Another Numeric optimization and Metaheuristics Library

A library to do your metaheuristics and numeric combinatorial stuff.

🎬 Visualization Highlights

ANMetaL now includes powerful visualization capabilities that create animated videos of metaheuristic optimization processes!

• 12 Population-based Algorithms: ABC, ACO, AFSA, Bat, Black Hole, Cuckoo, Firefly, Harmony Search, PSO, Greedy, and more
• 2D & 3D Plotting: Watch particles move in 2D space or explore 3D fitness landscapes
• Automatic Video Generation: Creates smooth MP4 animations with customizable frame rates
• Multiple Test Functions: Visualize optimization on various benchmark problems

Quick Start Visualization:

python test/mh_graph_each_it.py --mh Firefly --problem Goldsteinprice --iterations 20 --plot3d 1 --fps 30

Installation

To install the core library:

pip install anmetal

For visualization and animation features, install with development dependencies:

pip install anmetal[test]
# or for development
pip install -e .[dev]

Required dependencies for visualization:

• matplotlib (plotting)
• opencv-python (video generation)
• numpy (numerical operations)

See /test folder for examples of use.

Content

Numeric optimization

Iterative optimization functions (one solution)

• Euler method
• Newton method

Metaheuristics

Real input (Population-based)

• Artificial Bee Colony (ABC)
• Ant Colony Optimization (ACO)
• Artificial Fish Swarm Algorithm (AFSA)
• Bat Algorithm
• Blackhole Algorithm
• Cuckoo Search
• Firefly Algorithm
• Harmony Search (HS)
• Particle Swarm Optimization (PSO)
• Particle Swarm Optimization with Leap
• Greedy
• Greedy with Leap

Categorical input

• Genetic Algorithm
• Genetic Algorithm with Leap

Problems and gold-standard functions

NP-hard problems

• Real problems

  • Partition problem
  • Subset problem

• Categorical problems

  • Knapsack
  • Sudoku (without initial matrix, just random)

Non linear functions

• One input (1-D)

  • F1 (https://doi.org/10.1007/s00521-017-3088-3)
  • F3 (https://doi.org/10.1007/s00521-017-3088-3)

• Two inputs (2-D)

  • Camelback (https://doi.org/10.1007/s00521-017-3088-3)
  • Goldsteinprice (https://doi.org/10.1007/s00521-017-3088-3)
  • Pshubert1 (https://doi.org/10.1007/s00521-017-3088-3)
  • Pshubert2 (https://doi.org/10.1007/s00521-017-3088-3)
  • Shubert (https://doi.org/10.1007/s00521-017-3088-3)
  • Quartic (https://doi.org/10.1007/s00521-017-3088-3)

• N inputs (N-D)

  • Brown1 (https://doi.org/10.1007/s00521-017-3088-3)
  • Brown3 (https://doi.org/10.1007/s00521-017-3088-3)
  • F10n (https://doi.org/10.1007/s00521-017-3088-3)
  • F15n (https://doi.org/10.1007/s00521-017-3088-3)
  • Sphere (https://doi.org/10.1007/s00521-018-3512-3)
  • Rosenbrock (https://doi.org/10.1007/s00521-018-3512-3)
  • Griewank (https://doi.org/10.1007/s00521-018-3512-3)
  • Rastrigrin (https://doi.org/10.1007/s00521-018-3512-3)
  • Sumsquares (https://doi.org/10.1007/s00521-018-3512-3)
  • Michalewicz (https://doi.org/10.1007/s00521-018-3512-3)
  • Quartic (https://doi.org/10.1007/s00521-018-3512-3)
  • Schwefel (https://doi.org/10.1007/s00521-018-3512-3)
  • Penalty (https://doi.org/10.1007/s00521-018-3512-3)

Additional Features

Metaheuristic Visualization and Animation

ANMetaL includes a powerful visualization tool (test/mh_graph_each_it.py) that creates animated visualizations of metaheuristic optimization processes:

Features:

• 2D and 3D Plotting: Visualize population movement in 2D space or 3D with fitness as Z-axis
• Video Generation: Automatically creates MP4 animations from image sequences
• All Population Algorithms: Supports all population-based metaheuristics (except genetic algorithm)
• Multiple Problems: Works with various 2D optimization functions

Supported Algorithms:

• AFSA (Artificial Fish Swarm Algorithm)
• PSO (Particle Swarm Optimization) and PSO with Leap
• ABC (Artificial Bee Colony)
• ACO (Ant Colony Optimization)
• Bat Algorithm
• Black Hole Algorithm
• Cuckoo Search
• Firefly Algorithm
• Harmony Search
• Greedy and Greedy with Leap

Usage Examples:

# 2D visualization with ABC algorithm
python test/mh_graph_each_it.py --mh ABC --problem Camelback --iterations 20 --population 30

# 3D visualization with fitness landscape
python test/mh_graph_each_it.py --mh Firefly --problem Goldsteinprice --iterations 15 --plot3d 1 --fps 30

# Quick test with custom parameters
python test/mh_graph_each_it.py --mh Bat --problem Shubert --iterations 10 --plot3d 1 --fps 20 --seed 42

Available Arguments:

• --mh: Algorithm (AFSA, PSO, PSOWL, ABC, ACO, Bat, Blackhole, Cuckoo, Firefly, Harmony, Greed, GreedWL)
• --problem: Test function (Camelback, Goldsteinprice, Pshubert1, Pshubert2, Shubert, Quartic)
• --iterations: Number of optimization iterations
• --population: Population size
• --plot3d: Enable 3D plotting (0 for 2D, 1 for 3D)
• --fps: Video frame rate
• --seed: Random seed for reproducibility
• --verbose: Print optimization progress

Output: The visualization tool creates:

• Individual PNG images for each iteration in mh_graphs/{algorithm}_{problem}/
• An MP4 video animation: {algorithm}_{problem}_animation.mp4
• Console output showing optimization progress and best fitness values

Binarization functions

• sShape1
• sShape2
• sShape3
• sShape4
• vShape1
• vShape2
• vShape3
• vShape4
• erf

Binarization strategies

• standard
• complement
• static_probability
• elitist

Example Usage

See the /test folder for complete examples. Here's a quick overview:

Basic Optimization

# Example with Partition Problem
from anmetal.problems.nphard_real import Partition_Real
from anmetal.population.PSO.PSOMH_Real import PSOMH_Real

# Create problem instance
problem = Partition_Real(seed=0, num_dims=200)

# Create and run metaheuristic
mh = PSOMH_Real(problem.min_x, problem.max_x, problem.ndim, False,
                problem.objective_function, problem.repair_function,
                problem.preprocess_function)

# Run optimization
fitness, solution = mh.run(verbose=True, iterations=100, population=30,
                         omega=0.8, phi_g=1, phi_p=0.5, seed=115)

Visualization and Animation

# Run from command line for visualization
python test/mh_graph_each_it.py --mh PSO --problem Goldsteinprice --iterations 50 --plot3d 1

# This creates:
# - Individual iteration images
# - MP4 animation video
# - Real-time optimization visualization

Algorithm Parameters

Each metaheuristic has its own set of parameters. Here are some common ones:

• Common Parameters

  • iterations: Number of iterations
  • population: Population size
  • seed: Random seed for reproducibility
  • verbose: Whether to print progress

• Algorithm-Specific Parameters

  • ABC: limit
  • ACO: evaporation_rate, alpha, beta
  • BAT: fmin, fmax, A, r0
  • CUCKOO: pa
  • FIREFLY: alpha, beta0, gamma
  • GA: mutation_rate, crossover_rate
  • HS: hmcr, par, bw
  • PSO: omega, phi_g, phi_p

For detailed parameter descriptions and recommended values, see the respective algorithm implementations in the source code.

Troubleshooting

Visualization Issues

OpenCV Installation Problems:

# If you encounter OpenCV issues, try:
pip install opencv-python-headless

Missing Dependencies:

# Install all visualization dependencies:
pip install matplotlib opencv-python numpy seaborn pandas

Video Generation Errors:

• Ensure you have write permissions in the output directory
• Check that OpenCV is properly installed
• Try reducing FPS if encountering codec issues

Algorithm-Specific Issues

Parameter Tuning:

• Start with default parameters and adjust gradually
• Use smaller populations for testing (5-15 individuals)
• Reduce iterations for quick tests (5-20 iterations)

Performance:

• Use --verbose 0 to reduce console output
• Lower FPS for faster video generation
• Consider 2D plotting for better performance