An Exponential Transformation Model for Solving Nonlinear Equations Systems

A novel objective function transformation model based on exponential functions is proposed to address the issue of weak specificity and strong generality in the objective function model used with single-objective optimization algorithms for solving systems of nonlinear equations through single-objective transformation techniques. During the problem transformation process, this new model, referred to as the exponential model, is introduced to effectuate the problem transformation. Various specifications of exponential functions are employed to increase diversity. Subsequently, we enhance the selected algorithm by incorporating a local search method with a Gaussian coefficient of 0.6. This method involves two searches within local spaces, effectively facilitating the identification of roots located near exceptional individuals. Experimental results on the selected test function set demonstrate that the proposed exponential model not only entirely substitutes existing models but also significantly enhances the algorithm's global search capability for solving single-objective optimization problems when compared to traditional models. When compared to the two current models, the proposed model exhibits superior performance in root-finding rate and success rate.