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.
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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.
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: Glass piecewise linear ODE models are frequently used for simulation of neural and gene regulatory networks. Efficient computa- tional tools for automatic synthesis of such models are highly desirable. However, the existing algorithms for the identification of desired models are limited to four-dimensional networks, and rely on numerical solutions of eigenvalue problems. We suggest a novel algebraic criterion to detect the type of the phase flow along network cyclic attractors that is based on a corollary of the Perron-Frobenius theorem. We show an application of the criterion to the analysis of bifurcations in the networks. We pro- pose to encode the identification of models with periodic orbits along cyclic attractors as a propositional formula, and solving it using state- of-the-art SAT-based tools for real linear arithmetic. New lower bounds for the number of equivalence classes are calculated for cyclic attractors in six-dimensional networks. Experimental results indicate that the run- time of our algorithm increases slower than the size of the search space of the problem.Algebraic Biology, Second International Conference, AB 2007, Castle of Hagenberg, Austria, July 2-4, 2007, Proceedings; 01/2007