Korean Management Science Review (경영과학)

The Korean Operations Research and Management Science Society (한국경영과학회)
권호 표지

Warm-Start of Interior Point Methods for Multicommodity Network Flow Problem

다수상품 유통문제를 위한 내부점 방법에서의 Warm-Start

  • Published : 2004.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we present a methodology for solving the multicommodity network flow problems using interior point methods. In our method, the minimum cost network flow problem extracted from the given multicommodity network flow problem is solved by primal-dual barrier method in which normal equations are solved partially using preconditioned conjugate gradient method. Based on the solution of the minimum cost network flow problem, a warm-start point is obtained from which Castro's specialized interior point method for multicommodity network flow problem starts. In the computational experiments, the effectiveness of our methodology is shown.

Keywords

References

  1. 설동렬, 조은영, 박순달, '네트워크 문제에서 내부점 방법의 활용(내부점 선형계획법에서 효율적인 공액경사법)', '한국군사운영 분석학회', 제24권, 제1호(1998), pp.146-156
  2. 임성묵, 설동렬, 박순달, '다수상품 흐름문제를 위한 내부점 방법', '대한산업공학회지' , 제27권, 제3호(2001), pp.274-280
  3. Ahuja, RK, T.L. Magnanti and lB. Orlin, Network Flows, Prentice Hall, Englewood Cliffs, NJ, 1993
  4. Castro,, J. 'A Specialized Interior Point Algorithm for Multicommodity Network Flows,' Technical Report, 1998
  5. Castro, I. and N. Nabona, 'An implementation of linear and nonlinear multicommodity network flows,' European Journal of Operations Research, Vol.92 (1996), pp.37-53
  6. Choi, I.C. and D. Goldfarb, 'Solving mulicommodity network flow problems by an interior ppoint method,' SIAM Proceedings on Applied Mathemtics, Vol.46(1990), pp.58-69
  7. Gondzio, J., Multiple Centrality Corrections in a Primal-Dual Method for Linear Programming, Computational Optimization and Applications, Vol.6 (1996), pp.137-156
  8. Gondzio, J., 'Warm start of the primal-dual method applied in the cutting plane scheme,' Logilab Technical Report, 1996
  9. Hipolito, A.L., 'A weighted least square study of robustness in interior point linear programming,' Computational optimization and Applications, Vol.2 (1993), pp. 29-46
  10. McBride, R.D., 'Progress Made in Solving The Multicommodity Flow Problem,' SIAM Journal on Optimization, Vol.9, No.4 (1998), pp.947-955