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Evolutionary Modeling of Systems of Ordinary Differential Equations with Genetic Programming

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Jingxian YuAuthors Info & Claims

Genetic Programming and Evolvable Machines, Volume 1, Issue 4

Pages 309 - 337

https://doi.org/10.1023/A:1010013106294

Published: 01 October 2000 Publication History

Abstract

This paper describes an approach to the evolutionary modeling problem of ordinary differential equations including systems of ordinary differential equations and higher-order differential equations. Hybrid evolutionary modeling algorithms are presented to implement the automatic modeling of one- and multi-dimensional dynamic systems respectively. The main idea of the method is to embed a genetic algorithm in genetic programming where the latter is employed to discover and optimize the structure of a model, while the former is employed to optimize its parameters. A number of practical examples are used to demonstrate the effectiveness of the approach. Experimental results show that the algorithm has some advantages over most available modeling methods.

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Cited By

Tonelli TPietropolli GSbaiz GManzoni LLi XHandl J(2024)Genetic Programming for the Reconstruction of Delay Differential Equations in EconomicsProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3638530.3664164(2119-2122)Online publication date: 14-Jul-2024
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Rastogi RMisra OMishra R(2024)A Chebyshev polynomial approach to approximate solution of differential equations using differential evolutionEngineering Applications of Artificial Intelligence10.1016/j.engappai.2023.107197126:PDOnline publication date: 27-Feb-2024
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Maslyaev MHvatov ASilva SPaquete L(2023)Comparison of Single- and Multi- Objective Optimization Quality for Evolutionary Equation DiscoveryProceedings of the Companion Conference on Genetic and Evolutionary Computation10.1145/3583133.3590601(603-606)Online publication date: 15-Jul-2023
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cover image Genetic Programming and Evolvable Machines

Genetic Programming and Evolvable Machines Volume 1, Issue 4

October 2000

72 pages

ISSN:1389-2576

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Copyright © Copyright © 2000 Kluwer Academic Publishers.

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Kluwer Academic Publishers

United States

Publication History

Published: 01 October 2000

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Cited By

Tonelli TPietropolli GSbaiz GManzoni LLi XHandl J(2024)Genetic Programming for the Reconstruction of Delay Differential Equations in EconomicsProceedings of the Genetic and Evolutionary Computation Conference Companion10.1145/3638530.3664164(2119-2122)Online publication date: 14-Jul-2024
https://dl.acm.org/doi/10.1145/3638530.3664164
Rastogi RMisra OMishra R(2024)A Chebyshev polynomial approach to approximate solution of differential equations using differential evolutionEngineering Applications of Artificial Intelligence10.1016/j.engappai.2023.107197126:PDOnline publication date: 27-Feb-2024
https://dl.acm.org/doi/10.1016/j.engappai.2023.107197
Maslyaev MHvatov ASilva SPaquete L(2023)Comparison of Single- and Multi- Objective Optimization Quality for Evolutionary Equation DiscoveryProceedings of the Companion Conference on Genetic and Evolutionary Computation10.1145/3583133.3590601(603-606)Online publication date: 15-Jul-2023
https://dl.acm.org/doi/10.1145/3583133.3590601
Maslyaev MHvatov A(2022)Solver-Based Fitness Function for the Data-Driven Evolutionary Discovery of Partial Differential Equations2022 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC55065.2022.9870370(1-8)Online publication date: 18-Jul-2022
https://dl.acm.org/doi/10.1109/CEC55065.2022.9870370
Sadollah ASu RKim JGao K(2021)Approximate solutions of heat transfer fins with convex and exponential profiles using fourier-based optimization method2016 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2016.7748337(5106-5112)Online publication date: 11-Mar-2021
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Wang YWang HZhang S(2020)Prediction of daily PM 2.5 concentration in China using data-driven ordinary differential equationsApplied Mathematics and Computation10.1016/j.amc.2020.125088375:COnline publication date: 15-Jun-2020
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Hoogendoorn Mvan Breda WRuwaard J(2019)GP-HD: Using Genetic Programming to Generate Dynamical Systems Models for Health CareIEEE/WIC/ACM International Conference on Web Intelligence10.1145/3350546.3352494(1-8)Online publication date: 14-Oct-2019
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Degrand EHemery MFages F(2019)On Chemical Reaction Network Design by a Nested Evolution AlgorithmComputational Methods in Systems Biology10.1007/978-3-030-31304-3_5(78-95)Online publication date: 18-Sep-2019
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Yang SLiu J(2018)Time-Series Forecasting Based on High-Order Fuzzy Cognitive Maps and Wavelet TransformIEEE Transactions on Fuzzy Systems10.1109/TFUZZ.2018.283164026:6(3391-3402)Online publication date: 1-Dec-2018
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Panda APani S(2018)Determining Approximate Solutions of Nonlinear Ordinary Differential Equations Using Orthogonal Colliding Bodies OptimizationNeural Processing Letters10.1007/s11063-017-9711-648:1(219-243)Online publication date: 1-Aug-2018
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