15 research outputs found
The influence of mutation on population dynamics in multiobjective genetic programming
Using multiobjective genetic programming with a complexity objective to overcome tree bloat is usually very successful but can sometimes lead to undesirable collapse of the population to all single-node trees. In this paper we report a detailed examination of why and when collapse occurs. We have used different types of crossover and mutation operators (depth-fair and sub-tree), different evolutionary approaches (generational and steady-state), and different datasets (6-parity Boolean and a range of benchmark machine learning problems) to strengthen our conclusion. We conclude that mutation has a vital role in preventing population collapse by counterbalancing parsimony pressure and preserving population diversity. Also, mutation controls the size of the generated individuals which tends to dominate the time needed for fitness evaluation and therefore the whole evolutionary process. Further, the average size of the individuals in a GP population depends on the evolutionary approach employed. We also demonstrate that mutation has a wider role than merely culling single-node individuals from the population; even within a diversity-preserving algorithm such as SPEA2 mutation has a role in preserving diversity
Slightly beyond Turing-Computability for studying Genetic Programming
International audienceInspired by genetic programming (GP), we study iterative algorithms for non-computable tasks and compare them to naive models. This framework justifies many practical standard tricks from GP and also provides complexity lower-bounds which justify the computational cost of GP thanks to the use of Kolmogorov's complexity in bounded time
A Statistical Learning Theory Approach of Bloat
Code bloat, the excessive increase of code size, is an important is- sue in Genetic Programming (GP). This paper proposes a theoreti- cal analysis of code bloat in the framework of symbolic regression in GP, from the viewpoint of Statistical Learning Theory, a well grounded mathematical toolbox for Machine Learning. Two kinds of bloat must be distinguished in that context, depending whether the target function lies in the search space or not. Then, important mathematical results are proved using classical results from Sta- tistical Learning. Namely, the Vapnik-Cervonenkis dimension of programs is computed, and further results from Statistical Learn- ing allow to prove that a parsimonious fitness ensures Universal Consistency (the solution minimizing the empirical error does con- verge to the best possible error when the number of samples goes to infinity). However, it is proved that the standard method consisting in choosing a maximal program size depending on the number of samples might still result in programs of infinitely increasing size whith their accuracy; a more complicated modification of the fit- ness is proposed that theoretically avoids unnecessary bloat while nevertheless preserving the Universal Consistency
Why Simulation-Based Approachs with Combined Fitness are a Good Approach for Mining Spaces of Turing-equivalent Functions
We show negative results about the automatic generation of programs within bounded-time. Combining recursion theory and statistics, we contrast these negative results with positive computability results for iterative approachs like genetic programming, provided that the fitness combines e.g. fastness and size. We then show that simulation-based approachs (approachs evaluating only by simulation the quality of programs) like GP are not too far from the minimal time required for evaluating these combined fitnesses
Universal Consistency and Bloat in GP
In this paper, we provide an analysis of Genetic Programming (GP) from the Statistical Learning Theory viewpoint in the scope of symbolic regression. Firstly, we are interested in Universal Consistency, i.e. the fact that the solution minimizing the empirical error does converge to the best possible error when the number of examples goes to infinity, and secondly, we focus our attention on the uncontrolled growth of program length (i.e. bloat), which is a well-known problem in GP. Results show that (1) several kinds of code bloats may be identified and that (2) Universal consistency can be obtained as well as avoiding bloat under some con- ditions. We conclude by describing an ad hoc method that makes it possible simultaneously to avoid bloat and to ensure universal consistency
Apprentissage statistique et programmation génétique: la croissance du code est-elle inévitable ?
Universal Consistency, the convergence to the minimum possible error rate in learning through genetic programming (GP), and Code bloat, the excessive increase of code size, are important issues in GP. This paper proposes a theoretical analysis of universal consistency and code bloat in the framework of symbolic regression in GP, from the viewpoint of Statistical Learning Theory, a well grounded mathematical toolbox for Machine Learning. Two kinds of bloat must be distinguished in that context, depending whether the target function has finite description length or not. Then, the Vapnik-Chervonenkis dimension of programs is computed, and we prove that a parsimonious fitness ensures Universal Consistency (i.e. the fact that the solution minimizing the empirical error does converge to the best possible error when the number of examples goes to infinity). However, it is proved that the standard method consisting in choosing a maximal program size depending on the number of examples might still result in programs of infinitely increasing size with their accuracy; a fitness biased by parsimony pressure is proposed. This fitness avoids unnecessary bloat while nevertheless preserving the Universal Consistency
A Field Guide to Genetic Programming
xiv, 233 p. : il. ; 23 cm.Libro ElectrónicoA Field Guide to Genetic Programming (ISBN 978-1-4092-0073-4) is an introduction to genetic programming (GP). GP is a systematic, domain-independent method for getting computers to solve problems automatically starting from a high-level statement of what needs to be done. Using ideas from natural evolution, GP starts from an ooze of random computer programs, and progressively refines them through processes of mutation and sexual recombination, until solutions emerge. All this without the user having to know or specify the form or structure of solutions in advance. GP has generated a plethora of human-competitive results and applications, including novel scientific discoveries and patentable inventions. The authorsIntroduction --
Representation, initialisation and operators in Tree-based GP --
Getting ready to run genetic programming --
Example genetic programming run --
Alternative initialisations and operators in Tree-based GP --
Modular, grammatical and developmental Tree-based GP --
Linear and graph genetic programming --
Probalistic genetic programming --
Multi-objective genetic programming --
Fast and distributed genetic programming --
GP theory and its applications --
Applications --
Troubleshooting GP --
Conclusions.Contents
xi
1 Introduction
1.1 Genetic Programming in a Nutshell
1.2 Getting Started
1.3 Prerequisites
1.4 Overview of this Field Guide I
Basics
2 Representation, Initialisation and GP
2.1 Representation
2.2 Initialising the Population
2.3 Selection
2.4 Recombination and Mutation Operators in Tree-based
3 Getting Ready to Run Genetic Programming 19
3.1 Step 1: Terminal Set 19
3.2 Step 2: Function Set 20
3.2.1 Closure 21
3.2.2 Sufficiency 23
3.2.3 Evolving Structures other than Programs 23
3.3 Step 3: Fitness Function 24
3.4 Step 4: GP Parameters 26
3.5 Step 5: Termination and solution designation 27
4 Example Genetic Programming Run
4.1 Preparatory Steps 29
4.2 Step-by-Step Sample Run 31
4.2.1 Initialisation 31
4.2.2 Fitness Evaluation Selection, Crossover and Mutation Termination and Solution Designation Advanced Genetic Programming
5 Alternative Initialisations and Operators in
5.1 Constructing the Initial Population
5.1.1 Uniform Initialisation
5.1.2 Initialisation may Affect Bloat
5.1.3 Seeding
5.2 GP Mutation
5.2.1 Is Mutation Necessary?
5.2.2 Mutation Cookbook
5.3 GP Crossover
5.4 Other Techniques 32
5.5 Tree-based GP 39
6 Modular, Grammatical and Developmental Tree-based GP 47
6.1 Evolving Modular and Hierarchical Structures 47
6.1.1 Automatically Defined Functions 48
6.1.2 Program Architecture and Architecture-Altering 50
6.2 Constraining Structures 51
6.2.1 Enforcing Particular Structures 52
6.2.2 Strongly Typed GP 52
6.2.3 Grammar-based Constraints 53
6.2.4 Constraints and Bias 55
6.3 Developmental Genetic Programming 57
6.4 Strongly Typed Autoconstructive GP with PushGP 59
7 Linear and Graph Genetic Programming 61
7.1 Linear Genetic Programming 61
7.1.1 Motivations 61
7.1.2 Linear GP Representations 62
7.1.3 Linear GP Operators 64
7.2 Graph-Based Genetic Programming 65
7.2.1 Parallel Distributed GP (PDGP) 65
7.2.2 PADO 67
7.2.3 Cartesian GP 67
7.2.4 Evolving Parallel Programs using Indirect Encodings 68
8 Probabilistic Genetic Programming
8.1 Estimation of Distribution Algorithms 69
8.2 Pure EDA GP 71
8.3 Mixing Grammars and Probabilities 74
9 Multi-objective Genetic Programming 75
9.1 Combining Multiple Objectives into a Scalar Fitness Function 75
9.2 Keeping the Objectives Separate 76
9.2.1 Multi-objective Bloat and Complexity Control 77
9.2.2 Other Objectives 78
9.2.3 Non-Pareto Criteria 80
9.3 Multiple Objectives via Dynamic and Staged Fitness Functions 80
9.4 Multi-objective Optimisation via Operator Bias 81
10 Fast and Distributed Genetic Programming 83
10.1 Reducing Fitness Evaluations/Increasing their Effectiveness 83
10.2 Reducing Cost of Fitness with Caches 86
10.3 Parallel and Distributed GP are Not Equivalent 88
10.4 Running GP on Parallel Hardware 89
10.4.1 Master–slave GP 89
10.4.2 GP Running on GPUs 90
10.4.3 GP on FPGAs 92
10.4.4 Sub-machine-code GP 93
10.5 Geographically Distributed GP 93
11 GP Theory and its Applications 97
11.1 Mathematical Models 98
11.2 Search Spaces 99
11.3 Bloat 101
11.3.1 Bloat in Theory 101
11.3.2 Bloat Control in Practice 104
III
Practical Genetic Programming
12 Applications
12.1 Where GP has Done Well
12.2 Curve Fitting, Data Modelling and Symbolic Regression
12.3 Human Competitive Results – the Humies
12.4 Image and Signal Processing
12.5 Financial Trading, Time Series, and Economic Modelling
12.6 Industrial Process Control
12.7 Medicine, Biology and Bioinformatics
12.8 GP to Create Searchers and Solvers – Hyper-heuristics xiii
12.9 Entertainment and Computer Games 127
12.10The Arts 127
12.11Compression 128
13 Troubleshooting GP
13.1 Is there a Bug in the Code?
13.2 Can you Trust your Results?
13.3 There are No Silver Bullets
13.4 Small Changes can have Big Effects
13.5 Big Changes can have No Effect
13.6 Study your Populations
13.7 Encourage Diversity
13.8 Embrace Approximation
13.9 Control Bloat
13.10 Checkpoint Results
13.11 Report Well
13.12 Convince your Customers
14 Conclusions
Tricks of the Trade
A Resources
A.1 Key Books
A.2 Key Journals
A.3 Key International Meetings
A.4 GP Implementations
A.5 On-Line Resources 145
B TinyGP 151
B.1 Overview of TinyGP 151
B.2 Input Data Files for TinyGP 153
B.3 Source Code 154
B.4 Compiling and Running TinyGP 162
Bibliography 167
Inde
Proposta de um algoritmo de programaçao genética baseado em estratégias evolucionárias
Orientadora: Aurora Trinidad Ramirez PozoDissertaçao (mestrado) - Universidade Federal do Paraná, Setor de Ciencias Exatas, Programa de Pós-Graduaçao em Informática. Defesa: Curitiba, 2006Inclui bibliografiaResumo: Este trabalho apresenta uma nova abordagem para a indu¸c˜ao de programas pela Programa ¸c˜ao Gen'etica (PG) utilizando as id'eias das Estrat'egias Evolucion'arias (ES). A meta deste trabalho 'e desenvolver uma varia¸c˜ao do algoritmo de Programa¸c˜ao Gen'etica, realizando altera¸c˜oes no algoritmo cl'assico e adicionando conceitos da teoria das estratégias
Evolucion'arias. A abordagem proposta 'e avaliada utilizando problemas de dois dom'ýnios diferentes: Problemas de Regress˜ao Simb'olica e o Problema da Formiga (Santa Fe Artificial Ant). Dentre os problemas de Regress˜ao Simb'olica, s˜ao estudados os problemas Binomial–3, que caracteriza-se como um problema de dificuldade ajust'avel; S'eries Temporais e Modelagem da Confiabilidade de Software. Os resultados obtidos s˜ao comparados com os resultados obtidos com a PG cl'assica. Para os problemas de Regress˜ao Simb'olica obteve-se excelentes resultados e um melhoramento de desempenho significativo foi atingido, entretanto isto n˜ao aconteceu com o problema Santa Fe Artificial An