# Anytime Bi-Objective Optimization with a Hybrid Multi-Objective CMA-ES (HMO-CMA-ES)

Source: [Anytime Bi-Objective Optimization with a Hybrid Multi-Objective CMA-ES (HMO-CMA-ES)](<https://www.sota2.com/research/paper/68fa62801e209131ce9f9abd>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:56:31.814Z

Authors: Ilya Loshchilov, Tobias Glasmachers

Published: 2016-05-09T19:58:29.000Z

## Abstract

We propose a multi-objective optimization algorithm aimed at achieving good anytime performance over a wide range of problems. Performance is assessed in terms of the hypervolume metric. The algorithm called HMO-CMA-ES represents a hybrid of several old and new variants of CMA-ES, complemented by BOBYQA as a warm start. We benchmark HMO-CMA-ES on the recently introduced bi-objective problem suite of the COCO framework (COmparing Continuous Optimizers), consisting of 55 scalable continuous optimization problems, which is used by the Black-Box Optimization Benchmarking (BBOB) Workshop 2016.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1605.02720>)

[PDF](<https://arxiv.org/pdf/1605.02720.pdf>)