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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 474852, 10 pages
http://dx.doi.org/10.1155/2013/474852
Research Article

A Memetic Lagrangian Heuristic for the 0-1 Multidimensional Knapsack Problem

1Future IT R&D Laboratory, LG Electronics Umyeon R&D Campus, 38 Baumoe-ro, Seocho-gu, Seoul 137-724, Republic of Korea
2Department of Computer Science and Engineering, Kwangwoon University, 20 Kwangwoon-ro, Nowon-gu, Seoul 139-701, Republic of Korea

Received 9 January 2013; Accepted 23 April 2013

Academic Editor: Xiaohui Liu

Copyright © 2013 Yourim Yoon and Yong-Hyuk Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a new evolutionary algorithm to solve the 0-1 multidimensional knapsack problem. We tackle the problem using duality concept, differently from traditional approaches. Our method is based on Lagrangian relaxation. Lagrange multipliers transform the problem, keeping the optimality as well as decreasing the complexity. However, it is not easy to find Lagrange multipliers nearest to the capacity constraints of the problem. Through empirical investigation of Lagrangian space, we can see the potentiality of using a memetic algorithm. So we use a memetic algorithm to find the optimal Lagrange multipliers. We show the efficiency of the proposed method by the experiments on well-known benchmark data.