Using evolutionary techniques to hunt for snakes and coils
ABSTRACT 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.
- Journal of Combinatorial Optimization 01/2013; · 1.04 Impact Factor
Conference Paper: An efficient SAT encoding of circuit codes[Show abstract] [Hide abstract]
ABSTRACT: Circuit codes in hypercubes are generalized snake-in-the-box codes and are used in analog-to-digital conversion devices. The construction of the longest known circuit codes is based on either an exhaustive search or an algorithm that restricts the search to the codes with periodic coordinate sequences. In this paper, we describe an efficient SAT encoding of circuit codes, which enabled us to obtain new circuit codes.Information Theory and Its Applications, 2008. ISITA 2008. International Symposium on; 01/2009
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ABSTRACT: Extremal Optimization (EO) is a relatively new single search-point optimization heuristic based on self-organized criticality. Unlike many traditional optimization heuristics, EO focuses on removing poor characteristics of a solution instead of preserving the good ones. This thesis will examine the physical and biological inspirations behind EO, and will explore the application of EO on four unique search problems in planning, diagnosis, path-nding, and scheduling. Some of the pros and cons of EO will be discussed, and it will be shown that, in many cases, EO can perform as well as or better than many standard search methods. Finally, this thesis will conclude with a survey of the state of the art of EO, mentioning several variations of the algorithm and the benets of using such modications.