# An Analysis of Phenotypic Diversity in Multi-Solution Optimization

arXiv: https://arxiv.org/abs/2105.04252 · HTML: https://mlsanity.com/paper/2105.04252/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 10 May 2021.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Robots that can adapt like animals](https://mlsanity.com/paper/1407.3501/) (2014)
- [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)
- [Autonomous skill discovery with Quality-Diversity and Unsupervised Descriptors](https://mlsanity.com/paper/1905.11874/) (2019)
- [PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization](https://mlsanity.com/paper/1701.00879/) (2017)

## Built on by (most cited first, 3 of 3)

- [Discovering and Exploiting Sparse Rewards in a Learned Behavior Space](https://mlsanity.com/paper/2111.01919/) (2021)
- [Full Domain Analysis in Fluid Dynamics](https://mlsanity.com/paper/2505.22275/) (2025)
- [Efficient Quality Diversity Optimization of 3D Buildings through 2D Pre-optimization](https://mlsanity.com/paper/2303.15896/) (2023)

## Abstract (arXiv)

More and more, optimization methods are used to find diverse solution sets. We compare solution diversity in multi-objective optimization, multimodal optimization, and quality diversity in a simple domain. We show that multiobjective optimization does not always produce much diversity, multimodal optimization produces higher fitness solutions, and quality diversity is not sensitive to genetic neutrality and creates the most diverse set of solutions. An autoencoder is used to discover phenotypic features automatically, producing an even more diverse solution set with quality diversity. Finally, we make recommendations about when to use which approach.