一类具有Tikhonov正则化的逆问题的遗传优化求解方法

Q3 Mathematics
Jamal Daoudi, Chakir Tajani
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引用次数: 0

摘要

在本文中,我们感兴趣的是求解拉普拉斯方程的数据补全问题。它包括从边界不可访问部分的过指定条件中确定边界不可访问部分的缺失数据。知道这个问题是严重病态的,我们认为它的表述是一个使用吉洪诺夫正则化的优化问题。然后,我们考虑了一种基于自适应实数编码遗传算法(RCGA)的优化方法,以最小化代价函数并恢复丢失的数据。通过对不同域的数值模拟,验证了该方法在正则化参数适当的情况下的准确性和有效性,以及数值解与给定数据的不同噪声水平之间的良好一致性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Genetic Algorithm-Based Optimization Approach for Solving a Class of Inverse Problems with Tikhonov Regularization
In this paper, we are interested in solving the data completion problem for the Laplace equation. It consists to determine the missing data on the inaccessible part of the boundary from overspecified conditions in the accessible part. Knowing that this problem is severely ill-posed, we consider its formulation as an optimization problem using Tikhonov regularization. Then, we consider an optimization approach based on adapted Real Coded Genetic Algorithm (RCGA) to minimize the cost function and recover the missing data. The performed numerical simulations, with different domains, illustrate the accuracy and efficiency of the proposed method with an adequate regularization parameter, in addition to the good agreement between the numerical solutions and different noise level of the given data.
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来源期刊
WSEAS Transactions on Mathematics
WSEAS Transactions on Mathematics Mathematics-Discrete Mathematics and Combinatorics
CiteScore
1.30
自引率
0.00%
发文量
93
期刊介绍: WSEAS Transactions on Mathematics publishes original research papers relating to applied and theoretical mathematics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with linear algebra, numerical analysis, differential equations, statistics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.
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