Title: Solution of Uncertain Multiobjective Optimization Problems by Using Nonlinear Conjugate Gradient Method Show Chinese title

Title: 使用非线性共轭梯度法求解不确定多目标优化问题

Abstract: This paper introduces a nonlinear conjugate gradient method (NCGM) for addressing the robust counterpart of uncertain multiobjective optimization problems (UMOPs). Here, the robust counterpart is defined as the minimum across objective-wise worst-case scenarios. There are some drawbacks to using scalarization techniques to solve the robust counterparts of UMOPs, such as the pre-specification and restrictions of weights, and function importance that is unknown beforehand. NCGM is free from any kind of priori chosen scalars or ordering information of objective functions as accepted in scalarization methods. With the help of NCGM, we determine the critical point for the robust counterpart of UMOP, which is the robust critical point for UMOP. To tackle this robust counterpart using the NCGM, the approach involves constructing and solving a subproblem to determine a descent direction. Subsequently, a new direction is derived based on parameter selection methods such as Fletcher-Reeves, conjugate descent, Dai-Yuan, Polak-Ribi$\grave{e}$re-Polyak, and Hestenes-Stiefel. An Armijo-type inexact line search is employed to identify an appropriate step length. Utilizing descent direction and step length, a sequence is generated, and convergence of the proposed method is established. The effectiveness of the proposed method is verified and compared against an existing method using a set of test problems. Show Chinese abstract

Abstract: 本文介绍了一种非线性共轭梯度法（NCGM），用于解决不确定多目标优化问题（UMOP）的鲁棒对策问题。在这里，鲁棒对策被定义为目标函数最坏情况下的最小值。使用标量化技术解决UMOP的鲁棒对策存在一些缺点，例如权重的预设和限制，以及事先未知的目标函数的重要性。NCGM无需采用标量化方法中接受的任何先验选择的标量或目标函数的排序信息。借助NCGM，我们确定了UMOP的鲁棒对策的关键点，即UMOP的鲁棒关键点。为了用NCGM解决此鲁棒对策，该方法涉及构建和求解一个子问题以确定下降方向。随后，基于Fletcher-Reeves、共轭下降、Dai-Yuan、Polak-Ribi$\grave{e}$重Polyak和Hestenes-Stiefel等参数选择方法得出新的方向。采用Armijo型非精确线搜索来确定适当的步长。利用下降方向和步长生成一个序列，并证明所提出方法的收敛性。通过一组测试问题验证并比较了所提出方法的有效性与现有方法。