Arc Routing Problems: Data Instances
This webpage is maintained by Ángel Corberán, Isaac Plana, Miguel Reula and José María Sanchis. Last updated on July 2022. You can find data for different types of Arc Routing Problems defined on undirected, directed, mixed, and windy graphs.
The results for the instances for each specific problem have been obtained in the following articles:
The Rural Postman Problem, the General Routing Problem and the Graphical Traveling Salesman Problem
Corberán, Plana and Sanchis. A Branch & Cut Algorithm for the Windy General Routing Problem and special cases, Networks 49, pp. 245-257, 2007.
The Maximum Benefit Chinese Postman Problem
Corberán, Plana. Rodríguez-Chía and Sanchis. A New Approach to the Maximum Benefit Chinese Postman Problem, Mathematical Programming, Vol. 141, pp. 21-48, 2013.
The Directed Rural Postman Problem, the Directed General Routing Problem and the Stacker Crane Problem
Corberán, Plana and Sanchis. A Branch & Cut Algorithm for the Windy General Routing Problem and special cases, Networks 49, pp. 245-257, 2007.
Ávila, Corberán, Plana and Sanchis. The Stacker Crane Problem and the Directed General Routing Problem, Networks, Vol. 65, pp. 43-55, 2015.
Close-Enough Arc Routing Problem (or Generalized Directed Rural Postman Problem)
Ávila, Corberán, Plana and Sanchis. A new branch-and-cut algorithm for the Generalized Directed Rural Postman Problem, Transportation Science, 50 (2):750-761, 2016.
The Profitable Close-Enough Arc Routing Problem
Bianchessi, Corberán, Plana, Reula and Sanchis. The Profitable Close Enough Arc Routing Problem, Computers & Operations Research, 140: 105663, 2022.
The Distance-Constrained Close-Enough Arc Routing Problem
Ávila, Corberán, Plana and Sanchis. Formulations and exact algorithms for the Distance-Constrained Generalized Directed Rural Postman Problem, EURO Journal on Computational Optimization, Vol. 5 (3), pp. 339-365, 2017
Corberán, Plana, Reula and Sanchis. A matheuristic for the Distance-Constrained Close-Enough Arc Routing Problem. TOP, Vol. 27, pp. 312-326, 2019.
Corberán, Plana, Reula and Sanchis. On the Distance-Constrained Close-Enough Arc Routing Problem. EJOR, Vol 291 (1), pp 32-51, 2021.
The Min-Max Close-Enough Arc Routing Problem
Bianchessi, Corberán, Plana, Reula and Sanchis. The Min-Max Close-Enough Arc Routing Problem, EJOR, Vol. 300, pp.837-851, 2022.
The Orienteering Arc Routing Problem
Archetti, Corberán, Plana, Sanchis, and Speranza. A branch-and-cut algorithm for the Orienteering Arc Routing Problem, Computers and Operations Research Vol. 66, pp. 95-104, 2016.
The Team Orienteering Arc Routing
Archetti, Corberán, Plana, Sanchis, and Speranza. The Team Orienteering Arc Routing Problem, Transportation Science, Vol. 48, pp. 442-457, 2014.
The Windy Postman Problem and Windy Rural Postman Problem
Corberán, Plana and Sanchis. A Branch & Cut Algorithm for the Windy General Routing Problem and special cases, Networks 49, pp. 245-257, 2007.
Corberán, Oswald, Plana, Reinelt and Sanchis. New results on the Windy Postman Problem, Mathematical Programming, Vol. 132, pp. 309-332, 2012.
The Min-Max K-vehicles WRPP
Benavent, Corberán, Plana and Sanchis. Min-Max K-vehicles Wind Rural Postman Problem, Networks, Vol. 54(4), pp. 216-226, 2009
Benavent, Corberán, Plana and Sanchis. New Facets and an enhanced Branch-and-Cut for the Min-Max K-vehicles Windy Rural Postman Problem, Networks, Vol. 58, pp. 255-272, 2011.
Benavent, Corberán, Desaulniers, Lessard, Plana, and Sanchis. A branch-price-and-cut algorithm for the min-max k-vehicle windy rural postman problem, Networks, Vol. 63, pp. 34-45, 2014.
The Profitable Windy Rural Postman Problem
Ávila, Corberán, Plana and Sanchis. A branch-and-cut algorithm for the Profitable Windy Rural Postman Problem, European Journal of Operational Research, Vol. 249(3), pp. 1092-1101, 2016.
The Periodic Rural Postman Problem with Irregular Services on Mixed Graphs
Benavent, Corberán, Laganà and Vocaturo. The Periodic Rural Postman Problem with Irregular Services on Mixed Graphs, European Journal of Operational Research, Vol. 276, pp. 826-839, 2019.
Benavent, Corberán, Laganà and Vocaturo. A two-phase hybrid algorithm for the periodic rural postman problem with irregular services on mixed graphs. Submitted, 2022.
Other contributions
The optimal values for the MCPP instance MB1055, and the MGRP instance GD427, as well as the best-known solutions for the MGRP instance GD525, and the WGRP instances GB322, and GB422 were provided by Michael Drexl (On the generalized directed rural postman problem, JORS, Vol. 65, pp. 1143-1154, 2015).
The upper bounds for the MCPP instance MB3065, the MGRP instances GD422 and GD425, WRPP instances D322, D421, and D422, and the WGRP instances GB321, GB322, GB421, and GB622 were provided by Keld Helsgaun (Solving the equality generalized traveling salesman problem using the Lin-Kernighan-Helsgaun algorithm, Mathematical Programming Computation, Vol. 7, pp. 269-287, 2015).
All the results are reported in the files linked in column Solutions values. The characteristics of the instances can be found in column Instance characteristics. For more details about the instances, read the file readme file of the corresponding problem.
Problem |
Instances |
Instance characteristics |
Solution values |
Readme files |
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Undirected Graphs |
Graphical TSP |
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Rural Postman Problem (RPP) |
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General Routing Problem (GRP) |
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Maximum Benefit CPP (MBCPP) |
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Length-Constrained K-Drones RPP (LC K-DRPP) |
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Directed Graphs |
Diected General Routing Problem (DGRP) |
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Stacker Crane Problem (SCP) |
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Close Enough Arc Roting Problem (CEARP) or Generalized Directed RPP (GDRPP) |
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Profitable CEARP (PCEARP) |
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Distance-Constrained CEARP (DC-CEARP) |
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Min-Max CEARP (MM-CEARP) |
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Orienteering ARP (OARP) |
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Team Orienteering ARP (TOARP) |
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Mixed Graphs |
Mixed Postman Problem (MCPP) |
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Mixed Rural Postman Problem (MRPP) |
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Mixed General Routing Problem (MGRP) |
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Hierarchichal Mixed Rural Postman Problem (HMRPP) |
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The Periodic Rural Postman Problem with Irregular Services on Mixed Graphs (PRPP-IS) | PRPP-IS instances | PRPP-IS char | PRPP-IS solutions | readme | |
Windy Graphs |
Windy Postman Problem (WPP) |
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Windy Rural Postman Problem (WRPP) |
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Windy General Routing Problem (WGRP) |
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Min-Max K-vehicles Windy RPP |
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Profitable Windy RPP (PWRPP) |