# Illuminating the Diversity-Fitness Trade-Off in Black-Box Optimization

arXiv: https://arxiv.org/abs/2408.16393 · HTML: https://mlsanity.com/paper/2408.16393/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 23 references that are in the map.
- First posted on arXiv 29 Aug 2024.

## Builds on (most cited first, 10 of 10)

- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting](https://mlsanity.com/paper/1603.08785/) (2016)
- [Quality and Diversity Optimization: A Unifying Modular Framework](https://mlsanity.com/paper/1708.09251/) (2017)
- [Using Centroidal Voronoi Tessellations to Scale Up the Multi-dimensional Archive of Phenotypic Elites Algorithm](https://mlsanity.com/paper/1610.05729/) (2016)
- [Procedural Content Generation through Quality Diversity](https://mlsanity.com/paper/1907.04053/) (2019)
- [IOHprofiler: A Benchmarking and Profiling Tool for Iterative Optimization Heuristics](https://mlsanity.com/paper/1810.05281/) (2018)
- [Empowering Quality Diversity in Dungeon Design with Interactive Constrained MAP-Elites](https://mlsanity.com/paper/1906.05175/) (2019)
- [Evolutionary Diversity Optimization Using Multi-Objective Indicators](https://mlsanity.com/paper/1811.06804/) (2018)
- [Discrepancy-based Evolutionary Diversity Optimization](https://mlsanity.com/paper/1802.05448/) (2018)
- [Benchmarking HillVallEA for the GECCO 2019 Competition on Multimodal Optimization](https://mlsanity.com/paper/1907.10988/) (2019)

## Abstract (arXiv)

In real-world applications, users often favor structurally diverse design choices over one high-quality solution. It is hence important to consider more solutions that decision makers can compare and further explore based on additional criteria. Alongside the existing approaches of evolutionary diversity optimization, quality diversity, and multimodal optimization, this paper presents a fresh perspective on this challenge by considering the problem of identifying a fixed number of solutions with a pairwise distance above a specified threshold while maximizing their average quality. We obtain first insight into these objectives by performing a subset selection on the search trajectories of different well-established search heuristics, whether they have been specifically designed with diversity in mind or not. We emphasize that the main goal of our work is not to present a new algorithm but to understand the capability of off-the-shelf algorithms to quantify the trade-off between the minimum pairwise distance within batches of solutions and their average quality. We also analyze how this trade-off depends on the properties of the underlying optimization problem. A possibly surprising outcome of our empirical study is the observation that naive uniform random sampling establishes a very strong baseline for our problem, hardly ever outperformed by the search trajectories of the considered heuristics. We interpret these results as a motivation to develop algorithms tailored to produce diverse solutions of high average quality.