Constructing evolutionary algorithms for bilevel multiobjective optimization

Abstract

We propose a procedure to construct evolutionary bilevel optimization algorithms based on recent theoretical advances that have established connections between bilevel optimization and multiobjective optimization. In the proposed procedure, a new algorithm is defined by integrating an evolutionary multiobjective optimization algorithm with a partial order that is compatible with bilevel optimization. The advantages of the procedure include the ability to harness the methodology of evolutionary multiobjective optimization for bilevel optimization and to systematically develop new algorithms for single-objective and multiobjective bilevel optimization. No regularity assumptions are used, which ensures maximal applicability of the optimization algorithms constructed by the procedure. The necessary theoretical foundation is developed and the steps of the procedure are illustrated with an example.