1,792 research outputs found
CES-480 Covariant Parsimony Pressure for Genetic Programming
The parsimony pressure method is perhaps the simplest and most frequently used method to control bloat in genetic programming. In this paper we ?rst reconsider the size evolution equation for genetic programming developed in [24] and rewrite it in a form that shows its direct relationship to Price's theorem. We then use this new formulation to derive theoretical results that show how to practically and optimally set the parsimony coe?cient dynamically during a run so as to achieve complete control over the growth of the programs in a population. Experimental results con?rm the e?ectiveness of the method, as we are able to tightly control the average program size under a variety of conditions. These include such unusual cases as dynamically varying target sizes such that the mean program size is allowed to grow during some phases of a run, while being forced to shrink in others
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
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
Multiobjective parsimony enforcement for superior generalisation performance
Program Bloat - phenomenon of ever-increasing program size during a GP run - is a recognised and widespread problem. Traditional techniques to combat program bloat are program size limitations of parsimony pressure (penalty functions). These techniques suffer from a number of problems, in particular their reliance on parameters whose optimal values it is difficult to a priori determine. In this paper, we introduce POPE-GP, a system that makes use of the NSGA-II multiobjective evolutionary algorithm as an alternative, parameter-free technique for eliminating program bloat. We test it on a classification problem and find that while vastly reducing program size, it does improve generalisation performance
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
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