# Multi-Objective Quality Diversity Optimization

arXiv: https://arxiv.org/abs/2202.03057 · HTML: https://mlsanity.com/paper/2202.03057/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 43 references that are in the map.
- First posted on arXiv 7 Feb 2022.

## Builds on (most cited first, 14 of 14)

- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [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)
- [Covariance Matrix Adaptation for the Rapid Illumination of Behavior Space](https://mlsanity.com/paper/1912.02400/) (2019)
- [Differentiable Quality Diversity](https://mlsanity.com/paper/2106.03894/) (2021)
- [Quality-Diversity Optimization: a novel branch of stochastic optimization](https://mlsanity.com/paper/2012.04322/) (2020)
- [Diversity Policy Gradient for Sample Efficient Quality-Diversity Optimization](https://mlsanity.com/paper/2006.08505/) (2020)
- [Discovering the Elite Hypervolume by Leveraging Interspecies Correlation](https://mlsanity.com/paper/1804.03906/) (2018)
- [Scaling MAP-Elites to Deep Neuroevolution](https://mlsanity.com/paper/2003.01825/) (2020)
- [Talakat: Bullet Hell Generation through Constrained Map-Elites](https://mlsanity.com/paper/1806.04718/) (2018)
- [Quality Diversity for Multi-task Optimization](https://mlsanity.com/paper/2003.04407/) (2020)
- [Fast and stable MAP-Elites in noisy domains using deep grids](https://mlsanity.com/paper/2006.14253/) (2020)
- [General Subpopulation Framework and Taming the Conflict Inside Populations](https://mlsanity.com/paper/1901.00266/) (2019)

## Built on by (most cited first, 19 of 19)

- [QDax: A Library for Quality-Diversity and Population-based Algorithms with Hardware Acceleration](https://mlsanity.com/paper/2308.03665/) (2023)
- [Agent Skill Acquisition for Large Language Models via CycleQD](https://mlsanity.com/paper/2410.14735/) (2024)
- [The Quality-Diversity Transformer: Generating Behavior-Conditioned Trajectories with Decision Transformers](https://mlsanity.com/paper/2303.16207/) (2023)
- [Dominated Novelty Search: Rethinking Local Competition in Quality-Diversity](https://mlsanity.com/paper/2502.00593/) (2025)
- [Communication-Robust Multi-Agent Learning by Adaptable Auxiliary Multi-Agent Adversary Generation](https://mlsanity.com/paper/2305.05116/) (2023)
- [Gradient-Informed Quality Diversity for the Illumination of Discrete Spaces](https://mlsanity.com/paper/2306.05138/) (2023)
- [Embodied Co-Design for Rapidly Evolving Agents: Taxonomy, Frontiers, and Challenges](https://mlsanity.com/paper/2512.04770/) (2025)
- [Don't Bet on Luck Alone: Enhancing Behavioral Reproducibility of Quality-Diversity Solutions in Uncertain Domains](https://mlsanity.com/paper/2304.03672/) (2023)
- [Improving the Data Efficiency of Multi-Objective Quality-Diversity through Gradient Assistance and Crowding Exploration](https://mlsanity.com/paper/2302.12668/) (2023)
- [Enhancing Multi-Objective Optimization through Machine Learning-Supported Multiphysics Simulation](https://mlsanity.com/paper/2309.13179/) (2023)
- [Many-objective Optimization via Voting for Elites](https://mlsanity.com/paper/2307.02661/) (2023)
- [Evolutionary Computation for the Design and Enrichment of General-Purpose Artificial Intelligence Systems: Survey and Prospects](https://mlsanity.com/paper/2407.08745/) (2024)
- [Preference-Conditioned Gradient Variations for Multi-Objective Quality-Diversity](https://mlsanity.com/paper/2411.12433/) (2024)
- [Amortized Multi-Objective Optimization Across Tasks with Generative Solution Modeling](https://mlsanity.com/paper/2511.09598/) (2025)
- [Dynamic Quality-Diversity Search](https://mlsanity.com/paper/2404.05769/) (2024)
- [Runtime Analysis of Evolutionary Diversity Optimization on the Multi-objective (LeadingOnes, TrailingZeros) Problem](https://mlsanity.com/paper/2404.11496/) (2024)
- [Quality-Diversity Optimization as Multi-Objective Optimization](https://mlsanity.com/paper/2602.00478/) (2026)
- [Loreley: Repository-Scale Program Evolution with Quality-Diversity Search](https://mlsanity.com/paper/2608.19703/) (2026)
- [Small but Mighty: Test Suites as Improvement Signals for Self-Evolving Agents](https://mlsanity.com/paper/2610.15964/) (2026)

## Abstract (arXiv)

In this work, we consider the problem of Quality-Diversity (QD) optimization with multiple objectives. QD algorithms have been proposed to search for a large collection of both diverse and high-performing solutions instead of a single set of local optima. Thriving for diversity was shown to be useful in many industrial and robotics applications. On the other hand, most real-life problems exhibit several potentially antagonist objectives to be optimized. Hence being able to optimize for multiple objectives with an appropriate technique while thriving for diversity is important to many fields. Here, we propose an extension of the MAP-Elites algorithm in the multi-objective setting: Multi-Objective MAP-Elites (MOME). Namely, it combines the diversity inherited from the MAP-Elites grid algorithm with the strength of multi-objective optimizations by filling each cell with a Pareto Front. As such, it allows to extract diverse solutions in the descriptor space while exploring different compromises between objectives. We evaluate our method on several tasks, from standard optimization problems to robotics simulations. Our experimental evaluation shows the ability of MOME to provide diverse solutions while providing global performances similar to standard multi-objective algorithms.