A modified quasi-Newton method for uncertain multiobjective optimization problems under a finite uncertainty set

ABSTRACT

In this article, a modified quasi-Newton method is developed for the robust counterpart (RC) of an uncertain multiobjective optimization problem (UMOP). Specifically, the RC of a UMOP is the minimum of an objective-wise worst-case (OWWC) type RC. To determine the descent direction for the RC, a subproblem using a common Hessian approximation is constructed. An inexact line search technique based on the Armijo technique is employed to find an appropriate step length. Furthermore, a modified version of the Davidon–Fletcher–Powell (DFP) update formula is developed for the RC. A modified quasi-Newton algorithm is built using descent direction step length, and DFP Hessian update formula. Furthermore, the convergence of the modified quasi-Newton algorithm is also discussed. Finally, the modified quasi-Newton algorithm is illustrated with a set of test problems and compared with the weighted sum method. Moreover, it is demonstrated that the algorithm is effective for both convex and non-convex problems.

KEYWORDS:

• Multiobjective optimization under uncertainty
• robust optimization
• robust efficiency
• quasi-Newton method
• line search techniques

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research contribution of Shubham Kumar is supported by a Government of India Council of Scientific and Industrial Research fellowship [Program No. 09/1174(0006)/2019-EMR-I, New Delhi]; Debdas Ghosh acknowledges a Mathematical Research Impact Centric Support research grant [MTR/2021/000696] and a Core Research Grant research grant [CRG/2022/001347] from Science and Engineering Research Board, India, to carry out this research work.