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European Conference on Genetic Programming

EuroGP 2016: Genetic Programming pp 294–310Cite as

Iterative Cartesian Genetic Programming: Creating General Algorithms for Solving Travelling Salesman Problems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9594))

Abstract

Evolutionary algorithms have been widely used to optimise or design search algorithms, however, very few have considered evolving iterative algorithms. In this paper, we introduce a novel extension to Cartesian Genetic Programming that allows it to encode iterative algorithms. We apply this technique to the Traveling Salesman Problem to produce human-readable solvers which can be then be independently implemented. Our experimental results demonstrate that the evolved solvers scale well to much larger TSP instances than those used for training.

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Notes

  1. 1.

    d1291, u2152, usa23505 and d18512 are benchmarks from the well-known TSPLIB. The remaining instances are benchmarks from real-life geographical data; these are wi29, dj38, qa194, zi929, ca4663, ym7663, ja9874, gr9882, sw24978. All these instances can be found at http://www.math.uwaterloo.ca/tsp/world/countries.html and http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/STSP.html.

  2. 2.

    http://www.asap.cs.nott.ac.uk/external/chesc2011/.

  3. 3.

    http://www.hyflex.org/chesc2014/.

  4. 4.

    http://www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95/.

References

  1. Alexander, B., Zacher, B.: Boosting search for recursive functions using partial call-trees. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds.) PPSN 2014. LNCS, vol. 8672, pp. 384–393. Springer, Heidelberg (2014)

    Google Scholar 

  2. Banzhaf, W.: The “molecular” traveling salesman. Biol. Cybern. 64(1), 7–14 (1990)

    Article  MATH  Google Scholar 

  3. Brave, S.: Evolving Recusive Programs for Tree Search. MIT Press, Cambridge (1996)

    Google Scholar 

  4. Brownlee, A.E., Swan, J., Özcan, E., Parkes, A.J.: Hyperion\(^2\): A toolkit for Meta-, Hyper- heuristic research. In: Proceedings of the 2014 Conference Companion on Genetic and Evolutionary Computation Companion, GECCO Comp 2014, NY, USA, pp. 1133–1140. ACM, New York (2014)

    Google Scholar 

  5. Burke, E.K., Gendreau, M., Hyde, M., Kendall, G., Ochoa, G., Özcan, E., Qu, R.: Hyper-heuristics: a survey of the state of the art. J. Oper. Res. Soc. 64(12), 1695–1724 (2013)

    Article  Google Scholar 

  6. Davis, L., et al.: Handbook of Genetic Algorithms, vol. 115. Van Nostrand Reinhold, New York (1991)

    Google Scholar 

  7. Fogel, D.B.: An evolutionary approach to the traveling salesman problem. Biol. Cybern. 60(2), 139–144 (1988)

    Article  MathSciNet  Google Scholar 

  8. Goldberg, D.E., Lingle, R.: Alleles, loci, and the traveling salesman problem. In: Proceedings of an International Conference on Genetic Algorithms and Their Applications, vol. 154, Lawrence Erlbaum, Hillsdale, NJ (1985)

    Google Scholar 

  9. Grefenstette, J.J.: Incorporating problem specific knowledge into genetic algorithms. Genet. Algorithms Simulated Annealing 4, 42–60 (1987)

    Google Scholar 

  10. Gutin, G., Karapetyan, D.: A memetic algorithm for the generalized traveling salesman problem. Nat. Comput. 9(1), 47–60 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Helsgaun, K.: An effective implementation of the lin-kernighan traveling salesman heuristic. Eur. J. Oper. Res. 126(1), 106–130 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hoos, H.H.: Programming by optimization. Commun. ACM 55(2), 70–80 (2012)

    Article  Google Scholar 

  13. Kant, E.: Understanding and automating algorithm design. IEEE Trans. Softw. Eng. SE–11(11), 1361–1374 (1985)

    Article  MathSciNet  Google Scholar 

  14. Kasturi, E., Narayanan, S.L.: A novel approach to hybrid genetic algorithms to solve symmetric TSP. Int. J. 2(2) (2014)

    Google Scholar 

  15. Katayama, K., Sakamoto, H., Narihisa, H.: The efficiency of hybrid mutation genetic algorithm for the travelling salesman problem. Math. Comput. Model. 31(10), 197–203 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  16. Koza, J.R., Andre, D.: Evolution of iteration in genetic programming. In: Evolutionary Programming, pp. 469–478 (1996)

    Google Scholar 

  17. Langdon, W.B.: Genetic programming and data structures. Ph.D. thesis, University College London (1996)

    Google Scholar 

  18. Larres, J., Zhang, M., Browne, W.N.: Using unrestricted loops in genetic programming for image classification. In: 2010 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8. IEEE (2010)

    Google Scholar 

  19. Lin, S., Kernighan, B.: An effective heuristic algorithm for the traveling-salesman problem. Oper. Res. 21(2), 498–516 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  20. López-Ibánez, M., Dubois-Lacoste, J., Stützle, T., Birattari, M.: The irace package, iterated race for automatic algorithm configuration. Technical report, Citeseer (2011)

    Google Scholar 

  21. López-Ibánez, M., Stützle, T.: The automatic design of multiobjective ant colony optimization algorithms. IEEE Trans. Evol. Comput. 16(6), 861–875 (2012)

    Article  Google Scholar 

  22. Mascia, F., López-Ibáñez, M., Dubois-Lacoste, J., Stützle, T.: Grammar-based generation of stochastic local search heuristics through automatic algorithm configuration tools. Comput. Oper. Res. 51, 190–199 (2014). http://dx.doi.org/10.1016/j.cor.2014.05.020

    Article  MathSciNet  Google Scholar 

  23. Miihlenbein, H., Kindermann, J.: The dynamics of evolution and learning-towards genetic neural networks. Connectionism Perspect. pp. 173–197 (1989)

    Google Scholar 

  24. Miller, J.: What bloat? cartesian genetic programming on boolean problems. In: 2001 Genetic and Evolutionary Computation Conference Late Breaking Papers, pp. 295–302 (2001)

    Google Scholar 

  25. Miller, J.F. (ed.): Cartesian Genetic Programming. Springer, Heidelberg (2011)

    MATH  Google Scholar 

  26. Nagata, Y., Soler, D.: A new genetic algorithm for the asymmetric traveling salesman problem. Expert Syst. Appl. 39(10), 8947–8953 (2012)

    Article  Google Scholar 

  27. Ozcan, E., Erenturk, M.: A brief review of memetic algorithms for solving Euclidean 2D traveling salesrep problem. In: Proceedings of the 13th Turkish Symposium on Artificial Intelligence and Neural Networks, pp. 99–108 (2004)

    Google Scholar 

  28. Pillay, N.: A review of hyper-heuristics for educational timetabling. Ann. Oper. Res. pp. 1–36 (2014)

    Google Scholar 

  29. Rokbani, N., Abraham, A., Alimil, A.M.: Fuzzy ant supervised by PSO and simplified ant supervised PSO applied to TSP. In: 2013 13th International Conference on Hybrid Intelligent Systems (HIS), pp. 251–255. IEEE (2013)

    Google Scholar 

  30. Ross, P.: Hyper-heuristics. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies, pp. 529–556. Springer, US (2005)

    Chapter  Google Scholar 

  31. Ross, P.: Hyper-heuristics. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies, pp. 611–638. Springer, US (2005)

    Google Scholar 

  32. Ross, P., Schulenburg, S., Marín-Blázquez, J.G., Hart, E.: Hyper-heuristics: learning to combine simple heuristics in bin-packing problems. In: GECCO 2002, Proceedings of the Genetic and Evolutionary Computation Conference, pp. 942–948. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA (2002)

    Google Scholar 

  33. Ryser-Welch, P., Miller, J.F.: A review of hyper-heuristic frameworks. In: Proceedings of the 50th Anniversary Convention of the AISB, London, 1–4 April 2014

    Google Scholar 

  34. Ryser-Welch, P., Miller, J.F., Asta, S.: Generating human-readable algorithms for the travelling salesman problem using hyper-heuristics. In: GECCO Companion 2015, Proceedings of the Companion Publication of the 2015 on Genetic and Evolutionary Computation Conference, pp. 1067–1074. ACM, New York, NY, USA (2015). http://doi.acm.org/10.1145/2739482.2768459

  35. Shirakawa, S., Nagao, T.: Graph structured program evolution with automatically defined nodes. In: Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation, pp. 1107–1114. ACM (2009)

    Google Scholar 

  36. Swan, J., Woodward, J.R., Özcan, E., Kendall, G., Burke, E.K.: Searching the hyper-heuristic design space. Cogn. Comput. 6(1), 66–73 (2014)

    Article  Google Scholar 

  37. Swan, J., Burles, N.: Templar - a framework for template-method hyper-heuristics. In: Machado, P., et al. (eds.) Genetic Programming. Lecture Notes in Computer Science, vol. 9025, pp. 205–216. Springer, Switzerland (2015)

    Google Scholar 

  38. Swan, J., Özcan, E., Kendall, G.: Hyperion – a recursive hyper-heuristic framework. In: Coello, C.A.C. (ed.) LION 2011. LNCS, vol. 6683, pp. 616–630. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  39. Tavares, J., Pereira, F.B.: Automatic design of ant algorithms with grammatical evolution. In: Moraglio, A., Silva, S., Krawiec, K., Machado, P., Cotta, C. (eds.) EuroGP 2012. LNCS, vol. 7244, pp. 206–217. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  40. Turner, A.J., Miller, J.F.: Neutral genetic drift: an investigation using cartesian genetic programming. Genet. Program. Evolvable Mach. 16(4), 531–558 (2015)

    Article  Google Scholar 

  41. Walker, J.A., Liu, Y., Tempesti, G., Timmis, J., Tyrrell, A.M.: Automatic machine code generation for a transport triggered architecture using cartesian genetic programming. Int. J. Adapt. Resilient Auton. Syst. (IJARAS) 3(4), 32–50 (2012)

    Article  Google Scholar 

  42. Wijesinghe, G., Ciesielski, V.: Evolving programs with parameters and loops. In: 2010 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8. IEEE (2010)

    Google Scholar 

  43. Yu, T., Clack, C.: Recursion, lambda-abstractions and genetic programming. In: Poli, R., Langdon, W.B., Schoenauer, M., Fogarty, T., Banzhaf, W. (eds.) Late Breaking Papers at EuroGP 1998: The First European Workshop on Genetic Programming, CSRP-98-10, pp. 26–30. The University of Birmingham, UK, Paris, France, 14–15 April 1998

    Google Scholar 

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Acknowledgements

The N8 HPC computer cluster used to host our evolutionary cross-domain hyper-heuristics and test their performance was provided and funded by the N8 consortium and EPSRC (Grant No.EP/K000225/1). The Centre is co-ordinated by the Universities of Leeds and Manchester.

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Authors and Affiliations

  1. The University of York, Heslington, UK

    Patricia Ryser-Welch, Julian F. Miller, Jerry Swan & Martin A. Trefzer

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  1. Patricia Ryser-Welch
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  2. Julian F. Miller
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  3. Jerry Swan
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  4. Martin A. Trefzer
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Corresponding author

Correspondence to Patricia Ryser-Welch .

Editor information

Editors and Affiliations

  1. Dalhousie University, Halifax, Nova Scotia, Canada

    Malcolm I. Heywood

  2. University College Dublin, Dublin, Ireland

    James McDermott

  3. Universidade Nova de Lisboa, Lisboa, Portugal

    Mauro Castelli

  4. CIUSC Dept Informatics Engg, University of Coimbra, Coimbra, Portugal

    Ernesto Costa

  5. Edinburgh Napier University, Edinburgh, United Kingdom

    Kevin Sim

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Ryser-Welch, P., Miller, J.F., Swan, J., Trefzer, M.A. (2016). Iterative Cartesian Genetic Programming: Creating General Algorithms for Solving Travelling Salesman Problems. In: Heywood, M., McDermott, J., Castelli, M., Costa, E., Sim, K. (eds) Genetic Programming. EuroGP 2016. Lecture Notes in Computer Science(), vol 9594. Springer, Cham. https://doi.org/10.1007/978-3-319-30668-1_19

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  • DOI: https://doi.org/10.1007/978-3-319-30668-1_19

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