Enabling dominance resistance in visualisable distance-based many-objective problems

Abstract

The results when optimising most multi- and many-objective problems are difficult to visualise, often requiring sophisticated approaches for compressing information into planar or 3D representations, which can be difficult to decipher. Given this, distance-based test problems are attractive: they can be constructed such that the designs naturally lie on the plane, and the Pareto set elements easy to identify. As such, distance-based problems have gained in popularity as a way to visualise the distribution of designs maintained by different optimisers. Some taxing problem aspects (many-to-one mappings and multi-modality) have been embedded into planar distance-based test problems, although the full range of problem characteristics which exist in other test problem frameworks (deceptive fronts, degeneracy, etc.) have not. Here we present an augmentation to the distance-based test problem formulation which induces dominance resistance regions, which are otherwise missing from these test problems. We illustrate the performance of two popular optimisers on test problems generated from this framework, and highlight particular problems with evolutionary search that can manifest due to the problem characteristics.