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Best Known Solutions Identified by Heuristics for Solomon's (1987) Benchmark Problems



Solutions are compared primarily on the criterion lowest number of vehicles utilised, and secondarily on shortest distance. A third criterion, waiting-time, may be considered as a further option for comparison.

Best Known Results for Solomon's Benchmark Problems
Case
Vehicles
Distance
Authors
Date
c101 10
828,94 RT

c102 10
828,94 RT

c103 10
828,06 RT

c104 10
824,78 RT

c105 10
828,94 RT

c106 10
828,94 RT

c107 10
828,94 RT

c108 10
828,94 RT

c109 10
828,94 RT


c201
3
591,56 RT

c202 3
591,56 RT

c203 3
591,17 RT

c204 3
590,60 RT

c205 3
588,88 RT

c206 3
588,49 RT

c207 3
588,29 RT

c208 3
588,32 RT


r101
19
1645,79 H

r102 17
1486,12 RT

r103 13
1292,68 LLH

r104 9
1007,24 MBD

r105 14
1377,11 RT

r106 12
1251,98 MBD

r107 10
1104,66 S97

r108 9
960,88 BBB

r109 11
1194,73 HG

r110 10
1118,59 MBD

r111
10
1096,72 RGP

r112
9
982,14 GTA


r201
4
1252,37 HG

r202 3
1191,70 RGP

r203 3
939,50 WL
2009-10-21
r204 2
825,52 BVH

r205 3
994,42 RGP

r206 3
906,14 SSSD

r207 2
890,61 RP
25-feb-05
r208 2
726,75 MBD

r209 3
909,16 H

r210 3
939,34 MBD

r211
2
885,71 WL
2009-10-21

rc101
14
1696,94 TBGGP

rc102 12
1554,75 TBGGP

rc103 11
1261,67 S98

rc104 10
1135,48 CLM

rc105 13
1629,44 BBB

rc106 11
1424,73 BBB

rc107 11
1230,48 S97

rc108 10
1139,82 TBGGP


rc201
4
1406,91 MBD

rc202 3
1365,645 GCC
22-mar-04
rc203 3
1049,62 CC

rc204 3
798,41 MBD

rc205 4
1297,19 MBD

rc206 3
1146,32 H

rc207 3
1061,14 BVH

rc208 3
828,14 IKMUY









Legend:

BBB - J. Berger, M. Barkaoui and O. Bräysy, "A Parallel Hybrid Genetic Algorithm for the Vehicle Routing Problem with Time Windows," Working paper, Defense Research Establishment Valcartier, Canada, 2001.

BVH - R. Bent and P. Van Hentenryck, "A Two-Stage Hybrid Local Search for the Vehicle Routing Problem with Time Windows," Technical Report CS-01-06, Department of Computer Science, Brown University, 2001.

CC - Z. J. Czech and P. Czarnas, "A Parallel Simulated Annealing for the Vehicle Routing Problem with Time Windows," Proc. 10th Euromicro Workshop on Parallel, Distributed and Network-based Processing, Canary Islands, Spain, (January 9--11, 2002), 376--383.

CLM - J.-F. Cordeau,  G. Laporte, and A. Mercier, "A Unified Tabu Search Heuristic for Vehicle Routing Problems with Time Windows," Working Paper CRT-00-03, Centre for Research on Transportation, Montreal, Canada, 2000.

GCC - Agnieszka Debudaj-Grabysz, Zbigniew J.Czech and Piotr Czarnas
Silesia University of Technology and University of Wroclaw, Poland (2004)

GTA - L. M. Gambardella, E. Taillard, and G. Agazzi, "MACS-VRPTW: A Multiple Ant Colony System for Vehicle Routing Problems with Time Windows," in New Ideas in Optimization, D. Corne, M. Dorigo and F. Glover (eds), 63-76, McGraw-Hill, London, 1999.

H - J. Homberger, "Verteilt-parallele Metaheuristiken zur Tourenplanung," Gaber, Wiesbaden (2000).

HG - J. Homberger and H. Gehring, "Two Evolutionary Metaheuristics for the Vehicle Routing Problem with Time Windows," INFOR, VOL. 37, 297-318, (1999).

IKMUY - T. Ibaraki, M. Kubo, T. Masuda, T. Uno and M. Yagiura, "Effective Local Search Algorithms for the Vehicle Routing Problem with General Time Windows," Working Paper, Department of Applied Mathematics and Physics, Kyoto University, Japan, 2001.

MBD - D. Mester, O. Bräysy and W. Dullaert. A Multi-parametric Evolution Strategies Algorithm for Vehicle Routing Problems. Working Paper, Institute of Evolution, University of Haifa, Israel (2005).

LLH - H. Li, A. Lim, and J. Huang, "Local Search with Annealing-like Restarts to Solve the VRPTW," Working Paper, Department of Computer Science, National University of Singapore, 2001.

RGP - L.M. Rousseau, M. Gendreau and G. Pesant, "Using Constraint-Based Operators to Solve the Vehicle Routing Problem with Time Windows," Journal of Heuristics, forthcoming.

RP S. Ropke & D.Pisinger. "A general heuristic for vehicle routing problems",  technical report, Department of Computer Science, University of Copenhagen.

RT - Y. Rochat and E.D. Taillard, "Probabilistic Diversification and Intensification in Local Search for Vehicle Routing," Journal of Heuristics 1, 147-167, (1995).

SSSD - G. Schrimpf, J. Schneider, H. Stamm-Wilbrandt and G. Dueck, "Record Breaking Optimization Results Using the Ruin and Recreate Principle," Journal of Computational Physics 159, 139-171, (2000).

S97 - P. Shaw, "A New Local Search Algorithm Providing High Quality Solutions to Vehicle Routing Problems," Working Paper, University of Strathclyde, Glasgow, Scotland, 1997.

S98 - P. Shaw, "Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems," In Principles and Practice of Constraint Programming - CP98, Lecture Notes in Computer Science, 417-431, M. Maher and J.-F. Puget (eds), Springer-Verlag, New York, 1998.

TBGGP - E. Taillard, P. Badeau, M. Gendreau, F. Geurtin, and J.Y. Potvin, "A Tabu Search Heuristic for the Vehicle Routing Problem with Time Windows," Transportation Science, 31, 170-186, (1997).

WL - Woch M., Lebkowski P.: "Sequential Simulated Annealing for the Vehicle Routing Problem with Time Windows." XIII Logistics Conference, Zakopane (2009).