Phương pháp tối ưu hóa dựa trên mô phỏng sử dụng hàm cơ sở bán kính

Springer Science and Business Media LLC - Tập 11 - Trang 501-532 - 2009
Stefan Jakobsson1, Michael Patriksson2,3, Johan Rudholm2,3, Adam Wojciechowski2,3
1Fraunhofer–Chalmers Research Centre for Industrial Mathematics, Gothenburg, Sweden
2Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden
3Department of Mathematical Sciences, University of Gothenburg, Gothenburg, Sweden

Tóm tắt

Chúng tôi đề xuất một thuật toán cho tối ưu hóa toàn cầu các hàm đen hộp tốn kém và có tiếng ồn bằng cách sử dụng mô hình đại diện dựa trên hàm cơ sở bán kính (RBFs). Một phương pháp xấp xỉ dựa trên RBF được giới thiệu nhằm xử lý tiếng ồn. Các điểm mới được chọn để giảm thiểu tổng độ không chắc chắn của mô hình được trọng số dựa trên giá trị của hàm đại diện. Thuật toán được mở rộng cho các hàm mục tiêu đa chiều bằng cách trọng số dựa vào khoảng cách tới mặt trước Pareto đại diện; như vậy nó trở thành thuật toán đầu tiên cho các bài toán đa mục tiêu tốn kém, có tiếng ồn trong tài liệu. Kết quả số học trên các hàm kiểm tra phân tích cho thấy tiềm năng so với các thuật toán khác (thương mại), cũng như các kết quả từ một bài toán tối ưu hóa dựa trên mô phỏng.

Từ khóa

#tối ưu hóa toàn cầu #hàm đen hộp #tiếng ồn #mô hình đại diện #hàm cơ sở bán kính #hàm mục tiêu đa chiều #mặt trước Pareto

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