A robust nonlinear conjugate gradient technique for uncertain multiobjective optimization problems

This paper addresses a class of uncertain multiobjective optimisation problems by reformulating them as deterministic objective-wise worst-case robust counterparts. To solve the resulting robust multiobjective optimisation problem, we develop a robust nonlinear conjugate gradient method in which a descent direction is first obtained by solving an auxiliary optimisation subproblem and then updated using classical conjugate gradient formulas, including Fletcher–Reeves, Conjugate Descent, Dai–Yuan, Polak–Ribi’ere–Polyak, and Hestenes–Stiefel. The proposed update strategy is designed to preserve the sufficient descent property, while employing an Armijo-type inexact line search to determine suitable step sizes. We establish the global convergence of the proposed algorithm under standard assumptions. Numerical experiments on a collection of benchmark test problems are conducted to evaluate the effectiveness of the proposed framework. The results are compared with those obtained from the classical weighted-sum approach and existing descent-based methods using performance profiles based on iteration counts, function evaluations, delta spread, and hypervolume metrics. The computational results demonstrate that the proposed robust nonlinear conjugate gradient framework is efficient, competitive, and capable of producing high-quality approximations of robust Pareto solutions for uncertain multiobjective optimisation problems.