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.
Conference Paper: Finding longest paths in hypercubes, snakes and coils[Show abstract] [Hide abstract]
ABSTRACT: Since the problem's formulation by Kautz in 1958 as an error detection tool, diverse applications for long snakes and coils have been found. These include coding theory, electrical engineering, and genetics. Over the years, the problem has been explored by many researchers in different fields using varied approaches, and has taken on additional meaning. The problem has become a benchmark for evaluating search techniques in combinatorially expansive search spaces (NP-complete Optimizations). We present an effective process for searching for long achordal open paths (snakes) and achordal closed paths (coils) in n-dimensional hypercube graphs. Stochastic Beam Search provides the overall structure for the search while graph theory based techniques are used in the computation of a generational fitness value. This novel fitness value is used in guiding the search. We show that our approach is likely to work in all dimensions of the SIB problem and we present new lower bounds for a snake in dimension 11 and coils in dimensions 10, 11, and 12. The best known solutions of the unsolved dimensions of this problem have improved over the years and we are proud to make a contribution to this problem as well as the continued progress in combinatorial search techniques.2014 IEEE Symposium on Computational Intelligence for Engineering Solutions, CIES'14, Orlando, Florida, U.S.A.; 12/2014
Journal of Combinatorial Optimization 01/2013; DOI:10.1007/s10878-013-9630-z · 1.04 Impact Factor
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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.