T-DominO: Exploring Multiple Criteria with Quality-Diversity and the Tournament Dominance Objective

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.