# Using Well-Understood Single-Objective Functions in Multiobjective Black-Box Optimization Test Suites

arXiv: https://arxiv.org/abs/1604.00359 · HTML: https://mlsanity.com/paper/1604.00359/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2016.

## Built on by (most cited first, 10 of 10)

- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Deep-ELA: Deep Exploratory Landscape Analysis with Self-Supervised Pretrained Transformers for Single- and Multi-Objective Continuous Optimization Problems](https://mlsanity.com/paper/2401.01192/) (2024)
- [Optimal Scalarizations for Sublinear Hypervolume Regret](https://mlsanity.com/paper/2307.03288/) (2023)
- [Faster Convergence in Multi-Objective Optimization Algorithms Based on Decomposition](https://mlsanity.com/paper/2112.11939/) (2021)
- [Adaptive Regret for Bandits Made Possible: Two Queries Suffice](https://mlsanity.com/paper/2401.09278/) (2024)
- [R2 v2: The Pareto-compliant R2 Indicator for Better Benchmarking in Bi-objective Optimization](https://mlsanity.com/paper/2407.01504/) (2024)
- [Beyond Numerical Features: CNN-Driven Algorithm Selection via Contour Plots for Continuous Black-Box Optimization](https://mlsanity.com/paper/2605.20797/) (2026)
- [BONO-Bench: A Comprehensive Test Suite for Bi-objective Numerical Optimization with Traceable Pareto Sets](https://mlsanity.com/paper/2601.16970/) (2026)
- [CoAction: Cross-task Correlation-aware Pareto Set Learning](https://mlsanity.com/paper/2605.01712/) (2026)
- [SIMS: Scale-Invariant Merit-Function-Based Scalarization for Multi-Task Learning](https://mlsanity.com/paper/2609.12599/) (2026)

## Abstract (arXiv)

Several test function suites are being used for numerical benchmarking of multiobjective optimization algorithms. While they have some desirable properties, like well-understood Pareto sets and Pareto fronts of various shapes, most of the currently used functions possess characteristics that are arguably under-represented in real-world problems. They mainly stem from the easier construction of such functions and result in improbable properties such as separability, optima located exactly at the boundary constraints, and the existence of variables that solely control the distance between a solution and the Pareto front. Here, we propose an alternative way to constructing multiobjective problems-by combining existing single-objective problems from the literature. We describe in particular the bbob-biobj test suite with 55 bi-objective functions in continuous domain, and its extended version with 92 bi-objective functions (bbob-biobj-ext). Both test suites have been implemented in the COCO platform for black-box optimization benchmarking. Finally, we recommend a general procedure for creating test suites for an arbitrary number of objectives. Besides providing the formal function definitions and presenting their (known) properties, this paper also aims at giving the rationale behind our approach in terms of groups of functions with similar properties, objective space normalization, and problem instances. The latter allows us to easily compare the performance of deterministic and stochastic solvers, which is an often overlooked issue in benchmarking.