Problem solution sustenance in XCS: Markov chain analysis of niche support distributions and the impact on computational complexity
Michigan-style learning classifier systems iteratively evolve a distributed solution to a problem in the form of potentially overlapping subsolutions. Each problem niche is covered by subsolutions that are represented by a set of predictive rules, termed classifiers. The genetic algorithm is designed to evolve classifier structures that together cover the whole problem space and represent a complete problem solution. An obvious challenge for such an online evolving, distributed knowledge representation is to continuously sustain all problem subsolutions covering all problem niches, that is, to ensure niche support. Effective niche support depends both on the probability of reproduction and on the probability of deletion of classifiers in a niche. In XCS, reproduction is occurrence-based whereas deletion is support-based. In combination, niche support is assured effectively. In this paper we present a Markov chain analysis of the niche support in XCS, which we validate experimentally. Evaluations in diverse Boolean function settings, which require non-overlapping and overlapping solution structures, support the theoretical derivations. We also consider the effects of mutation and crossover on niche support. With respect to computational complexity, the paper shows that XCS is able to maintain (partially overlapping) niches with a computational effort that is linear in the inverse of the niche occurrence frequency.

title: Classifier Systems and Genetic Algorithms
abstract: 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.

title: Population sizing for entropy-based model building in discrete estimation of distribution algorithms
abstract: 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.

title: Construction of high-order deceptive functions using low-order Walsh coefficients
abstract: This paper constructs deceptive functions over bit strings of any length using low-order Walsh coefficients. Specifically, a partially deceptive construct is achieved with coefficients no higher than second order, and a fully deceptive construct is achieved with coefficients no higher than third order. Previous work on deception tacitly assumed that the very highest order Walsh coefficient, the order-l coefficient in a length-l problem, must be non-zero to achieve full deception, that condition where all schemata of orderl−1 or less containing the complement of the global optimum are superior to their competitors. The constructions of this paper show such assumptions to be false and lead to a more general theory of functions whose value only depends on the number of ones (or zeros) in the function's argument, so-calledfunctions of unitation. These results also help shed some light on Tanese's puzzling results on functions that contained large numbers of Walsh terms of fixed order.

title: Substructural Surrogates for Learning Decomposable Classification Problems
abstract: This paper presents a learning methodology based on a substructural classification model to solve decomposable classification problems. The proposed method consists of three important components: (1) a structural model, which represents salient interactions between attributes for a given data, (2) a surrogate model, which provides a functional approximation of the output as a function of attributes, and (3) a classification model, which predicts the class for new inputs. The structural model is used to infer the functional form of the surrogate. Its coefficients are estimated using linear regression methods. The classification model uses a maximally-accurate, least-complex surrogate to predict the output for given inputs. The structural model that yields an optimal classification model is searched using an iterative greedy search heuristic. Results show that the proposed method successfully detects the interacting variables in hierarchical problems, groups them in linkages groups, and builds maximally accurate classification models. The initial results on non-trivial hierarchical test problems indicate that the proposed method holds promise and also shed light on several improvements to enhance the capabilities of the proposed method.

title: SEARCH, Blackbox Optimization, And Sample Complexity
abstract: 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.

title: Teching PL/I using a microcomputer
abstract: Until the Fall 1983 semester, the introductory programming course at Brooklyn College had been taught (in the PL/C dialect of PL/I) using keypunch equipment in a batch environment. However, that term two experimental sections used IBM Personal Computer (PC's) instead of keypunches. The experiment was expanded in the Spring 1984 semester to include almost one third of all sections of the introductory course, and then expanded again in the Fall 1984 semester to all sections of the first PL/I course, plus three sections of second-level courses. Although the PC's were quite easy to use, the PL/I-86 PC-DOS compiler produced by Digital Research caused many problems. A number of advantages and disadvantages of the experiment are discussed. Other implications of the use of PC's are also noted, including the possible change of language and the extension to more advanced courses in the curriculum.