IE interfaces (산업공학)

Korean Institute of Industrial Engineers (대한산업공학회)
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Finding Optimal Small Networks by Mathematical Programming Models

수리계획 모형을 이용한 최적의 작은 네트워크 찾기

  • Choi, Byung-Joo (Department of Systems Management Engineering, Sungkyunkwan University) ;
  • Lee, Hee-Sang (Department of Systems Management Engineering, Sungkyunkwan University)
  • 최병주 (성균관대학교 산업공학과) ;
  • 이희상 (성균관대학교 산업공학과)
  • Received : 20070100
  • Accepted : 20070800
  • Published : 2008.03.31
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Abstract

In this paper we study the Minimum Edge Addition Problem(MEAP) to decrease the diameter of a graph. MEAP can be used for improving the serviceability of telecommunication networks with a minimum investment. MEAP is an NP-hard optimization problem. We present two mathematical programming models : One is a multi-commodity flow formulation and the other is a path partition formulation. We propose a branch-and-price algorithm to solve the path partition formulation to the optimality. We develop a polynomial time column generation sub-routine conserving the mathematical structure of a sub problem for the path partition formulation. Computational experiments show that the path partition formulation is better than the multi-commodity flow formulation. The branch-and-price algorithm can find the optimal solutions for the immediate size graphs within reasonable time.

Keywords

References

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