带有对称编码的遗传算法在动力学系统中的应用

Genetic Algorithm with Symmetric Code and Its Application to Dynamic System

本文通过对动力学系统模型和对带有约束条件的优化控制问题的分析，以系统的动力学优化控制问题为对象，进一步将带有对称编码的遗传算法应用于带有约束条件的优化问题的求解中．根据系统的终点和初始状态，提出了泛横向对称编码和泛纵向对称编码理论，为进一步拓展对称编码理论的应用空间提供了理论基础．在讨论了单输入和双输入的系统模型后，由定理１、定理２和定理３描述了对称编码自动满足系统的终点和初始状态约束的特点，这一理论的初步应用成果表明，以对称编码理论为核心的遗传算法的性能远好于普通的遗传算法，并可望其在机器学习、神经网络技术等领域中得到进一步应用．

This paper studys the application of Symmetric Code theory to optimization problem with constraints after the analysis of dynamic system.A dynamic optimal control problem is considered as an application.With regard to a system with no zero initial and final states conditions,General Horizontal Symmetric Code and General Vertical Symmetric Code theory is given out.After discussing one input and bi input linear system dynamic model,we propose Theorem 1,Theorem 2 and Theorem 3 to describe the property of Symmetric Code,which can automatically satisfy the final states constraints of a dynamic system.This theory offers a foundation to expend the applications of Symmetric Code theory.The initial application of Symmetric Code is of much better performance than classical Genetic Algorithms.We can also find its applications in machine learning and neural network technique.