Solving symbolic regression problems with formal constraints

2019 ◽  
Author(s):  
Iwo Błądek ◽  
Krzysztof Krawiec
Keyword(s):  
Symbolic Regression ◽  
Regression Problems ◽  
Formal Constraints

scholarly journals A NEW LINEAR GENETIC PROGRAMMING APPROACH BASED ON STRAIGHT LINE PROGRAMS: SOME THEORETICAL AND EXPERIMENTAL ASPECTS

2009 ◽  
Vol 18 (05) ◽  
pp. 757-781 ◽  
Author(s):  
CÉSAR L. ALONSO ◽  
JOSÉ LUIS MONTAÑA ◽  
JORGE PUENTE ◽  
CRUZ ENRIQUE BORGES
Keyword(s):  
Data Structure ◽  
Genetic Programming ◽  
Computer Programs ◽  
Symbolic Regression ◽  
Programming Approach ◽  
Linear Genetic Programming ◽  
Straight Line ◽  
Structured Representations ◽  
Regression Problems ◽  
Straight Line Programs

Tree encodings of programs are well known for their representative power and are used very often in Genetic Programming. In this paper we experiment with a new data structure, named straight line program (slp), to represent computer programs. The main features of this structure are described, new recombination operators for GP related to slp's are introduced and a study of the Vapnik-Chervonenkis dimension of families of slp's is done. Experiments have been performed on symbolic regression problems. Results are encouraging and suggest that the GP approach based on slp's consistently outperforms conventional GP based on tree structured representations.

scholarly journals Shape-constrained Symbolic Regression – Improving Extrapolation with Prior Knowledge

2021 ◽  
pp. 1-24
Author(s):  
G. Kronberger ◽  
F. O. de Franca ◽  
B. Burlacu ◽  
C. Haider ◽  
M. Kommenda
Keyword(s):  
Evolutionary Algorithms ◽  
Prior Knowledge ◽  
Polynomial Regression ◽  
Predictive Accuracy ◽  
Symbolic Regression ◽  
Training Set ◽  
Test Set ◽  
Regression Algorithms ◽  
Selection Step ◽  
Regression Problems

Abstract We investigate the addition of constraints on the function image and its derivatives for the incorporation of prior knowledge in symbolic regression. The approach is called shape-constrained symbolic regression and allows us to enforce e.g. monotonicity of the function over selected inputs. The aim is to find models which conform to expected behaviour and which have improved extrapolation capabilities. We demonstrate the feasibility of the idea and propose and compare two evolutionary algorithms for shapeconstrained symbolic regression: i) an extension of tree-based genetic programming which discards infeasible solutions in the selection step, and ii) a two population evolutionary algorithm that separates the feasible from the infeasible solutions. In both algorithms we use interval arithmetic to approximate bounds for models and their partial derivatives. The algorithms are tested on a set of 19 synthetic and four real-world regression problems. Both algorithms are able to identify models which conform to shape constraints which is not the case for the unmodified symbolic regression algorithms. However, the predictive accuracy of models with constraints is worse on the training set and the test set. Shape-constrained polynomial regression produces the best results for the test set but also significantly larger models.

An improved Gene Expression Programming approach for symbolic regression problems

2014 ◽  
Vol 137 ◽  
pp. 293-301 ◽  
Author(s):  
YuZhong Peng ◽  
ChangAn Yuan ◽  
Xiao Qin ◽  
JiangTao Huang ◽  
YaBing Shi
Keyword(s):  
Gene Expression ◽  
Gene Expression Programming ◽  
Symbolic Regression ◽  
Programming Approach ◽  
Regression Problems

scholarly journals A Study On Financial Time Series Forecasting And Symbolic Regression By Means Of A Hybrid Probabilistic Model-Building Cartesian Genetic Programming Methodology

2021 ◽  
Author(s):  
Mahsa Mostowfi
Keyword(s):  
Time Series ◽  
Stock Market ◽  
Genetic Programming ◽  
Probabilistic Model ◽  
Stock Price ◽  
Model Building ◽  
Symbolic Regression ◽  
Time Series Forecasting ◽  
Fusion Model ◽  
Regression Problems

This work proposes a hybrid algorithm called Probabilistic Incremental Cartesian Genetic Pro- gramming (PI-CGP), which integrates an Estimation of Distribution Algorithm (EDA) with Carte- sian Genetic Programming (CGP). PI-CGP uses a fixed-length problem representation and the algorithm constructs a probabilistic model of promising solutions. PI-CGP was evaluated on sym- bolic regression problems and next trading day stock price forecasting. On the symbolic regression problems PI-CGP did not outperform other approaches. The reason could be premature convergence and being trapped at a local minimum. However, PI-CGP was competitive at stock market forecasting. It was comparable to a fusion model employing a Hidden Markov Model (HMM). HMMs are extensively used for time-series forecasting. This result is promising considering the volatile nature of the stock market and that PI-CGP was not customized toward forecasting.

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