کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
1139019 1489395 2016 19 صفحه PDF سفارش دهید دانلود رایگان
عنوان انگلیسی مقاله ISI
Solving the Pareto front for multiobjective Markov chains using the minimum Euclidean distance gradient-based optimization method
ترجمه فارسی عنوان
حل تقسیم پارتو برای زنجیرهای چند منظوره مارکوف با استفاده از روش بهینه سازی فاصله مبتنی بر فاصله اکولدی
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کلمات کلیدی
بهینه سازی چند هدفه، زنجیره مارکوف، پارتو جلو، سیاست های قوی پارتو، فاصله ی اقلیدسی
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی کنترل و سیستم های مهندسی
چکیده انگلیسی

• Present a novel method based on minimizing the Euclidean distance.
• Introduce Tikhonov’s regularization method for ensuring strict-convexity of Pareto front.
• Propose a linear constraints over the nonlinear problem employing the cc-variable method.
• Generate an even representation of the entire Pareto surface employing a distance restriction.
• Present an algorithm for solving multi-objective Markov chains problems.

A novel method based on minimizing the Euclidean distance is proposed for generating a well-distributed Pareto set in multi-objective optimization for a class of ergodic controllable Markov chains. The proposed approach is based on the concept of strong Pareto policy. We consider the case where the search space is a non-strictly convex set. For solving the problem we introduce the Tikhonov’s regularization method and implement the Lagrange principle. We formulate the original problem introducing linear constraints over the nonlinear problem employing the cc-variable method and constraining the cost-functions allowing points in the Pareto front to have a small distance from one another. As a result, the proposed method generates an even representation of the entire Pareto surface. Then, we propose an algorithm to compute the Pareto front and provide all the details needed to implement the method in an efficient and numerically stable way. As well, we prove the main Theorems for describing the dependence of the saddle point for the regularizing parameter and analyzes its asymptotic behavior. Moreover, we analyze the step size parameter of the Lagrange principle and also its asymptotic behavior. The suggested approach is validated theoretically and verified by a numerical example related to security patrolling that present a technique for visualizing the Pareto front.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Mathematics and Computers in Simulation - Volume 119, January 2016, Pages 142–160
نویسندگان
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