Alden Wright

University of Montana, Computer Science, Faculty Member

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I am doing research on the evolution of complexity of genotype-phenotype maps. This research is related to biological and artificial evolution (such as evolutionary computation.I continue to be active in the University of Montana Computer Science department.

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Perturbation Theory and the Renormalization Group in Genetic Dynamics

Lecture Notes in Computer Science, 2005

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Allele Diffusion in Linear Genetic Programming and Variable-Length Genetic Algorithms with Subtree Crossover

Lecture Notes in Computer Science, 2002

In this paper we study, theoretically, the search biases produced by GP subtree crossover when ap... more In this paper we study, theoretically, the search biases produced by GP subtree crossover when applied to linear representations, such as those used in linear GP or in variable length GAs. The study naturally leads to generalisations of Geiringer's theorem and of the notion of linkage equilibrium, which, until now, were applicable only to fixed-length representations. This indicates the presence of a diffusion process by which, even in the absence of selective pressure and mutation, the alleles in a particular individual tend not just to be swapped with those of other individuals in the population, but also to diffuse within the representation of each individual. More precisely, crossover attempts to push the population towards distributions of primitives where each primitive is equally likely to be found in any position in any individual.

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Proceedings of the 8th international conference on Foundations of Genetic Algorithms

The Walsh Transform and the Theory of the Simple Genetic Algorithm

Genetic Algorithms for Pattern Recognition, 2017

The Walsh Transform and the Theory of the Simple Genetic Algorithm Michael D. Vose and Alden H. W... more The Walsh Transform and the Theory of the Simple Genetic Algorithm Michael D. Vose and Alden H. Wright Abstract This chapter surveys a number of recent developments concerning the Simple Genetic Algorithm, its formalism, and the application of the Walsh transform to the theory of the Simple Genetic Algorithm. 2.1 Introduction The Walsh transform has a history of applications to signal processing and pattern recognition. Genetic algorithms are also being successfully applied to problems in these areas. This chapter is about both the Walsh transform and ...

Foundations of Genetic Algorithms

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An Estimation of Distribution Algorithm Based on Maximum Entropy

Springer eBooks, 2004

Estimation of distribution algorithms (EDA) are similar to genetic algorithms except that they re... more Estimation of distribution algorithms (EDA) are similar to genetic algorithms except that they replace crossover and mutation with sampling from an estimated probability distribution. We develop a framework for estimation of distribution algorithms based on the principle of maximum entropy and the conservation of schema frequencies. An algorithm of this type gives better performance than a standard genetic algorithm (GA) on a number of standard test problems involving deception and epistasis (i.e. Trap and NK).

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On mutation and crossover in the theory of evolutionary algorithms

Variation in fact is Evolution. The readiest way then of studying the problem of Evolution is to ... more

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Evolvability and complexity properties of the digital circuit genotype-phenotype map

Proceedings of the Genetic and Evolutionary Computation Conference, 2021

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An adaptive function identification system

[1993] Proceedings IEEE International Conference on Developing and Managing Intelligent System Projects

Abstract Given data in the form of a collection of (x, y) pairs of real numbers, the symbolic fun... more Abstract Given data in the form of a collection of (x, y) pairs of real numbers, the symbolic function identification problem is to find a functional model of the form y= f (x) that fits the data. This paper describes an adaptive system for solution of symbolic function identification problems that combines a genetic algorithm and the Levenberg-Marquardt nonlinear regression algorithm. The genetic algorithm uses an expression-tree representation rather than the more usual binary-string representation. Experiments were run with data ...

Boundary-preserving mappings of $3$-manifolds onto cubes-with-handles

Illinois Journal of Mathematics, 1976

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Exploiting Quotients of Markov Chains to Derive Properties of the Stationary Distribution of the Markov Chain Associated to an Evolutionary Algorithm

Lecture Notes in Computer Science, 2006

Abstract. In this work, a method is presented for analysis of Markov chains modeling evolutionary... more Abstract. In this work, a method is presented for analysis of Markov chains modeling evolutionary algorithms through use of a suitable quotient construction. Such a notion of quotient of a Markov chain is frequently referred to as “coarse graining” in the evolutionary computation literature. We shall discuss the construction of a quotient of an irreducible Markov chain with respect to an arbitrary equivalence relation on the state space. The stationary distribution of the quotient chain is “coherent” with the stationary distribution of ...

O (k) parallel algorithm for approximate string matching

Mappings from 3-Manifolds onto 3-Manifolds

Transactions of the American Mathematical Society, 1972

Let/be a compact, boundary preserving mapping from the 3-manifold M3 onto the 3-manifold N3. Let ... more Let/be a compact, boundary preserving mapping from the 3-manifold M3 onto the 3-manifold N3. Let Zv denote the integers mod a prime/», or, if p = 0, the integers. (1) If each point inverse of/is connected and strongly 1-acyclic over Z", and if M3 is orientable for p > 2, then all but a locally finite collection of point inverses of/ are cellular. (2) If the image of the singular set of/is contained in a compact set each component of which is strongly acyclic overZ,,, and if M3 is orientable forp/2, then N3 can be obtained from M3 by cutting out of Int M3 a compact 3-manifold with 2-sphere boundary, and replacing it by a Zp-homology 3-cell. (3) If the singular set of /is contained in a O-dimensional set, then all but a locally finite collection of point inverses of/are cellular. I. Introduction. We suppose throughout the introduction that /: M3 -»-A'3 is a compact, boundary preserving mapping from the 3-manifold M3 onto the 3-manifold TV3 (where A/3 and N3 may or may not have boundary). Let Zp denote the integers modulo a prime p, or, if p = 0, the integers. If/_1(x) is connected and strongly 1-acyclic over Zp for all x e N3, and if M3 is orientable for p > 2, then in Corollary 1 it is shown that all but a locally finite collection of point inverses are cellular. This implies that N3 can be obtained from M3 by cutting out of Int M3 a locally finite collection of compact 2-manifolds, each bounded by a 2-sphere, and replacing them by a 3-cell (see Corollary 3). Thus, if M3 is compact, N3 is a factor in a connected sum decomposition of M3. Now suppose that the image of the singular set of/is contained in a compact set X each component of which is strongly acyclic over Z". If M3 is orientable for p¥"2, then N3 can be obtained from M3 by cutting out of M3 a finite number of compact 3-manifolds, each bounded by a 2-sphere, and replacing each by a Zp-homology 3-cell. In particular, if Jfhas a neighborhood which is an irreducible 3-manifold with boundary (or if N3 is irreducible), then TV3 is a factor in a connected sum decomposition of M3. This extends Theorem 1 of Lambert in . In the special case where the image of the singular set is contained in a Cantor set,

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A new and constructive proof of the Borsuk-Ulam theorem

Proceedings of the American Mathematical Society, 1979

The Borsuk-Ulam Theorem [1] states that if f is a continuous function from the n-sphere to n-spac... more

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Embedding open 3-manifolds in compact 3-manifolds

Pacific Journal of Mathematics, 1979

We consider open 3-maniίolds that are monotone unions of compact 3-manifolds each bounded by a to... more We consider open 3-maniίolds that are monotone unions of compact 3-manifolds each bounded by a torus. We give necessary and sufficient conditions for embedding such an open 3-manifold in a compact 3-manifold. We also show that if the open 3-manif old embeds in a compact 3-manif old, then it embeds in a compact 3-manifold as the complement of the intersection of a decreasing sequence of solid tori.

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Periodical switching between related goals for improving evolvability to a fixed goal in multi-objective problems

Information Sciences, 2009

Evolutionary computation plays a principal role in intelligent design automation. Evolutionary ap... more Evolutionary computation plays a principal role in intelligent design automation. Evolutionary approaches have discovered novel and patentable designs. Nonetheless, evolutionary techniques may lead to designs that lack robustness. This critical issue is strongly connected to the concept of evolvability. In nature, highly evolvable species tend to be found in rapidly changing environments. Such species can be considered robust against environmental changes. Consequently, to create robust engineering designs it could be ...

The computational complexity of N-K fitness functions

IEEE Transactions on Evolutionary Computation, 2000

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Finiteness of the Fixed Point Set for the Simple Genetic Algorithm

Evolutionary Computation, 1995

The infinite population simple genetic algorithm is a discrete dynamical system model of a geneti... more The infinite population simple genetic algorithm is a discrete dynamical system model of a genetic algorithm. It is conjectured that trajectories in the model always converge to fixed points. This paper shows that an arbitrarily small perturbation of the fitness will result in a model with a finite number of fixed points. Moreover, every sufficiently small perturbation of fimess preserves the finiteness of the fixed point set. These results allow proofs and constructions that require finiteness of the fixed point set. For example, applying the stable manifold theorem to a fixed point requires the hyperbolicity of the differential of the transition map of the genetic algorithm, which requires (among other things) that the fixed point be isolated.

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An advisory expert system for designing fire prescriptions

Ecological Modelling, 1989

Abstract Prescribed fire is used to manipulate forest ecosystems to accomplish a variety of resou... more Abstract Prescribed fire is used to manipulate forest ecosystems to accomplish a variety of resource management objectives. To develop prescriptions that successfully achieve these objectives, managers use information from a variety of sources. These include results of scientific research and of their own experience. Much of the knowledge of expert practitioners has never been collected and made available to others. An expert system is being developed using rule-based inference and frame-based inheritance to integrate ...

A hierarchical genetic system for symbolic function identification

COMPUTING SCIENCE AND STATISTICS, 1993

Given data in the form of a collection of (x, y) pairs of real numbers, the symbolic function ide... more Given data in the form of a collection of (x, y) pairs of real numbers, the symbolic function identification problem is to find a functional model of the form y= f (x) that fits the data. This paper describes a system for solution of symbolic function identification problems that combines a genetic algorithm and the Levenberg-Marquardt nonlinear regression algorithm. The genetic algorithm uses an expression-tree representation rather than the more usual binary-string representation. Experiments were run with data generated using ...

Alden Wright

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