یافتن جواب‌های بهین دسته‌ای از مسائل بهینه‌سازی پارامتری بر حسب مقادیر پارامتر با استفاده از شبکه‌های عصبی چندلایه

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه ریاضی، دانشگاه آزاد واحد تبریز، تبریز، ایران.

چکیده

در این مقاله، مسائل‎‎‎ بهینه‌سازی پارامتر‏ی مورد بررسی قرار گرفته‌اند. ‎‎‎‎‎‎‎‎‎در یک مساله بهینه‌سازی پارامتری فرض می‌شود ‎‎$‎‎lambdain‎mathbb{R}^n‎$‎‏ بردار پارامترها و ‎$x^*in‎mathbb{R}^n‎$‎‏ جواب بهین متناظر با ‎$lambda$‎‏ باشد. هدف این تحقیق مشخص کردن تابعی مانند ‎‎$‎‎‎psi‎$‎‏ است که ‎$psi(‎lambda‎)=x^*$‎‏ جواب بهین متناظر با ‎$‎lambda‎‎$‎‏ باشد. برای این کار ابتدا به ازای هر مقدار ‎‎$‎‎‎lambda‎$‎‏‏، جواب بهین متناظر محاسبه می‌شود. بدین ترتیب یک مجموعه از داده‌های آموزشی متشکل از پارامترها و مقادیر بهین آنها بدست می‌آید. یک شبکه عصبی چندلایه داده‌های ‌آموزشی را آموزش دیده و در نتیجه عملکرد ‎$psi$‎‏ در یک دامنه معلوم توسط این شبکه عصبی مشخص می‌شود. در واقع تابع ‎‎$‎‎psi$‎‏ به ازای هر مقدار از پارامتر(پارامترها)‏، جواب بهین متناظر را توسط شبکه چندلایه آموزش دیده مشخص می‎‌کند. در نهایت چند مثال برای بررسی کارایی روش ارائه می‌شود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Finding Optimal Solutions to a Class of Parametric Optimization Problems in Terms of Parameter Values by using Multilayer Neural Networks

نویسندگان [English]

  • Kobra Mohammadsalahi
  • Farzin Modarres Khyiabani
  • Nima Azarmir
Department of Mathematics, Tabriz Branch, Islamic azad University, Tabriz, Iran.
چکیده [English]

‎‎In this paper, parametric optimization problems are investigated. ‎In a‎ ‎parametric ‎optimization ‎problem ‎we ‎assume ‎‏‎$‎‎‎‎‎‏‎‎lambda‎in‎mathbb{R}^n‎$‎‎ ‎is ‎the ‎vector ‎of ‎the ‎parameters ‎and ‎‎$‎‎x^*$ ‎is ‎the ‎optimal ‎answer ‎corresponding ‎to ‎it. ‎The ‎purpose ‎of ‎this ‎paper ‎is ‎to ‎determine a‎ ‎function ‎such ‎as ‎‎$‎‎psi$ ‎so ‎that ‎we ‎have ‎‎$‎‎psi(‎lambda‎)=x^*$.‎ To do this, first for each ‎$‎‎‎lambda‎$‎, the corresponding optimal answer is calculated. In this way, a set of data bases consisting of parameters and the corresponding optimal values are obtained. A multilayer network of data base is trained to obtain the function ‎$‎‎psi$‎ in a domain. In fact, the function ‎$‎‎psi$‎ for each value of the parameter specifies the corresponding answer by the trained multilayer network.‎‎ Finally, we conduct several numerical examples to test our method.

کلیدواژه‌ها [English]

  • Parametric Optimization&lrm
  • Multilayer Neural Networks&lrm
  • Recurrent Neural Networks&lrm
  • &lrm
  • Free Derivative Optimizatiuon
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