# Incorporating Surprisingly Popular Algorithm and Euclidean Distance-based Adaptive Topology into PSO

arXiv: https://arxiv.org/abs/2108.11173 · HTML: https://mlsanity.com/paper/2108.11173/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Aug 2021.

## Built on by (most cited first, 5 of 5)

- [Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectives](https://mlsanity.com/paper/2406.00415/) (2024)
- [An Efficient Diffusion-based Non-Autoregressive Solver for Traveling Salesman Problem](https://mlsanity.com/paper/2501.13767/) (2025)
- [EFormer: An Effective Edge-based Transformer for Vehicle Routing Problems](https://mlsanity.com/paper/2506.16428/) (2025)
- [Efficient Neural Combinatorial Optimization Solver for the Min-max Heterogeneous Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/2507.21386/) (2025)
- [Towards Efficient Few-shot Graph Neural Architecture Search via Partitioning Gradient Contribution](https://mlsanity.com/paper/2506.01231/) (2025)

## Abstract (arXiv)

While many Particle Swarm Optimization (PSO) algorithms only use fitness to assess the performance of particles, in this work, we adopt Surprisingly Popular Algorithm (SPA) as a complementary metric in addition to fitness. Consequently, particles that are not widely known also have the opportunity to be selected as the learning exemplars. In addition, we propose a Euclidean distance-based adaptive topology to cooperate with SPA, where each particle only connects to k number of particles with the shortest Euclidean distance during each iteration. We also introduce the adaptive topology into heterogeneous populations to better solve large-scale problems. Specifically, the exploration sub-population better preserves the diversity of the population while the exploitation sub-population achieves fast convergence. Therefore, large-scale problems can be solved in a collaborative manner to elevate the overall performance. To evaluate the performance of our method, we conduct extensive experiments on various optimization problems, including three benchmark suites and two real-world optimization problems. The results demonstrate that our Euclidean distance-based adaptive topology outperforms the other widely adopted topologies and further suggest that our method performs significantly better than state-of-the-art PSO variants on small, medium, and large-scale problems.