# Local Optima Networks: A New Model of Combinatorial Fitness Landscapes

arXiv: https://arxiv.org/abs/1402.2959 · HTML: https://mlsanity.com/paper/1402.2959/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2014.

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

- [Fitness Landscape of Large Language Model-Assisted Automated Algorithm Search](https://mlsanity.com/paper/2504.19636/) (2025)
- [Understanding fitness landscapes in morpho-evolution via local optima networks](https://mlsanity.com/paper/2402.07822/) (2024)
- [Behaviour Space Analysis of LLM-driven Meta-heuristic Discovery](https://mlsanity.com/paper/2507.03605/) (2025)
- [Constraint Programming to Discover One-Flip Local Optima of Quadratic Unconstrained Binary Optimization Problems](https://mlsanity.com/paper/2104.01709/) (2021)
- [A Survey of Features Used for Representing Black-box Single-objective Continuous Optimization](https://mlsanity.com/paper/2406.06629/) (2024)
- [Complexity Scaling Laws for Neural Models using Combinatorial Optimization](https://mlsanity.com/paper/2506.12932/) (2025)
- [Local Optima Correlation Assisted Adaptive Operator Selection](https://mlsanity.com/paper/2305.02805/) (2023)
- [ClustOpt: A Clustering-based Approach for Representing and Visualizing the Search Dynamics of Numerical Metaheuristic Optimization Algorithms](https://mlsanity.com/paper/2507.02337/) (2025)
- [Nearest-Better Network for Visualizing and Analyzing Combinatorial Optimization Problems: A Unified Tool](https://mlsanity.com/paper/2507.22440/) (2025)
- [Proximal basin hopping: global optimization with guarantees](https://mlsanity.com/paper/2605.18364/) (2026)
- [Semantic Space Search Trajectory Networks](https://mlsanity.com/paper/2607.25122/) (2026)

## Abstract (arXiv)

This chapter overviews a recently introduced network-based model of combinatorial landscapes: Local Optima Networks (LON). The model compresses the information given by the whole search space into a smaller mathematical object that is a graph having as vertices the local optima and as edges the possible weighted transitions between them. Two definitions of edges have been proposed: basin-transition and escape-edges, which capture relevant topological features of the underlying search spaces. This network model brings a new set of metrics to characterize the structure of combinatorial landscapes, those associated with the science of complex networks. These metrics are described, and results are presented of local optima network extraction and analysis for two selected combinatorial landscapes: NK landscapes and the quadratic assignment problem. Network features are found to correlate with and even predict the performance of heuristic search algorithms operating on these problems.