بهبود الگوریتم های بهینه سازی اجتماع ذرات و تکامل تفاضلی با استفاده از نظریه چانه زنی نش

مرضیه دادور ¹ ( گروه مهندسی کامپیوتر ، واحد علوم و تحقیقات ، دانشگاه آزاد اسلامی ، تهران ، ایران )
حمید رضا نویدی ² ( گروه ریاضیات و علوم کامپیوتر ، دانشگاه شاهد ، تهران ، ایران )
حمید حاج سید جوادی ³ ( گروه ریاضیات و علوم کامپیوتر ، دانشگاه شاهد ، تهران ، ایران )
میترا میرزارضایی ⁴ ( گروه مهندسی کامپیوتر ، واحد علوم و تحقیقات ، دانشگاه آزاد اسلامی ، تهران ، ایران )

تاریخ ارسال : 1403/02/09 تاریخ تایید : 1403/05/16

کلید واژه: بهینه سازی ازدحام ذرات (PSO), تکامل تفاضلی (DE), تئوری بازی همکارانه , نظریه چانه زنی نش .,

چکیده مقاله :

این مقاله، رویکرد جدیدی را به منظور حل مسائل بهینه‌سازی ارائه می­کند، که دو الگوریتم شناخته شده‌ی بهینه­سازی ازدحام ذرات (Particle Swarm Optimization) و تکامل تفاضلی (Differential Evolution) با هم همکاری می‌نماید. در رویکرد پیشنهادی برای حفظ تعادل بین توانایی اکتشاف و استخراج با جلوگیری از سکون جمعیت، اجتناب از بهینه محلی و بهبود در الگوریتم­های PSO و DE از مدل ائتلافی یا همکاری در تئوری بازی‌ها استفاده می‌شود. در واقع الگوریتم­های PSO و DE به عنوان دو بازیکن در فضای جستجو هستند، که با استفاده نظریه چانه زنی­نش (Nash bargaining theory) در هر مرحله با هم بازی همکارانه (Cooperative game) انجام داده تا بهترین راه­حل را در فضای جستجو بدست آورند. مطابق با ساختارCEC2005، بیست و پنج تابع معیار (Benchmark functions) برای ارزیابی کارایی الگوریتم پیشنهادی مورد استفاده قرار می‌گیرند. روش پیشنهادی با دو الگوریتم‌ کلاسیک PSO وDE  و الگوریتم‌های ترکیبی که اخیرا پیشنهاد شده است مقایسه می‌شود. نتایج نشان می‌دهد، رویکرد ارائه شده در مقایسه با الگوریتم­های‌ کلاسیک و سایر مدل های ترکیبی عملکرد بهتری دارد.

چکیده انگلیسی :

 This article proposes a new approach in solving optimization (issues) problems in which two known optimization algorithm of particle swarm algorithm (PSO) and differential evolution (DE) a cooperate. The proposed approach uses a coalition or cooperation model in the game theory to improve the DE and PSO algorithms. This is done in an attempt to keep a balance between the exploration and exploitation capabilities by preventing population stagnation and avoiding the local optimum. The DE and PSO algorithms are two players in the state space, which play cooperative games together using the Nash bargaining theory to find the best solution. To evaluate the performance of the proposed algorithm, 25 benchmark functions are used in terms of the CEC2005 structure. The proposed algorithm is then compared with the classical DE and PSO algorithms and the hybrid algorithms recently proposed. The results indicated that the proposed hybrid algorithm outperformed the classical algorithms and other hybrid models.

highlight:

محیط بازی یک فضای رقابتی را در بین الگوریتم ها ایجاد می کند و باعث می شود توانایی جستجوی الگوریتم ها تا حد زیادی افزایش پیدا کند.

سود حاصل از چانه زنی نش با توجه به خاصیت بهینه پرتو بودن بهترین جوابی هست که برای هر دو الگوریتم بدست می آید.

تبادل سود حاصل از بازی در بین الگوریتم ها باعث اکتشاف نواحی جدید در فضای جستجو و افزایش تنوع و اجتناب از بهینه محلی می شود.

شرط قضیه چانه زنی نش به حفظ تعادل در بین توانایی اکتشاف و استخراج در روش پیشنهادی کمک می کند.

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