  Real-world design problems are a messy combination of constraints,
objectives, and features. Exploring these problem spaces can be defined as a
Multi-Criteria Exploration (MCX) problem, whose goals are to produce a set of
diverse solutions with high performance across many objectives, while avoiding
low performance across any objectives. Quality-Diversity algorithms produce the
needed design variation, but typically consider only a single objective. We
present a new ranking, T-DominO, specifically designed to handle multiple
objectives in MCX problems. T-DominO ranks individuals relative to other
solutions in the archive, favoring individuals with balanced performance over
those which excel at a few objectives at the cost of the others. Keeping only a
single balanced solution in each MAP-Elites bin maintains the visual
accessibility of the archive -- a strong asset for design exploration. We
illustrate our approach on a set of easily understood benchmarks, and showcase
its potential in a many-objective real-world architecture case study.
