Genetic programming: on the programming of computers by means of natural selection
Genetic programming: on the programming of computers by means of natural selection
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Improving Gene Expression Programming Performance by Using Differential Evolution
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Genetic Algorithms and Genetic Programming: Modern Concepts and Practical Applications
Genetic Algorithms and Genetic Programming: Modern Concepts and Practical Applications
Evolution Strategies for Constants Optimization in Genetic Programming
ICTAI '09 Proceedings of the 2009 21st IEEE International Conference on Tools with Artificial Intelligence
Improving symbolic regression with interval arithmetic and linear scaling
EuroGP'03 Proceedings of the 6th European conference on Genetic programming
A simple but theoretically-motivated method to control bloat in genetic programming
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
Proceedings of the 13th annual conference companion on Genetic and evolutionary computation
Two fast tree-creation algorithms for genetic programming
IEEE Transactions on Evolutionary Computation
Random sampling technique for overfitting control in genetic programming
EuroGP'12 Proceedings of the 15th European conference on Genetic Programming
Differential evolution of constants in genetic programming improves efficacy and bloat
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Better GP benchmarks: community survey results and proposals
Genetic Programming and Evolvable Machines
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In this publication a constant optimization approach for symbolic regression is introduced to separate the task of finding the correct model structure from the necessity to evolve the correct numerical constants. A gradient-based nonlinear least squares optimization algorithm, the Levenberg-Marquardt (LM) algorithm, is used for adjusting constant values in symbolic expression trees during their evolution. The LM algorithm depends on gradient information consisting of partial derivations of the trees, which are obtained by automatic differentiation. The presented constant optimization approach is tested on several benchmark problems and compared to a standard genetic programming algorithm to show its effectiveness. Although the constant optimization involves an overhead regarding the execution time, the achieved accuracy increases significantly as well as the ability of genetic programming to learn from provided data. As an example, the Pagie-1 problem could be solved in 37 out of 50 test runs, whereas without constant optimization it was solved in only 10 runs. Furthermore, different configurations of the constant optimization approach (number of iterations, probability of applying constant optimization) are evaluated and their impact is detailed in the results section.