scholarly journals Genetic programming with separability detection for symbolic regression

2021 ◽  
Author(s):  
Wei-Li Liu ◽  
Jiaquan Yang ◽  
Jinghui Zhong ◽  
Shibin Wang
Keyword(s):  
Genetic Programming ◽  
Least Squares Method ◽  
Optimal Solution ◽  
Symbolic Regression ◽  
Final Solution ◽  
Intrinsic Structure ◽  
Regression Problem ◽  
Structure Information ◽  
Wide Range ◽  
Chromosome Representation

AbstractGenetic Programming (GP) is a popular and powerful evolutionary optimization algorithm that has a wide range of applications such as symbolic regression, classification and program synthesis. However, existing GPs often ignore the intrinsic structure of the ground truth equation of the symbolic regression problem. To improve the search efficacy of GP on symbolic regression problems by fully exploiting the intrinsic structure information, this paper proposes a genetic programming with separability detection technique (SD-GP). In the proposed SD-GP, a separability detection method is proposed to detect additive separable characteristics of input features from the observed data. Then based on the separability detection results, a chromosome representation is proposed, which utilizes multiple sub chromosomes to represent the final solution. Some sub chromosomes are used to construct separable sub functions by using separate input features, while the other sub chromosomes are used to construct sub functions by using all input features. The final solution is the weighted sum of all sub functions, and the optimal weights of sub functions are obtained by using the least squares method. In this way, the structure information can be learnt and the global search ability of GP can be maintained. Experimental results on synthetic problems with differing characteristics have demonstrated that the proposed SD-GP can perform better than several state-of-the-art GPs in terms of the success rate of finding the optimal solution and the convergence speed.

Competent Geometric Semantic Genetic Programming for Symbolic Regression and Boolean Function Synthesis

2018 ◽  
Vol 26 (2) ◽  
pp. 177-212 ◽  
Author(s):  
Tomasz P. Pawlak ◽  
Krzysztof Krawiec
Keyword(s):  
Genetic Programming ◽  
Boolean Function ◽  
Performance Indicators ◽  
Mate Selection ◽  
Semantic Space ◽  
Symbolic Regression ◽  
Test Set ◽  
Theoretical Rationale ◽  
Fitness Test ◽  
Wide Range

Program semantics is a promising recent research thread in Genetic Programming (GP). Over a dozen semantic-aware search, selection, and initialization operators for GP have been proposed to date. Some of these operators are designed to exploit the geometric properties of semantic space, while others focus on making offspring effective, that is, semantically different from their parents. Only a small fraction of previous works aimed at addressing both of these features simultaneously. In this article, we propose a suite of competent operators that combine effectiveness with geometry for population initialization, mate selection, mutation, and crossover. We present a theoretical rationale behind these operators and compare them experimentally to operators known from literature on symbolic regression and Boolean function synthesis benchmarks. We analyze each operator in isolation as well as verify how they fare together in an evolutionary run, concluding that the competent operators are superior on a wide range of performance indicators, including best-of-run fitness, test-set fitness, and program size.

scholarly journals Adjustment models for multivariate geodetic time series with vector-autoregressive errors

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Boris Kargoll ◽  
Alexander Dorndorf ◽  
Mohammad Omidalizarandi ◽  
Jens-André Paffenholz ◽  
Hamza Alkhatib
Keyword(s):  
Least Squares Method ◽  
Functional Model ◽  
Expectation Maximization Algorithm ◽  
Two Dimensions ◽  
Vector Autoregressive ◽  
Wide Range ◽  
Engineering Geodesy ◽  
Cross Correlations ◽  
T Distribution ◽  
Multivariate T

Abstract In this contribution, a vector-autoregressive (VAR) process with multivariate t-distributed random deviations is incorporated into the Gauss-Helmert model (GHM), resulting in an innovative adjustment model. This model is versatile since it allows for a wide range of functional models, unknown forms of auto- and cross-correlations, and outlier patterns. Subsequently, a computationally convenient iteratively reweighted least squares method based on an expectation maximization algorithm is derived in order to estimate the parameters of the functional model, the unknown coefficients of the VAR process, the cofactor matrix, and the degree of freedom of the t-distribution. The proposed method is validated in terms of its estimation bias and convergence behavior by means of a Monte Carlo simulation based on a GHM of a circle in two dimensions. The methodology is applied in two different fields of application within engineering geodesy: In the first scenario, the offset and linear drift of a noisy accelerometer are estimated based on a Gauss-Markov model with VAR and multivariate t-distributed errors, as a special case of the proposed GHM. In the second scenario real laser tracker measurements with outliers are adjusted to estimate the parameters of a sphere employing the proposed GHM with VAR and multivariate t-distributed errors. For both scenarios the estimated parameters of the fitted VAR model and multivariate t-distribution are analyzed for evidence of auto- or cross-correlations and deviation from a normal distribution regarding the measurement noise.

Simultaneous determination of thickness, thermal conductivity and porosity in textile material design

2016 ◽  
Vol 24 (1) ◽  
Author(s):  
Dinghua Xu ◽  
Peng Cui
Keyword(s):  
Thermal Conductivity ◽  
Human Body ◽  
Moisture Transfer ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Optimal Solution ◽  
Comfort Level ◽  
Textile Material ◽  
Heat And Moisture Transfer ◽  
Heat And Moisture

AbstractThe thickness, thermal conductivity and porosity of textile material are three key factors which determine the heat-moisture comfort level of the human body to a large extent based on the heat and moisture transfer process in the human body-clothing-environment system. This paper puts forward an Inverse Problem of Textile Thickness-Heat conductivity-Porosity Determination (IPT(THP)D) based on the steady-state model of heat and moisture transfer and the heat-moisture comfort indexes. Adopting the idea of the weighted least-squares method, we formulate IPT(THP)D into a function minimization problem. We employ the Particle Swarm Optimization (PSO) method to stochastically search the optimal solution of the objective function. We put the optimal solution into the corresponding direct problem to verify the effectiveness of the proposed numerical algorithms and the validity of the IPT(THP)D.

scholarly journals Control Synthesis as Machine Learning Control by Symbolic Regression Methods

2021 ◽  
Vol 11 (12) ◽  
pp. 5468
Author(s):  
Elizaveta Shmalko ◽  
Askhat Diveev
Keyword(s):  
Machine Learning ◽  
Genetic Programming ◽  
Mathematical Formulation ◽  
Small Variation ◽  
Learning Control ◽  
Symbolic Regression ◽  
Control Technique ◽  
Control Synthesis ◽  
Basic Solution ◽  
Regression Methods

The problem of control synthesis is considered as machine learning control. The paper proposes a mathematical formulation of machine learning control, discusses approaches of supervised and unsupervised learning by symbolic regression methods. The principle of small variation of the basic solution is presented to set up the neighbourhood of the search and to increase search efficiency of symbolic regression methods. Different symbolic regression methods such as genetic programming, network operator, Cartesian and binary genetic programming are presented in details. It is shown on the computational example the possibilities of symbolic regression methods as unsupervised machine learning control technique to the solution of MLC problem of control synthesis for obtaining the stabilization system for a mobile robot.

scholarly journals Temporal concatenation for Markov decision processes

2021 ◽  
pp. 1-28
Author(s):  
Ruiyang Song ◽  
Kuang Xu
Keyword(s):  
Markov Decision Processes ◽  
Large Scale ◽  
Optimal Solution ◽  
Upper Bounds ◽  
Black Box ◽  
Decision Processes ◽  
Optimal Solutions ◽  
Wide Range ◽  
Markov Decision ◽  
Speed Up

We propose and analyze a temporal concatenation heuristic for solving large-scale finite-horizon Markov decision processes (MDP), which divides the MDP into smaller sub-problems along the time horizon and generates an overall solution by simply concatenating the optimal solutions from these sub-problems. As a “black box” architecture, temporal concatenation works with a wide range of existing MDP algorithms. Our main results characterize the regret of temporal concatenation compared to the optimal solution. We provide upper bounds for general MDP instances, as well as a family of MDP instances in which the upper bounds are shown to be tight. Together, our results demonstrate temporal concatenation's potential of substantial speed-up at the expense of some performance degradation.

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