A trust region method for uncertain multiobjective optimization: comparative analysis with existing descent methods

Uncertain optimization problems play a crucial role in fields that involve decision-making under uncertainty, such as finance, supply chain management, energy systems, healthcare, transportation, engineering design, risk management, telecommunications, and agriculture. This paper develops a trust region method for uncertain multiobjective optimization problems (UMOPs). To find the solution of UMOP, an objective-wise worst-case-type robust counterpart (OWRC) is considered, which transforms the UMOP into a deterministic multiobjective optimization problem (MOP). To solve the OWRC, a trust region algorithm is developed, and the global convergence of this algorithm is also presented. After that, the trust region algorithm is compared with existing methods (e.g., steepest descent method, Newton’s method, modified quasi-Newton method, weighted sum method) for UMOP. The algorithm’s effectiveness is validated through numerical test problems using performance profiles.