# Uncrowded Hypervolume Improvement: COMO-CMA-ES and the Sofomore framework

arXiv: https://arxiv.org/abs/1904.08823 · HTML: https://mlsanity.com/paper/1904.08823/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2019.

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

- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [EVO-LRP: Evolutionary Optimization of LRP for Interpretable Model Explanations](https://mlsanity.com/paper/2509.23585/) (2025)
- [Expected Hypervolume Maximization for Multiobjective Optimization under Uncertainties](https://mlsanity.com/paper/2609.19858/) (2026)

## Abstract (arXiv)

We present a framework to build a multiobjective algorithm from single-objective ones. This framework addresses the p × n-dimensional problem of finding p solutions in an n-dimensional search space, maximizing an indicator by dynamic subspace optimization. Each single-objective algorithm optimizes the indicator function given p - 1 fixed solutions. Crucially, dominated solutions minimize their distance to the empirical Pareto front defined by these p - 1 solutions. We instantiate the framework with CMA-ES as single-objective optimizer. The new algorithm, COMO-CMA-ES, is empirically shown to converge linearly on bi-objective convex-quadratic problems and is compared to MO-CMA-ES, NSGA-II and SMS-EMOA.