A Feature Rich Distance-Based Many-Objective Visualisable Test Problem Generator

Abstract

In optimiser analysis and design it is informative to visualise how a search point/population moves through the design space over time. Visualisable distance-based many-objective optimisation problems have been developed whose design space is in two-dimensions with arbitrarily many objective dimensions. Previous work has shown how disconnected Pareto sets may be formed, how problems can be projected to and from arbitrarily many design dimensions, and how dominance resistant regions of design space may be defined. Most recently, a test suite has been proposed using distances to lines rather than points. However, active use of visualisable problems has been limited. This may be because the type of problem characteristics available has been relatively limited compared to many practical problems (and non-visualisable problem suites). Here we introduce the mechanisms required to embed several widely seen problem characteristics in the existing problem framework. These include variable density of solutions in objective space, landscape discontinuities, varying objective ranges, neutrality, and non-identical disconnected Pareto set regions. Furthermore, we provide an automatic problem generator (as opposed to hand-tuned problem definitions). The flexibility of the problem generator is demonstrated by analysing the performance of popular optimisers on a range of sampled instances.