Nghiên cứu phân tích khám phá và ổn định của thuật toán điện trường nhân tạo

Springer Science and Business Media LLC - Tập 52 - Trang 10805-10828 - 2022
Anita Sajwan1, Anupam Yadav2
1Department of Mathematics, National Institute of Technology, Uttarakhand, Srinagar, India
2Department of Mathematics, Dr. B.R. Ambedkar National Institute of Technology Jalandhar, Jalandhar, India

Tóm tắt

Sự hội tụ lý thuyết, phân tích khám phá và ổn định của bất kỳ thuật toán heuristic nào là một khía cạnh quan trọng để làm cho nó trở nên hiệu quả và đáng tin cậy hơn đối với cộng đồng nghiên cứu. Thuật toán điện trường nhân tạo (AEFA) (Yadav et al., Swarm Evol Comput 48:93–108, 54) là một thuật toán tối ưu hóa mới trong lớp các thuật toán tối ưu hóa heuristic. Nó được lấy cảm hứng từ định luật Coulomb về lực tĩnh điện. Trong bài báo này, một nghiên cứu về hội tụ và phân tích ổn định của quỹ đạo hạt của thuật toán AEFA được thiết lập. Một nghiên cứu lý thuyết về ổn định bậc nhất và bậc hai của thuật toán AEFA được thiết lập và được mô tả bởi một quan hệ hồi tiếp ngẫu nhiên. Sự hội tụ của kỳ vọng và phương sai của vị trí các hạt được chứng minh và thảo luận chi tiết. Hơn nữa, các điều kiện biên cho sự hội tụ của kỳ vọng và phương sai của vị trí các hạt được thiết lập cùng với ổn định bậc nhất và bậc hai của chúng. Những điều kiện biên này gợi ý các giá trị tham số tốt hơn cho thuật toán AEFA. Các ranh giới hệ số cho vị trí các hạt liên quan đến các loại hành vi dao động khác nhau, chẳng hạn như dao động đơn, dao động điều hòa và dao động zigzag, được thảo luận trong cả miền thời gian và miền tần số. Ngoài ra, các phát hiện lý thuyết được xác thực bằng cách giải quyết 23 bài toán tối ưu hóa tham khảo và một số bài toán tối ưu hóa trong thực tế.

Từ khóa


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