A scalar optimization approach for averaged Hausdorff approximations of the Pareto front

This article presents a novel method to compute averaged Hausdorff (Δ_p) approximations of the Pareto fronts of multi-objective optimization problems. The underlying idea is to utilize directly the scalar optimization problem that is induced by the Δ_p performance indicator. This method can be viewed as a certain set based scalarization approach and can be addressed both by mathematical programming techniques and evolutionary algorithms (EAs). In this work, the focus is on the latter where a first single objective EA for such Δ_p approximations is proposed. Finally, the strength of the novel approach is demonstrated on some bi-objective benchmark problems with different shapes of the Pareto front.