حل عددی دستگاه معادلات غیرخطی با الگوریتم فراابتکاری ARO بهبودیافته

حمدی پور, علی; بصیری, عبدالعلی; زارع, مصطفی

doi:10.22052/scj.2025.254888.1244

حل عددی دستگاه معادلات غیرخطی با الگوریتم فراابتکاری ARO بهبودیافته

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده ریاضی و علوم کامپیوتر، دانشگاه دامغان، دامغان، ایران.

10.22052/scj.2025.254888.1244

چکیده

حل دستگاه معادلات غیرخطی یکی از سخت‌ترین مسائل در محاسبات عددی است. روش‌های عددی سنتی مانند روش‌های نیوتن و انواع آن‌ نیاز به حدس اولیه خوب برای حل دستگاه معادلات غیرخطی دارند. حدس اولیه نامناسب می‌تواند تاثیر سوء در عملکرد و همگرایی این روش‌ها داشته باشد. در عمل، دست‌یابی به این حدس اولیه دشوار و از نظر زمانی پرهزینه خواهد بود. با هدف غلبه بر این مشکل، در این مقاله بهره‌گیری از الگوریتم فراابتکاری بهبود‌یافته (IARO) برای حل عددی دستگاه معادلات غیرخطی پیشنهاد شده است. از آنجا که حل دستگاه معادلات غیرخطی را می‌توان به حل یک مساله بهینه‌سازی تقلیل داد، الگوریتم فراابتکاری توانایی خوبی در پیدا کردن جواب آن خواهد داشت. الگوریتم فراابتکاری ARO از رفتار خرگوش‌ها در هنگام تغذیه الگو گرفته است و می‌تواند مسائل بهینه‌سازی پیچیده را در زمان مناسب حل کند. در روش پیشنهاد شده، الگوریتم ARO به کمک جدول حافظه بهبود یافته تا عملکرد مناسبی برای حل دستگاه معادلات غیرخطی داشته باشد. برای سنجش عملکرد روش پیشنهاد شده، جواب چندین دستگاه معادلات غیرخطی پیچیده توسط آن محاسبه شده که نتایج آن عملکرد خوب روش پیشنهادی را نمایش می‌دهد.

کلیدواژه‌ها

موضوعات

الگوریتم های تکاملی

عنوان مقاله [English]

Numerical solution of nonlinear equations systems with improved meta-heuristic ARO algorithm

نویسندگان [English]

Ali Hamdipour
Abdolali Basiri
Mostafa Zaare

Department of Mathematics and Computer Sciences, Damghan University, Damghan, Iran.

چکیده [English]

In the field of numerical analysis, one of the most difficult problems to solve is nonlinear equations. Traditional numerical techniques like Newton's methods and their variations typically demand a well-informed initial guess to successfully solve these nonlinear systems. An improper initial guess can significantly hinder the performance and convergence of these methods, making it difficult and time-consuming to achieve the desired results in practice. To overcome these issues, this paper presents a novel approach that employed the Improved ARO (IARO) meta-heuristic algorithm for solving nonlinear equation systems numerically. Given that solving nonlinear equation systems can be transformed into an optimization problem, meta-heuristic algorithms exhibit strong potential for finding solutions efficiently. The ARO meta-heuristic algorithm, inspired by the feeding behavior of rabbits, has demonstrated its ability to solve intricate optimization problems within acceptable time. In the proposed method, the ARO algorithm is improved with adding a memory table to have a suitable performance for solving nonlinear equation systems. To assess the effectiveness of the proposed method, it is applied to solve several complex nonlinear equations. The results clearly demonstrate the robust performance of the approach.

کلیدواژه‌ها [English]

Nonlinear equations systems
numerical analysis
meta-heuristic algorithms
ARO algorithm
optimization

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