基于遗传支持向量机的城市扩张非线性组合模型

A Nonlinear Polynomial Model for Urban Expansion Incorporating Genetic Algorithm and Support Vector Machines

在分析当前城市扩张模拟模型优缺点的基础上,利用支持向量机能有效表达、拟合复杂非线性系统的功能,将多个单项城市扩张模型进行非线性组合,有机融合各单项模型优点,最后构建支持向量机的城市空间扩张非线性组合模拟模型。利用遗传算法优化支持向量机的参数,减小参数设置不合理对支持向量机建模精度引起的影响,有效提高支持向量机模型精度。通过分析组合模型误差和各参与组合的单项模型之间的关系,总结出提高支持向量机的城市扩张非线性组合模型精度的方法是:①提高参与组合的各单项模型精度;②增加单项模型之间的差异性。以长沙市为例,分别构建多元回归、GM(1,8)、BP网络和LS-SVM单项城市空间扩张模拟模型,并在此基础上建立线性组合城市扩张模型和遗传支持向量机非线性组合城市扩张模型。通过各模型精度对比分析证明,遗传支持向量机的城市扩张非线性组合模型精度远优于各单项模型,并且优于线性组合模型,是一种有效的城市扩张新模型。

With comparative analysis of strengths and weaknesses of current urban expansion simulation models and nonlinearly combining the advantages of best individual-based models,a nonlinear polynomial model of urban spatial expansion has been proposed by using the powerful functions of support vector machine to describe highly complicated nonlinear systems and then to make a better fit for them.The accuracy of the proposed model has been effectively improved by using the parameters of support vector machine optimized with genetic algorithm to reduce the negative influence,exerted by the non-rational design of parameters,on the modeling accuracy of support vector machine.With analyzing the relationship between the error arising from the combined model and all individual-based models,we conclude the ways to improve the accuracy of the nonlinear polynomial model of urban expansion equipped with support vector machine as follows：The first is to improve the accuracy of individual-based models;the second is to enlarge differences between individual models.In the case study of Changsha city,individual-based simulation models of urban spatial expansion constructed by multiple regression model,GM（1,8）,BP network and LS-SVM are used to build a linear combination model of urban spatial expansion and a nonlinear combination model of urban spatial expansion equipped with genetic algorithm and support vector machine.A comparison of accuracy of selected models shows that the accuracy of nonlinear polynomial model of urban expansion equipped with genetic algorithm and support vector machine is much higher than any individual-based simulation model,and also higher than the linear combination model,and therefore,an efficient new model of urban expansion is established.