메뉴 건너뛰기




Volumn 14, Issue , 2010, Pages 1-12

Almost 20 years of combinatorial optimization for railway planning: From lagrangian relaxation to column generation

Author keywords

Column generation; Integer linear programming formulations; Integer multicommodity flow; Lagrangian relaxation; Railway planning

Indexed keywords

COLUMN GENERATION; INTEGER LINEAR PROGRAMMING FORMULATION; LAGRANGIAN RELAXATION; MULTI-COMMODITY FLOW; RAILWAY PLANNING;

EID: 84882960736     PISSN: 21906807     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.4230/OASIcs.ATMOS.2010.1     Document Type: Conference Paper
Times cited : (9)

References (24)
  • 1
    • 0030282457 scopus 로고    scopus 로고
    • A dynamic subgradient-based branch-and-bound procedure for set covering
    • E. Balas and M.C. Carrera, "A Dynamic Subgradient-Based Branch-and-Bound Procedure for Set Covering", Operations Research 44 (1996), 875-890.
    • (1996) Operations Research , vol.44 , pp. 875-890
    • Balas, E.1    Carrera, M.C.2
  • 4
    • 0025383362 scopus 로고
    • A lagrangian heuristic for set covering problems
    • J.E. Beasley, "A Lagrangian Heuristic for Set Covering Problems", Naval Research Logistics 37 (1990), 151-164.
    • (1990) Naval Research Logistics , vol.37 , pp. 151-164
    • Beasley, J.E.1
  • 7
    • 43949092779 scopus 로고    scopus 로고
    • A column generation approach to train timetabling on a corridor
    • V. Cacchiani, A. Caprara, P. Toth, "A Column Generation Approach to Train Timetabling on a Corridor", 4OR 6 (2008), 125-142.
    • (2008) 4OR , vol.6 , pp. 125-142
    • Cacchiani, V.1    Caprara, A.2    Toth, P.3
  • 8
    • 77955173320 scopus 로고    scopus 로고
    • Solving a real-world train unit assignment problem
    • V. Cacchiani, A. Caprara, P. Toth, "Solving a Real-World Train Unit Assignment Problem", Mathematical Programming 124 (2010), 207-232.
    • (2010) Mathematical Programming , vol.124 , pp. 207-232
    • Cacchiani, V.1    Caprara, A.2    Toth, P.3
  • 9
  • 10
    • 0033351565 scopus 로고    scopus 로고
    • A heuristic method for the set covering problem
    • A. Caprara, M. Fischetti, P. Toth, "A Heuristic Method for the Set Covering Problem", Operations Research 47 (1999), 730-743.
    • (1999) Operations Research , vol.47 , pp. 730-743
    • Caprara, A.1    Fischetti, M.2    Toth, P.3
  • 14
    • 0036759198 scopus 로고    scopus 로고
    • Modeling and solving the train timetabling problem
    • A. Caprara, M. Fischetti, P. Toth, "Modeling and Solving the Train Timetabling Problem", Operations Research 50 (2002), 851-861.
    • (2002) Operations Research , vol.50 , pp. 851-861
    • Caprara, A.1    Fischetti, M.2    Toth, P.3
  • 17
    • 0001140270 scopus 로고    scopus 로고
    • A lagrangian-based heuristic for large-scale set covering problems
    • S. Ceria, P. Nobili and A. Sassano, "A Lagrangian-Based Heuristic for Large-Scale Set Covering Problems", Mathematical Programming 81 (1998), 215-228.
    • (1998) Mathematical Programming , vol.81 , pp. 215-228
    • Ceria, S.1    Nobili, P.2    Sassano, A.3
  • 18
    • 77957089136 scopus 로고
    • Time constrained routing and scheduling
    • M.O. Ball et al. (Eds.) Elsevier Science
    • J. Desrosiers, Y. Dumas, M.M. Solomon and F. Soumis, "Time Constrained Routing and Scheduling", in M.O. Ball et al. (Eds.), Handbooks in OR & MS, Vol. 8, Elsevier Science, 1995, 35-139.
    • (1995) Handbooks in or & MS , vol.8 , pp. 35-139
    • Desrosiers, J.1    Dumas, Y.2    Solomon, M.M.3    Soumis, F.4
  • 19
    • 0019477279 scopus 로고
    • The lagrangian relaxation method for solving integer programming problems
    • M.L. Fisher, "The Lagrangian Relaxation Method for Solving Integer Programming Problems", Management Science 27 (1981), 1-18.
    • (1981) Management Science , vol.27 , pp. 1-18
    • Fisher, M.L.1
  • 20
    • 35248871154 scopus 로고    scopus 로고
    • The bundle method for hard combinatorial optimization problems
    • M. Jünger, G. Reinelt, G. Rinaldi (eds.) You Shrink!, Springer-Verlag
    • G. Gruber F. Rendl, "The Bundle Method for Hard Combinatorial Optimization Problems", in M. Jünger, G. Reinelt, G. Rinaldi (eds.), Combinatorial Optimization - Eureka, You Shrink!, Springer-Verlag (2003), 78-88.
    • (2003) Combinatorial Optimization - Eureka , pp. 78-88
    • Gruber, G.1    Rendl, F.2
  • 23
    • 0024014124 scopus 로고
    • Dual formulations and subgradient optimization strategies for linear programming relaxations of mixed-integer programs
    • H.D. Sherali, D.C. Myers, "Dual Formulations and Subgradient Optimization Strategies for Linear Programming Relaxations of Mixed-Integer Programs", Discrete Applied Mathematics 20 (1988), 51-68
    • (1988) Discrete Applied Mathematics , vol.20 , pp. 51-68
    • Sherali, H.D.1    Myers, D.C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.