动态系统的常微分方程组建模—基于不同搜索技术的实验研究

以人口模型和化学反应模型为例，通过大量实验研究比较了分别采用基于两种传统的搜索方法即局部搜索算法和模拟退火算法、遗传算法（简称GA）四者相结合的14种不同算法建立动态系统的常微分方程组模型的实验结果，得到了有关各算法性能比较的一些新的结论。两个实例的实验结果表明：在14种算法中，GP＋GA＋LS－MU算法（即在采用GP的模型结构的优化过程中嵌入采用GA的模型参数的优化过程，并且在每一演化代对种群中的部分个体进行基于GP的标准变异算子产生邻域解的局域搜索过程）是目前解决常微分方程组建模问题的最好算法。

MODELING OF SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS FOR DYNAMIC SYSTEMS

Using the population model and the chemical reaction model as examples, the experimental results of building the ordinary differential equation (ODE) models for dynamical systems by using fourteen kinds of algorithms which are based on two traditional searching methods (i.e. the local search algorithm and the simulated annealing algorithm), genetic programming (GP), genetic algorithm (GA) and their combinations are studied in detail. Some new conclusions about the comparisons of the performance of those algorithms are drawn at the end of this paper. The results of both examples show that of the fourteen kinds of algorithms the algorithm called GP+GA+LS MU is the best one in solving the modeling problem of ODE, which is performed by embedding a parameter optimization process using GA into the structure optimization process using GP, and adding local search for some individuals in the population at the end of each generation based on the standard GP mutation operators to generate their neighbor solutions.