# Challenges of Convex Quadratic Bi-objective Benchmark Problems

arXiv: https://arxiv.org/abs/1810.09690 · HTML: https://mlsanity.com/paper/1810.09690/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2018.

## Built on by (most cited first, 1 of 1)

- [BONO-Bench: A Comprehensive Test Suite for Bi-objective Numerical Optimization with Traceable Pareto Sets](https://mlsanity.com/paper/2601.16970/) (2026)

## Abstract (arXiv)

Convex quadratic objective functions are an important base case in state-of-the-art benchmark collections for single-objective optimization on continuous domains. Although often considered rather simple, they represent the highly relevant challenges of non-separability and ill-conditioning. In the multi-objective case, quadratic benchmark problems are under-represented. In this paper we analyze the specific challenges that can be posed by quadratic functions in the bi-objective case. Our construction yields a full factorial design of 54 different problem classes. We perform experiments with well-established algorithms to demonstrate the insights that can be supported by this function class. We find huge performance differences, which can be clearly attributed to two root causes: non-separability and alignment of the Pareto set with the coordinate system.