通用遗传算法的优化过程

Alexander Zemliak, Andrei Osadchuk, Christian Serrano
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摘要

早先开发的基于广义优化的方法已成功应用于使用确定性优化方法设计电子电路的问题。本文将类似方法扩展到使用遗传算法(GA)作为主要优化方法的电子电路优化问题。广义优化的基本要素是人为引入控制向量,在优化过程中产生多种不同的策略,并决定优化问题的自变量数量以及 GA 中染色体的长度和结构。在这种情况下,GA 会形成一组种群,这些种群由适合度函数定义,适合度函数根据在广义优化思想框架内选择的策略以不同方式指定。通过控制向量可以生成不同的策略,也可以建立复合策略,从而显著提高解决方案的准确性。这反过来又使得在解决电路优化问题时,与传统 GA 相比,可以减少 GA 运行过程中所需的代数,并将处理器时间减少 3-5 个数量级。对一些电子电路优化程序的分析表明了这种方法的有效性。获得的结果证明,对遗传算法进行修改后,可以克服过早收敛的问题,并将最小化精度提高 3-4 个数量级。
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Optimization Process by Generalized Genetic Algorithm
The approach developed earlier, based on generalized optimization, was successfully applied to the problem of designing electronic circuits using deterministic optimization methods. In this paper, a similar approach is extended to the problem of optimizing electronic circuits using a genetic algorithm (GA) as the main optimization method. The fundamental element of generalized optimization is an artificially introduced control vector that generates many different strategies within the optimization process and determines the number of independent variables of the optimization problem, as well as the length and structure of chromosomes in the GA. In this case, the GA forms a set of populations defined by a fitness function specified in different ways depending on the strategy chosen within the framework of the idea of generalized optimization. The control vector allows you to generate different strategies, as well as build composite strategies that significantly increase the accuracy of the resulting solution. This, in turn, makes it possible to reduce the number of generations required during the operation of the GA and reduce the processor time by 3–5 orders of magnitude when solving the circuit optimization problem compared to the traditional GA. An analysis of the optimization procedure for some electronic circuits showed the effectiveness of this approach. The obtained results prove that the applied modification of the GA makes it possible to overcome premature convergence and increase the minimization accuracy by 3-4 orders of magnitude.
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