Skip to main content

Distance-Based Heuristic Solvers for Cooperative Path Planning with Heterogeneous Agents

  • 494 Accesses

Part of the Lecture Notes in Computer Science book series (LNAI,volume 12568)


Cooperation among different vehicles is a promising concept for transportation services. For instance, vehicle platooning on highways with self-driving vehicles is known to decrease fuel consumption. This makes us construct paths on graphs, where many vehicles share sub-paths to form platoons. The platooning model has been recently generalized to model different types (e.g., trucks and UAVs) but existing exact solvers using Integer Programming (IP) are not experimentally evaluated on various settings and heuristic solvers are underdeveloped; hence solving large instances remains difficult. In this study, we propose heuristic solvers using a distance-based grouping of vehicles. Our solver first finds groups of vehicles and constructs paths in each group independently. We also experimentally investigate both exact and heuristic solvers. Experimental results suggest that IP-based solvers only solve small instances due to the overhead of compiling IP models. We observed that our solvers were almost fifth magnitude faster than the exact solver with at most 25% additional travel costs. Also, our method achieved roughly 15% additional costs if requests are clustered in terms of their locations, meaning that distance-based heuristic solvers could find moderate solutions within typically a few seconds.


  • Path-planning
  • Cooperation
  • Heterogeneous agents

This is a preview of subscription content, access via your institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions


  1. 1.

    Our previous extended abstract paper also discusses this topic [25].

  2. 2.

    Typically, the modern IP solvers first try to transform the given problem instance into more convenient formulations for the strategy adopted in the solvers. This process (at least in Gurobi) is named presolve.

  3. 3.

    More precisely, this parameter cannot be compared the resulted gaps directly since MIPGap is the gap between the upper and lower bounds. However, the value MIPGap is often related to the obtained gap as checked in Fig. 3.

  4. 4. (accessed 2020/11/4).

  5. 5. (accessed 2020/11/4).


  1. Agatz, N., Erera, A., Savelsbergh, M., Xign, W.: Opimization for dynamic ride-sharing: a review. Eur. J. Oper. Res. 223, 295–303 (2012)

    CrossRef  Google Scholar 

  2. Beck, Z., Teacy, L., Rogers, A., Jennings, N.R.: Online planning for collaborative search and rescue by heterogeneous robot teams. In: Proceedings of AAMAS2016, pp. 1024–1033 (2016)

    Google Scholar 

  3. Bit-Monnot, A., Artigues, C., Huguet, M.J., Killijian, M.O.: Carpooling: the 2 synchronization points shortest paths problem. In: Proceedings of ATMOS2013, pp. 150–163 (2013)

    Google Scholar 

  4. Bonnet, C., Fritz, H.: Fuel consumption reduction in a platoon: experimental results with two electronically coupled trucks at close spacing. Technical report, SAE Technical Paper (No. 2000–01-3056) (2000)

    Google Scholar 

  5. Eppstein, D.: Finding the k shortest paths. SIAM J. Comput. 28(2), 652–673 (1998)

    CrossRef  MathSciNet  Google Scholar 

  6. Flushing, E.F., Gambardella, L.M., Di Caro, G.A.: A mathematical programming approach to collaborative missions with heterogeneous teams. In: Proceedings of IROS2014, pp. 396–403 (2014)

    Google Scholar 

  7. Flushing, E.F., Gambardella, L.M., Di Caro, G.A.: On decenteralized coordination for spatial task allocation and scheduling in heterogeneous teams. In: Proceedings of AAMAS2016, pp. 988–996 (2016)

    Google Scholar 

  8. Furuhata, M., Dessouky, M., Ordóñez, F., Brunet, M.E., Wang, X., Koenig, S.: Ridesharing: the state-of-the-art and future directions. Transp. Res. Part B 57, 28–46 (2013)

    CrossRef  Google Scholar 

  9. Geisberger, R., Luxen, D., Neubauer, S., Sanders, P., Volker, L.: Fast detour computation for ride sharing. arXiv preprint arXiv:0907.5269 (2009)

  10. Gurobi Optimization, LLC: Gurobi optimizer reference manual (2018).

  11. Ha, M.H., Bostel, N., Lagngevin, A., Rousseau, L.M.: An exact algorithm and a metaheuristic for the multi-vehicle covering tour problem with a constraint on the number of vehicles. Eur. J. Oper. Res. 226(2), 211–220 (2013)

    CrossRef  Google Scholar 

  12. Hietanen, S.: Mobility as a service, pp. 2–4 (2014)

    Google Scholar 

  13. van de Hoef, S., Johansson, K.H., Dimarogonas, D.V.: Coordinating truck platooning by clustering pairwise fuel-optimal plans. In: Proceedings of ITSC2015, pp. 408–415 (2015)

    Google Scholar 

  14. van de Hoef, S., Johansson, K.H., Dimarogonas, D.V.: Fuel-efficient en route formation of truck platoons. IEEE Trans. Intell. Transp. Syst. 19(1), 102–112 (2017)

    CrossRef  Google Scholar 

  15. Korte, B., Vygen, J.: Combinatorial Optimization: Theory and Algorithms, 4th edn. Springer, Heidelberg (2007).

    CrossRef  MATH  Google Scholar 

  16. Ladier, A.L., Alpan, G.: Cross-docking operations: current research versus industry practice. Omega 62, 145–162 (2016)

    CrossRef  Google Scholar 

  17. Larsson, E., Sennton, G., Larson, J.: The vehicle platooning problem: computational complexity and heuristics. Transp. Res. Part C Emerg. Technol. 60, 258–277 (2015)

    CrossRef  Google Scholar 

  18. Ma, S., Zheng, Y., Wolfson, O.: Real-time city-scale taxi ridesharing. IEEE Trans. Knowl. Data Eng. 27(7), 1782–1795 (2015)

    CrossRef  Google Scholar 

  19. Miller, C.E., Tucker, A.W., Zemlin, R.A.: Integer programming formulation of traveling salesman problems. J. ACM (JACM) 7(4), 326–329 (1960)

    CrossRef  MathSciNet  Google Scholar 

  20. Nikolopoulou, A.I., Repoussis, P.P., Tarantilis, C.D., Zachariadis, E.E.: Moving products between location pairs: cross-docking versus direct-shipping. Eur. J. Oper. Res. 256(3), 803–819 (2017)

    CrossRef  MathSciNet  Google Scholar 

  21. Nishi, T., Otaki, K., Okoso, A., Fukunaga, A.: Cooperative routing problem between customers and vehicles for on-demand mobile facility services. In: Proceedings of ITSC2020 (2020)

    Google Scholar 

  22. Ondráček, J., Vanek, O., Pěchouček, M.: Solving infrastracture monitoring problems with multiple heterogeneous unmanned aerial vehicles. In: Proceedings of AAMAS2015, pp. 1597–1605 (2015)

    Google Scholar 

  23. Otaki, K., Koide, S., Keiichiro, H., Okoso, A., Nishi, T.: Multi-agent path planning with heterogeneous cooperation. In: Proceedings of ICTAI2019, pp. 93–100 (2019)

    Google Scholar 

  24. Otaki, K., Koide, S., Okoso, A., Nishi, T.: Cooperative routing with heterogeneous vehicles. In: Proceedings of AAMAS2019, pp. 2150–2152 (2019)

    Google Scholar 

  25. Otaki, K., Koide, S., Okoso, A., Nishi, T.: Cooperative path planning for heterogeneous agents. In: Proceedings of SoCS2020, pp. 133–134 (2020)

    Google Scholar 

  26. Shang, S., Chen, L., Wei, Z., Jensen, C.S., Wen, J., Kalnis, P.: Collective travel planning in spatial networks. IEEE Trans. Knowl. Data Eng. 28(5), 1132–1146 (2016)

    CrossRef  Google Scholar 

  27. Sharon, G., Stern, R., Felner, A., Sturtevant, N.R.: Conflict-based search for optimal multi-agent pathfinding. Artif. Intell. 219, 40–66 (2015)

    CrossRef  MathSciNet  Google Scholar 

  28. Takise, K., Asano, Y., Yoshikawa, M.: Multi-user routing to single destination with confluence. In: Proceedings of the 24th ACM SIGSPATIAL, pp. 72:1–72:4 (2016)

    Google Scholar 

  29. Yen, J.Y.: Finding the \(k\) shortest loopless paths in a network. Manage. Sci. 17(11), 712–716 (1971)

    CrossRef  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Keisuke Otaki .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Otaki, K., Koide, S., Okoso, A., Nishi, T. (2021). Distance-Based Heuristic Solvers for Cooperative Path Planning with Heterogeneous Agents. In: Uchiya, T., Bai, Q., Marsá Maestre, I. (eds) PRIMA 2020: Principles and Practice of Multi-Agent Systems. PRIMA 2020. Lecture Notes in Computer Science(), vol 12568. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-69321-3

  • Online ISBN: 978-3-030-69322-0

  • eBook Packages: Computer ScienceComputer Science (R0)