Tree based models and algorithms for the preemptive asymmetric Stacker Crane problem
RAIRO - Operations Research - Recherche Opérationnelle, Tome 45 (2011) no. 3, pp. 179-207.

In this paper we deal with the preemptive asymmetric stacker crane problem in a heuristic way. We first present some theoretical results which allow us to turn this problem into a specific tree design problem. We next derive from this new representation an integer linear programming model together with simple and efficient greedy and local search heuristics. We conclude by presenting experimental results which aim at both testing the efficiency of our heuristic and evaluating the impact of the preemption hypothesis.

DOI : 10.1051/ro/2011110
Classification : 99-XX
Mots-clés : preemptive stacker crane problem, routing, local search, heuristics
@article{RO_2011__45_3_179_0,
     author = {Kerivin, Herv\'e and Lacroix, Mathieu and Quilliot, Alain and Toussaint, H\'el\`ene},
     title = {Tree based models and algorithms for the preemptive asymmetric {Stacker} {Crane} problem},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {179--207},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {3},
     year = {2011},
     doi = {10.1051/ro/2011110},
     mrnumber = {2865232},
     zbl = {1246.90018},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2011110/}
}
TY  - JOUR
AU  - Kerivin, Hervé
AU  - Lacroix, Mathieu
AU  - Quilliot, Alain
AU  - Toussaint, Hélène
TI  - Tree based models and algorithms for the preemptive asymmetric Stacker Crane problem
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2011
SP  - 179
EP  - 207
VL  - 45
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro/2011110/
DO  - 10.1051/ro/2011110
LA  - en
ID  - RO_2011__45_3_179_0
ER  - 
%0 Journal Article
%A Kerivin, Hervé
%A Lacroix, Mathieu
%A Quilliot, Alain
%A Toussaint, Hélène
%T Tree based models and algorithms for the preemptive asymmetric Stacker Crane problem
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2011
%P 179-207
%V 45
%N 3
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro/2011110/
%R 10.1051/ro/2011110
%G en
%F RO_2011__45_3_179_0
Kerivin, Hervé; Lacroix, Mathieu; Quilliot, Alain; Toussaint, Hélène. Tree based models and algorithms for the preemptive asymmetric Stacker Crane problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 45 (2011) no. 3, pp. 179-207. doi : 10.1051/ro/2011110. http://www.numdam.org/articles/10.1051/ro/2011110/

[1] S. Anily and R. Hassin, The swapping problem. Networks 22 (1992) 419-433. | MR | Zbl

[2] S. Anily, M. Gendreau and G. Laporte, The preemptive swapping problem on a tree. Submitted to Networks (2009). | MR | Zbl

[3] N. Ascheuer, L. Escudero, M. Grötschel and M. Stoer, A cutting plane approach to the sequential ordering problem (with applications to job scheduling in manufacturing). SIAM J. Optim. 3 (1993) 25-42. | MR | Zbl

[4] N. Ascheuer, M. Jünger and G. Reinelt, A Branch and Cut algorithm for the Asymmetric Traveling Salesman Problem with Precedence Constraints. Comput. Optim. Appl. 17 (2000) 61-84. | MR | Zbl

[5] M.J. Atallah and S.R. Kosaraju, Efficient solutions to some transportation problems with applications to minimizing robot arm travel. SIAM J. Comput. 17 (1988) 849. | MR | Zbl

[6] E. Balas, M. Fischetti and W. Pulleyblank, The precedence constrained asymmetric traveling salesman problem. Math. Program. 68 (1995) 241-265. | MR | Zbl

[7] G. Berbeglia, J.F. Cordeau, I. Gribkovskaia and G. Laporte, Static pickup and delivery problems: a classification scheme and survey. TOP: An Official Journal of the Spanish Society of Statistics and Operations Research 15 (2007) 1-31. | MR | Zbl

[8] C. Bordenave, M. Gendreau and G. Laporte, A branch-and-cut algorithm for the preemptive swapping problem. Technical Report CIRRELT-2008-23 (2008). | MR | Zbl

[9] C. Bordenave, M. Gendreau and G. Laporte, Heuristics for the mixed swapping problem. Comput. Oper. Res. 37 (2010) 108-114. | MR | Zbl

[10] S. Chen and S. Smith, Commonality and genetic algorithms. Technical Report CMU-RI-TR-96-27, Robotics Institute, Carnegie Mellon University, Pittsburgh, PA (1996).

[11] J.F. Cordeau, M. Iori, G. Laporte and J.J. Salazar-González, A branch-and-cut algorithm for the pickup and delivery traveling salesman problem with LIFO loading. Networks 55 (2010) 46-59. | MR | Zbl

[12] C.E. Cortés, M Matamala and C. Contardo, The Pickup and Delivery Problem with Transfers: Formulation and Solution Approaches, in VII French - Latin American Congress on Applied Mathematics. Springer (2005). | Zbl

[13] I. Dumitrescu, Polyhedral results for the pickup and delivery travelling salesman problem. Technical Report, CRT-2005-27 (2005).

[14] M.T. Fiala Timlin, Precedence constrained routing and helicopter scheduling. M. Sc. thesis, Department of Combinatorics and Optimization University of Waterloo (1989).

[15] M.T. Fiala Timlin and W.R. Pulleyblank, Precedence constrained routing and helicopter scheduling: heuristic design. Interfaces 22 (1992) 100-111.

[16] G.N. Frederickson and D.J. Guan, Preemptive ensemble motion planning on a tree. SIAM J. Comput. 21 (1992) 1130. | MR | Zbl

[17] G.N. Frederickson and D.J. Guan, Nonpreemptive ensemble motion planning on a tree. J. Algorithms 15 (1993) 29-60. | MR | Zbl

[18] G.N. Frederickson, M.S. Hecht and C.E. Kim, Approximation algorithms for some routing problems. SIAM J. Comput. 7 (1978) 178. | MR

[19] L.M. Gambardella and M. Dorigo, An ant colony system hybridized with a new local search for the sequential ordering problem. INFORMS J. Comput. 12 (2000) 237-255. | MR | Zbl

[20] L. Gouveia and P. Pesneau, On extended formulations for the precedence constrained asymmetric traveling salesman problem. Networks 48 (2006) 77-89. | MR | Zbl

[21] H. Hernández-Pérez and J. Salazar-González, The multicommodity one-to-one pickup-and-delivery traveling salesman problem. Eur. J. Oper. Res. 196 (2009) 987-995. | Zbl

[22] B. Kalantari, A.V. Hill and S.R. Arora, An algorithm for the traveling salesman problem with pickup and delivery customers. Eur. J. Oper. Res. 22 (1985) 377-386. | MR | Zbl

[23] M. Lacroix, Le problème de ramassage et livraison préemptif : complexité, modèles et polyèdres. Ph.D. thesis, Université Blaise Pascal, Clermont-Ferrand II (2009).

[24] S. Lin, Computer solutions to the traveling salesman problem. Bell System Technical Journal 44 (1965) 2245-2269. | MR | Zbl

[25] J. Little, K. Murty, D. Sweeney and C. Karel, An algorithm for the traveling salesman problem. Oper. Res. 11 (1963) 972-989. | Zbl

[26] S. Mitrovic-Minic and G. Laporte, The pickup and delivery problem with time windows and transshipment. INFOR 44 (2006) 217-227. | MR

[27] R. Montemanni, D.H. Smith and L.M. Gambardella, A heuristic manipulation technique for the sequential ordering problem. Comput. Oper. Res. 35 (2008) 3931-3944. | Zbl

[28] P. Oertel, Routing with Reloads. Doktorarbeit, Universität zu Köln (2000).

[29] S.N. Parragh, K.F. Doerner and R.F. Hartl, A survey on pickup and delivery problems: Part II: Transportation between pickups and delivery locations. Journal für Betriebswirtschaft 58 (2008) 21-51.

[30] H.N. Psaraftis, A Dynamic Programming solution to the single-vehicle many to-many immediate request dial-a-ride problem. Transp. Sci. 14 (1980) 130-154.

[31] H.N. Psaraftis, k-interchange procedures for local search in a precedence constrained routing problem. Eur. J. Oper. Res. 13 (1983) 391-402. | Zbl

[32] J. Renaud, F. Boctor and J. Ouenniche, A heuristic for the pickup and delivery traveling salesman problem. Comput. Oper. Res. 27 (2000) 905-916. | MR | Zbl

[33] J. Renaud, F. Boctor and G. Laporte, Perturbation heuristics for the pickup and delivery traveling salesman problem. Comput. Oper. Res. 29 (2002) 1129-1141. | Zbl

[34] K.M. Ruland and E.Y. Rodin, The pickup and delivery problem: Faces and branch-and-cut algorithm. Comput. Math. Appl. 33 (1997) 1-13. | MR | Zbl

[35] H. Toussaint, Algorithmique rapide pour les problèmes de tournées et d'ordonnancement. Ph.D. thesis, Université Blaise Pascal, Clermont-Ferrand II (2010).

Cité par Sources :