文档介绍：ic Programming and Evolvable Machines, 1, 309–337, 2000
© 2000 Kluwer Academic Publishers. Manufactured in herlands.
Evolutionary Modeling of Systems of Ordinary
Differential Equations with ic Programming
HONGQING CAO, LISHAN KANG, AND
YUPING CHEN ******@.; ******@whu.
State Key Laboratory of Software Engineering, Wuhan University, Wuhan 430072, P. R. China
State Key Laboratory of Parallel and Distributed Processing, P. R. China
JINGXIAN YU jxyu@
Institute of Electrochemistry, Department of Chemistry, Wuhan University, Wuhan 430072, P. R. China
Received May 18, 1999; Revised March 8, 2000
Abstract. This paper describes an approach to the evolutionary modeling problem of ordinary differen-
tial 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 ic
algorithm in ic 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.
Keywords: evolutionary modeling, ic programming, ic algorithm, system of ordinary differ-
ential equations, higher-order ordinary differential equation
1. Introduction
plex systems and nonlinear phenomena that change over time exist in
engineering, economic management, natural sciences, social sciences and many
other fields. Examples include price fluctuations, the change of temperature during
a chemical process, weather changes, population growth, and so on. Researchers
have long sought reasonable mathematical models for those systems based on the
observed data so as to provide a basis for system analys