# Towards the Inferrence of Structural Similarity of Combinatorial Landscapes

arXiv: https://arxiv.org/abs/2312.02720 · HTML: https://mlsanity.com/paper/2312.02720/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 83 references that are in the map.
- First posted on arXiv 5 Dec 2023.

## Builds on (most cited first, 9 of 9)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)
- [Network Representation Learning: A Survey](https://mlsanity.com/paper/1801.05852/) (2017)
- [Automated Algorithm Selection on Continuous Black-Box Problems By Combining Exploratory Landscape Analysis and Machine Learning](https://mlsanity.com/paper/1711.08921/) (2017)
- [Comprehensive Feature-Based Landscape Analysis of Continuous and Constrained Optimization Problems Using the R-Package flacco](https://mlsanity.com/paper/1708.05258/) (2017)
- [HPO X ELA: Investigating Hyperparameter Optimization Landscapes by Means of Exploratory Landscape Analysis](https://mlsanity.com/paper/2208.00220/) (2022)
- [Benchmarking Feature-based Algorithm Selection Systems for Black-box Numerical Optimization](https://mlsanity.com/paper/2109.08377/) (2021)
- [On the Hyperparameter Loss Landscapes of Machine Learning Models: An Exploratory Study](https://mlsanity.com/paper/2311.14014/) (2023)
- [A Local Optima Network Analysis of the Feedforward Neural Architecture Space](https://mlsanity.com/paper/2206.06903/) (2022)

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

- [Rethinking Performance Analysis for Configurable Software Systems: A Case Study from a Fitness Landscape Perspective](https://mlsanity.com/paper/2412.16888/) (2024)

## Abstract (arXiv)

One of the most common problem-solving heuristics is by analogy. For a given problem, a solver can be viewed as a strategic walk on its fitness landscape. Thus if a solver works for one problem instance, we expect it will also be effective for other instances whose fitness landscapes essentially share structural similarities with each other. However, due to the black-box nature of combinatorial optimization, it is far from trivial to infer such similarity in real-world scenarios. To bridge this gap, by using local optima network as a proxy of fitness landscapes, this paper proposed to leverage graph data mining techniques to conduct qualitative and quantitative analyses to explore the latent topological structural information embedded in those landscapes. By conducting large-scale empirical experiments on three classic combinatorial optimization problems, we gain concrete evidence to support the existence of structural similarity between landscapes of the same classes within neighboring dimensions. We also interrogated the relationship between landscapes of different problem classes.