Natural and extended formulations for the Time-Dependent Traveling Salesman Problem

Discrete Applied Mathematics

Volumn 164, Issue PART 1, 2014, Pages 138-153

  Godinho, Maria Teresa ^a   Gouveia, Luis ^b   Pesneau, Pierre ^c  

^a INSTITUTO POLITÉCNICO DE BEJA   (Portugal)

^b UNIVERSITY OF LISBON   (Portugal)

^c UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

Extended formulations; Projection; Time Dependent Traveling Salesman Problem

Indexed keywords

LINEAR PROGRAMMING;

COMPUTATIONAL EXPERIMENT; EXTENDED FORMULATIONS; FEASIBLE SET; LINEAR PROGRAMMING RELAXATION; PROBLEM INSTANCES; PROJECTION; SUB-PROBLEMS; TIME DEPENDENT TRAVELING SALESMAN PROBLEM; TIME-DEPENDENT TRAVELING SALESMAN;

TRAVELING SALESMAN PROBLEM;

EID: 84893796204     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2011.11.019     Document Type: Article

References (27)

1. H. Abeledo, R. Fukasawa, A. Pessoa, and E. Uchoa The time dependent traveling salesman problem: polyhedra and branch-cut-and-price algorithm SEA 2010 2010, Nápoles Lecture Notes in Computer Science vol. 6049 2010 Springer Berlin 202 213
2. L. Bianco, A. Mingozzi, and S. Ricciardelli The traveling salesman problem with cumulative costs Networks 23 1993 81 91
3. L.-P. Bigras, M. Gamache, and G. Savard The time-dependent traveling salesman problem and single machine scheduling problems with sequence dependent setup times Discrete Optimization 5 2008 685 699
4. A. Claus A new formulation for the Travelling Salesman Problem SIAM Journal on Algebraic and Discrete Methods 5 1984 21 25
5. A. Costa, J.F. Cordeau, and G. Laporte Models and branch-and-cut algorithms for the Steiner tree problem with revenues, budget and hop constraints Networks 53 2009 141 159
6. M. Fischetti, G. Laporte, and S. Martello The delivery man problem and cumulative matroids Operations Research 41 1992 1055 1064
7. L.R. Fox, B. Gavish, and S.C. Graves A N-constrained formulation of the (time-dependent) traveling salesman problem Operations Research 28 1980 1018 1021
8. M.T. Godinho, L. Gouveia, and T. Magnanti Combined route capacity and route length models for unit demand vehicle routing problems Discrete Optimization 5 2008 350 372 (special issue in honor of George Dantzig)
9. M.T. Godinho, L. Gouveia, T. Magnanti, P. Pesneau, J. Pires, On time-dependent models for unit demand vehicle routing problems, in: Proceedings of the INOC2007 Conference, Spa 2007.
10. M.T. Godinho, L. Gouveia, and P. Pesneau On a time-dependent formulation and an updated classification of ATSP formulations R. Mahjoub, Progress in Combinatorial Optimization 2011 ISTE-Wiley
11. L. Gouveia Using hop-indexed models for constrained spanning and Steiner tree models B. Samso, P. Soriano, Telecommunications Network Planning 1999 21 32
12. L. Gouveia, and P. Pesneau On extended formulations for the precedence constrained asymmetric Travelling Salesman Problem Networks 48 2006 77 89
13. L. Gouveia, and J.M. Pires Uma análise comparativa de formulações para o Problema do Caixeiro Viajante Investigação Operacional 16 1996 89 114
14. L. Gouveia, and J.M. Pires The asymmetric Travelling Salesman Problem: on generalisations of disaggregated Miller-Tucker-Zemlin constraints Discrete Applied Mathematics 112 1-3 2001 129 145
15. L. Gouveia, L. Simonetti, and E. Uchoa Modelling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs Mathematical Programming 128 2011 123 148
16. L. Gouveia, and S. Voss A classification of formulations for the time-dependent Travelling Salesman Problem European Journal of Operational Research 83 1995 69 82
17. A. Langevin, F. Soumis, and J. Desrosiers Classification of travelling salesman formulations Operations Research Letters 9 1990 127 132
18. E. Lawler, J. Lenstra, A. Rinnooy StateKan, and D. Shmoys The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization 1985 Wiley New York
19. A. Lucena The time-dependent traveling salesman problem - the deliveryman case Networks 20 1990 753 763
20. I. Méndez-Díaz, P. Zabala, and A. Lucena A new formulation for the traveling deliveryman problem Discrete Applied Mathematics 156 2008 3223 3237
21. T. Oncan, I.K. Atinel, and G. Laporte A comparative analysis of several asymmetric traveling salesman problem formulations Computers and Operations Research 36 3 2009 637 654
22. J.C. Picard, and M. Queyranne The time-dependent traveling salesman problem and its application to the tardiness in one-machine scheduling Operations Research 26 1978 86 110
23. S.C. Sarin, H.D. Sherali, and A. Bhootra New tighter polynomial length formulations for the asymmetric travelling salesman problem with and without precedence constraints Operations Research Letters 33 2005 62 70
24. H.D. Sherali, and P.J. Driscoll On tightening the relaxations of Miller-Tucker-Zemlin formulations for asymmetric traveling salesman problems Operations Research 50 2002 656 669
25. H.D. Sherali, S.C. Sarin, and P.F. Tsai A class of lifted path and flow-based formulations for the asymmetric traveling salesman problem with and without precedence constraints Discrete Optimization 3 2006 20 32
26. M. Van Vyve, and L.A. Wolsey Approximate extended formulations Mathematical Programming Series B 105 2006 501 522
27. R.T. Wong, Integer programming formulations of the traveling salesman problem. in: Proceedings of the IEEE International Conference of Circuits and Computers, 1980, pp. 149-152.