Abstract
The “Snake-In-The-Box” problem is a hard combinatorial search problem, first described more than 50 years ago, which consists in finding longest induced paths in hypercube graphs. Solutions to the problem have diverse and some quite surprising practical applications, but optimal solutions are known only for problems of small dimension, as the search space grows super-exponentially in the hypercube dimension. Incomplete search algorithms based on Evolutionary Computation techniques have been considered the state-of-the-art for finding near-optimal solutions, and have until recently held most significant records. This study presents the latest results of a new technique, based on Monte-Carlo search, which finds significantly improved solutions compared to prior techniques, is considerably faster, and, unlike EC techniques, requires no tuning.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abbott, H., Katchalski, M.: On the construction of snake in the box codes. Utilitas Mathematica 40, 97–116 (1991)
Adelson, L., Alter, R., Curtz, T.: Computation of d-dimensional snakes. In: Procs. 4th S-E Conf. Combinatorics, Graph Theory and Computing, pp. 135–139 (1973)
Carlson, B., Hougen, D.: Phenotype feedback genetic algorithm operators for heuristic encoding of snakes within hypercubes. In: Procs. GECCO 2010, pp. 791–798. ACM (2010)
Casella, D., Potter, W.: New lower bounds for the snake-in-the-box problem: Using evolutionary techniques to hunt for snakes and coils. In: Proceedings of the Florida AI Research Society Conference (2005)
Cazenave, T.: Nested monte-carlo search. In: Proceedings of IJCAI 2009, pp. 456–461 (2009)
Davies, D.: Longest ’separated’ paths and loops in an n cube. IEEE Transactions on Electronic Computers 14(261) (1965)
Hiltgen, A.P., Paterson, K.G.: Single-track circuit codes. IEEE Transactions on Information Theory 47, 2587–2595 (2000)
Hood, S., Recoskie, D., Sawada, J., Wong, C.H.: Snakes, coils, and single-track circuit codes with spread k (2011), http://www.socs.uoguelph.ca/~sawada/papers/coil.pdf
Kautz, W.H.: Unit-distance error-checking codes. IRE Transactions on Electronic Computers 7(2), 179–180 (1958)
Kochut, K.J.: Snake-in-the-box codes for dimension 7. Combinatorial Mathematics and Combinatorial Computations 20, 175–185 (1996)
Lukito, A.: Upper and lower bounds for the length of snake-in-the-box codes. Tech. Rep. 98-07, Delft University of Technology (1998)
Paterson, K., Tuliani, J.: Some new circuit codes. IEEE Transactions on Information Theory 44(3), 1305–1309 (1998)
Potter, W., Robinson, R., Miller, J., Kochut, K., Redys, D.: Using the genetic algorithm to find snake-in-the-box codes. In: Procs. 7th International Conference on Industrial and Engineering Applications of Artificial Intelligence and Expert Systems, pp. 421–426 (1994)
Rimmel, A., Teytaud, F., Cazenave, T.: Optimization of the Nested Monte-Carlo Algorithm on the Traveling Salesman Problem with Time Windows. In: Di Chio, C., Brabazon, A., Di Caro, G.A., Drechsler, R., Farooq, M., Grahl, J., Greenfield, G., Prins, C., Romero, J., Squillero, G., Tarantino, E., Tettamanzi, A.G.B., Urquhart, N., Uyar, A.Ş. (eds.) EvoApplications 2011, Part II. LNCS, vol. 6625, pp. 501–510. Springer, Heidelberg (2011)
Shilpa, H.: An Ant Colony approach to the Snake-In-the-Box Problem. Master’s thesis, University of Georgia (2005)
Snevily, H.S.: The snake-in-the-box problem: A new upper bound. Discrete Mathematics 133(1-3), 307–314 (1994)
Solov´jeva, F.: An upper bound for the length of a cycle in an n-dimensional unit cube. Diskret. Anal. 45, 71–76 (1987)
Tuohy, D.R., Potter, W.D., Casella, D.A.: Searching for snake-in-the-box codes with evolved pruning models. In: Procs. of the 2007 International Conference on Genetic and Evolutionary Methods, GEM 2007, Las Vegas, NV, pp. 25–29 (2007)
Wynn, E.: Constructing circuit codes by permuting initial sequences (2012), http://arxiv.org/pdf/1201.1647
Yehezkeally, Y., Schwartz, M.: Snake-in-the-box codes for rank modulation (2011), http://arxiv.org/abs/1107.3372
Zinovik, I., Chebiryak, Y., Kroening, D.: Periodic orbits and equilibria in glass models for gene regulatory networks. IEEE Transactions on Information Theory 56(2), 805–820 (2010)
Zinovik, I., Kroening, D., Chebiryak, Y.: Computing binary combinatorial gray codes via exhaustive search with sat solvers. IEEE Transactions on Information Theory 54(4), 1819–1823 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kinny, D. (2012). Monte-Carlo Search for Snakes and Coils. In: Sombattheera, C., Loi, N.K., Wankar, R., Quan, T. (eds) Multi-disciplinary Trends in Artificial Intelligence. MIWAI 2012. Lecture Notes in Computer Science(), vol 7694. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35455-7_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-35455-7_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35454-0
Online ISBN: 978-3-642-35455-7
eBook Packages: Computer ScienceComputer Science (R0)