[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-137812-105":59,"doc-detail-137812-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","using-approximations-to-accelerate-engineering-design-optimization","Using Approximations to Accelerate Engineering Design Optimization","","Engineering design optimization problems often include computationally intensive objective-function evaluations that make standard nonlinear optimization impractical, since each iteration requires expensive function assessments. This work applies surrogate strategies that are cheaper to evaluate, emphasizing algebraic approximations of the objective. The paper introduces merit functions that explicitly balance improving the current objective approximation throughout the optimization while also enhancing both the final solution quality and approximation accuracy. The approach aims to increase effectiveness without compromising 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are engineering design optimization problems difficult with standard nonlinear methods?","Question",{"text":113,"@type":114},"Because the objective functions are defined through costly computer simulations, making repeated evaluations at every iteration prohibitively expensive and potentially problematic for higher-order methods.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What alternative strategy does the paper propose to handle expensive objective evaluations?",{"text":118,"@type":114},"It uses surrogate models, specifically algebraic approximations of the objective, chosen to reduce evaluation cost while still supporting optimization progress.",{"name":120,"@type":111,"acceptedAnswer":121},"How do merit functions fit into the optimization framework in this work?",{"text":122,"@type":114},"The paper introduces merit functions that explicitly promote improving the current approximation during the optimization, simultaneously targeting better objective solutions and improved approximation quality.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},137812,1787447959,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145},8796095461564,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","# Using Approximations to Accelerate EngineeringDesign Optimization\n\nVirginia Torczon and Michael W.TrossetThe College of William&Mary,Williamsburg,Virginia  \nInstitute for Computer Applications in Science and EngineeringNASA Langley Research CenterHampton,VA  \nOperated by Universities Space Research Association  \nNational Aeronautics andSpace Administration  \nLangley Research CenterHampton,Virginia 23681-2199  \nAugust 1998  \nAvailable from the following:  \n# USING APPROXIMATIONS TO ACCELERATE ENGINEERING DESIGNOPTIMIZATION*\n\nVIRGINIA TORCZONt AND MICHAEL W.TROSSET  \nAbstract.Optimization problems that arise in engineering design are often characterized by severalfeatures that hinder the use of standard nonlinear optimization techniques.Foremost among these featuresis that the functions used to define the engineering optimization problem often are computationally intensive.Within a standard nonlinear optimization algorithm,the computational expense of evaluating the functionsthat define the problem would necessarily be incurred for each iteration of the optimization algorithm.  \nFaced with such prohibitive computational costs,an attractive alternative is to make use of surrogateswithin an optimization context since surrogates can be chosen or constructed so that they are typicallymuch less expensive to compute.For the purposes of this paper,we will focus on the use of algebraicapproximations as surrogates for the objective.  \nIn this paper we introduce the use of so-called merit functions that explicitly recognize the desirabilityof improving the current approximation to the objective during the course of the optimization.We defineand experiment with the use of merit functions chosen to simultaneously improve both the solution to theoptimization problem(the objective)and the quality of the approximation.Our goal is to further improvethe effectiveness of our general approach without sacrificing any of its rigor.  \nKey words.design optimization,computer simulation,pattern search,kriging,nonparametric responscsurface methodology.  \nSubject classification.Applied &Numerical Mathematics  \n1.Introduction.The presentation that follows is intended to illustrate that global approximationscan be helpful in facilitating optimization.We present several simple examples,selected to illustrate twofundamental perspectives that have guided our recent research:  \n·When one uses algebraic approximations within an iterative optimization framework,the initialstages of the optimization should concentrate on the predictive ability of the approximation.Theaccuracy of the approximation should be a concern only when in the vicinity of a minimizer orwhen it becomes clear that the approximation is not doing a good job of identifying trends in theobjective.  \n● It is desirable to compromise between the single-minded pursuit of a minimizer and the constructionof an approximation that gives a reasonable“picture”of the behavior of the objective—particularlywhen a problem is known to have many local minimizers.  \nNeither of these observations is unique to us;however,they motivate us to introduce merit functionsthat explicitly recognize the desirability of improving the current approximation to the expensive simulation  \n*This research was supported in part by the National Science Foundation under Grant CCR-9734044 and by the NationalAeronautics and Space Administration under NASA Contract No.NAS1-97046 while the authors were in residence at theInstitute for Computer Applications in Science and Engineering(ICASE),NASA Langley Research Center,Hampton,Virginia23681-2199.  \nAssistant Professor,Department of Computer Science,College of William &Mary,P.O.Box 8795,Williamsburg,Virginia23187-8795,va@cs.wm.edu  \n\\#Associate Professor,Department of Mathernatics,College of William &Mary,P.O.Box 8795,Williamsburg,Virginia23187-8795,trosset@math.m.edu  \nin certain regions.In other words,we introduce a criterion that balances the expenditure of expensiveevaluations of the ","cbCaisUxb0Kbctyr","https://ap.wps.com/l/cbCaisUxb0Kbctyr","pdf",922324,18,"English","# Introduction\n## Problem\n## Operating Assumptions\n## Consequences\n## Goals","[{\"question\":\"Why are engineering design optimization problems difficult with standard nonlinear methods?\",\"answer\":\"Because the objective functions are defined through costly computer simulations, making repeated evaluations at every iteration prohibitively expensive and potentially problematic for higher-order methods.\"},{\"question\":\"What alternative strategy does the paper propose to handle expensive objective evaluations?\",\"answer\":\"It uses surrogate models, specifically algebraic approximations of the objective, chosen to reduce evaluation cost while still supporting optimization progress.\"},{\"question\":\"How do merit functions fit into the optimization framework in this work?\",\"answer\":\"The paper introduces merit functions that explicitly promote improving the current approximation during the optimization, simultaneously targeting better objective solutions and improved approximation quality.\"}]","Using Approximations to Accelerate Engineering Design Optimization | PDF",45]