Skip to main content
SpringerLink
Log in

Logic-Based Encodings for Ricochet Robots

  • Conference paper
  • First Online:
Progress in Artificial Intelligence (EPIA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10423))

Included in the following conference series:

  • 2736 Accesses

Abstract

Studying the performance of logic tools on solving a specific problem can bring new insights on the use of different paradigms. This paper provides an empirical evaluation of logic-based encodings for a well known board game: Ricochet Robots. Ricochet Robots is a board game where the goal is to find the smallest number of moves needed for one robot to move from the initial position to a target position, while taking into account the existing barriers and other robots. Finding a solution to the Ricochet Robots problem is NP-hard. In this work we develop logic-based encodings for the Ricochet Robots problem to feed into Boolean Satisfiability (SAT) solvers. When appropriate, advanced techniques are applied to further boost the performance of a solver. A comparison between the performance of SAT solvers and an existing ASP solution clearly shows that SAT is by far the more adequate technology to solve the Ricochet Robots problem.

This work was partially supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) with reference UID/CEC/50021/2013.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Notes

  1. 1.

    For the sake of clarity, some of the clauses are not written in CNF. In any case, the translation to CNF is trivial.

  2. 2.

    This encoding is available from https://potassco.org/doc/apps/2016/09/20/ricochet-robots.html. Note that the more recent encoding described in [13] is not publicly available.

  3. 3.

    http://potassco.sourceforge.net/.

  4. 4.

    http://www.labri.fr/perso/lsimon/glucose/.

  5. 5.

    https://github.com/Z3Prover/z3.

  6. 6.

    http://www.minizinc.org/index.html.

References

  1. Ansótegui, C., Manyà, F.: Mapping problems with finite-domain variables into problems with Boolean variables. In: International Conference on Theory and Applications of Satisfiability Testing, pp. 1–15 (2004)

    Google Scholar 

  2. Audemard, G., Lagniez, J.-M., Simon, L.: Improving glucose for incremental SAT solving with assumptions: application to MUS extraction. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 309–317. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39071-5_23

    Chapter  MATH  Google Scholar 

  3. Audemard, G., Simon, L.: Lazy clause exchange policy for parallel SAT solvers. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 197–205. Springer, Cham (2014). doi:10.1007/978-3-319-09284-3_15

    Chapter  MATH  Google Scholar 

  4. Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)

    Book  Google Scholar 

  5. Barták, R., Dovier, A., Zhou, N.F.: Multiple-origin-multiple-destination path finding with minimal arc usage: complexity and models. In: International Conference on Tools with Artificial Intelligence (ICTAI), pp. 91–97. IEEE (2016)

    Google Scholar 

  6. Butko, N., Lehmann, K.A., Ramenzoni, V.: Ricochet robots-a case study for human complex problem solving. Project thesis from the Complex System Summer School, Santa Fe Institute (2006)

    Google Scholar 

  7. Chen, J.: A new SAT encoding of the at-most-one constraint. In: International Workshop on Modelling and Reformulating Constraint Satisfaction Problems (2010)

    Google Scholar 

  8. Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008). doi:10.1007/978-3-540-78800-3_24

    Chapter  Google Scholar 

  9. Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004). doi:10.1007/978-3-540-24605-3_37

    Chapter  Google Scholar 

  10. Engels, B., Kamphans, T.: Randolphs robot game is NP-hard!. Electron. Notes Discret. Math. 25, 49–53 (2006)

    Article  MathSciNet  Google Scholar 

  11. Frisch, A.M., Peugniez, T.J., Doggett, A.J., Nightingale, P.: Solving non-Boolean satisfiability problems with stochastic local search: a comparison of encodings. J. Autom. Reason. 35(1–3), 143–179 (2005)

    MathSciNet  MATH  Google Scholar 

  12. Gebser, M., Jost, H., Kaminski, R., Obermeier, P., Sabuncu, O., Schaub, T., Schneider, M.: Ricochet robots: a transverse ASP benchmark. In: Cabalar, P., Son, T.C. (eds.) LPNMR 2013. LNCS, vol. 8148, pp. 348–360. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40564-8_35

    Chapter  Google Scholar 

  13. Gebser, M., Kaminski, R., Obermeier, P., Schaub, T.: Ricochet Robots reloaded: a case-study in multi-shot ASP solving. In: Eiter, T., Strass, H., Truszczyński, M., Woltran, S. (eds.) Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation. LNCS, vol. 9060, pp. 17–32. Springer, Cham (2015). doi:10.1007/978-3-319-14726-0_2

    Chapter  MATH  Google Scholar 

  14. Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: clasp: a conflict-driven answer set solver. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS, vol. 4483, pp. 260–265. Springer, Heidelberg (2007). doi:10.1007/978-3-540-72200-7_23

    Chapter  Google Scholar 

  15. Gebser, M., Schaub, T., Thiele, S.: GrinGo: a new grounder for answer set programming. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS, vol. 4483, pp. 266–271. Springer, Heidelberg (2007). doi:10.1007/978-3-540-72200-7_24

    Chapter  Google Scholar 

  16. Gent, I.P., Nightingale, P.: A new encoding of All different into SAT. In: International Workshop on Modelling and Reformulating Constraint Satisfaction Problems (2004)

    Google Scholar 

  17. Klieber, W., Kwon, G.: Efficient CNF encoding for selecting 1 from N objects. In: International Workshop on Constraints in Formal Verification (2007)

    Google Scholar 

  18. Martins, R., Joshi, S., Manquinho, V., Lynce, I.: Incremental cardinality constraints for MaxSAT. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 531–548. Springer, Cham (2014). doi:10.1007/978-3-319-10428-7_39

    Chapter  Google Scholar 

  19. Nethercote, N., Stuckey, P.J., Becket, R., Brand, S., Duck, G.J., Tack, G.: MiniZinc: towards a standard CP modelling language. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 529–543. Springer, Heidelberg (2007). doi:10.1007/978-3-540-74970-7_38

    Chapter  Google Scholar 

  20. Prestwich, S.: Variable dependency in local search: prevention is better than cure. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 107–120. Springer, Heidelberg (2007). doi:10.1007/978-3-540-72788-0_14

    Chapter  Google Scholar 

  21. Russell, S.J., Norvig, P.: Artificial Intelligence - A Modern Approach, 3rd edn. Pearson Education, London (2010)

    MATH  Google Scholar 

  22. Sharma, A., Sharma, D.: An incremental approach to solving dynamic constraint satisfaction problems. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds.) ICONIP 2012. LNCS, vol. 7665, pp. 445–455. Springer, Heidelberg (2012). doi:10.1007/978-3-642-34487-9_54

    Chapter  Google Scholar 

  23. Shtrichman, O.: Pruning techniques for the SAT-based bounded model checking problem. In: Margaria, T., Melham, T. (eds.) CHARME 2001. LNCS, vol. 2144, pp. 58–70. Springer, Heidelberg (2001). doi:10.1007/3-540-44798-9_4

    Chapter  Google Scholar 

  24. Surynek, P.: Simple direct propositional encoding of cooperative path finding simplified yet more. In: Gelbukh, A., Espinoza, F.C., Galicia-Haro, S.N. (eds.) MICAI 2014. LNCS, vol. 8857, pp. 410–425. Springer, Cham (2014). doi:10.1007/978-3-319-13650-9_36

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. INESC-ID/Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

    Filipe Gouveia, Pedro T. Monteiro, Vasco Manquinho & Inês Lynce

Authors
  1. Filipe Gouveia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pedro T. Monteiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vasco Manquinho
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Inês Lynce
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Inês Lynce .

Editor information

Editors and Affiliations

  1. Universidade do Porto, Porto, Portugal

    Eugénio Oliveira

  2. Universidade do Porto, Porto, Portugal

    João Gama

  3. Polytechnic Institute of Porto, Porto, Portugal

    Zita Vale

  4. Universidade do Porto, Porto, Portugal

    Henrique Lopes Cardoso

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Gouveia, F., Monteiro, P.T., Manquinho, V., Lynce, I. (2017). Logic-Based Encodings for Ricochet Robots. In: Oliveira, E., Gama, J., Vale, Z., Lopes Cardoso, H. (eds) Progress in Artificial Intelligence. EPIA 2017. Lecture Notes in Computer Science(), vol 10423. Springer, Cham. https://doi.org/10.1007/978-3-319-65340-2_54

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-65340-2_54

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-65339-6

  • Online ISBN: 978-3-319-65340-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation