A Probabilistic Linear Genetic Programming with Stochastic Context-Free Grammar for solving Symbolic Regression problems

Traditional Linear Genetic Programming (LGP) algorithms are based only on the selection mechanism to guide the search. Genetic operators combine or mutate random portions of the individuals, without knowing if the result will lead to a fitter individual. Probabilistic Model Building Genetic Programming (PMB-GP) methods were proposed to overcome this issue through a probability model that captures the structure of the fit individuals and use it to sample new individuals. This work proposes the use of LGP with a Stochastic Context-Free Grammar (SCFG), that has a probability distribution that is updated according to selected individuals. We proposed a method for adapting the grammar into the linear representation of LGP. Tests performed with the proposed probabilistic method, and with two hybrid approaches, on several symbolic regression benchmark problems show that the results are statistically better than the obtained by the traditional LGP.Comment: Genetic and Evolutionary Computation Conference (GECCO) 2017, Berlin, German

Study on probabilistic model building genetic network programming

制度:新 ; 報告番号:甲3776号 ; 学位の種類:博士(工学) ; 授与年月日:2013/3/15 ; 早大学位記番号:新6149Waseda Universit

Surrogate probabilistic seismic demand modelling of inelastic single-degree-of-freedom systems for efficient earthquake risk applications

This paper proposes surrogate models (or metamodels) mapping the parameters controlling the dynamic behaviour of inelastic single-degree-of-freedom (SDoF) systems (i.e., force-displacement capacity curve, hysteretic behaviour) and the parameters of their probabilistic seismic demand model (PSDM, i.e., conditional distribution of an engineering demand parameter [EDP] given a ground-motion intensity measure [IM]). These metamodels allow the rapid derivation of fragility curves of SDoF representation of structures. Gaussian Process (GP) regression is selected as the metamodelling approach because of their flexibility in implementation, the resulting accuracy and computational efficiency. The metamodel training dataset includes 10,000 SDoF systems analysed via cloud-based non-linear time-history analysis (NLTHA) using recorded ground motions. The proposed GP regressions are tested in predicting the PSDM of both the SDoF database (through ten-fold cross validation) and eight realistic reinforced concrete (RC) frames, benchmarking the results against NLTHA. An application is conducted to propagate such modelling uncertainty to both fragility and vulnerability/loss estimations. Error levels are deemed satisfactory for practical applications, especially considering the low required modelling effort and analysis time. Regarding single-building applications enabled by the proposed metamodel, this paper presents a first attempt at a direct loss-based design procedure, which allows setting a target loss level for the designed structure (shown for a realistic RC frame). An earthquake risk model involving dynamic exposure and vulnerability modules is illustrated as an example of building portfolio applications. Specifically, the proposed application considers a retrofit-based seismic risk-reduction policy for a synthetic building portfolio, for which it is possible estimating the loss evolution over time

CES-479 A Linear Estimation-of-Distribution GP System

We present N-gram GP, an estimation of distribution algorithm for the evolution of linear computer programs. The algorithm learns and samples the joint probability distribution of triplets of instructions (or 3-grams) at the same time as it is learning and sampling a program length distribution. We have tested N-gram GP on symbolic regressions problems where the target function is a polynomial of up to degree 12 and lawn-mower problems with lawn sizes of up to 12 ? 12. Results show that the algorithm is e?ective and scales better on these problems than either linear GP or simple stochastic hill-climbing

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

Learning Computer Programs with the Bayesian Optimization Algorithm

The hierarchical Bayesian Optimization Algorithm (hBOA) [24, 25] learns bit-strings by constructing explicit centralized models of a population and using them to generate new instances. This thesis is concerned with extending hBOA to learning open-ended program trees. The new system, BOA programming (BOAP), improves on previous probabilistic model building GP systems (PMBGPs) in terms of the expressiveness and open-ended flexibility of the models learned, and hence control over the distribution of individuals generated. BOAP is studied empirically on a toy problem (learning linear functions) in various configurations, and further experimental results are presented for two real-world problems: prediction of sunspot time series, and human gene function inference

A hybrid computational approach for seismic energy demand prediction

In this paper, a hybrid genetic programming (GP) with multiple genes is implemented for developing prediction models of spectral energy demands. A multi-objective strategy is used for maximizing the accuracy and minimizing the complexity of the models. Both structural properties and earthquake characteristics are considered in prediction models of four demand parameters. Here, the earthquake records are classified based on soil type assuming that different soil classes have linear relationships in terms of GP genes. Therefore, linear regression analysis is used to connect genes for different soil types, which results in a total of sixteen prediction models. The accuracy and effectiveness of these models were assessed using different performance metrics and their performance was compared with several other models. The results indicate that not only the proposed models are simple, but also they outperform other spectral energy demand models proposed in the literature

Competent Program Evolution, Doctoral Dissertation, December 2006

Heuristic optimization methods are adaptive when they sample problem solutions based on knowledge of the search space gathered from past sampling. Recently, competent evolutionary optimization methods have been developed that adapt via probabilistic modeling of the search space. However, their effectiveness requires the existence of a compact problem decomposition in terms of prespecified solution parameters. How can we use these techniques to effectively and reliably solve program learning problems, given that program spaces will rarely have compact decompositions? One method is to manually build a problem-specific representation that is more tractable than the general space. But can this process be automated? My thesis is that the properties of programs and program spaces can be leveraged as inductive bias to reduce the burden of manual representation-building, leading to competent program evolution. The central contributions of this dissertation are a synthesis of the requirements for competent program evolution, and the design of a procedure, meta-optimizing semantic evolutionary search (MOSES), that meets these requirements. In support of my thesis, experimental results are provided to analyze and verify the effectiveness of MOSES, demonstrating scalability and real-world applicability

Direct loss-based seismic design of reinforced concrete frame and wall structures

This paper presents a procedure to design reinforced concrete (RC) buildings to achieve an acceptable target level of earthquake-induced loss (e.g., deaths, dollars, downtime) under a site-specific hazard profile. The procedure is called “direct” since the target loss level is specified at the first step of the process, and virtually no iteration is required. The procedure is based on a simplified loss assessment involving a surrogate model for the seismic demand (i.e., probability distribution of peak horizontal deformation given ground-motion intensity) and simplified loss models for direct and indirect losses. For an arbitrarily-selected target loss level and structural geometry, the procedure provides the force-displacement curve of the corresponding equivalent single degree of freedom system. The principles of displacement-based design are adopted to provide member detailings (beams, columns, walls) consistent with such force-displacement curve. The procedure is applied to 16 realistic RC case studies with a lateral resisting system composed of frames in one direction and cantilever walls in the perpendicular one. They show different geometries, hazard profiles, and target values of direct economic expected annual loss. A benchmark loss estimation is obtained using cloud-based non-linear time-history analyses of multi-degree of freedom models. The procedure is conservative since the benchmark loss levels are always smaller than the targets. Such discrepancy is within 10% for 12 out of 32 case studies, between 10% and 20% for 13, between 20% and 31% for the remaining six. Therefore, the proposed procedure is deemed dependable for preliminary design