), Xin Han and Jacek Blazewicz
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Jiaxin Li: Software School, Dalian University of Technology, Dalian, P. R. China
Yan Lan: Dalian Minzu University, Dalian, P. R. China
Feng Chen: Software Technology Research Laboratory, De Montfort University, UK
Xin Han: Software School, Dalian University of Technology, Dalian, P. R. China
Jacek Blazewicz: Institute of Computing Science, Poznań University of Technology, Poznań, Poland5Institute of Bioorganic Chemistry, Polish Academy of Sciences, Poznań, Poland6European Center for Bioinformatics and Genomics, Poznań, Poland

Asia-Pacific Journal of Operational Research (APJOR), 2021, vol. 38, issue 06, 1-34

Abstract: In this paper, we propose a fast algorithm based on a new algorithm to calculate the upper bound for the knapsack problem with conflict graph (KPCG). The KPCG is an extension of the 0-1 knapsack problem. A pre-defined conflict graph defines the incompatibility properties between pairs of items. The goal is to determine which items should be packed into the knapsack to maximize the total profit on the premise of satisfying the capacity constraint and the incompatibility constraints. The experimental results show that for the graph with density greater than or equal to 0.1, the branch-and-bound algorithm based on the new algorithm is 1.6458 and 1.6352 times faster than the state-of-the-art algorithm on random and correlated instances, respectively, and can achieve speedups of up to 4.6477 for some low density instances. Moreover, the branch-and-bound algorithm based on the new algorithm can optimally solve more instances than the state-of-the-art algorithm in a given time limit.

Keywords: Combinatorial optimization; branch-and-bound; knapsack problem with conflict graph; maximum weight stable set problem (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S021759592150010X

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