Preferences-Based Choice Prediction in Evolutionary Multi-objective Optimization

Abstract

Evolutionary multi-objective algorithms (EMOAs) of the type of NSGA-2 approximate the Pareto-front, after which a decision-maker (DM) is confounded with the primary task of selecting the best solution amongst all the equally good solutions on the Pareto-front. In this paper, we complement the popular NSGA-2 EMOA by posteriori identifying a DM’s best solution among the candidate solutions on the Pareto-front, generated through NSGA-2. To this end, we employ a preference-based learning approach to learn an abstract ideal reference point of the DM on the multi-objective space, which reflects the compromises the DM makes against a set of conflicting objectives. The solution that is closest to this reference-point is then predicted as the DM’s best solution. The pairwise comparisons of the candidate solutions provides the training information for our learning model. The experimental results on ZDT1 dataset shows that the proposed approach is not only intuitive, but also easy to apply, and robust to inconsistencies in the DM’s preference statements.

A Benchmark Function

Problem ZDT1 minimizes the two objective functions $f_1(\mathbf {x})$ and $f_2(\mathbf {x})$ with $f_1(\mathbf {x}) = x_1$ and $f_2(\mathbf {x},\mathbf {z}) = g(\mathbf {z}) h(f_1(\mathbf {x}),g(\mathbf {z}))$ with $g(\mathbf {z}) = 1+ \sum _{i=1}^N z_i /N$ and $h(f_1(\mathbf {x}),g(\mathbf {z})) = 1- \sqrt{f_1(\mathbf {x}) / g(\mathbf {z}})$.