Many-Objective Quality Measures

A key concern when undertaking any form of optimisation is how to characterise the quality of the putative solution returned. In many-objective optimisation an added complication is that such measures are on a set of trade-off solutions. We present and discuss the commonly used quality measures for many-objective optimisation, which are a subset of those used in multi-objective optimisation. We discuss the computational aspects and theoretical properties of these measures, highlighting measures for both a posteriori and a priori approaches, where the latter incorporate preference information from a decision maker (DM). We also discuss open areas in this field and forms of many-objective optimisation which are relatively under-explored, and where appropriate quality measures are much less developed including challenges related to developing measures for interactive methods.