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Sparse Surrogate Model for Optimization: Example of the Bus Stops Spacing Problem

  • Conference paper
Evolutionary Computation in Combinatorial Optimization (EvoCOP 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14632))

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Abstract

Combinatorial optimization problems can involve computationaly expensive fitness function, making their resolution challenging. Surrogate models are one of the effective techniques used to solve such black-box problems by guiding the search towards potentially good solutions. In this paper, we focus on the use of surrogate based on multinomial approaches, particularly based on Walsh functions, to tackle pseudo-Boolean problems. Although this approach can be effective, a potential drawback is the growth of the polynomial expansion with problem dimension. We introduce a method for analyzing real-world combinatorial black-box problems defined through numerical simulation. This method combines Walsh spectral analysis and polynomial regression. Consequently, we propose a sparse surrogate model that incorporates selected, relevant terms and is simpler to optimize. To demonstrate our approach, we apply it to the bus stop spacing problem, an exemplary combinatorial pseudo-Boolean challenge.

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Notes

  1. 1.

    Recommended parameters values, and stopping criterion at 2 s of computation.

References

  1. Armas, R., Aguirre, H., Tanaka, K.: Multi-objective optimization of level of service in urban transportation. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 1057–1064 (2017)

    Google Scholar 

  2. Armas, R., Aguirre, H., Zapotecas-Martínez, S., Tanaka, K.: Traffic signal optimization: minimizing travel time and fuel consumption. In: Bonnevay, S., Legrand, P., Monmarché, N., Lutton, E., Schoenauer, M. (eds.) EA 2015. LNCS, vol. 9554, pp. 29–43. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-31471-6_3

    Chapter  Google Scholar 

  3. Aurore Sallard, M.B., Hörl, S.: An open data-driven approach for travel demand synthesis: an application to são paulo. Reg. Stud. Reg. Sci. 8(1), 371–386 (2021). https://doi.org/10.1080/21681376.2021.1968941

    Article  Google Scholar 

  4. Bai, Z., Nguyen, H., Davidson, I.: Block model guided unsupervised feature selection. In: Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 1201–1211 (2020)

    Google Scholar 

  5. Balac, M., Hörl, S.: Synthetic population for the state of California based on open data: examples of the San Francisco bay area and San Diego county, February 2021

    Google Scholar 

  6. Baptista, R., Poloczek, M.: Bayesian optimization of combinatorial structures. In: International Conference on Machine Learning, pp. 462–471. PMLR (2018)

    Google Scholar 

  7. Bartz-Beielstein, T., Zaefferer, M.: Model-based methods for continuous and discrete global optimization. Appl. Soft Comput. 55, 154–167 (2017)

    Article  Google Scholar 

  8. Branke, J.: Simulation optimisation: tutorial. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, pp. 862–889 (2019)

    Google Scholar 

  9. Chicano, F., Derbel, B., Verel, S.: Fourier transform-based surrogates for permutation problems. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 275–283 (2023)

    Google Scholar 

  10. Chicano, F., Whitley, D., Ochoa, G., Tinós, R.: Optimizing one million variable NK landscapes by hybridizing deterministic recombination and local search. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 753–760 (2017)

    Google Scholar 

  11. Dadkhahi, H., Rios, J., Shanmugam, K., Das, P.: Fourier representations for black-box optimization over categorical variables. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 36, pp. 10156–10165 (2022)

    Google Scholar 

  12. Dadkhahi, H., et al.: Combinatorial black-box optimization with expert advice. In: Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 1918–1927 (2020)

    Google Scholar 

  13. Derbel, B., Pruvost, G., Liefooghe, A., Verel, S., Zhang, Q.: Walsh-based surrogate-assisted multi-objective combinatorial optimization: a fine-grained analysis for pseudo-Boolean functions. Appl. Soft Comput. 136, 110061 (2023)

    Article  Google Scholar 

  14. Dushatskiy, A., Alderliesten, T., Bosman, P.A.: A novel approach to designing surrogate-assisted genetic algorithms by combining efficient learning of Walsh coefficients and dependencies. ACM Trans. Evol. Learn. Optim. 1(2), 1–23 (2021)

    Article  Google Scholar 

  15. Dushatskiy, A., Mendrik, A.M., Alderliesten, T., Bosman, P.A.: Convolutional neural network surrogate-assisted GOMEA. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 753–761 (2019)

    Google Scholar 

  16. Gosavi, A., et al.: Simulation-Based Optimization. Springer, New York (2015). https://doi.org/10.1007/978-1-4899-7491-4

  17. Han, L., Wang, H.: A random forest assisted evolutionary algorithm using competitive neighborhood search for expensive constrained combinatorial optimization. Memetic Comput. 13, 19–30 (2021)

    Article  Google Scholar 

  18. Hordijk, W., Stadler, P.F.: Amplitude spectra of fitness landscapes. Adv. Complex Syst. 1(01), 39–66 (1998)

    Article  Google Scholar 

  19. Hörl, S., Balac, M.: Introducing the eqasim pipeline: from raw data to agent-based transport simulation. Procedia Comput. Sci. 184, 712–719 (2021). the 12th International Conference on Ambient Systems, Networks and Technologies (ANT)/The 4th International Conference on Emerging Data and Industry 4.0 (EDI40) / Affiliated Workshops

    Google Scholar 

  20. Hörl, S., Balac, M.: Synthetic population and travel demand for Paris and île-de-France based on open and publicly available data. Transp. Res. Part C: Emerg. Technol. 130, 103291 (2021)

    Article  Google Scholar 

  21. Horni, A., Nagel, K., Axhausen, K. (eds.): Multi-Agent Transport Simulation MATSim. Ubiquity Press, London, August 2016

    Google Scholar 

  22. Ibeas, A., della Olio, L., Alonso, B., Sainz, O.: Optimizing bus stop spacing in urban areas. Transp. Res. Part E: Logist. Transp. Rev. 46(3), 446–458 (2010)

    Google Scholar 

  23. Leprêtre, F., Fonlupt, C., Verel, S., Marion, V.: Combinatorial surrogate-assisted optimization for bus stops spacing problem. In: Biennial International Conference on Artificial Evolution (EA 2019). Mulhouse, France, October 2019

    Google Scholar 

  24. Leprêtre, F.: Fitness landscapes analysis and adaptive algorithms design for traffic lights optimization on SIALAC benchmark. Appl. Soft Comput. 85, 105869 (2019)

    Article  Google Scholar 

  25. Leprêtre, F., Verel, S., Fonlupt, C., Marion, V.: Walsh functions as surrogate model for pseudo-Boolean optimization problems. In: The Genetic and Evolutionary Computation Conference (GECCO 2019), pp. 303–311. Proceedings of the Genetic and Evolutionary Computation Conference, ACM, Prague, Czech Republic, July 2019

    Google Scholar 

  26. Li, J., et al.: Feature selection: a data perspective. ACM Comput. Surv. (CSUR) 50(6), 94 (2018)

    Article  MathSciNet  Google Scholar 

  27. Moraglio, A., Kattan, A.: Geometric generalisation of surrogate model based optimisation to combinatorial spaces. In: Merz, P., Hao, J.-K. (eds.) EvoCOP 2011. LNCS, vol. 6622, pp. 142–154. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20364-0_13

    Chapter  Google Scholar 

  28. O’Donnell, R.: Analysis of Boolean Functions. Cambridge University Press, Cambridge (2014)

    Google Scholar 

  29. Oh, C., Tomczak, J., Gavves, E., Welling, M.: Combo: combinatorial Bayesian optimization using graph representations. In: ICML Workshop on Learning and Reasoning with Graph-Structured Data (2019)

    Google Scholar 

  30. Pires, F., Cachada, A., Barbosa, J., Moreira, A.P., Leitão, P.: Digital twin in industry 4.0: technologies, applications and challenges. In: 2019 IEEE 17th International Conference on Industrial Informatics (INDIN), vol. 1, pp. 721–726. IEEE (2019)

    Google Scholar 

  31. Saka, A.A.: Model for determining optimum bus-stop spacing in urban areas. J. Transp. Eng. 127(3), 195–199 (2001)

    Article  Google Scholar 

  32. Saka, A.A.: Effect of bus-stop spacing on mobile emissions in urban areas (2003)

    Google Scholar 

  33. Saltiel, D., Benhamou, E.: Feature selection with optimal coordinate ascent (OCA). arXiv preprint arXiv:1811.12064 (2018)

  34. Stadler, P.F.: Landscapes and their correlation functions. J. Math. Chem. 20(1), 1–45 (1996)

    Article  MathSciNet  Google Scholar 

  35. Stadler, P.F.: Spectral landscape theory. Evolutionary dynamics: exploring the interplay of selection, accident, neutrality, and function, pp. 221–272 (2003)

    Google Scholar 

  36. Sutton, A.M., Whitley, L.D., Howe, A.E.: Computing the moments of k-bounded Pseudo-Boolean functions over hamming spheres of arbitrary radius in polynomial time. Theor. Comput. Sci. 425, 58–74 (2012)

    Article  MathSciNet  Google Scholar 

  37. Tinós, R., Przewozniczek, M.W., Whitley, D.: Iterated local search with perturbation based on variables interaction for pseudo-Boolean optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 296–304 (2022)

    Google Scholar 

  38. Verel, S., Derbel, B., Liefooghe, A., Aguirre, H., Tanaka, K.: A surrogate model based on Walsh decomposition for Pseudo-Boolean functions. In: Auger, A., Fonseca, C.M., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds.) PPSN 2018. LNCS, vol. 11102, pp. 181–193. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99259-4_15

    Chapter  Google Scholar 

  39. Whitley, L.D., Chicano, F., Goldman, B.W.: Gray box optimization for MK landscapes (NK landscapes and MAX-kSAT). Evol. Comput. 24(3), 491–519 (2016)

    Article  Google Scholar 

  40. Wright, A.H., Thompson, R.K., Zhang, J.: The computational complexity of NK fitness functions. IEEE Trans. Evol. Comput. 4(4), 373–379 (2000)

    Article  Google Scholar 

  41. Zaefferer, M., Horn, D.: A first analysis of kernels for kriging-based optimization in hierarchical search spaces. In: Auger, A., Fonseca, C.M., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds.) PPSN 2018. LNCS, vol. 11102, pp. 399–410. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99259-4_32

    Chapter  Google Scholar 

  42. Zaefferer, M., Stork, J., Friese, M., Fischbach, A., Naujoks, B., Bartz-Beielstein, T.: Efficient global optimization for combinatorial problems. In: Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation, pp. 871–878 (2014)

    Google Scholar 

  43. Zheng, C., Zheng, S., Ma, G.: The bus station spacing optimization based on game theory. Adv. Mech. Eng. 7(2), 453979 (2015). https://doi.org/10.1155/2014/453979

    Article  Google Scholar 

  44. Zhu, Z., Guo, X., Chen, H., Zeng, J., Wu, J.: Optimization of urban mini-bus stop spacing: a case study of Shanghai (China). Tehnicki Vjesnik 24, 949–955 (2017)

    Google Scholar 

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Acknowledgments

Experiments presented in this paper were carried out using the CALCULCO computing platform, supported by DSI/ULCO. We thank Sébastian Hörl for his help in setting up the Eqasim environment and the modification he made for our research project.

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Authors and Affiliations

  1. Univ. Littoral Côte d’Opale, LISIC, 62100, Calais, France

    Valentin Vendi, Sébastien Verel & Cyril Fonlupt

Authors
  1. Valentin Vendi
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  2. Sébastien Verel
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  3. Cyril Fonlupt
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Corresponding authors

Correspondence to Sébastien Verel or Cyril Fonlupt .

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Editors and Affiliations

  1. IRIDIA, Université libre de Bruxelles, Brussels, Belgium

    Thomas Stützle

  2. Monash University, Clayton, VIC, Australia

    Markus Wagner

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Vendi, V., Verel, S., Fonlupt, C. (2024). Sparse Surrogate Model for Optimization: Example of the Bus Stops Spacing Problem. In: Stützle, T., Wagner, M. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2024. Lecture Notes in Computer Science, vol 14632. Springer, Cham. https://doi.org/10.1007/978-3-031-57712-3_2

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  • DOI: https://doi.org/10.1007/978-3-031-57712-3_2

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