# Lazy Parameter Tuning and Control: Choosing All Parameters Randomly From a Power-Law Distribution

arXiv: https://arxiv.org/abs/2104.06714 · HTML: https://mlsanity.com/paper/2104.06714/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 57 references that are in the map.
- First posted on arXiv 14 Apr 2021.

## Builds on (most cited first, 19 of 19)

- [Fast Genetic Algorithms](https://mlsanity.com/paper/1703.03334/) (2017)
- [Probabilistic Tools for the Analysis of Randomized Optimization Heuristics](https://mlsanity.com/paper/1801.06733/) (2018)
- [Does Comma Selection Help To Cope With Local Optima](https://mlsanity.com/paper/2004.01274/) (2020)
- [Self-Adjusting Evolutionary Algorithms for Multimodal Optimization](https://mlsanity.com/paper/2004.03266/) (2020)
- [The Runtime of the Compact Genetic Algorithm on Jump Functions](https://mlsanity.com/paper/1908.06527/) (2019)
- [Stagnation Detection with Randomized Local Search](https://mlsanity.com/paper/2101.12054/) (2021)
- [Runtime Analysis of a Heavy-Tailed (1+(λ,λ)) Genetic Algorithm on Jump Functions](https://mlsanity.com/paper/2006.03523/) (2020)
- [Fixed-Target Runtime Analysis](https://mlsanity.com/paper/2004.09613/) (2020)
- [First Steps Towards a Runtime Analysis When Starting With a Good Solution](https://mlsanity.com/paper/2006.12161/) (2020)
- [A Tight Runtime Analysis for the (μ + λ) EA](https://mlsanity.com/paper/1812.11061/) (2018)
- [A Rigorous Runtime Analysis of the (1 + (λ, λ)) GA on Jump Functions](https://mlsanity.com/paper/2004.06702/) (2020)
- [Stagnation Detection in Highly Multimodal Fitness Landscapes](https://mlsanity.com/paper/2104.04395/) (2021)
- [Runtime Analysis of the (1+(λ,λ)) Genetic Algorithm on Random Satisfiable 3-CNF Formulas](https://mlsanity.com/paper/1704.04366/) (2017)
- [Evolutionary Algorithms and Submodular Functions: Benefits of Heavy-Tailed Mutations](https://mlsanity.com/paper/1805.10902/) (2018)
- [Runtime Analysis for Self-adaptive Mutation Rates](https://mlsanity.com/paper/1811.12824/) (2018)
- [Artificial Immune Systems Can Find Arbitrarily Good Approximations for the NP-Hard Number Partitioning Problem](https://mlsanity.com/paper/1806.00300/) (2018)
- [A Tight Runtime Analysis for the cGA on Jump Functions---EDAs Can Cross Fitness Valleys at No Extra Cost](https://mlsanity.com/paper/1903.10983/) (2019)
- [Solving Problems with Unknown Solution Length at (Almost) No Extra Cost](https://mlsanity.com/paper/1506.05913/) (2015)
- [Optimal Parameter Settings for the (1+(λ, λ)) Genetic Algorithm](https://mlsanity.com/paper/1604.01088/) (2016)

## Built on by (most cited first, 11 of 11)

- [A First Runtime Analysis of the NSGA-II on a Multimodal Problem](https://mlsanity.com/paper/2204.13750/) (2022)
- [Choosing the Right Algorithm With Hints From Complexity Theory](https://mlsanity.com/paper/2109.06584/) (2021)
- [How the Move Acceptance Hyper-Heuristic Copes With Local Optima: Drastic Differences Between Jumps and Cliffs](https://mlsanity.com/paper/2304.10414/) (2023)
- [An Extended Jump Functions Benchmark for the Analysis of Randomized Search Heuristics](https://mlsanity.com/paper/2105.03090/) (2021)
- [The (1+(λ,λ)) Global SEMO Algorithm](https://mlsanity.com/paper/2210.03618/) (2022)
- [Approximation Guarantees for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)](https://mlsanity.com/paper/2203.02693/) (2022)
- [Towards a Stronger Theory for Permutation-based Evolutionary Algorithms](https://mlsanity.com/paper/2204.07637/) (2022)
- [Multi-parameter Control for the (1+(λ,λ))-GA on OneMax via Deep Reinforcement Learning](https://mlsanity.com/paper/2505.12982/) (2025)
- [Runtime Analysis for Permutation-based Evolutionary Algorithms](https://mlsanity.com/paper/2207.04045/) (2022)
- [Larger Offspring Populations Help the (1 + (λ, λ)) Genetic Algorithm to Overcome the Noise](https://mlsanity.com/paper/2305.04553/) (2023)
- [Discovering Interpretable Multi-Parameter Control Policies for Evolutionary Algorithms Using Deep Reinforcement Learning](https://mlsanity.com/paper/2606.10129/) (2026)

## Abstract (arXiv)

Most evolutionary algorithms have multiple parameters and their values drastically affect the performance. Due to the often complicated interplay of the parameters, setting these values right for a particular problem (parameter tuning) is a challenging task. This task becomes even more complicated when the optimal parameter values change significantly during the run of the algorithm since then a dynamic parameter choice (parameter control) is necessary. In this work, we propose a lazy but effective solution, namely choosing all parameter values (where this makes sense) in each iteration randomly from a suitably scaled power-law distribution. To demonstrate the effectiveness of this approach, we perform runtime analyses of the (1+(λ,λ)) genetic algorithm with all three parameters chosen in this manner. We show that this algorithm on the one hand can imitate simple hill-climbers like the (1+1) EA, giving the same asymptotic runtime on problems like OneMax, LeadingOnes, or Minimum Spanning Tree. On the other hand, this algorithm is also very efficient on jump functions, where the best static parameters are very different from those necessary to optimize simple problems. We prove a performance guarantee that is comparable to the best performance known for static parameters. For the most interesting case that the jump size k is constant, we prove that our performance is asymptotically better than what can be obtained with any static parameter choice. We complement our theoretical results with a rigorous empirical study confirming what the asymptotic runtime results suggest.