Hot Off the Press: A Newton Method for Hausdorff Approximations of the Pareto Front within Multi-objective Evolutionary Algorithms

Here we briefly summarize the main findings of the above mentioned paper by Hao Wang et al., 2024. In this work, a novel set-based Newton method for Hausdorff approximations of the Pareto front is proposed for the use within multi-objective evolutionary algorithms (MOEAs). To this end, first a previously proposed set-based Newton step is generalized for the treatment of both equality and inequality constraints and for the use of general reference sets. Since the target reference set (i.e., the Pareto front) is not given, in a next step a particular strategy is proposed to obtain an approximation of this set via using the information of the used MOEA during its run. Finally, the strength of the resulting Newton method as post-processing step is demonstrated on several test functions and different base MOEAs.