{"title":"一类具有Tikhonov正则化的逆问题的遗传优化求解方法","authors":"Jamal Daoudi, Chakir Tajani","doi":"10.37394/23206.2023.22.92","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"22 2","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Genetic Algorithm-Based Optimization Approach for Solving a Class of Inverse Problems with Tikhonov Regularization\",\"authors\":\"Jamal Daoudi, Chakir Tajani\",\"doi\":\"10.37394/23206.2023.22.92\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":55878,\"journal\":{\"name\":\"WSEAS Transactions on Mathematics\",\"volume\":\"22 2\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"WSEAS Transactions on Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37394/23206.2023.22.92\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"WSEAS Transactions on Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/23206.2023.22.92","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
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.
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.