Genetic programming: on the programming of computers by means of natural selection
Genetic programming: on the programming of computers by means of natural selection
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
The Use of Neutral Genotype-Phenotype Mappings for Improved Evolutionary Search
BT Technology Journal
Numeric Mutation as an Improvement to Symbolic Regression in Genetic Programming
EP '98 Proceedings of the 7th International Conference on Evolutionary Programming VII
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)
Representations for Genetic and Evolutionary Algorithms
Representations for Genetic and Evolutionary Algorithms
Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence (Studies in Computational Intelligence)
Using gene expression programming to construct sentence ranking functions for text summarization
COLING '04 Proceedings of the 20th international conference on Computational Linguistics
Self-emergence of structures in gene expression programming
Self-emergence of structures in gene expression programming
Improving Gene Expression Programming Performance by Using Differential Evolution
ICMLA '07 Proceedings of the Sixth International Conference on Machine Learning and Applications
Improving symbolic regression with interval arithmetic and linear scaling
EuroGP'03 Proceedings of the 6th European conference on Genetic programming
Analysis of a digit concatenation approach to constant creation
EuroGP'03 Proceedings of the 6th European conference on Genetic programming
An analysis of diversity of constants of genetic programming
EuroGP'03 Proceedings of the 6th European conference on Genetic programming
Evolving accurate and compact classification rules with gene expression programming
IEEE Transactions on Evolutionary Computation
Symbolic regression using nearest neighbor indexing
Proceedings of the 12th annual conference companion on Genetic and evolutionary computation
Artificial bee colony programming for symbolic regression
Information Sciences: an International Journal
Differential evolution of constants in genetic programming improves efficacy and bloat
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Solving the unknown complexity formula problem with genetic programming
IWANN'13 Proceedings of the 12th international conference on Artificial Neural Networks: advances in computational intelligence - Volume Part I
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One problem that has plagued Genetic Programming (GP) and its derivatives is numerical constant creation. Given a mathematical formula expressed as a tree structure, the leaf nodes are either variables or constants. Such constants are usually unknown in Symbolic Regression (SR) problems, and GP, as well as many of its derivatives, lack the ability to precisely approximate these values. This is due to the inherently discrete encoding of GP-like methods which are more suited to combinatorial searches than real-valued optimization tasks. Previously, several attempts have been made to resolve this issue, and the dominant solutions have been to either embed a real-valued local optimizer or to develop additional numerically oriented operators. In this paper, an entirely new approach is proposed for constant creation. Through the adoption of a robust, real-valued optimization algorithm known as Differential Evolution (DE), constants and GP-like programs will be simultaneously evolved in such a way that the values of the leaf nodes will be approximated as the tree structure is itself changing. Experimental results from several SR benchmarks are presented and analyzed. The results demonstrate the feasibility of the proposed algorithm and suggest that exotic or computationally expensive methods are not necessary for successful constant creation.