Optimization Algorithm Based on Weighted Triangular Barycentric Monte Carlo Method

In traditional Monte Carlo algorithms, the issues of blind sampling and the risk of falling into local optima are significant limitations, which can hinder the search for optimal solutions. To overcome these challenges, this paper introduces a Monte Carlo optimization algorithm based on a weighted triangular center of gravity. The proposed algorithm constructs the search space by initializing a population of triangles, where each triangle is defined by its three vertices. Instead of relying on random sampling, the algorithm calculates the center of gravity of each triangle by incorporating the fitness weights of the vertices. This approach ensures that the center of gravity moves toward the better-performing vertices, thereby enhancing the guidance towards high-quality solutions. Additionally, the algorithm implements a fitness sorting mechanism, retaining the best-performing triangles and discarding the lower-ranked individuals to refine the search process and improve the convergence rate. As a result, the algorithm effectively avoids local optima and promotes global optimization. To verify the performance and effectiveness of the proposed method, we tested it on several well-known benchmark functions, including Sphere, Rastrigin, and Griewank. The experimental results show that compared to the traditional Monte Carlo method, the weighted triangular barycentric Monte Carlo method significantly improves both the accuracy and stability of the optimization process. This novel optimization technique provides an efficient and reliable solution for complex optimization problems, demonstrating its potential for broader applications in the field of computational optimization.