In the evolving landscape of artificial intelligence and machine learning, the choice of optimization algorithm can significantly impact the success of model training and the accuracy of predictions. This paper embark...In the evolving landscape of artificial intelligence and machine learning, the choice of optimization algorithm can significantly impact the success of model training and the accuracy of predictions. This paper embarks on a rigorous and comprehensive exploration of widely adopted optimization techniques, specifically focusing on their performance when applied to the notoriously challenging Rosenbrock function. As a benchmark problem known for its deceptive curvature and narrow valleys, the Rosenbrock function provides a fertile ground for examining the nuances and intricacies of algorithmic behavior. The study delves into a diverse array of optimization methods, including traditional Gradient Descent, its stochastic variant (SGD), and the more sophisticated Gradient Descent with Momentum. The investigation further extends to adaptive methods like RMSprop, AdaGrad, and the highly regarded Adam optimizer. By meticulously analyzing and visualizing the optimization paths, convergence rates, and gradient norms, this paper uncovers critical insights into the strengths and limitations of each technique. Our findings not only illuminate the intricate dynamics of these algorithms but also offer actionable guidance for their deployment in complex, real-world optimization problems. This comparative analysis promises to intrigue and inspire researchers and practitioners alike, as it reveals the subtle yet profound impacts of algorithmic choices in the quest for optimization excellence.展开更多
The Rosenbrock function optimization belongs to unconstrained optimization problems, and its global minimum value is located at the bottom of a smooth and narrow valley of the parabolic shape. It is very difficult to ...The Rosenbrock function optimization belongs to unconstrained optimization problems, and its global minimum value is located at the bottom of a smooth and narrow valley of the parabolic shape. It is very difficult to find the global minimum value of the function because of the little information provided for the optimization algorithm. According to the characteristics of the Rosenbrock function, this paper specifically proposed an improved differential evolution algorithm that adopts the self-adaptive scaling factor F and crossover rate CR with elimination mechanism, which can effectively avoid premature convergence of the algorithm and local optimum. This algorithm can also expand the search range at an early stage to find the global minimum of the Rosenbrock function. Many experimental results show that the algorithm has good performance of function optimization and provides a new idea for optimization problems similar to the Rosenbrock function for some problems of special fields.展开更多
文摘In the evolving landscape of artificial intelligence and machine learning, the choice of optimization algorithm can significantly impact the success of model training and the accuracy of predictions. This paper embarks on a rigorous and comprehensive exploration of widely adopted optimization techniques, specifically focusing on their performance when applied to the notoriously challenging Rosenbrock function. As a benchmark problem known for its deceptive curvature and narrow valleys, the Rosenbrock function provides a fertile ground for examining the nuances and intricacies of algorithmic behavior. The study delves into a diverse array of optimization methods, including traditional Gradient Descent, its stochastic variant (SGD), and the more sophisticated Gradient Descent with Momentum. The investigation further extends to adaptive methods like RMSprop, AdaGrad, and the highly regarded Adam optimizer. By meticulously analyzing and visualizing the optimization paths, convergence rates, and gradient norms, this paper uncovers critical insights into the strengths and limitations of each technique. Our findings not only illuminate the intricate dynamics of these algorithms but also offer actionable guidance for their deployment in complex, real-world optimization problems. This comparative analysis promises to intrigue and inspire researchers and practitioners alike, as it reveals the subtle yet profound impacts of algorithmic choices in the quest for optimization excellence.
文摘The Rosenbrock function optimization belongs to unconstrained optimization problems, and its global minimum value is located at the bottom of a smooth and narrow valley of the parabolic shape. It is very difficult to find the global minimum value of the function because of the little information provided for the optimization algorithm. According to the characteristics of the Rosenbrock function, this paper specifically proposed an improved differential evolution algorithm that adopts the self-adaptive scaling factor F and crossover rate CR with elimination mechanism, which can effectively avoid premature convergence of the algorithm and local optimum. This algorithm can also expand the search range at an early stage to find the global minimum of the Rosenbrock function. Many experimental results show that the algorithm has good performance of function optimization and provides a new idea for optimization problems similar to the Rosenbrock function for some problems of special fields.
