یک مدل عصبی پویای کارا برای حل مسایل بهینه سازی ناهموار مقید با محدودیت‌های آفین و کران‌دار

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه ریاضی، دانشگاه دریانوردی و علوم دریایی چابهار، چابهار، ایران

2 بلوار شهید ریگی، دانشگاه دریانوردی و علوم دریایی چابهار، استادیار

10.22034/jfsa.2022.316313.1103

چکیده

در اﯾﻦ ﻣﻘﺎﻟﻪ ﯾﮏ ﻣﺪل ﻏﯿﺮﺟﺮﯾﻤﻪای ﻣﺒﺘﻨﯽ ﺑﺮ ﺷﻤﻮل دﯾﻔﺮاﻧﺴﯿﻠﯽ ﺑﺮای ﺣﻞ ﻣﺴﺎﯾﻞ ﺑﻬﯿﻨﻪﺳﺎزی ﻣﻘﯿﺪ ﺑﺎ ﻗﯿﻮد ﮐﺮاندار و ﺗﺴﺎوی ﺧﻄﯽ ﭘﯿﺸﻨﻬﺎد ﮔﺮدﯾﺪه اﺳﺖ. ﻫﻤﮕﺮاﯾﯽ ﺧﻂ ﺳﯿﺮﻫﺎ ﺑﻪ ﻧﺎﺣﯿﻪی ﺷﺪﻧﯽ ﻣﺴﺎوی در زﻣﺎن ﻣﺘﻨﺎﻫﯽ را اﺛﺒﺎت ﻧﻤﻮدهاﯾﻢ. ﻫﻢﭼﻨﯿﻦ ﻣﻌﺎدل ﺑﻮدن ﻧﻘﻄﻪ ﺗﻌﺎدﻟﯽ ﺷﺒﮑﻪ ﻋﺼﺒﯽ ﭘﯿﺸﻨﻬﺎدی ﺑﺎ ﺟﻮاب ﺑﻬﯿﻨﻪی ﻣﺴﺄﻟﻪ ﺑﻬﯿﻨﻪﺳﺎزی اﺻﻠﯽ را ﻧﺸﺎن دادهاﯾﻢ. ﺑﻪﻋ ﻼوه ﭘﺎﯾﺪاری ﺷﺒﮑﻪی ﭘﯿﺸﻨﻬﺎدی ﺑﻪ ﻣﻔﻬﻮم ﻟﯿﺎﭘﺎﻧﻮف و ﻫﻤﮕﺮاﯾﯽ ﺳﺮاﺳﺮی آن ﺑﻪ ﺟﻮاب ﺑﻬﯿﻨﻪی دﻗﯿﻖ ﻣﺴﺄﻟﻪ ﺑﻬﯿﻨﻪﺳﺎزی اﺻﻠﯽ اﺛﺒﺎت ﮔﺮدﯾﺪه اﺳﺖ. ﻣﺪل ﭘﯿﺸﻨﻬﺎدی در ﻣﻘﺎﯾﺴﻪ ﺑﺎ ﻣﺪلﻫﺎی ﻣﻮﺟﻮد ﺑﺮای ﺣﻞ ﻣﺴﺎﯾﻞ ﺑﻬﯿﻨﻪﺳﺎزی ﻣﺤﺪب ﻧﺎﻫﻤﻮار ﻓﺎﻗﺪ ﭘﺎراﻣﺘﺮﺟﺮﯾﻤﻪ ﯾﺎ ﺗﺎﺑﻊ ﺟﺮﯾﻤﻪ ﺑﻮده و ﭘﯿﺎدهﺳﺎزی آن آﺳﺎنﺗﺮ ﻣﯽﺑﺎﺷﺪ. ﺑﻪﻋﻨﻮان ﮐﺎرﺑﺮد، ﺷﺒﮑﻪ ﻋﺼﺒﯽ ﭘﯿﺸﻨﻬﺎدی ﺑﻪ ﯾﮏ ﻣﺪل ﺑﺮای ﺣﻞ ﻣﺴﺎﯾﻞ ﺑﻬﯿﻨﻪﺳﺎزی ﻣﺤﺪب ﻧﺎﻫﻤﻮار ﻣﻘﯿﺪ ﺑﺎ ﻗﯿﻮد ﻣﺴﺎوی ﺧﻄﯽ و ٠ x ﺗﺒﺪﯾﻞ ﺷﺪه اﺳﺖ. در اﻧﺘﻬﺎ ﺑﺮای ﻧﺸﺎن دادن ﮐﺎراﯾﯽ ﻣﺪل ﭘﯿﺸﻨﻬﺎدی ﺗﻌﺪادی ﻣﺜﺎل اراﯾﻪ ﮔﺮدﯾﺪه اﺳﺖ.

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