산업공학 (IE interfaces)

  • 제21권1호
  • /
  • Pages.1-7
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  • 2008
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  • 1225-0996(pISSN)
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  • 2234-6465(eISSN)
대한산업공학회 (Korean Institute of Industrial Engineers)
권호 표지

수리계획 모형을 이용한 최적의 작은 네트워크 찾기

Finding Optimal Small Networks by Mathematical Programming Models

  • 최병주 (성균관대학교 산업공학과) ;
  • 이희상 (성균관대학교 산업공학과)
  • Choi, Byung-Joo (Department of Systems Management Engineering, Sungkyunkwan University) ;
  • Lee, Hee-Sang (Department of Systems Management Engineering, Sungkyunkwan University)
  • 투고 : 20070100
  • 심사 : 20070800
  • 발행 : 2008.03.31
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초록

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.

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참고문헌

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