Skip to main content
SpringerLink
Log in

An evolutionary-based hyper-heuristic approach for the Jawbreaker puzzle

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

In this paper a hyper-heuristic algorithm is designed and developed for its application to the Jawbreaker puzzle. Jawbreaker is an addictive game consisting in a matrix of colored balls, that must be cleared by popping sets of balls of the same color. This puzzle is perfect to be solved by applying hyper-heuristics algorithms, since many different low-level heuristics are available, and they can be applied in a sequential fashion to solve the puzzle. We detail a set of low-level heuristics and a global search procedure (evolutionary algorithm) that conforms to a robust hyper-heuristic, able to solve very difficult instances of the Jawbreaker puzzle. We test the proposed hyper-heuristic approach in Jawbreaker puzzles of different size and difficulty, with excellent results.

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
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  1. Note that in this paper we consider the first type of HHs approach, i.e., HHs for heuristic selection, since we try to optimize the sequence of basic (existing) heuristic that produces the best solution the Jawbreaker.

  2. In this paper we consider, of course, online learning to solve the Jawbreaker puzzle.

References

  1. Hartmann D, van den Herik HJ, Iida H (eds) (2000) Games in AI research. ICGA J (special issue) 23(2)

  2. Laird JE (2001) Using a computer game to develop advanced AI. Computer 34(7):70–75

    Article  Google Scholar 

  3. Khoo A, Zubek R (2002) Applying inexpensive AI techniques to computer games. IEEE Intell Syst 17(4):48–53

    Article  Google Scholar 

  4. Wallace SA, McCartney R, Russell I (2010) Games and machine learning: a powerful combination in an artificial intelligence course. Comput Sci Educ 20(1):17–36

    Article  Google Scholar 

  5. Joyner D (2002) Adventures in group theory: Rubik’s cube, Merlin’s machine, and other mathematical toys. Johns Hopkins Press, Baltimore

    Google Scholar 

  6. Kunkle D, Cooperman G (2009) Harnessing parallel disks to solve Rubik’s cube. J Symb Comput 44(7):872–890

    Article  MATH  MathSciNet  Google Scholar 

  7. Ryabogin D (2012) On the continual Rubik’s cube. Adv Math 231(6):3429–3444

    Article  MATH  MathSciNet  Google Scholar 

  8. Kendall G, Parkes A, Spoerer K (2008) A survey of NP-complete puzzles. ICGA J 31(1):13–34

    Google Scholar 

  9. Mantere T, Koljonen J (2007) Solving, rating and generating Sudoku puzzles with GA. In: Proc of the IEEE congress on evolutionary computation, pp 1382–1389

    Google Scholar 

  10. Hereford JM, Gerlach H (2008) Integer-valued particle swarm optimization applied to Sudoku puzzles. In: Proc of the IEEE swarm intelligence symposium, pp 1–7

    Google Scholar 

  11. Berghman L, Goossens D, Leus R (2009) Efficient solutions for MasterMind using genetic algorithms. Comput Oper Res 36(6):1880–1885

    Article  MATH  Google Scholar 

  12. Merelo-Guervós JJ, Castillo P, Rivas V (2006) Finding a needle in a haystack using hints and evolutionary computation: the case of evolutionary MasterMind. Appl Soft Comput 6(2):170–179

    Article  Google Scholar 

  13. Chen KH (2000) Some practical techniques for global search in go. ICGA J 23(2):67–74

    Google Scholar 

  14. Drake P (2009) The last-good-reply policy for Monte-Carlo go. ICGA J 32(4):221–227

    MathSciNet  Google Scholar 

  15. Tsai JT (2012) Solving Japanese nonograms by Taguchi-based genetic algorithm. Appl Intell 37(3):405–419

    Article  Google Scholar 

  16. Batenburg KJ, Kosters WA (2009) Solving nonograms by combining relaxations. Pattern Recognit 42(8):1672–1683

    Article  MATH  Google Scholar 

  17. Jefferson C, Miguel A, Miguel I, Armagan-Tarim S (2006) Modelling and solving English peg solitaire. Comput Oper Res 33(10):2935–2959

    Article  MATH  MathSciNet  Google Scholar 

  18. Gindre F, Trejo Pizzo DA, Barrera G, Lopez De Luise MD (2010) A criterion-based genetic algorithm solution to the Jigsaw puzzle NP-complete problem. In: Proc of the world congress on engineering and computer science, pp 367–372

    Google Scholar 

  19. van Eck NJ, van Wezel M (2008) Application of reinforcement learning to the game of Othello. Comput Oper Res 35(6):1999–2017

    Article  MATH  MathSciNet  Google Scholar 

  20. Lucas SS, Kendall G (2006) Evolutionary computation and games. IEEE Comput Intell Mag 1(1):10–18

    Article  Google Scholar 

  21. Salcedo-Sanz S, Portilla-Figueras J, Bellido AP, Ortiz-García E, Yao X (2007) Teaching advanced features of evolutionary algorithms using Japanese puzzles. IEEE Trans Ed 50(2):151–155

    Article  Google Scholar 

  22. Tsai JT, Chou PY, Fang JC (2012) Learning intelligent genetic algorithms using Japanese nonograms. IEEE Trans Ed 55(2):164–168

    Article  Google Scholar 

  23. Pocket PC Jawbreaker Game, The ultimate guide to PDA games. http://www.pdagameguide.com/jawbreaker-game.html

  24. Schadd MP, Winands MH, van den Herik HJ, Chaslot GM, Uiterwijk JW (2008) Single-player Monte-Carlo tree search. In: Proc of the 6th international conference on computers and games, pp 24–26

    Google Scholar 

  25. Schadd MP, Winands MH, van den Herik HJ, Chaslot GM, Uiterwijk JW (2012) Single-player Monte-Carlo tree search for SameGame. Knowl-Based Syst 34:3–11

    Article  Google Scholar 

  26. Burke EK, Hart E, Kendall G, Newall J, Ross P, Schulenburg S (2003) Hyper-heuristics: an emerging direction in modern search technology. In: Glover F, Kochenberger G (eds) Handbook of metaheuristics. Kluwer Academic, Norwell, pp 457–474

    Google Scholar 

  27. Burke EK, Hyde M, Kendall G, Ochoa G, Ozcan E, Qu R (2013) Hyper-heuristics: a survey of the state of the art. J. Oper. Res. Soc., in press

  28. Han L, Cowling PI, Kendall G (2002) An investigation of a hyperheuristic genetic algorithm applied to a trainer scheduling problem. In: Proceedings of congress on evolutionary computation (CEC2002), pp 1185–1190

    Google Scholar 

  29. Sabar NR, Ayob M, Qu R, Kendall G (2011) A graph coloring constructive hyper-heuristic for examination timetabling problems. Applied Intelligence

  30. Soghier A, Qu R (2013) Adaptive selection of heuristics for assigning time slots and rooms in exam timetables. Applied Intelligence, in press

  31. Abuhamdah A, Ayob M, Kendall G, Sabar NR (2013) Population based local search for university course timetabling problems. Appl. Intell. (in press)

  32. Hunt R, Neshatian K, Zhang M (2012) A genetic programming approach to hyper-heuristic feature selection. In: Proc of the 9th international conference on simulated evolution and learning (SEAL12). LNCS, vol 7673. Hanoi, Vietnam

    Google Scholar 

  33. Shafi K, Bender A, Abbass HA (2012) Multi-objective learning classifier systems based hyperheuristics for modularised fleet mix problem. In: Proc of the 9th international conference on simulated evolution and learning (SEAL12). LNCS, vol 7673/2012. Hanoi, Vietnam

    Google Scholar 

  34. Wauters T, Vancrooenburg W, Vanden Berghe G (2010) A two phase hyper-heuristic approach for solving the Eternity II puzzle. In: Proc of the 2nd international conference on metaheuristics and nature inspired computing (META10), Djerba Island, Tunisia

    Google Scholar 

  35. Wauters T, Vancrooenburg W, Vanden Berghe G (2012) A guide-and-observe hyper-heuristic approach to the Eternity II puzzle. Journal of Mathematical Modelling and Algorithms 11(3)

  36. Burke EK, Kendall G, Soubeiga E (2003) A tabu-search hyper-heuristic for timetabling and rostering. J Heuristics 9(6):451–470

    Article  Google Scholar 

  37. Burke EK, McCollum B, Meisels A, Petrovic S, Qu R (2007) A graph-based hyperheuristic for educational timetabling problems. Eur J Oper Res 176:177–192

    Article  MATH  MathSciNet  Google Scholar 

  38. Cowling P, Kendall G, Soubeiga E (2001) A parameter-free hyperheuristic for scheduling a sales summit. In: Proc of the 4th metaheuristic international conference, pp 127–131

    Google Scholar 

  39. Cowling P, Kendall G, Soubeiga E (2002) Hyperheuristics: a tool for rapid prototyping in scheduling and optimisation. In: Proc of EvoWorkshops 2002. Lecture notes in computer science, vol 2279, pp 1–10

    Google Scholar 

  40. Burke EK, Hyde MR, Kendall G, Woodward J (2010) A genetic programming hyperheuristic approach for evolving two dimensional strip packing heuristics. IEEE Trans Evol Comput 14(6):942–958

    Article  Google Scholar 

  41. Burke EK, Hyde MR, Kendall G, Woodward J (2007) The scalability of evolved on line bin packing heuristics. In: Proc of the IEEE congress on evolutionary computation, pp 2530–2537

    Google Scholar 

  42. Bai R, Kendall G (2008) A model for fresh produce shelf-space allocation and inventory management with freshness-condition-dependent demand. INFORMS J Comput 20(1):78–85

    Article  MATH  MathSciNet  Google Scholar 

  43. Bai R, Burke EK, Kendall G (2008) Heuristic, meta-heuristic and hyper-heuristic approaches for fresh produce inventory control and shelf space allocation. J Oper Res Soc 59:1387–1397

    Article  MATH  Google Scholar 

  44. Remde S, Cowling P, Dahal K, Colledge N, Selensky E (2011) An empirical study of hyperheuristics for managing very large sets of low level heuristics. J Oper Res Soc 63(3):392–405

    Article  Google Scholar 

  45. Kendall G, Mohamad M (2004) Channel assignment in cellular communication using a great deluge hyper-heuristic. In: Proc of the IEEE international conference on network, pp 769–773

    Google Scholar 

  46. Kendall G, Mohamad M (2004) Channel assignment optimisation using a hyper-heuristic. In: Proc of the IEEE conference on cybernetic and intelligent systems, pp 790–795

    Google Scholar 

  47. Li J, Burke EK, Qu R (2011) Integrating neural networks and logistic regression to underpin hyper-heuristic search. Knowl-Based Syst 24(2):322–330

    Article  Google Scholar 

  48. Furtuna R, Curteanu S, Leon F (2012) Multi-objective optimization of a stacked neural network using an evolutionary hyper-heuristic. Appl Soft Comput 12(1):133–144

    Article  Google Scholar 

  49. Burke EK, Hyde M, Kendall G, Ochoa G, Ozcan E, Woodward J (2009) A classification of hyper-heuristics approaches. In: Gendreau M, Potvin J-Y (eds) Handbook of metaheuristics. International series in operations research and management science. Springer, Berlin

    Google Scholar 

  50. Ozcan E, Bilgin B, Korkmaz EE (2008) A comprehensive analysis of hyper-heuristics. Intell Data Anal 12(1):3–23

    Google Scholar 

  51. Ross P (2005) In: Burke EK, Kendall G (eds) Hyper-heuristics, search methodologies: introductory tutorials in optimization and decision support techniques. Springer, Berlin, pp 529–556

    Chapter  Google Scholar 

  52. http://allserv.kahosl.be/~mustafa.misir/hh.html

  53. http://www.hyper-heuristic.org

  54. Eiben AE, Smith JE (2003) Introduction to evolutionary computing, 1st edn. Natural computing series. Springer, Berlin

    Book  MATH  Google Scholar 

  55. http://www.js-games.de/eng/games/samegame

  56. Billings D (2007) Personal communication. University of Alberta, Canada

    Google Scholar 

  57. Takes FW, Kosters WA (2009) Solving SameGame and its chessboard variants. In: Proc of the 21st Benelux conference on artificial intelligence, Eindhoven, The Netherlands, pp 249–256

    Google Scholar 

Download references

Acknowledgements

This work has been partially supported by Spanish Ministry of Science and Innovation, under project number ECO2010-22065-C03-02.

Author information

Authors and Affiliations

  1. Department of Signal Theory and Communications, Escuela Politécnica Superior, Universidad de Alcalá, 28871 Alcalá de Henares, Madrid, Spain

    S. Salcedo-Sanz, J. M. Matías-Román, S. Jiménez-Fernández, A. Portilla-Figueras & L. Cuadra

Authors
  1. S. Salcedo-Sanz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. M. Matías-Román
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Jiménez-Fernández
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Portilla-Figueras
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. L. Cuadra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Salcedo-Sanz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Salcedo-Sanz, S., Matías-Román, J.M., Jiménez-Fernández, S. et al. An evolutionary-based hyper-heuristic approach for the Jawbreaker puzzle. Appl Intell 40, 404–414 (2014). https://doi.org/10.1007/s10489-013-0470-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-013-0470-4

Keywords

Search

Navigation