# Multimodal Multi-objective Optimization: Comparative Study of the State-of-the-Art

arXiv: https://arxiv.org/abs/2207.04730 · HTML: https://mlsanity.com/paper/2207.04730/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2022.

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

- [A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges](https://mlsanity.com/paper/2412.11936/) (2024)
- [Preference-Conditioned Gradient Variations for Multi-Objective Quality-Diversity](https://mlsanity.com/paper/2411.12433/) (2024)
- [GaussianPSL: Soft partitioning for complex PSL problem](https://mlsanity.com/paper/2509.17889/) (2025)

## Abstract (arXiv)

Multimodal multi-objective problems (MMOPs) commonly arise in real-world problems where distant solutions in decision space correspond to very similar objective values. To obtain all solutions for MMOPs, many multimodal multi-objective evolutionary algorithms (MMEAs) have been proposed. For now, few studies have encompassed most of the recently proposed representative MMEAs and made a comparative comparison. In this study, we first review the related works during the last two decades. Then, we choose 12 state-of-the-art algorithms that utilize different diversity-maintaining techniques and compared their performance on existing test suites. Experimental results indicate the strengths and weaknesses of different techniques on different types of MMOPs, thus providing guidance on how to select/design MMEAs in specific scenarios.