A hybrid Bayesian approach for pessimistic bilevel problems with a new formulation

Dogan, Vedat; Prestwich, Steven D.; O'Sullivan, Barry

A hybrid Bayesian approach for pessimistic bilevel problems with a new formulation

Files

MODeM2024_paper_21.pdf(232.9 KB)

Accepted Version

Date

2024

Authors

Dogan, Vedat

Prestwich, Steven D.

O'Sullivan, Barry

Abstract

In many real-world problems, finding the optimal decision for a decision-maker depends on another decision-maker’s response, and it is called bilevel optimization in mathematical programming. It contains two levels of optimization problems while one appears as a constraint of another one called follower and leader, respectively. In many real-world scenarios, the lower level has multiple global optima and the upper level needs to make worst-case assumptions about the decision of the lower level, called the pessimistic case of the bilevel problem. Various approaches have been implemented over the years to solve generic bilevel problems, but few of them could be extended to pessimistic cases. In this short paper, we first propose a new formulation for the pessimistic case. In this way, we take advantage of the hierarchical structure of bilevel problems to make the results more accurate for pessimistic cases. Then, we implement a black-box approach to solve the pessimistic upper level problem to decrease the necessary function evaluations. The performance of the problem is examined by solving a test benchmark problem from the literature.

Keywords

Bayesian approach , Hybrid , Pessimistic bilevel problems , Black-box approach

Citation

Dogan V.; Preswich S. and O'Sullivan B. (2024) 'A hybrid Bayesian approach for pessimistic bilevel problems with a new formulation', 27th European Conference on Artificial Intelligence (ECAI 2024) , 19-24 October, Santiago de Compostela, Spain.