One serious problem of standard Genetic Programming (GP) is that evolved structures appear to drift towards large and slow forms on average. This paper presents a novel analysis of the role played by variable complexity in the selection and survival of GP expressions. It defines a particular property of GP representations, called rooted tree-schema, that sheds light on the role of variable complexity of evolved structures. A rooted tree-schema is a relation on the space of tree-shaped structures which provides a quantifiable partitioning of the search space. The paper analyzes the influence of parsimony pressure on selection and growth of structures. Experimental evidence confirms theoretical predictions. 1 Introduction Genetic programming (GP) uses open-ended complexity representations of flexible semantics (Koza1992). GP evolves a population of expressions in some problem dependent language that encode problem solutions. Evolved expressions are tree structured and can be interpret...

Two important problems in genetic programming (GP) are its tendency to find unnecessarily large trees (bloat), and the general evolutionary algorithms problem that diversity in the population can be lost prematurely. The prevention of these problems is frequently an implicit goal of basic GP. We explore the potential of techniques from multi-objective optimization to aid GP by adding explicit objectives to avoid bloat and promote diversity. The even 3, 4, and 5-parity problems were solved efficiently compared to basic GP results from the literature. Even though only non-dominated individuals were selected and populations thus remained extremely small, appropriate diversity was maintained. The size of individuals visited during search consistently remained small, and solutions of what we believe to be the minimum size were found for the 3, 4, and 5-parity problems.

Parsimony pressure, the explicit penalization of larger programs, has been increasingly used as a means of controlling code growth in genetic programming. However, in many cases parsimony pressure degrades the performance of the genetic program. In this paper we show that poor average results with parsimony pressure are a result of "failed" populations that overshadow the results of populations that incorporate parsimony pressure successfully. Additionally, we show that the effect of parsimony pressure can be measured by calculating the relationship between program size and performance within the population. This measure can be used as a partial indicator of success or failure for individual populations. Keywords Code growth, code bloat, parsimony, genetic programming, introns. 1. Introduction The use of parsimony pressure as a means of controlling the size of programs generated with genetic programming (GP) has grown considerably in recent years. In many cases parsimony pr...

Evolutionary computation (EC) consists of the design and analysis of probabilistic algorithms inspired by the principles of natural selection and variation. Genetic Programming (GP) is one subfield of EC that emphasizes desirable features such as the use of procedural representations, the capability to discover and exploit intrinsic characteristics of the application domain, and the flexibility to adapt the shape and complexity of learned models. Approaches that learn monolithic representations are considerably less likely to be effective for complex problems, and standard GP is no exception. The main goal of this dissertation is to extend GP capabilities with automatic mechanisms to cope with problems of increasing complexity. Humans succeed here by skillfully using hierarchical decomposition and abstraction mechanisms. The translation of such mechanisms into a general computer implementation is a tremendous challenge, which requires a firm understanding of the interplay between repr...

In this paper we introduce experiments on neuro-evolution mechanisms applied to predator /prey multi-character computer games. Our test-bed is a modified version of the well-known Pac-Man game. By viewing the game from the predators' (i.e. opponents') perspective, we attempt o#-line to evolve neural-controlled opponents capable of playing e#ectively against computer-guided fixed strategy players. However, emergent near-optimal behaviors make the game less interesting to play. We therefore discuss the criteria that make a game interesting and, furthermore, we introduce a generic measure of predator/prey computer games' interest. Computer

Genetic programming trees have a strong tendency to grow rapidly and relatively independent of fitness, a serious flaw which has received considerable attention in the genetic programming literature. Much of this literature has implicated introns, subtree structures with no effect on the an individual's fitness assessment. The propagation of inviable code, a certain kind of intron, has been especially linked to tree growth. However this paper presents evidence which shows that denying inviable code the opportunity to propagate actually increases tree growth. The paper argues that rather than causing tree growth, a rise in inviable code is in fact an expected result of tree growth. Lastly, this paper proposes a more general theory of growth for which introns are merely a symptom. 1 INTRODUCTION An unforseen result of genetic programming's tree-based chromosome is bloat, the uncontrolled growth in the size of individuals over the course of a run. This phenomenon has bee...

One serious problem of standard Genetic Programming (GP) is that evolved expressions appear to drift towards large and slow forms on average. This report presents a novel analysis of the role played by variable complexity in the selection and survival of GP expressions. It defines a particular property of GP representations, called rooted tree-schema, that sheds light on the role of variable complexity of evolved representations. A tree-schema is a relation on the space of tree-shaped structures which provides a quantifiable partitioning of the search space. The present analysis answers questions such as: What role does variable complexity play in the selection and survival of evolved expressions? What is the influence of a parsimony penalty? How heavy should parsimony penalty be weighted or how should it be adapted in order to preserve the underlying optimization process? Are there alternative approaches to simulating a parsimony penalty that do not result in a change of the fitness l...

Pac-Man is a well-known, real-time computer game that provides an interesting platform for research. This paper describes an initial approach to developing an artificial agent that replaces the human to play a simplified version of Pac-Man. The agent is specified as a simple finite state machine and ruleset, with parameters that control the probability of movement by the agent given the constraints of the maze at some instant of time. In contrast to previous approaches, the agent represents a dynamic strategy for playing Pac-Man, rather than a pre-programmed maze-solving method. The agent adaptively "learns" through the application of population-based incremental learning (PBIL) to adjust the agents' parameters. Experimental results are presented that give insight into some of the complexities of the game, as well as highlighting the limitations and difficulties of the representation of the agent.

Variable length methods for evolutionary computation can lead to a progressive and mainly unnecessary growth of individuals, known as bloat. First, we propose to measure performance in genetic programming as a function of the number of nodes, rather than trees, that have been evaluated. Evolutionary Multi-Objective Optimization (EMOO) constitutes a principled way to optimize both size and fitness and may provide parameterless size control. Reportedly, its use can also lead to minimization of size at the expense of fitness. We replicate this problem, and an empirical analysis suggests that multi-objective size control particularly requires diversity maintenance. Experiments support this explanation. The multi-

Using deliberately designed primitive sets, we investigate the relationship between context-based expression mechanisms and the size, height and density of genetic program trees during the evolutionary process. We show that contextual semantics influence the composition, location and flows of operative code in a program. In detail we analyze these dynamics and discuss the impact of our findings on micro-level descriptions of genetic programming.