Dung beetle optimizer for mixed additive and multiplicative error model with inequality constraints

Establishing constraint relationships for parameters based on prior information is beneficial for improving the accuracy of geodetic measurements. However, there is limited research on constraint relationships in the form of inequalities for mixed additive and multiplicative error models. Addressing the limitations and algorithm improvements of existing research, with a focus on universality, stability, and efficiency, the parameter estimation method for mixed additive and multiplicative error model with inequality constraints needs to meet various requirements such as handling invalid constraints, excellent computational speed, certain robustness, addressing the impact of multiplicative errors on gradient calculations, or even not requiring gradient calculations, and having a high fault tolerance rate during the iterative process. This paper integrates the dung beetle optimizer with the aggregation function method, improves the original algorithm based on the differences between additive and multiplicative errors, analyzes and solves the issues that need to be considered when using the aggregation function method, proposes new ideas such as parallel operation of two formulas and value range contraction mechanisms, and provides recommendations for setting various operational parameters in optimizing the dung beetle algorithm for different mixed additive and multiplicative error models. The algorithm in this article has undergone repeated experiments with various models and thousands of samples. In all experiments, it effectively utilizes prior information for constraints and achieves more accurate parameter estimates. The universality, efficiency, and stability of the algorithm have been demonstrated.