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International Conference on Evolutionary Multi-Criterion Optimization

EMO 2021: Evolutionary Multi-Criterion Optimization pp 375–386Cite as

Many-Objective Pathfinding Based on Fréchet Similarity Metric

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12654))

Abstract

Route planning, also known as pathfinding is one of the essential elements in logistics, mobile robotics and other applications, where engineers face many conflicting objectives. One major challenge in dealing with multi-objective pathfinding problems is that several different paths can map to the same objective values. Since typical multi-objective optimization algorithms focus on the selection mechanism in the objective space, such multi-modal solutions cannot be easily found. In this paper, we propose a new methodology for preserving a good diversity of solutions in the decision space, which is tailored for pathfinding problems. We measure the similarity between the solutions in the decision space using the discrete Fréchet distance measurement, which is meant as a replacement for the well-known crowding distance measurement. We examine the proposed approach in three different variations on a variety of benchmark instances.

This work is funded by the German Federal Ministry of Education and Research through the MOSAIK project (grant no. 01IS18070B).

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References

  1. Ahmed, F., Deb, K.: Multi-objective optimal path planning using elitist non-dominated sorting genetic algorithms. Soft Comput. 17(7), 1283–1299 (2013)

    Google Scholar 

  2. Alt, H., Godau, M.: Computing the Fréchet distance between two polygonal curves. Int. J. Comput. Geom. Appl. 05(01n02), 75–91 (1995)

    Google Scholar 

  3. Anguelov, B.: Video game pathfinding and improvements to discrete search on grid-based maps. Ph.D. thesis (2011)

    Google Scholar 

  4. Beke, L., Weiszer, M., Chen, J.: A comparison of genetic representations for multi-objective shortest path problems on multigraphs. In: Paquete, L., Zarges, C. (eds.) EvoCOP 2020. LNCS, vol. 12102, pp. 35–50. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-43680-3_3

    Chapter  Google Scholar 

  5. Besada-Portas, E., de la Torre, L., Moreno, A., Risco-Martín, J.L.: On the performance comparison of multi-objective evolutionary UAV path planners. Inf. Sci. 238, 111–125 (2013)

    Google Scholar 

  6. Cai, X., Sun, H., Fan, Z.: A diversity indicator based on reference vectors for many-objective optimization. Inf. Sci. 430–431, 467–486 (2018)

    Google Scholar 

  7. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  8. Deb, K., Tiwari, S.: Omni-optimizer: a procedure for single and multi-objective optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 47–61. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31880-4_4

    Chapter  MATH  Google Scholar 

  9. Efrat, A., Guibas, L.J., Har-Peled, S., Mitchell, J.S., Murali, T.M.: New similarity measures between polylines with applications to morphing and polygon sweeping. Discrete Comput. Geom. 28(4), 535–569 (2002)

    Article  MathSciNet  Google Scholar 

  10. Eiter, T., Mannila, H.: Computing Discrete Fréchet Distance (1994)

    Google Scholar 

  11. Fan, C., Luo, J., Zhu, B.: Fréchet-distance on road networks. In: Akiyama, J., Bo, J., Kano, M., Tan, X. (eds.) CGGA 2010. LNCS, vol. 7033, pp. 61–72. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24983-9_7

    Chapter  Google Scholar 

  12. Fréchet, M.M.: Sur quelques points du calcul fonctionnel. Rendiconti del Circolo Matematico di Palermo (1884–1940) 22(1), 1–72 (1906)

    Google Scholar 

  13. Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. 4(2), 100–107 (1968)

    Article  Google Scholar 

  14. Hu, J., Zhu, Q., Jun, H., Qingbao, Z.: Multi-objective mobile robot path planning based on improved genetic algorithm. In: 2010 International Conference on Intelligent Computation Technology and Automation, vol. 2, pp. 752–756. IEEE (2010)

    Google Scholar 

  15. Ishibuchi, H., Masuda, H., Nojima, Y.: A study on performance evaluation ability of a modified inverted generational distance indicator. In: Proceedings of the 2015 on Genetic and Evolutionary Computation Conference - GECCO 2015. pp. 695–702. ACM Press, New York (2015)

    Google Scholar 

  16. Javadi, M., Zille, H., Mostaghim, S.: Modified crowding distance and mutation for multimodal multi-objective optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, pp. 211–212. ACM, New York (2019)

    Google Scholar 

  17. Jiang, M., Xu, Y., Zhu, B.: Protein structure-structure alignment with discrete Fréchet distance. J. Bioinform. Comput. Biol. 06(01), 51–64 (2008)

    Google Scholar 

  18. Maheshwari, A., Sack, J.R., Shahbaz, K., Zarrabi-Zadeh, H.: Fréchet distance with speed limits. Comput. Geom. 44(2), 110–120 (2011)

    Google Scholar 

  19. Mandow, L., De La Cruz, J.L.P.: Multiobjective A* search with consistent heuristics. J. ACM 57(5), 1–25 (2010)

    Google Scholar 

  20. Munkres, J.R.: Topology. Featured Titles for Topology. Prentice Hall, Incorporated (2000)

    Google Scholar 

  21. Patil, M.B.: Improved performance in multi-objective optimization using external archive. Sādhanā 45(1), 70 (2020)

    Google Scholar 

  22. Pulido, F.J.J., Mandow, L., Pérez-De-La-Cruz, J.L.L.: Dimensionality reduction in multiobjective shortest path search. Comput. Oper. Res. 64, 60–70 (2015)

    Google Scholar 

  23. Anbuselvi, R.: Path finding solutions for grid based graph. Adv. Comput. Int. J. 4(2), 51–60 (2013)

    Google Scholar 

  24. Sriraghavendra, E., Karthik, K., Bhattacharyya, C.: Fréchet distance based approach for searching online handwritten documents. In: Ninth International Conference on Document Analysis and Recognition (ICDAR 2007), vol. 1, pp. 461–465. IEEE, September 2007

    Google Scholar 

  25. Sturtevant, N.R.: Benchmarks for grid-based pathfinding. IEEE Trans. Comput. Intell. AI Games 4(2), 144–148 (2012)

    Article  Google Scholar 

  26. Toth, P., Vigo, D.: Vehicle Routing: Problems, Methods, and Applications. SIAM (2014)

    Google Scholar 

  27. Tozer, B., Mazzuchi, T., Sarkani, S.: Many-objective stochastic path finding using reinforcement learning. Expert Syst. Appl. 72, 371–382 (2017)

    Google Scholar 

  28. Weise, J., Mai, S., Zille, H., Mostaghim, S.: On the scalable multi-objective multi-agent pathfinding problem. In: 2020 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8. IEEE, July 2020

    Google Scholar 

  29. Weise, J., Mostaghim, S.: A many-objective route planning benchmark problem for navigation. In: Proceedings of the 2020 Genetic and Evolutionary Computation Conference Companion, GECCO 2020, pp. 183–184. ACM, New York, July 2020

    Google Scholar 

  30. Weise, J., Mostaghim, S.: Scalable many-objective pathfinding benchmark suite. [Manuscript submitted for publication] (2020). https://ci.ovgu.de/Publications/TEVC_WM_2020-p-910.html

  31. Xiao, J., Michalewicz, Z.: An evolutionary computation approach to robot planning and navigation. Soft Comput. Mechatron. 32, 117–141 (1999)

    Google Scholar 

  32. Yap, P.: Grid-based path-finding. In: Cohen, R., Spencer, B. (eds.) AI 2002. LNCS (LNAI), vol. 2338, pp. 44–55. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-47922-8_4

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Faculty of Computer Science, Otto von Guericke University, Magdeburg, Germany

    Jens Weise & Sanaz Mostaghim

Authors
  1. Jens Weise
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  2. Sanaz Mostaghim
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Corresponding author

Correspondence to Jens Weise .

Editor information

Editors and Affiliations

  1. Southern University of Science and Technology, Shenzhen, China

    Hisao Ishibuchi

  2. City University of Hong Kong, Kowloon Tong, China

    Qingfu Zhang

  3. Southern University of Science and Technology, Shenzhen, China

    Ran Cheng

  4. University of Exeter, Exeter, UK

    Ke Li

  5. Xi'an Jiaotong University, Xi'an, China

    Hui Li

  6. Xidian University, Xi'an, China

    Handing Wang

  7. East China Normal University, Shanghai, China

    Aimin Zhou

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Weise, J., Mostaghim, S. (2021). Many-Objective Pathfinding Based on Fréchet Similarity Metric. In: Ishibuchi, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2021. Lecture Notes in Computer Science(), vol 12654. Springer, Cham. https://doi.org/10.1007/978-3-030-72062-9_30

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  • DOI: https://doi.org/10.1007/978-3-030-72062-9_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-72061-2

  • Online ISBN: 978-3-030-72062-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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