A Penalty-Based Guardrail Algorithm

This repository presents the Penalty-Based Guardrail Algorithm (PGA) for solving large-scale, nonlinear, and nonconvex constrained minimization problems with increasing objective function and non-decreasing inequality constraints under tight time constraints.

Key Idea

PGA adapts the traditional penalty-based algorithm -- which applies a low-strength penalty term for constraint violations –- by introducing a guardrail variable that dynamically adjusts the right-hand side of the constraints. This variable is updated iteratively based on historical constraint values. This approach helps balance constraint violations and the minimization of the objective function.

Comparison Benchmarks

We compare PGA against four well-known five algorithms:

• Standard penalty-based algorithm with a small value of the penalty parameter ($PA_{C \searrow}$),
• Standard penalty-based algorithm with a large penalty parameter ($PA_{C \nearrow}$),
• Increasing penalty dual decomposiion (IPDD) algorithm,
• Gradiet descent perturbed ascent (GDPA) algorithm,
• Baseline mathematical programming solver (MPS).

Evaluation Domains

• Three linear evaluation domains,
• Three nonlinear evaluation domains,
• Neural network-based control of a district heating system domain.

Installation and Operation

To install this package:

git clone https://github.com/AlgTUDelft/A-Penalty-Based-Guardrail-Algorithm.git
cd /A-Penalty-Based-Guardrail-Algorithm
pip install -r requirements.txt

To run algorithms on linear domains:

cd /path/to/A-Penalty-Based-Guardrail-Algorithm
python -m src.linear.algorithms_run.run

To run algorithms on nonlinear domains:

cd /path/to/A-Penalty-Based-Guardrail-Algorithm
python -m src.nonlinear.algorithms_run.run

To run algorithm on the neural network-based control of a district heating system domain:

cd /path/to/A-Penalty-Based-Guardrail-Algorithm
python -m src.dnn.algorithms_run.run