[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85872-en":3,"doc-seo-85872-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85872,1099514068035,"Ezra","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Complex Permittivity Extraction of Polymer Materials Using Gradient-Enhanced NSGA-II Algorithm","A gradient-enhanced NSGA-II (G-NSGA-II) hybrid optimization framework is presented to solve complex permittivity extraction for polymer materials, targeting local optima and solution non-uniqueness. The method combines NSGA-II global exploration with gradient-based local refinement activated by population-stagnation detection. Multi-dimensional constraints are enforced by jointly optimizing transmission and reflection coefficients across multiple sample thicknesses. Experiments on six polymers in the 20–40 GHz band show strong agreement with literature and measurements, cutting convergence generations by about 50% for robust broadband dielectric characterization in building and electromagnetic engineering.","Complex Permittivity Extraction of Polymer Materials Using Gradient-Enhanced NSGA-II Algorithm  \nHanqing Zhang, Zhuowei Li, Member, IEEE, Jiliang Zhang, Senior Member, IEEE, Xi Liao, Senior Member, IEEE, Yang  \nWang Senior Member, IEEE  \narXiv :2607 . 1026 1v 1 [ cs .CE] 11 Jul 2026  \nAbstract—This paper presents gradient-enhanced non-dominated sorting genetic algorithm II (G-NSGA-II) to address the challenges of local optima and solution non-uniqueness in the complex permittivity extraction problem for the first time. This adaptive hybrid algorithm integrates the global exploration capability of NSGA-II with gradientbased local refinement, triggered by a population-stagnation detection mechanism. Furthermore, multi-dimensional constraints are incorporated by jointly optimizing transmission and reflection coefficients across multiple sample thicknesses. Experimental validation conducted on six typical polymers in the 20–40 GHz band demonstrates that the retrieved relative permittivity and thicknesses are in high agreement with literature values and physical measurements. Compared to standard heuristic and gradient-based algorithms, the proposed G-NSGA-II reduces the number of generations required for convergence by approximately 50% . This significant improvement in speed, combined with enhanced robustness, provides a highly reliable and efficient solution for broadband dielectric characterization in architectural and electromagnetic engineering. The simple measurement method and the proposed efficient algorithm allow for a rapid evalutaion of wireless performance within indoor environments. This approach serves as a valuable tool for optimizing existing wireless layouts and improving network performance.  \nIndex Terms—Complex permittivity, building wireless performance, millimeter-wave, NSGA-II, polymer materials.  \nI. INTRODUCTION  \nTHE integration of 5G and 6G millimeter-wave systems into indoor  \nenvironments has intensified interest in the electromagnetic properties of building materials [1] . As internal structures and infill patterns of polymers significantly influence their effective permittivity, accurate characterization of material-wave interaction is vital for predicting transmission, reflection, and attenuation [2], [3] . Accurate electromagnetic parameters are fundamental to metrics such as spatially averaged capacity (SAC) [4], enabling precise channel simulation [5] and interference prediction, such as far-end crosstalk [6] . Consequently, achieving high-precision, non-destructive extraction of complex permittivity and permeability across a wide spectrum remains a primary challenge [7] .  \nTraditional characterization relies on waveguide and resonant cavity techniques [8]–[13], which, despite their precision in millimeter-wave bands, require destructive and rigorous sample machining to avoid airgap errors [8],[12] . In contrast, the free-space method is more suitable  \nCorresponding Author: Jiliang Zhang ([zhangjiliang1@mail.neu.edu.cn](zhangjiliang1@mail.neu.edu.cn))  \nH. Zhang, Z. Li and J. Zhang are with the College of Information Science and Engineering, Northeastern University, China, 110819 .  \nX. Liao is with the School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing, China, 400065.  \nY. Wang is with the International College, Chongqing University of Postsand Telecommunications, Chongqing, China, 400065  \nThis work was supported by the National Key R&D Program of China under Grant 2025YFE0122200, the National Natural Science Foundation of China (NSFC) under Grant 62573096 and 62401644, the Postdoctoral Fellowship Program and China Postdoctoral Science Foundation under Grant BX20250343, the LiaoNing Revitalization Talents Program under Grant XLYC2403116, the Opening Fund of Liaoning Key Laboratory of Urban and Architectural Digital Technology under Grant UADT2024A05, the Fundamental Research Funds for the Central Universities under Grant N25XQD","cbCaivDVnPcLcQwr","https://ap.wps.com/l/cbCaivDVnPcLcQwr","pdf",27579955,1,6,"English","en",105,"# Abstract\n# Introduction","[{\"question\":\"What problem does the proposed G-NSGA-II algorithm address in complex permittivity extraction?\",\"answer\":\"It targets challenges of local optima and solution non-uniqueness that often arise in complex permittivity extraction for polymer materials.\"},{\"question\":\"How does G-NSGA-II improve search performance compared with standard NSGA-II?\",\"answer\":\"It integrates gradient-based local refinement into NSGA-II, triggered by a population-stagnation detection mechanism, improving robustness and reducing the number of generations needed for convergence by about 50%.\"},{\"question\":\"How are multi-dimensional constraints incorporated in the extraction process?\",\"answer\":\"The approach jointly optimizes transmission and reflection coefficients across multiple sample thicknesses, enabling more reliable broadband dielectric parameter extraction.\"}]",1784206828,15,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"complex-permittivity-extraction-of-polymer-materials-using-gradient-enhanced-nsga-ii-algorithm","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/complex-permittivity-extraction-of-polymer-materials-using-gradient-enhanced-nsga-ii-algorithm/85872/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What problem does the proposed G-NSGA-II algorithm address in complex permittivity extraction?","Question",{"text":74,"@type":75},"It targets challenges of local optima and solution non-uniqueness that often arise in complex permittivity extraction for polymer materials.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does G-NSGA-II improve search performance compared with standard NSGA-II?",{"text":79,"@type":75},"It integrates gradient-based local refinement into NSGA-II, triggered by a population-stagnation detection mechanism, improving robustness and reducing the number of generations needed for convergence by about 50%.",{"name":81,"@type":72,"acceptedAnswer":82},"How are multi-dimensional constraints incorporated in the extraction process?",{"text":83,"@type":75},"The approach jointly optimizes transmission and reflection coefficients across multiple sample thicknesses, enabling more reliable broadband dielectric parameter 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