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首页> 外文期刊>The journal of physical chemistry, A. Molecules, spectroscopy, kinetics, environment, & general theory >Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface
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Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface

机译：组合遗传算法和多元线性回归（GA-MLR）优化器：在多指数荧光衰减表面上的应用

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摘要

The optimization approach based on the genetic algorithm ( GA) combined with multiple linear regression ( MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection ( VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Frechet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear combinations of nonlinear functions, is indicated. The VP algorithm does not distinguish the weakly nonlinear parameters from the nonlinear ones and it does not apply to the model functions which are multi-linear combinations of nonlinear functions.
机译：讨论了基于遗传算法（GA）和多元线性回归（MLR）方法的优化方法。 GA-MLR优化器设计用于非线性最小二乘问题，其中模型函数是非线性函数的线性组合。 GA优化了非线性参数，并根据MLR计算了线性参数。 GA-MLR是一种直观的优化方法，它利用了遗传算法技术的所有优势。该优化方法是由两种众所周知的优化方法的适当组合得出的。 MLR方法嵌入在GA优化器中，并且并行优化了线性和非线性模型参数。 MLR方法是GA-MLR中唯一涉及的严格数学“工具”。 GA-MLR方法简化并大大加快了优化过程，因为线性参数不是拟合参数。通过分析与双激发态互变过程相对应的动力学双指数荧光衰变表面来举例说明其性质。简短讨论了针对相同类别的优化问题而设计的可变投影（VP）算法。 VP是一种非常高级的数学形式主义，涉及非线性函数方法，线性投影仪的代数以及Frechet导数和伪逆的形式主义。在最近引入的GA-NR优化器的应用程序上添加了其他解释性注释，以同时恢复在同一优化问题中出现的线性和弱非线性参数以及非线性参数。 GA-NR优化器将GA方法与NR方法结合在一起，在其中，通过牛顿的方法，从chi（2）的泰勒级数展开中获得了对chi（2）的二次近似的最小值条件。 -Raphson算法。指出了GA-NR优化器在建模非线性函数的多线性组合的函数中的应用。 VP算法不能将弱非线性参数与非线性参数区分开，并且不适用于作为非线性函数的多线性组合的模型函数。

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