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Solving the 8-puzzle problem using genetic programming

Published: 07 October 2013 Publication History

Abstract

The 8-puzzle problem is a classic artificial intelligence problem which has been well-researched. The research in this domain has focused on evaluating traditional search methods such as the breadth-first search and the A* algorithm and deriving and testing various heuristics for use with informed searches to solve the 8-puzzle problem. The study presented in this paper evaluates a machine learning technique, namely genetic programming, as means of solving the 8-puzzle problem. The genetic programming algorithm uses the grow method to create an initial population which is iteratively refined using tournament selection to choose parents which the reproduction, mutation and crossover operators are applied to, thereby producing successive generations. The edit operator has been used to exert parsimony pressure in order to reduce the size of solution trees and hence the number of moves to solve a problem instance. The genetic programming system was successfully applied to 20 problem instances of differing difficulty, producing solutions to all 20 problems. Furthermore, for a majority of the problems the solutions produced solve the problem instance using the known minimum number of moves.

References

[1]
Reinefeld, A. 1993. Complete Solution of the EightPuzzle Problem and the Benefit of Node Ordering in IDA*. In Proceedings of the 13th Joint Conference on Artificial Intelligence (IJCAI '93), Vol. 1, 248--253, Morgan Kaufmann Publishers, Inc., USA.
[2]
Kunkle, D. R. 2001. Solving the 8 Puzzle Problem in a Minimum Number of Moves: An Application of the A* Algorithm. http://web.mit.edu/6.034/wwwbob/EightPuzzle.pdf. Accessed 31 May 2013.
[3]
Bhasin, H., Singla, N. 2012. Genetic Based Algorithms for N-Puzzle Problem. International Journal of Computer Applications, Vol. 51, No. 22, 44--50.
[4]
Luger, G. F., Stubblefield, W. 1998. Artificial Intelligence: Structures and Strategies for Complex Problem Solving. Addison-Wesley Longman.
[5]
Shaban, R. Z., Alkallak, I. N., Sulaiman, M. M. 2010. Genetic Programming to Solve Sliding Tile 8-Puzzle Problem. Journal of Education and Science, Vol. 23, No. 3, 145--157.
[6]
Banzhaf, W., Nordin, P., Keller, R. E., Francone, F. D. 1998. Genetic Programming - An Introduction - On the Automatic Evolution of Computer Programs and its Applications, Morgan Kaufmann Publishers, Inc.
[7]
Barnes, J. M., Hasan, S. H., Lee, S. 2006. Solving the 8-Puzzle Problem: A Genetic Programming Approach. http://sha.ddih.org/f/Barnes-Hasan-Lee-Project-3.pdf. Accessed 31 May 2013.
[8]
Marshall, C. 2007. Heuristics for Solving the Eight Puzzle Problem. http://www.soe.ucsc.edu/~csm/240/Report.pdf. Accessed 31 May 2013.
[9]
Koza, J. R. 1992. Genetic Programming I: On the Programming of Computers by Means of Natural Selection, MIT Press.

Cited By

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  • (2023)Informedness and Effectiveness in Search: Heuristic Simplicity and Algorithm Complexity2023 IEEE 3rd International Maghreb Meeting of the Conference on Sciences and Techniques of Automatic Control and Computer Engineering (MI-STA)10.1109/MI-STA57575.2023.10169436(12-17)Online publication date: 21-May-2023
  • (2021)Transition Graph Analysis of Sliding Tile Puzzle HeuristicsRecent Advances in Soft Computing and Cybernetics10.1007/978-3-030-61659-5_13(149-156)Online publication date: 6-Feb-2021
  • (2020)Attractiveness of Single-Agent Game: Case Study Using Sliding Puzzle2020 International Conference on Advanced Information Technologies (ICAIT)10.1109/ICAIT51105.2020.9261794(76-81)Online publication date: 4-Nov-2020

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cover image ACM Other conferences
SAICSIT '13: Proceedings of the South African Institute for Computer Scientists and Information Technologists Conference
October 2013
398 pages
ISBN:9781450321129
DOI:10.1145/2513456
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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  • Rhodes Univ.: Rhodes University
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 07 October 2013

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Author Tags

  1. 8-puzzle problem
  2. genetic programming

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  • Research-article

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SAICSIT '13
Sponsor:
  • Amazon
  • Rhodes Univ.
  • IBM

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SAICSIT '13 Paper Acceptance Rate 48 of 89 submissions, 54%;
Overall Acceptance Rate 187 of 439 submissions, 43%

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Cited By

View all
  • (2023)Informedness and Effectiveness in Search: Heuristic Simplicity and Algorithm Complexity2023 IEEE 3rd International Maghreb Meeting of the Conference on Sciences and Techniques of Automatic Control and Computer Engineering (MI-STA)10.1109/MI-STA57575.2023.10169436(12-17)Online publication date: 21-May-2023
  • (2021)Transition Graph Analysis of Sliding Tile Puzzle HeuristicsRecent Advances in Soft Computing and Cybernetics10.1007/978-3-030-61659-5_13(149-156)Online publication date: 6-Feb-2021
  • (2020)Attractiveness of Single-Agent Game: Case Study Using Sliding Puzzle2020 International Conference on Advanced Information Technologies (ICAIT)10.1109/ICAIT51105.2020.9261794(76-81)Online publication date: 4-Nov-2020

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