46040947
Genetic Algorithm Difficulty and the Modality of Fitness Landscapes
Abstract We assume that the modality (i.e., number of local optima) of a fitness landscape is related to the difficulty of finding the best point on that landscape by evolutionary computation (e.g., hillclimbers and genetic algorithms (GAs)). We first examine the limits of modality by constructing a unimodal function and a maximally multimodal function. At such extremes our intuition breaks down. A fitness landscape consisting entirely of a single hill leading to the global optimum proves to be harder for hillclimbers than GAs. A provably maximally multimodal function, in which half the points in the search space are local optima, can be easier than the unimodal, single hill problem for both hillclimbers and GAs. Exploring the more realistic intermediate range between the extremes of modality, we construct local optima with varying degrees of “attraction” to our evolutionary algorithms. Most work on optima and their basins of attraction has focused on hills and hillclimbers, while some research has explored attraction for the GA's crossover operator. We extend the latter results by defining and implementing maximal partial deception in problems with k arbitrarily placed global optima. This allows us to create functions, such as the minimum distance function f mdG , with k isolated global optima and multiple local optima attractive to both crossover and hillclimbers. The function f mdG seems to be a powerful new tool for generalizing deception and relating hillclimbers (and Hamming space) to GAs and crossover.
207507686
Classifier Systems and Genetic Algorithms
Classifier systems are massively parallel, message-passing, rule-based systems that learn through credit assignment (the bucket brigade algorithm) and rule discovery (the genetic algorithm). They typically operate in environments that exhibit one or more of the following characteristics: (1) perpetually novel events accompanied by large amounts of noisy or irrelevant data; (2) continual, often real-time, requirements for action; (3) implicitly or inexactly defined goals; and (4) sparse payoff or reinforcement obtainable only through long action sequences. Classifier systems are designed to absorb new information continuously from such environments, devising sets of competing hypotheses (expressed as rules) without disturbing significantly capabilities already acquired. This paper reviews the definition, theory, and extant applications of classifier systems, comparing them with other machine learning techniques, and closing with a discussion of advantages, problems, and possible extensions of classifier systems.
45531719
The Nonuniform Walsh-Schema Transform
Abstract The Walsh-schema transform allows useful analysis of the expected performance of genetic algorithms. Until recently, its use has been restricted to the static analysis of functions, codings, and operators. In this paper, we present a form of the Walsh-schema transform that accounts for nonuniformly distributed populations, and thereby extend its use to the dynamic analysis of genetic algorithms. We also show the relationship between the nonuniform Walsh-schema transform and the hyperplane transform.
14443613
SEARCH, Blackbox Optimization, And Sample Complexity
The SEARCH (Search Envisioned As Relation and Class Hierarchizing) framework developed elsewhere (Kargupta, 1995; Kargupta and Goldberg, 1995) offered an alternate perspective toward blackbox optimization -- optimization in presence of little domain knowledge. The SEARCH framework investigates the conditions essential for transcending the limits of random enumerative search using a framework developed in terms of relations, classes and partial ordering. This paper presents a summary of some of the main results of that work. A closed form bound on the sample complexity in terms of the cardinality of the relation space, class space, desired quality of the solution and the reliability is presented. This also leads to the identification of the class of order-k delineable problems that can be solved in polynomial sample complexity. These results are applicable to any blackbox search algorithms, including evolutionary optimization techniques.
14286903
Classifier prediction based on tile coding
This paper introduces XCSF extended with tile coding prediction: each classifier implements a tile coding approximator; the genetic algorithm is used to adapt both classifier conditions (i.e., to partition the problem) and the parameters of each approximator; thus XCSF evolves an ensemble of tile coding approximators instead of the typical monolithic approximator used in reinforcement learning. The paper reports a comparison between (i) XCSF with tile coding prediction and (ii) plain tile coding. The results show that XCSF with tile coding always reaches optimal performance, it usually learns as fast as the best parametrized tile coding, and it can be faster than the typical tile coding setting. In addition, the analysis of the evolved tile coding ensembles shows that XCSF actually adapts local approximators following what is currently considered the best strategy to adapt the tile coding parameters in a given problem.
14360251
Population sizing for entropy-based model building in discrete estimation of distribution algorithms
This paper proposes a population-sizing model for entropy-based model building in discrete estimation of distribution algorithms. Specifically, the population size required for building an accurate model is investigated. The effect of selection pressure on population sizing is also preliminarily incorporated. The proposed model indicates that the population size required for building an accurate model scales as Θ(m log m), where m is the number of substructures of the given problem and is proportional to the problem size. Experiments are conducted to verify the derivations, and the results agree with the proposed model.
60847515
Two analysis tools to describe the operation of classifier systems
Anti-Microbial Quaternary Ammonium Co-Polymers formed by the condensation of at least two di-functional tertiary amines and a molar quantity of 1,4-dihalo-2-butene that is equal to the molar sum of the di-functional tertiary amines in the mixture.