Finding reliable solutions in bi level optimization problems under uncertainties

Abstract

Bilevel optimization problems are referred to as having a nested inner optimization problem as a constraint to a outer optimization problem in the domain of mathematical programming. It is also known as Stackelberg problems in game theory. In the recent past, bilevel optimization problems have received a growing attention because of its relevance in practice applications. However, the hierarchical structure makes these problems difficult to handle and they are commonly optimized with a deterministic setup. With presence of constrains, bilevel optimization problems are considered for finding reliable solutions which are subjected to a possess a minimum reliability requirement under decision variable uncertainties. Definition of reliable bilevel solution, the effect of lower and upper level uncertainties on reliable bilevel solution, development of efficient reliable bilevel evolutionary algorithm, and supporting simulation results on test and engineering design problems amply demonstrate their further use in other practical bilevel problems.