Journal of the Korea Society of Computer and Information (한국컴퓨터정보학회논문지)

Korean Society of Computer Information (한국컴퓨터정보학회)
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An Integer Programming-based Local Search for the Multiple-choice Multidimensional Knapsack Problem

  • Hwang, Junha (Dept. of Computer Engineering, Kumoh National Institute of Technology)
  • Received : 2018.09.17
  • Accepted : 2018.11.12
  • Published : 2018.12.31
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Abstract

The multiple-choice multidimensional knapsack problem (MMKP) is a variant of the well known 0-1 knapsack problem, which is known as an NP-hard problem. This paper proposes a method for solving the MMKP using the integer programming-based local search (IPbLS). IPbLS is a kind of a local search and uses integer programming to generate a neighbor solution. The most important thing in IPbLS is the way to select items participating in the next integer programming step. In this paper, three ways to select items are introduced and compared on 37 well-known benchmark data instances. Experimental results shows that the method using linear programming is the best for the MMKP. It also shows that the proposed method can find the equal or better solutions than the best known solutions in 23 data instances, and the new better solutions in 13 instances.

Keywords

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Fig. 1. General Integer Programming-based Local Search

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Fig. 2. Selection Method using Linear Programming

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Fig. 3. Selection Method using Profit/Weight Ratio

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Fig. 4. Sum Graph of Objective Values for Selection Rate

Table 1. MMKP Data Instances

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Table 2. An Example of MMKP

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Table 3. Experimental Results for Selection Methods

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Table 4. Comparison with Other Methods

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