A neural network transformation based global optimization algorithm

Abstract

In the field of global optimization, finding the global optimum for complex problems remains a significant challenge. Traditional optimization methods often struggle to escape local minima and achieve global solutions, particularly when the initial solutions are far from the global optimum. This study addresses these challenges by introducing a novel algorithm called neural network transformation based global optimization. Our approach transforms original decision variables into higher-dimensional neural network parameters and constructs an empirical loss function using multiple sample points. By employing stochastic gradient descent for training, our approach effectively navigates the optimization landscape, escaping local minima and reaching low-loss solutions with high probability, even from distant starting points. We also propose a hybrid optimization method that combines the strength of metaheuristic strategies. The experimental results show that our hybrid method surpasses traditional global optimization algorithms, achieving an average 5% improvement in the success rate across benchmark functions. In practical applications, such as the B-spline curve approximation, our method reduces the fitting error by at least 10% compared with conventional approaches, delivering more accurate results. This study contributes a new gradient-based algorithm to the global optimization field, particularly effective for complex real-world problems where the initial points are far from the global minima.