Mathematical Programming Computation

, Volume 11, Issue 3, pp 587–629 | Cite as

OAR Lib: an open source arc routing library

  • Oliver LumEmail author
  • Bruce Golden
  • Edward Wasil
Full Length Paper


We present an open source, arc routing Java library that has a flexible graph architecture with solvers for several uncapacitated arc routing problems and the ability to dynamically generate and visualize real-world street networks. The library is hosted at ( We describe the algorithms in the library, report computational performance, and discuss implementation issues.

Mathematics Subject Classification

90B06 90B10 90C27 90C59 



  1. 1.
    Arc Routing Problems: Data Instances.
  2. 2.
    Ahr, D., Reinelt, G.: New heuristics and lower bounds for the min-max k-Chinese postman problem. Algorithms-ESA 2002, pp. 64–74. Springer, Berlin (2002)CrossRefGoogle Scholar
  3. 3.
    Bastian, M., Heymann, S., Jacomy, M.: Gephi: an open source software for exploring and manipulating networks. ICWSM 8, 361–362 (2009)Google Scholar
  4. 4.
    Benavent, E., Corberán, A., Piñana, E., Plana, I., Sanchis, J.M.: New heuristic algorithms for the windy rural postman problem. Comput. Oper. Res. 32(12), 3111–3128 (2005)zbMATHCrossRefGoogle Scholar
  5. 5.
    Campos, V., Savall, J.V.: A computational study of several heuristics for the DRPP. Comput. Optim. Appl. 4(1), 67–77 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Corberán, A., Golden, B., Lum, O., Plana, I., Sanchis, J.: Aesthetic considerations for the min-max k windy rural postman problem. Networks 70(3), 216–232 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Derigs, U.: Optimization and Operations Research. Eolss Publishers Company Limited, New York (2009)Google Scholar
  8. 8.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1(1), 269–271 (1959)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Dussault, B., Golden, B., Groër, C., Wasil, E.: Plowing with precedence: a variant of the windy postman problem. Comput. Oper. Res. 40(4), 1047–1059 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Edmonds, J., Johnson, E.L.: Matching, Euler tours and the Chinese postman. Math. Program. 5(1), 88–124 (1973)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Eiselt, H.A., Gendreau, M., Laporte, G.: Arc routing problems, part I: the Chinese postman problem. Oper. Res. 43(2), 231–242 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Eiselt, H.A., Gendreau, M., Laporte, G.: Arc routing problems, part II: the rural postman problem. Oper. Res. 43(3), 399–414 (1995)zbMATHCrossRefGoogle Scholar
  13. 13.
    Floyd, R.W.: Algorithm 97: shortest path. Commun. ACM 5(6), 345 (1962)CrossRefGoogle Scholar
  14. 14.
    Frederickson, G.N.: Approximation algorithms for some postman problems. J. ACM 26(3), 538–554 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
  16. 16.
    Groër, C., Golden, B., Wasil, E.: A library of local search heuristics for the vehicle routing problem. Math. Program. Comput. 2(2), 79–101 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Grötschel, M., Win, Z.: A cutting plane algorithm for the windy postman problem. Math. Program. 55(1–3), 339–358 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Haklay, M., Weber, P.: Openstreetmap: user-generated street maps. IEEE Pervasive Comput. 7(4), 12–18 (2008)CrossRefGoogle Scholar
  19. 19.
    Hierholzer, C., Wiener, C.: Über die Möglichkeit, einen Linienzug ohne Wiederholung und ohne Unterbrechung zu umfahren. Math. Ann. 6(1), 30–32 (1873)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359–392 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Kolmogorov, V., Blossom, V.: A new implementation of a minimum cost perfect matching algorithm. Math. Program. Comput. 1(1), 43–67 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Lau, H.T.: A Java Library of Graph Algorithms and Optimization. CRC Press, London (2010)Google Scholar
  23. 23.
    Letchford, A.N., Reinelt, G., Theis, D.O.: A faster exact separation algorithm for blossom inequalities. In: Integer Programming and Combinatorial Optimization, pp. 196–205. Springer, Berlin (2004)Google Scholar
  24. 24.
    Lum, O., Cerrone, C., Golden, B., Wasil, E.: Partitioning a street network into compact, balanced, and visually appealing routes. Networks 69(3), 290–303 (2016)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Lum, O., Zhang, R., Golden, B., Wasil, E.: A hybrid heuristic for the windy rural postman problem with time-dependent zigzag options. Comput. Oper. Res. 88, 247–257 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
  27. 27.
    Padberg, M.W., Rao, M.R.: Odd minimum cut-sets and b-matchings. Math. Oper. Res. 7(1), 67–80 (1982)MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Prim, R.C.: Shortest connection networks and some generalizations. Bell Syst. Tech. J. 36(6), 1389–1401 (1957)CrossRefGoogle Scholar
  29. 29.
    Tahchiev, P., Leme, F., Massol, V., Gregory, G.: JUnit in Action. Manning Publications Co, New York (2010)Google Scholar
  30. 30.
    Thimbleby, H.: The directed Chinese postman problem. Softw. Pract. Exp. 33(11), 1081–1096 (2003)CrossRefGoogle Scholar
  31. 31.
    Win, Z.: On the windy postman problem on Eulerian graphs. Math. Program. 44(1–3), 97–112 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    Yaoyuenyong, K., Charnsethikul, P., Chankong, V.: A heuristic algorithm for the mixed Chinese postman problem. Optim. Eng. 3(2), 157–187 (2002)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2019

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Scientific ComputationUniversity of MarylandCollege ParkUSA
  2. 2.Robert H. Smith School of BusinessUniversity of MarylandCollege ParkUSA
  3. 3.Kogod School of BusinessAmerican UniversityWashingtonUSA

Personalised recommendations