Generalized ordered weighted aggregation robustness to solve uncertain single objective optimization problems

Abstract

Robust optimization aims to find optimum points from the collection of points that are feasible for every possible scenario of a given uncertain set. An optimum solution to a robust optimization problem is commonly found by the min-max robust counterpart or by the best out of the worst-cases analysis. In this article, we introduce a new counterpart with the help of the generalized or-dered weighted aggregation (GOWA) operator to solve uncertain single objective optimization problems. After introducing GOWA robustness, we analyze a few elementary properties of the GOWA robust objective function, like continuity, monotonicity, coerciveness, local Lipschitz property, and subdifferential regular-ity. An approach to computing the Clarke subdifferential of the GOWA robust objective function is also provided. We discuss the relationship between the con-cept of GOWA robustness with other existing robustness flimsily, highly, min-max, light, and min-min robustness. We show that in a particular case, GOWA robustness reduces to the commonly used min-max robustness. The entire paper is supported by several geometrical and numerical illustrations. © 2025 Yokohama Publications. All rights reserved.