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Hybrid Augmented Lagrangian Method

Code for replicating the experiments found on the paper Hybrid Augmented Lagrangian Method for General Constrained Optimization via Evolutionary Algorithms.

Install dependencies

  • Eigen

  • TBB

  • Algevo:

    • git clone https://github.com/NOSALRO/algevo.git
    • cd algevo
    • ./waf configure
    • ./waf
    • [sudo] ./waf install

Compilation

  • ./waf configure
  • ./waf

Running experiments

Use the Python script below to run the experiments and save the results automatically:

python run_all_and_save_results.py --help

Run method

Choose one of the following:

  • --run-method al for the Augmented Lagrangian approach
  • --run-method pen for the Penalty Method

Evolutionary algorithms

Available EA IDs:

  • 1 = PSO
  • 2 = DE
  • 3 = CEM
  • 4 = SGA

For al:

  • --eas all runs all 4 EAs
  • --eas 1,3,4 runs only the selected EAs

For pen:

  • only EA 1 (PSO) is allowed
  • --eas all is accepted and resolves to 1

Optimization problems

Available problem IDs:

  • 1 = Rosenbrock
  • 2 = Quadratic
  • 3 = Power
  • 4 = LinearPolynomial
  • 5 = Mishra
  • 6 = GomezLevy
  • 7 = DropWave
  • 8 = EggHolder
  • 9 = Griewank
  • 10 = DoubleIntegrator

Use:

  • --problems all to run all 10 problems
  • --problems 1,7,8,9 to run a subset

Examples

python run_all_and_save_results.py --run-method al --eas all --problems all
python run_all_and_save_results.py --run-method al --eas 1,3,4 --problems 1,7,8,9
python run_all_and_save_results.py --run-method pen --eas all --problems 1,7,8,9
python run_all_and_save_results.py --run-method pen --problems all

Output folders

Results are saved automatically in:

  • al_results/ for --run-method al
  • pen_results/ for --run-method pen

Citing halm

If you use halm in a scientific publication, please use the following citation (pdf:

@article{printzios2026hybrid,
  title={Hybrid Augmented Lagrangian Method for General Constrained Optimization via Evolutionary Algorithms},
  author={Printzios, Lampros and Chatzilygeroudis, Konstantinos},
  journal={arXiv preprint arXiv:2607.16876},
  year={2026}
}

Acknowledgments

This work was supported by the Hellenic Foundation for Research and Innovation (H.F.R.I.) under the "3rd Call for H.F.R.I. Research Projects to support Post-Doctoral Researchers" (Project Acronym: NOSALRO, Project Number: 7541).

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This work was conducted within the Computational Intelligence Lab (CILab), Department of Mathematics, and the Laboratory of Automation and Robotics (LAR), Department of Electrical & Computer Engineering, University of Patras, Greece.

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License

BSD 2-Clause "Simplified" License