Conference Paper

Using evolutionary techniques to hunt for snakes and coils

Artificial Intelligence Center, Georgia Univ., Athens, Georgia
DOI: 10.1109/CEC.2005.1555007 Conference: Evolutionary Computation, 2005. The 2005 IEEE Congress on, Volume: 3
Source: IEEE Xplore


The snake-in-the-box problem is a difficult problem in mathematics and computer science that deals with finding the longest-possible constrained path that can be formed by following the edges of a multidimensional hypercube. This problem was first described by Kautz in the late 1950's (Kautz, 1958). Snake-in-the-box codes, or 'snakes,' are the node or transition sequences of constrained open paths through an n-dimensional hypercube. Coil-in-the-box codes, or 'coils,' are the node or transition sequences of constrained closed paths, or cycles, through an n-dimensional hypercube. Snakes and coils have many applications in electrical engineering, coding theory, and computer network topologies. Generally, the longer the snake or coil for a given dimension, the more useful it is in these applications (Klee, 1970). By applying a relatively recent evolutionary search algorithm known as a population-based stochastic hill-climber, new lower bounds were achieved for (1) the longest-known snake in each of the dimensions nine through twelve and (2) the longest-known coil in each of the dimensions nine through eleven.

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    • "The search for snakes is motivated by the theory of error-correcting codes (as the vertices of a solution to the snake or coil in the box problems can be used as a Gray code that can detect singlebit errors), electrical engineering, computer network topologies [1], Systems Biology [9], etc. Approaches to find long snakes range from studies of mathematical constructions (e.g. binary necklaces [17]) and certain patterns in lower dimensions [20] [19] to genetic algorithms [1] [2] [22]. R. C. Singleton generalized the concept of snakein-the-box codes to circuit codes with a parameter spread [21]. "
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