Skip to main content

Advertisement

SpringerLink
Log in

A hyperheuristic approach based on low-level heuristics for the travelling thief problem

  • Published:
Genetic Programming and Evolvable Machines Aims and scope Submit manuscript

Abstract

In this paper, we investigate the use of hyper-heuristics for the travelling thief problem (TTP). TTP is a multi-component problem, which means it has a composite structure. The problem is a combination between the travelling salesman problem and the knapsack problem. Many heuristics were proposed to deal with the two components of the problem separately. In this work, we investigate the use of automatic online heuristic selection in order to find the best combination of the different known heuristics. In order to achieve this, we propose a genetic programming based hyper-heuristic called GPHS*, and compare it to state-of-the-art algorithms. The experimental results show that the approach is competitive with those algorithms on small and mid-sized TTP instances.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. We apply the Lexicographic Parsimony Pressure technique [30]. If two individuals are equally fit, the tree with less nodes is chosen as the best. This technique has shown to effectively control bloat in different types of problems [40].

  2. Our implementation of GPHS is available at https://bitbucket.org/yafrani/gphs-offline.

  3. The GPHS* implementation is publically available at https://bitbucket.org/yafrani/gphs-online.

  4. All TTP instances can be found in the website: http://cs.adelaide.edu.au/optlog/research/ttp.php.

  5. Our GA source codes can be found at: https://bitbucket.org/yafrani/gahs-ttp.

References

  1. M. Birattari, Z. Yuan, P. Balaprakash, T. Stützle, F-Race and Iterated F-Race: An Overview (Springer, Berlin, 2010)

    MATH  Google Scholar 

  2. A. Bölte, U.W. Thonemann, Optimizing simulated annealing schedules with genetic programming. Eur. J. Oper. Res. 92(2), 402–416 (1996)

    Article  MATH  Google Scholar 

  3. M. R. Bonyadi, Z. Michalewicz, L. Barone, The travelling thief problem: the first step in the transition from theoretical problems to realistic problems, in Proceedings of the 2013 IEEE Congress on Evolutionary Computation, (2013), pp. 1037–1044

  4. M. R. Bonyadi, Z. Michalewicz, M. R. Przybylek, A. Wierzbicki, Socially inspired algorithms for the travelling thief problem, in Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation, GECCO’14, (ACM, 2014), pp. 421–428

  5. E. K. Burke, M. R. Hyde, G. Kendall, J. Woodward, Automatic heuristic generation with genetic programming: evolving a jack-of-all-trades or a master of one, in Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, GECCO’07, London, vol. 2 (ACM, 2007), pp. 1559–1565

  6. E.K. Burke, M.R. Hyde, G. Kendall, G. Ochoa, E. Ozcan, J.R. Woodward, Exploring Hyper-Heuristic Methodologies with Genetic Programming (Springer, Berlin, 2009)

    Book  MATH  Google Scholar 

  7. E.K. Burke, M. Hyde, G. Kendall, G. Ochoa, E. Özcan, J.R. Woodward, A Classification of Hyper-Heuristic Approaches (Springer, Boston, 2010)

    Book  MATH  Google Scholar 

  8. E.K. Burke, G. Kendall, E. Soubeiga, A tabu-search hyperheuristic for timetabling and rostering. J. Heuristics 9(6), 451–470 (2003)

    Article  Google Scholar 

  9. M. Castelli, L. Manzoni, L. Vanneschi, S. Silva, A. Popovič, Self-tuning geometric semantic genetic programming. Genet. Program. Evolvable Mach. 17(1), 55–74 (2016)

    Article  Google Scholar 

  10. W.J. Conover, Practical Nonparametric Statistics (Wiley, Hoboken, 1999)

    Google Scholar 

  11. P. Cowling, G. Kendall, E. Soubeiga, A hyperheuristic approach to scheduling a sales summit, in Proceedings of the Third International Conference on Practice and Theory of Automated Timetabling, PATAT 2000, Konstanz, Germany (Springer, Berlin, 2000), pp. 176–190

  12. P. Cowling, G. Kendall, E. Soubeiga, A parameter-free hyperheuristic for scheduling a sales summit, in Proceedings of the 4th Metaheuristic International Conference, MIC 2001 (2001), pp. 127–131

  13. A. Cuesta-Cañada, L. Garrido, H. Terashima-Marín, Building hyper-heuristics through ant colony optimization for the 2D bin packing problem, in Proceedings of the 9th International Conference, KES 2005, Melbourne, Australia (Springer, Berlin, 2005), pp. 654–660

  14. B. Delaunay, Sur la sphere vide. Izv. Akad. Nauk SSSR, Otdelenie Matematicheskii i Estestvennyka Nauk 7(793–800), 1–2 (1934)

    MATH  Google Scholar 

  15. K.A. Dowsland, E. Soubeiga, E. Burke, A simulated annealing based hyperheuristic for determining shipper sizes for storage and transportation. Eur. J. Oper. Res. 179(3), 759–774 (2007)

    Article  MATH  Google Scholar 

  16. J.H. Drake, M. Hyde, K. Ibrahim, E. Ozcan, A genetic programming hyper-heuristic for the multidimensional knapsack problem. Kybernetes 43(9/10), 1500–1511 (2014)

    Article  Google Scholar 

  17. M. El Yafrani, B. Ahiod, Cosolver2B: an efficient local search heuristic for the travelling thief problem, in Proceedings of the 2015 IEEE/ACS 12th International Conference of Computer Systems and Applications, AICCSA (2015), pp. 1–5. doi:10.1109/AICCSA.2015.7507099

  18. M. El Yafrani, B. Ahiod, A local search based approach for solving the travelling thief problem. Appl. Soft Comput. (2016). ISSN 1568-4946. doi:10.1016/j.asoc.2016.09.047

  19. M. El Yafrani, B. Ahiod, Population-based vs. single-solution heuristics for the travelling thief problem, in Proceedings of the Genetic and Evolutionary Computation Conference 2016, GECCO’16, Denver, Colorado, USA (ACM, 2016), pp. 317–324. ISBN 978-1-4503-4206-3

  20. H. Faulkner, S. Polyakovskiy, T. Schultz, M. Wagner, Approximate approaches to the traveling thief problem, in Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation, GECCO’15, Madrid, Spain (2015), pp. 385–392. ISBN 978-1-4503-3472-3

  21. A. S. Fukunaga, Automated discovery of local search heuristics for satisfiability testing. Evolut. Comput. 16(1), 31–61 (2008). ISSN 1063-6560

  22. R. Hunt, K. Neshatian, M. Zhang, A genetic programming approach to hyper-heuristic feature selection, in Proceedings of the 9th International Conference on Simulated Evolution and Learning, SEAL 2012, Hanoi, Vietnam (Springer, Berlin, 2012), pp. 320–330

  23. M. Kovačič, Modeling of total decarburization of spring steel with genetic programming. Mater. Manuf. Process. 30(4), 434–443 (2015)

    Article  Google Scholar 

  24. M. Kovačič, F. Dolenc, Prediction of the natural gas consumption in chemical processing facilities with genetic programming. Genet. Program. Evolvable Mach. 17(3), 231–249 (2016)

    Article  Google Scholar 

  25. J.R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection (MIT Press, Cambridge, 1992)

    MATH  Google Scholar 

  26. N. Krasnogor, J. Smith, Emergence of profitable search strategies based on a simple inheritance mechanism, in Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation, GECCO’01, San Francisco, California (Morgan Kaufmann Publishers Inc., 2001), pp. 432–439. ISBN 1-55860-774-9

  27. W.B. Langdon, R. Poli, N.F. McPhee, J.R. Koza, Genetic Programming: An Introduction and Tutorial, with a Survey of Techniques and Applications (Springer, Berlin, 2008)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  29. M. López-Ibáñez, J. Dubois-Lacoste, T. Stützle, M. Birattari, The irace Package: iterated racing for automatic algorithm configuration. IRIDIA Technical Report Series 2011-004, Université Libre de Bruxelles, Bruxelles, Belgium (2011)

  30. S. Luke, L. Panait, Lexicographic parsimony pressure, in Proceedings of the Genetic and Evolutionary Computation Conference, GECCO’02, San Francisco, CA, USA (Morgan Kaufmann Publishers Inc., 2002), pp. 829–836. ISBN 1-55860-878-8

  31. Y. Mei, X. Li, X. Yao, Improving efficiency of heuristics for the large scale traveling thief problem, in Proceedings of the Asia-Pacific Conference on Simulated Evolution and Learning (Springer, 2014), pp. 631–643

  32. Y. Mei, X. Li, F. Salim, X. Yao, Heuristic evolution with genetic programming for traveling thief problem, in Proceedings of the 2015 IEEE Congress on Evolutionary Computation, CEC (IEEE, 2015), pp. 2753–2760

  33. Y. Mei, X. Li, X. Yao, On investigation of interdependence between sub-problems of the travelling thief problem. Soft. Comput. 20(1), 157–172 (2016)

    Article  Google Scholar 

  34. S. Nguyen, M. Zhang, M. Johnston, A genetic programming based hyper-heuristic approach for combinatorial optimisation, in Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, GECCO’11, Dublin, Ireland (ACM, 2011), pp. 1299–1306. ISBN 978-1-4503-0557-0

  35. S. Polyakovskiy, M. R. Bonyadi, M. Wagner, Z. Michalewicz, F. Neumann, A comprehensive benchmark set and heuristics for the traveling thief problem, in Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation, GECCO’14, Vancouver, BC, Canada (ACM, 2014), pp. 477–484. ISBN 978-1-4503-2662-9

  36. G. Reinelt, Tspliba traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991)

    Article  MATH  Google Scholar 

  37. P. Ross, Hyper-Heuristics (Springer US, Boston, 2005)

    Book  Google Scholar 

  38. P. Ross, J. G. Marín-Blázquez, S. Schulenburg, E. Hart, Learning a procedure that can solve hard bin-packing problems: a new GA-based approach to hyper-heuristics, in Proceedings of the Genetic and Evolutionary Computation 2003, GECCO’03, Chicago, IL, USA (Springer, Berlin, 2003), pp. 1295–1306

  39. S. Silva, Gplaba genetic programming toolbox for matlab, version 4.0 (2015). University of Coimbra (2009). http://gplab.sourceforge.net/download.html

  40. S. Silva, J. Almeida, Gplab-a genetic programming toolbox for matlab, in Proceedings of the Nordic MATLAB Conference (NMC-2003) (2005), pp. 273–278

  41. A. Sosa-Ascencio, G. Ochoa, H. Terashima-Marin, S.E. Conant-Pablos, Grammar-based generation of variable-selection heuristics for constraint satisfaction problems. Genet. Program. Evolvable Mach. 17(2), 119–144 (2016)

    Article  Google Scholar 

  42. A. Vargha, H.D. Delaney, A critique and improvement of the CL common language effect size statistics of McGraw and Wong. J. Educ. Behav. Stat. 25(2), 101–132 (2000)

    Google Scholar 

  43. M. Wagner, Stealing items more efficiently with ants: a swarm intelligence approach to the travelling thief problem, in Proceedings of the 10th International Conference on Swarm Intelligence, ANTS 2016, Brussels, Belgium (Springer International Publishing, 2016), pp. 273–281

  44. M. Wagner, M. Lindauer, M. Mısır, S. Nallaperuma, F. Hutter, A case study of algorithm selection for the traveling thief problem. J. Heuristics, 1–26 (2017). ISSN 1572-9397. doi:10.1007/s10732-017-9328-y

  45. J. Wu, S. Polyakovskiy, F. Neumann, On the impact of the renting rate for the unconstrained nonlinear knapsack problem, in Proceedings of the 2016 on Genetic and Evolutionary Computation Conference, GECCO’16 (ACM, 2016), pp. 413–419

Download references

Acknowledgements

M. Martins acknowledges CAPES/Brazil. M. Delgado acknowledges CNPq Grant Nos.: 309197/2014-7 (Brazil Government).

Author information

Authors and Affiliations

  1. LRIT, associated unit to CNRST (URAC 29), Mohammed V University in Rabat, B.P. 1014, Rabat, Morocco

    Mohamed El Yafrani & Belaïd Ahiod

  2. Optimisation and Logistics, School of Computer Science, University of Adelaide, Adelaide, Australia

    Markus Wagner

  3. Federal University of Technology - Paraná (UTFPR), Av. Sete de Setembro, 3165, Curitiba, PR, Brazil

    Marcella Martins, Myriam Delgado & Ricardo Lüders

Authors
  1. Mohamed El Yafrani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marcella Martins
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Markus Wagner
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Belaïd Ahiod
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Myriam Delgado
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ricardo Lüders
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamed El Yafrani.

A Appendix

A Appendix

In this appendix we provide a closer look of the average approximation ratio achieved in 10 independent runs (stated as trend lines in Sect. 5).

According to Figs. 3, 4, 5, 6, 7, 8, 9, for some instances, the average approximation ratios are close to \(100\%\), while the same achievement seems to be very difficult on others. For example, GPHS* regularly achieves better results than S5 on almost all instances of small size (eil51, berlin52, eil76 and kroA100), as can be seen in Figs. 3, 4, 5 and 6. Another example can be seen in Figs. 7 and 8, where GPHS*  presents similar results as S5 for almost all instances of a280 and pr439 set. Finally, in Fig. 9 we observe that GPHS* presents similar results as MA2B and MATLS but worse than S5 for almost all instances of rat783 set.

Fig. 3
figure 3

Average approximation ratios over 10 independent runs of the eil51 instances

Full size image
Fig. 4
figure 4

Average approximation ratios over 10 independent runs of the berlin52 instances

Full size image
Fig. 5
figure 5

Average approximation ratios over 10 independent runs of the eil76 instances

Full size image
Fig. 6
figure 6

Average approximation ratios over 10 independent runs of the kroA100 instances

Full size image
Fig. 7
figure 7

Average approximation ratios over 10 independent runs of the a280 instances

Full size image
Fig. 8
figure 8

Average approximation ratios over 10 independent runs of the pr439 instances

Full size image
Fig. 9
figure 9

Average approximation ratios over 10 independent runs of the rat783 instances

Full size image

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

El Yafrani, M., Martins, M., Wagner, M. et al. A hyperheuristic approach based on low-level heuristics for the travelling thief problem. Genet Program Evolvable Mach 19, 121–150 (2018). https://doi.org/10.1007/s10710-017-9308-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10710-017-9308-x

Keywords

Search

Navigation