Nonlinear least square regression by adaptive domain method with multiple genetic algorithms
Nonlinear least square regression by adaptive domain method with multiple genetic algorithms
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DOI：
10.1109/tevc.2006.876363
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发表时间：
2007-02-01
影响因子：
14.3
通讯作者：
Enoto, Takeaki
中科院分区：
文献类型：
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作者：
Tomioka, Satoshi;Nisiyama, Shusuke;Enoto, Takeaki
在非线性问题的传统最小二乘 (LS) 回归中，获得包含一组正规方程的目标参数的解析导数并不容易。即使可以通过分析或数值方式获得导数，也必须注意为求解方程的迭代过程选择正确的初始值，因为一些不需要的局部优化解也可能满足正规方程。在非线性LS的遗传算法（GA）应用中，不需要使用正规方程，并且遗传算法还能够避免局部最优。然而，种群的收敛性和解的可靠性取决于参数的初始域，类似于上述使用正规方程的方法中初始值的选择。为了克服将 GA 用于非线性 LS 的缺点，我们提出使用自适应域方法 (ADM)，其中参数域可以通过使用多个寿命较短的实数编码 GA 动态变化。通过一个示例问题，我们展示了 ADM 在收敛性和可靠性方面的改进。该方法的另一个优点是它不需要任何有关 GA 或其调整的专业知识。因此，普通科学家可以利用 ADM 和 GA 的非线性 LS 来实现许多领域的各种应用。
In conventional least square (LS) regressions for nonlinear problems, it is not easy to obtain analytical derivatives with respect to target parameters that comprise a set of normal equations. Even if the derivatives can be obtained analytically or numerically, one must take care to choose the correct initial values for the iterative procedure of solving an equation, because some undesired, locally optimized solutions may also satisfy the normal equation. In the application of genetic algorithms (GAs) for nonlinear LS, it is not necessary to use normal equations, and a GA is also capable of avoiding localized optima. However, convergence of population and reliability of solutions depends on the initial domain of parameters, similarly to the choice of initial values in the abovementioned method using the normal equation. To overcome this disadvantage of applying GAs for nonlinear LS, we propose to use an adaptive domain method (ADM) in which the parameter domain can change dynamically by using several real-coded GAs with short lifetimes.Through an example problem, we demonstrate improvements in terms of both the convergence and the reliability by ADM. A further merit in the proposed method is that it does not require any specialized knowledge about GAs or their tuning. Therefore, the nonlinear LS by ADM with GAs are accessible to general scientists for various applications in many fields.