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.







Similar content being viewed by others
Explore related subjects
Discover the latest articles and news from researchers in related subjects, suggested using machine learning.Notes
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.
In this paper we consider, of course, online learning to solve the Jawbreaker puzzle.
References
Hartmann D, van den Herik HJ, Iida H (eds) (2000) Games in AI research. ICGA J (special issue) 23(2)
Laird JE (2001) Using a computer game to develop advanced AI. Computer 34(7):70–75
Khoo A, Zubek R (2002) Applying inexpensive AI techniques to computer games. IEEE Intell Syst 17(4):48–53
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
Joyner D (2002) Adventures in group theory: Rubik’s cube, Merlin’s machine, and other mathematical toys. Johns Hopkins Press, Baltimore
Kunkle D, Cooperman G (2009) Harnessing parallel disks to solve Rubik’s cube. J Symb Comput 44(7):872–890
Ryabogin D (2012) On the continual Rubik’s cube. Adv Math 231(6):3429–3444
Kendall G, Parkes A, Spoerer K (2008) A survey of NP-complete puzzles. ICGA J 31(1):13–34
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
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
Berghman L, Goossens D, Leus R (2009) Efficient solutions for MasterMind using genetic algorithms. Comput Oper Res 36(6):1880–1885
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
Chen KH (2000) Some practical techniques for global search in go. ICGA J 23(2):67–74
Drake P (2009) The last-good-reply policy for Monte-Carlo go. ICGA J 32(4):221–227
Tsai JT (2012) Solving Japanese nonograms by Taguchi-based genetic algorithm. Appl Intell 37(3):405–419
Batenburg KJ, Kosters WA (2009) Solving nonograms by combining relaxations. Pattern Recognit 42(8):1672–1683
Jefferson C, Miguel A, Miguel I, Armagan-Tarim S (2006) Modelling and solving English peg solitaire. Comput Oper Res 33(10):2935–2959
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
van Eck NJ, van Wezel M (2008) Application of reinforcement learning to the game of Othello. Comput Oper Res 35(6):1999–2017
Lucas SS, Kendall G (2006) Evolutionary computation and games. IEEE Comput Intell Mag 1(1):10–18
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
Tsai JT, Chou PY, Fang JC (2012) Learning intelligent genetic algorithms using Japanese nonograms. IEEE Trans Ed 55(2):164–168
Pocket PC Jawbreaker Game, The ultimate guide to PDA games. http://www.pdagameguide.com/jawbreaker-game.html
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
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
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
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
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
Sabar NR, Ayob M, Qu R, Kendall G (2011) A graph coloring constructive hyper-heuristic for examination timetabling problems. Applied Intelligence
Soghier A, Qu R (2013) Adaptive selection of heuristics for assigning time slots and rooms in exam timetables. Applied Intelligence, in press
Abuhamdah A, Ayob M, Kendall G, Sabar NR (2013) Population based local search for university course timetabling problems. Appl. Intell. (in press)
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
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
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
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)
Burke EK, Kendall G, Soubeiga E (2003) A tabu-search hyper-heuristic for timetabling and rostering. J Heuristics 9(6):451–470
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
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
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
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
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
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
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
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
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
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
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
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
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
Ozcan E, Bilgin B, Korkmaz EE (2008) A comprehensive analysis of hyper-heuristics. Intell Data Anal 12(1):3–23
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
Eiben AE, Smith JE (2003) Introduction to evolutionary computing, 1st edn. Natural computing series. Springer, Berlin
Billings D (2007) Personal communication. University of Alberta, Canada
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
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
Corresponding author
Rights 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
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10489-013-0470-4