不确定多目标优化问题的标量化与鲁棒化研究——基于极小极大鲁棒优化方法分析

Scalarization and Robustification for Uncertain Multi-Objective Optimization Problems—An Analysis Based on Minimax Robust Optimization

摘要: 本文针对不确定多目标优化问题，采用标量化与极小极大鲁棒优化结合的方法，以应对不确定性与多目标之间的冲突性。通过标量函数的序保持性质与序表示性质，建立鲁棒充分和必要最优性条件。在适当假设条件下证明标量化与鲁棒化的可交换性。并基于Gerstewitz函数构造的非线性标量化函数说明方法的有效性与适用性。

Abstract: This paper proposes a method for uncertain multi-objective optimization problems that combines scalarization with minimax robust optimization to handle both uncertainty and conflicts among multiple objectives. Using scalarizing functions with order-preserving and order-representing properties, necessary and sufficient robust optimality conditions are established. Under appropriate assumptions, the commutativity between scalarization and robustification is proved. Furthermore, a nonlinear scalarization function constructed based on the Gerstewitz function is employed to illustrate the effectiveness and applicability of the method.