Nonstationary Function Optimization Using Genetic Algorithms with Dominance and Diploidy
Specifically, we apply genetic algorithms that include diploid genotypes and dominance operators to a simple nonstationary problem in function optimization: an oscillating, blind knapsack problem. In doing this, we find that diploidy and dominance induce a form of long term distributed memory that stores and occasionally remembers good partial solutions that were once desirable. This memory permits faster adaptation to drastic environmental shifts than is possible without the added structures and operators. This paper investigates the use of diploid representations and dominance operators in genetic algorithms (GAs) to improve performance in environments that vary with time. The mechanics of diploidy and dominance in natural genetics are briefly discussed, and the usage of these structures and operators in other GA investigations is reviewed. An extension of the schema theorem is developed which illustrates the ability of diploid GAs with dominance to hold alternative alleles in abeyance. Both haploid and diploid GAs are applied to a simple time varying problem: an oscillating, blind knapsack problem. Simulation results show that a diploid GA with an evolving dominance map adapts more quickly to the sudden changes in this problem environment than either a haploid GA or a diploid GA with a fixed dominance map. These proof-of-principle results indicate that diploidy and dominance can be used to induce a form of long term distributed memory within a population of structures. In the remainder of this paper, we explore the mechanism, theory, and implementation of dominance and diploidy in artificial genetic search. We start by examining the role of diploidy and dominance in natural genetics, and we briefly review examples of their usage in genetic algorithm circles. We extend the schema theorem to analyze the effect of these structures and mechanisms. We present results from computational experiments on a 17-object, oscillating, blind 0-1 knapsack problem. Simulations with adaptive dominance maps and diploidy are able to adapt more quickly to sudden environmental shifts than either a haploid genetic algorithm or a diploid genetic algorithm with fixed dominance map. These results are encouraging and suggest the investigation of dominance and diploidy in other GA applications in search and machine learning.  Real world problems are seldom independent of time. If you don't like the weather, wait five minutes and it will change. If this week gasoline costs $1.30 a gallon, next week it may cost $0.89 a gallon or perhaps $2.53 a gallon. In these and many more complex ways, real world environments are both nonstationary and noisy. Searching for good solutions or good behavior under such conditions is a difficult task; yet, despite the perpetual change and uncertainty, all is not lost. History does repeat itself, and what goes around does come around. The horrors of Malthusian extrapolation rarely come to pass, and solutions that worked well yesterday are at least somewhat likely to be useful when circumstances are somewhat similar tomorrow or the day after. The temporal regularity implied in these observations places a premium on search augmented by selective memory. In other words, a system which does not learn the lessons of its history is doomed to repeat its mistakes. THE MECHANICS OF NATURAL DOMINANCE AND DIPLOIDY It is surprising to some genetic algorithm newcomers that tpe most commonly used GA is modeled after the mechanics of haploid genetics. After all, don't most elementary genetics textbooks start off with a discussion of Mendel's pea plants and some mention of diploidy and dominance? The reason for this disparity between genetic algorithm practice and genetics textbook coverage is due to the success achieved by early GA investigators (Hollstien, 1971; De Jong, 1975) using haploid chromosome models on stationary problems. It was found that surprising efficacy and efficiency could be obtained using single stranded (haploid) chromosomes under the action of reproduction and crossover. As a result, later investigators of artificial genetic search have tended to ignore diploidy and dominance. In this section we examine the mechanics of diploidy and dominance to understand their roles in shielding alternate In this paper, we investigate the behavior of a genetic algorithm augmented by structures and operators capable of exploiting the regularity and repeatability of many nonstationary environments.

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: 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: 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: 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: 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: Two analysis tools to describe the operation of classifier systems
abstract: 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.