Holistic Swarm Optimization (HSO) - MATLAB Implementation

Metaphor-less optimization using full-population guidance. MATLAB implementation from the published open-access paper.

Holistic Swarm Optimization (HSO)

Holistic Swarm Optimization (HSO) is a metaphor-less, population-based optimization algorithm that utilizes the entire population's fitness landscape to guide search agents. Unlike traditional algorithms that rely on local or partial data, HSO balances exploration and exploitation through:

• Utilizing entire population data
• Root Mean Squared (RMS)-based displacement coefficients
• Simulated Annealing-based selection
• Adaptive mutation

This MATLAB implementation follows the algorithm proposed in:

Holistic Swarm Optimization: A Novel Metaphor-less Algorithm Guided by Whole Population Information for Addressing Exploration-Exploitation Dilemma

Ebrahim Akbari, Abolfazl Rahimnejad, Stephen Andrew Gadsden

📄 https://doi.org/10.1016/j.cma.2025.118208

📘 *Computer Methods in Applied Mechanics and Engineering*, Elsevier, 2025

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🔧 How to Run

1. Open `HSO.m` in MATLAB.

2. Ensure `CostFunction.m` is in the same directory.

3. Press **Run** or type:

```matlab

HSO

```

By default, the algorithm minimizes the Sphere function:

```matlab

z = sum(x.^2);

```

You can replace `CostFunction.m` with any benchmark or real-world objective function of your choice.

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📊 Sample Output

The algorithm prints iteration-wise best cost and plots a **convergence curve**:

```

Iter = 1, Best Cost = 2.764838e+04

Iter = 2, Best Cost = 1.974029e+04

...

Iter = 10000, Best Cost = 9.721004e-16

```

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📌 Features

- Entire population used to compute directional displacement

- Displacement coefficients based on RMS fitness (global structure)

- Adaptive mutation with time-decaying parameters

- Simulated annealing-based acceptance to escape local optima

- Supports real-valued, high-dimensional optimization

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📎 Requirements

- MATLAB R2016a or later

- No additional toolboxes needed

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📜 License

- Code License: This project is released under the MIT License. See the [LICENSE](LICENSE) file for details.

- Article License: The article is open access under the Creative Commons Attribution–NonCommercial 4.0 International (CC BY-NC 4.0) license.

For details, see: https://creativecommons.org/licenses/by-nc/4.0/

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📬 Contact

For academic questions, contact:

Abolfazl Rahimnejad

📧 [e-mail]

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⭐ Acknowledgments

This implementation was created as a reference implementation of the HSO algorithm proposed in the published paper.

Please cite the paper if you use this code in your work.