Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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A Lagrangian Heuristic for the Multidimensional 0-1 Knapsack Problem

다중 배낭 문제를 위한 라그랑지안 휴리스틱

  • 윤유림 (서울대학교 컴퓨터공학부) ;
  • 김용혁 (광운대학교 컴퓨터소프트웨어학과)
  • Received : 2010.07.12
  • Accepted : 2010.11.20
  • Published : 2010.12.25
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Abstract

In general, Lagrangian method for discrete optimization is a kind of technique to easily manage constraints. It is traditionally used for finding upper bounds in the branch-and-bound method. In this paper, we propose a new Lagrangian search method for the 0-1 knapsack problem with multiple constraints. A novel feature of the proposed method different from existing Lagrangian approaches is that it can find high-quality lower bounds, i.e., feasible solutions, efficiently based on a new property of Lagrangian vector. We show the performance improvement of the proposed Lagrangian method over existing ones through experiments on well-known large scale benchmark data.

일반적으로 이산 최적화에서의 라그랑지안 방법은 제약조건을 쉽게 다루기 위한 기법이다. 이 방법은 전형적으로 분지한계법에서 상한을 찾을 때 사용한다. 본 논문은 여러 개의 제약조건이 있는 다중 배낭 문제를 위한 새로운 라그랑지안 방법을 제안한다. 기존 라그랑지안 접근법과는 달리 제안한 방법은 라그랑지안 벡터의 새로운 특징에 기초하여 품질 좋은 하한(즉, 가능 해)을 효율적으로 찾을 수 있다. 잘 알려진 큰 규모의 벤치마크 데이터에서 실험을 하였고 제안한 라그랑지안 방법은 기존 방법의 성능을 개선하였다.

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References

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