Weakly robust global optimization of max-plus linear systems with non-negative constraint sets and its application to optimizing time parameters in data transmission systems

This paper considers the weakly robust global optimization problem of max-plus linear systems with non-negative constraint sets. A characteristic of the weak robustness of global optimization is given, and the weakly robust perturbation bound is constructed to ensure that the parameter perturbations within the bound do not affect the original global minimum and one globally optimal solution. The maximal element of each row in a max-plus matrix is used to characterize the variable elements and invariable elements, and their maximum number is determined. The relatively maximal perturbation bounds are derived by using all variable and invariable elements, and a polynomial algorithm for finding these bounds is provided. The proposed weakly robust global optimization is applied to optimizing time parameters in data transmission systems. The effectiveness of the proposed method is demonstrated by examples.