Thuật toán tối ưu hóa bầy đàn cho bài toán vị trí Fermat-Weber trên mặt cầu
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Abstract
The Fermat-Weber problem on a sphere is a natural extension of its planar counterpart. Due to the nonlinearity and unique geometric properties of the spherical space, the problem poses significant challenges in finding optimal solutions using traditional methods. In this study, we propose an alternative approach based on the Particle Swarm Optimization (PSO) algorithm. The algorithm is redesigned to ensure all particles remain constrained to the sphere's surface by employing a coordinate transformation technique.
Tóm tắt
Bài toán Fermat-Weber trên mặt cầu là một mở rộng tự nhiên của bài toán ấy trên mặt phẳng. Do tính phi tuyến và các tính chất hình học đặc biệt của không gian cầu, bài toán đã đặt ra nhiều thách thức trong việc tìm nghiệm tối ưu bằng các phương pháp truyền thống. Trong nghiên cứu này, một cách tiếp cận khác cho bài toán dựa trên thuật toán Tối ưu bầy đàn (Particle Swarm Optimization - PSO) được đề xuất. Thuật toán được thiết kế lại để bảo đảm các cá thể luôn di chuyển trên mặt cầu thông qua kỹ thuật đổi tọa độ.
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