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Problem Difficulty and Code Growth in Genetic Programming
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Evolutionary Computation
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Evolutionary Computation
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GECCO '96 Proceedings of the 1st annual conference on Genetic and evolutionary computation
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EuroGP'03 Proceedings of the 6th European conference on Genetic programming
The root causes of code growth in genetic programming
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Crossover bias in genetic programming
EuroGP'07 Proceedings of the 10th European conference on Genetic programming
On the limiting distribution of program sizes in tree-based genetic programming
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IEEE Transactions on Evolutionary Computation
Performance assessment of multiobjective optimizers: an analysis and review
IEEE Transactions on Evolutionary Computation
Evolutionary Model Type Selection for Global Surrogate Modeling
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Open issues in genetic programming
Genetic Programming and Evolvable Machines
Nonlinear regression model generation using hyperparameter optimization
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LION'10 Proceedings of the 4th international conference on Learning and intelligent optimization
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Drawing boundaries: using individual evolved class boundaries for binary classification problems
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Random sampling technique for overfitting control in genetic programming
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A library to run evolutionary algorithms in the cloud using mapreduce
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The Journal of Machine Learning Research
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This paper presents a novel approach to generate data-driven regression models that not only give reliable prediction of the observed data but also have smoother response surfaces and extra generalization capabilities with respect to extrapolation. These models are obtained as solutions of a genetic programming (GP) process, where selection is guided by a tradeoff between two competing objectives--numerical accuracy and the order of nonlinearity. The latter is a novel complexity measure that adopts the notion of the minimal degree of the best-fit polynomial, approximating an analytical function with a certain precision. Using nine regression problems, this paper presents and illustrates two different strategies for the use of the order of nonlinearity in symbolic regression via GP. The combination of optimization of the order of nonlinearity together with the numerical accuracy strongly outperforms "conventional" optimization of a size-related expressional complexity and the accuracy with respect to extrapolative capabilities of solutions on all nine test problems. In addition to exploiting the new complexity measure, this paper also introduces a novel heuristic of alternating several optimization objectives in a 2-D optimization framework. Alternating the objectives at each generation in such a way allows us to exploit the effectiveness of 2-D optimization when more than two objectives are of interest (in this paper, these are accuracy, expressional complexity, and the order of nonlinearity). Results of the experiments on all test problems suggest that alternating the order of nonlinearity of GP individuals with their structural complexity produces solutions that are both compact and have smoother response surfaces, and, hence, contributes to better interpretability and understanding.