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@gorkemulas2005 gorkemulas2005 commented Jan 5, 2026

📑 Description

This PR introduces the Improved Chameleon Swarm Algorithm (ICSA) to the swarm_based module. ICSA is a nature-inspired metaheuristic based on the 2024 paper published in Biomimetics. The implementation focuses on multi-strategy fusion to enhance population diversity and avoid local optima, utilizing fully vectorized NumPy operations for maximum efficiency within the Mealpy framework.

✨ Key Features Implemented

Stage Strategy Description Reference
Initialization Logistic Chaotic Map Enhances initial population diversity and ergodic properties. Eq. 9, 10
Prey Searching Sub-population Hybrid Balances exploration via a hybrid spiral search mechanism. Eq. 11
Eyes' Rotation Lévy Flight Stage Adaptive rotation using Lévy flight and cosine factors. Eq. 15
Prey Capture Refraction Reverse-Learning Prevents stagnation by modeling light refraction principles. Eq. 20

🛠 Implementation Checklist

  • Full vectorized ICSA implementation in mealpy/swarm_based/ICSA.py
  • Proper export in mealpy/swarm_based/__init__.py and mealpy/__init__.py
  • Comprehensive unit tests in tests/swarm_based/test_ICSA.py
  • Docstrings and mathematical references added to the class

✅ Checks

  • My pull request adheres to the code style of this project
  • My code requires changes to the documentation
  • I have updated the documentation as required (Docstrings added)
  • All the tests have passed

ℹ️ Additional Information

The algorithm's robustness was verified on a 16-core system using two benchmark suites.

1. Classic Benchmark Results (F1 - F18)

The implementation matches the global optima and convergence characteristics of the original article.

Func Best (Min) Mean Std AvgTime(s)
F1 0.0000e+00 0.0000e+00 0.0000e+00 1.26
F2 0.0000e+00 0.0000e+00 0.0000e+00 1.68
F3 0.0000e+00 0.0000e+00 0.0000e+00 18.21
F4 0.0000e+00 0.0000e+00 0.0000e+00 1.20
F5 2.8950e+01 2.8975e+01 1.1124e-02 4.68
F6 4.2906e+00 6.0516e+00 6.3142e-01 1.40
F7 6.4002e-07 1.0960e-05 1.2816e-05 2.90
F8 -6.6905e+03 -5.5618e+03 5.3885e+02 1.50
F9 0.0000e+00 0.0000e+00 0.0000e+00 2.06
F10 4.4409e-16 4.4409e-16 0.0000e+00 2.50
F11 0.0000e+00 0.0000e+00 0.0000e+00 2.23
F12 2.5722e-01 7.5567e-01 2.7886e-01 7.27
F13 1.9366e+00 2.9157e+00 2.1140e-01 6.46
F14 2.0000e-03 2.0000e-03 5.4857e-19 4.45
F15 3.0847e-04 6.4443e-03 7.8868e-03 3.47
F16 -1.0316e+00 -1.0308e+00 4.3406e-03 0.76
F17 3.9789e-01 3.9789e-01 1.1300e-06 0.89
F18 3.0000e+00 5.7403e+00 8.0895e+00 1.04

2. High-Complexity Benchmarks (CEC 2017 via opfunu)

ICSA performance comparison against Mealpy's PSO on shifted and rotated functions.

Function ICSA Mean PSO Mean ICSA Std PSO Std ICSA Time(s)
CEC17_F15 4.3325e+03 2.7233e+03 4.1379e+03 2.6290e+03 15.00
CEC17_F19 4.7720e+03 2.4826e+03 5.4133e+02 3.1292e+02 49.00
CEC17_F20 3.7261e+03 2.5334e+03 1.1981e+03 4.1964e+02 7.64

Verification Result: 1 passed in 1.09s

📚 References

  1. Chen, Y.; Cao, L.; Yue, Y. Hybrid Multi-Objective Chameleon Optimization Algorithm Based on Multi-Strategy Fusion and Its Applications. Biomimetics 2024, 9, 583.
  2. Malik, B.S. Chameleon Swarm Algorithm: A bio-inspired optimizer for solving engineering design problems. Expert Systems with Applications, 2021, 174, 114685.

*Submitted by Kazan Ulaş Görkem

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