A central problem in the theory of genetic algorithms is the characterization of problems that are difficult for GAs to optimize. Many attempts to characterize such problems focus on the notion of Deception, defined in terms of the static average fitness of competing schemas. This article examines the Static Building Block Hypothesis (SBBH), the underlying assumption used to define Deception. Exploiting contradictions between the SBBH and the Schema Theorem, we show that Deception is neither necessary nor sufficient for problems to be difficult for GAs. This article argues that the characterization of hard problems must take into account the basic features of genetic algorithms, especially their dynamic, biased sampling strategy. Keywords: Deception, building block hypothesis 1 INTRODUCTION Since Holland's early work on the analysis of genetic algorithms (GAs), the usual approach has been to focus on the allocation of search effort to subspaces described by schemas representing hyper...

In the light of a recently derived evolution equation for genetic algorithms we consider the schema theorem and the building block hypothesis. We derive a schema theorem based on the concept of effective fitness showing that schemata of higher than average effective fitness receive an exponentially increasing number of trials over time. The equation makes manifest the content of the building block hypothesis showing how fit schemata are constructed from fit sub-schemata. However, we show that generically there is no preference for short, low-order schemata. In the case where schema reconstruction is favored over schema destruction large schemata tend to be favored. As a corollary of the evolution equation we prove Geiringer’s theorem.

A set of executable equations are defined which model the ideal behavior of a simple genetic algorithm. The equations assume an infinitely large population and require the enumeration of all points in the search space.

We analyze the schema theorem and the building block hypothesis using a recently derived, exact schemata evolution equation. We derive a new schema theorem based on the concept of effective fitness showing that schemata of higher than average effective fitness receive an exponentially increasing number of trials over time. The building block hypothesis is a natural consequence in that the equation shows how fit schemata are constructed from fit sub-schemata. However, we show that generically there is no preference for short, low-order schemata. In the case where schema reconstruction is favoured over schema destruction large schemata tend to be favoured. As a corollary of the evolution equation we prove Geiringer’s theorem. We give supporting numerical evidence for our claims in both non-epsitatic and epistatic landscapes. 1

We analyze the schema theorem and the building block hypothesis using a recently derived, exact schemata evolution equation. We derive a new schema theorem based on the concept of effective fitness showing that schemata of higher than average effective fitness receive an exponentially increasing number of trials over time. The building block hypothesis is a natural consequence in that the equation shows how fit schemata are constructed from fit sub-schemata. However, we show that generically there is no preference for short, low-order schemata. In the case where schema reconstruction is favoured over schema destruction large schemata tend to be favoured. As a corollary of the evolution equation we prove Geiringer's theorem. We give supporting numerical evidence for our claims in both non-epsitatic and epistatic landscapes. e-mail: stephens@nuclecu.unam.mx y e-mail: hwael@nuclecu.unam.mx z e-mail: rosalia@nuclecu.unam.mx 1 Introduction A very large proportion of scientific end...

This paper aims to analyse the robustness of Genetic Algorithms (GA) technique for its application in the field of trading systems design for the Stock Exchange. The functioning of the GA is driven by the control parameters: crossover and mutation probabilities, number of generations, and size of population. Whether the results generated by the application of GA to a specific problem are conditioned by the value assess to these parameters, becomes a main research field. The purpose of this paper is to develop a sensibility analyses about the dependency of the GA to the value of these parameters. The sensibility analyses is developed in part by a hierarchic GA (a GA which is used to the optimisation of the control parameters of a second GA which is used to design the trading system). The results find that the GA is a very robustness technique when logical ranges are considered for these parameters (taken into account that there is a high level of complementation between them), with a wide optimisation capacity. 1.- GENETIC ALGORITHMS METHODOLOGY This paper aims to analyse the robustness of the GA technique for its application in the field of trading systems design for the Stock Exchange. At the same time, the optimisation power of the GA methodology will be tested.

We extend a recently developed exact schema based, or coarse grained, formulation of genetic dynamics [12, 13, 14] and its associated exact Schema theorem to an arbitrary selection scheme and a general crossover operator. We show that the intuitive“building block” interpretation of the former is preserved leading to hierarchical formal solutions of the equations that upon iteration lead to new results for the limiting distribution of a population in the case of 1-point crossover and “weak ” selection, where we define quantitatively “weak”. We also derive an exact, analytic form for the population distribution as a function of time for a flat landscape and 1-point crossover. 1

We extend a recently developed exact schema based, or coarse grained, formulation of genetic dynamics [12, 13, 14] and its associated exact Schema theorem to an arbitrary selection scheme and a general crossover operator. We show that the intuitive“building block” interpretation of the former is preserved leading to hierarchical formal solutions of the equations that upon iteration lead to new results for the limiting distribution of a population in the case of 1-point crossover and “weak ” selection, where we define quantitatively “weak”. We also derive an exact, analytic form for the population distribution as a function of time for a flat landscape and 1-point crossover. 1