# A Literature Survey of Benchmark Functions For Global Optimization Problems

arXiv: https://arxiv.org/abs/1308.4008 · HTML: https://mlsanity.com/paper/1308.4008/

## Key facts

- Cited by 77 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2013.

## Built on by (most cited first, 30 of 77)

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- [SP2: A Second Order Stochastic Polyak Method](https://mlsanity.com/paper/2207.08171/) (2022)
- [Born-Infeld (BI) for AI: Energy-Conserving Descent (ECD) for Optimization](https://mlsanity.com/paper/2201.11137/) (2022)
- [Bayesian Optimization of Function Networks with Partial Evaluations](https://mlsanity.com/paper/2311.02146/) (2023)
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- [Quantum Langevin Dynamics for Optimization](https://mlsanity.com/paper/2311.15587/) (2023)
- [Bandits with Preference Feedback: A Stackelberg Game Perspective](https://mlsanity.com/paper/2406.16745/) (2024)
- [No-Regret Constrained Bayesian Optimization of Noisy and Expensive Hybrid Models using Differentiable Quantile Function Approximations](https://mlsanity.com/paper/2305.03824/) (2023)
- [Improving Energy Conserving Descent for Machine Learning: Theory and Practice](https://mlsanity.com/paper/2306.00352/) (2023)
- [Optimizing Algorithms From Pairwise User Preferences](https://mlsanity.com/paper/2308.04571/) (2023)
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- [Agent-based Collaborative Random Search for Hyper-parameter Tuning and Global Function Optimization](https://mlsanity.com/paper/2303.03394/) (2023)
- [Gradient is All You Need? How Consensus-Based Optimization can be Interpreted as a Stochastic Relaxation of Gradient Descent](https://mlsanity.com/paper/2306.09778/) (2023)
- [Deterministic Global Optimization of the Acquisition Function in Bayesian Optimization: To Do or Not To Do?](https://mlsanity.com/paper/2503.03625/) (2025)
- [Bayesian Optimization from Human Feedback: Near-Optimal Regret Bounds](https://mlsanity.com/paper/2505.23673/) (2025)
- [Evolutionary Multi-Task Optimization for LLM-Guided Program Discovery](https://mlsanity.com/paper/2605.22613/) (2026)
- [Hierarchical Collaborative Hyper-parameter Tuning](https://mlsanity.com/paper/2205.05272/) (2022)
- [LABCAT: Locally adaptive Bayesian optimization using principal-component-aligned trust regions](https://mlsanity.com/paper/2311.11328/) (2023)
- [Evolving Benchmark Functions to Compare Evolutionary Algorithms via Genetic Programming](https://mlsanity.com/paper/2403.14146/) (2024)
- [BEACON: A Bayesian Optimization Inspired Strategy for Efficient Novelty Search](https://mlsanity.com/paper/2406.03616/) (2024)
- [Discovering Quality-Diversity Algorithms via Meta-Black-Box Optimization](https://mlsanity.com/paper/2502.02190/) (2025)
- [Optimizing over an ensemble of neural networks](https://mlsanity.com/paper/2112.07007/) (2021)

## Abstract (arXiv)

Test functions are important to validate and compare the performance of optimization algorithms. There have been many test or benchmark functions reported in the literature; however, there is no standard list or set of benchmark functions. Ideally, test functions should have diverse properties so that can be truly useful to test new algorithms in an unbiased way. For this purpose, we have reviewed and compiled a rich set of 175 benchmark functions for unconstrained optimization problems with diverse properties in terms of modality, separability, and valley landscape. This is by far the most complete set of functions so far in the literature, and tt can be expected this complete set of functions can be used for validation of new optimization in the future.