ANMetaL - Another Numeric optimization and Metaheuristics Library

A comprehensive Python library for metaheuristic optimization, numeric methods, and NP-hard problem solving with powerful visualization capabilities.

Whether you're optimizing complex functions, solving combinatorial problems, or researching metaheuristic algorithms, ANMetaL provides battle-tested implementations with beautiful visualizations.

✨ Key Features

🎬 Stunning Visualizations

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
• Genetic Algorithm Visualization: Track evolution on categorical problems like Knapsack and Sudoku

Quick Start Visualization:

anmetal mh_graph_each_it --mh Firefly --problem Goldsteinprice --iterations 20 --plottype 3d --fps 30

For complete documentation of all visualization commands and options, see the CLI Documentation section below.

🤖 12+ Metaheuristic Algorithms

Population-Based Algorithms (for continuous/real-valued problems):

• 🐝 ABC - Artificial Bee Colony
• 🐜 ACO - Ant Colony Optimization
• 🐟 AFSA - Artificial Fish Swarm Algorithm
• 🦇 Bat Algorithm - Echolocation-based optimization
• ⚫ Black Hole Algorithm - Gravitational search
• 🐦 Cuckoo Search - Lévy flight optimization
• 🔥 Firefly Algorithm - Bio-luminescence inspired
• 🎵 Harmony Search - Music-inspired optimization
• 🌊 PSO - Particle Swarm Optimization (with Leap variant)
• 🎯 Greedy Search (with Leap variant)

Evolutionary Algorithms (for categorical/discrete problems):

• 🧬 Genetic Algorithm - Evolution-inspired optimization (with Leap variant)

📊 Comprehensive Problem Suite

NP-Hard Problems:

• 🎒 Knapsack Problem - Classic combinatorial optimization
• 🔢 Sudoku Solver - Constraint satisfaction (standard & optimized)
• ⚖️ Partition Problem - Subset partitioning
• ➕ Subset Sum Problem - Target sum finding

Benchmark Functions (20+ optimization test functions):

• 2D Functions: Camelback, Goldstein-Price, Shubert variants, Quartic
• N-Dimensional: Sphere, Rosenbrock, Rastrigin, Griewank, Schwefel, and more
• 1D Functions: F1, F3 test functions

🔧 Numeric Optimization Tools

Single-Solution Iterative Methods:

• Newton Method
• Euler Method

Binary Optimization Utilities:

• 9 binarization functions (sShape1-4, vShape1-4, erf)
• 4 binarization strategies (standard, complement, static_probability, elitist)

🎨 Flexible Visualization Options

• 2D and 3D plotting
• Multiple category visualization types (character, color, icon, number, value)
• Trajectory tracking and convergence analysis
• Automated video generation
• Customizable frame rates and plot styles

🚀 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)

---

🛠️ Command Line Interface

ANMetaL provides a powerful CLI for running optimizations and creating visualizations. All commands follow the pattern:

anmetal <command> [arguments]

Available commands:

• mh_graph_each_it - Create animated visualizations of metaheuristic optimization
• genetic_categorical_plot - Visualize genetic algorithm on categorical problems
• trajectory_plot_npcomp - Plot trajectories for NP-complete problems
• nonlinear_mh_optimization - Run metaheuristics on nonlinear functions
• basic_mh_optimization_npcomp - Run metaheuristics on NP-hard problems
• basic_math_it_optimization - Test iterative optimization methods
• categorical_mh_optimization - Run genetic algorithms on categorical problems

See /pytests folder for additional examples of programmatic use.

📖 Quick Start Examples

Basic Optimization

# Example with Partition Problem
from anmetal.problems.nphard_real import Partition_Real
from anmetal.optimizer.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
anmetal mh_graph_each_it --mh PSO --problem Goldsteinprice --iterations 50 --plottype 3d

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

For more detailed command-line options, see the Command Line Interface section.

📚 Complete API Reference

Optimization Methods

Single-Solution Iterative Methods

• Newton Method - Root finding and optimization
• Euler Method - Numerical differential equation solving

Metaheuristic Algorithms

Population-Based (Real/Continuous Input)

Algorithm	Description	Variants
ABC	Artificial Bee Colony	Standard
ACO	Ant Colony Optimization	Standard
AFSA	Artificial Fish Swarm Algorithm	Standard
Bat	Bat Algorithm	Standard
Black Hole	Black Hole Algorithm	Standard
Cuckoo	Cuckoo Search	Standard
Firefly	Firefly Algorithm	Standard
Harmony Search	Harmony Search	Standard
PSO	Particle Swarm Optimization	Standard, With Leap
Greedy	Greedy Search	Standard, With Leap

Evolutionary (Categorical/Discrete Input)

Algorithm	Description	Variants
Genetic Algorithm	Evolution-based optimization	Standard, With Leap

Test Problems

NP-Hard Problems

Real-Valued:

• Partition Problem - Divide set into equal-sum subsets
• Subset Sum Problem - Find subset with target sum

Categorical:

• Knapsack Problem - Maximize value within weight constraint
• Sudoku - Fill 9×9 grid with constraints (standard & optimized versions)

Benchmark Functions

1-Dimensional Functions:

• F1, F3 (Ref)

2-Dimensional Functions:

• Camelback, Goldstein-Price, Pshubert1, Pshubert2, Shubert, Quartic (Ref)

N-Dimensional Functions:

• Brown1, Brown3, F10n, F15n (Ref)
• Sphere, Rosenbrock, Griewank, Rastrigin, Sumsquares, Michalewicz, Quartic, Schwefel, Penalty (Ref)

Utility Functions

Binarization Functions

Transform continuous values to binary for discrete optimization:

• S-Shape family: sShape1, sShape2, sShape3, sShape4
• V-Shape family: vShape1, vShape2, vShape3, vShape4
• Error function: erf

Binarization Strategies

Methods for applying binarization in optimization:

• standard - Basic threshold-based conversion
• complement - Inverted threshold
• static_probability - Fixed probability approach
• elitist - Elite-preserving conversion

---

🛠️ Command Line Interface

1. Metaheuristic Animation (mh_graph_each_it)

Creates animated visualizations of population-based metaheuristic optimization processes with 2D or 3D plots.

Basic Usage:

anmetal mh_graph_each_it --mh <algorithm> --problem <function> [options]

Common Arguments:

• --folder <path> - Output folder for plots and videos (default: mh_graphs)
• --seed <int> - Random seed for reproducibility (default: 0)
• --mh <algorithm> - Algorithm to use (required)
  • Options: AFSA, PSO, PSOWL, Greed, GreedWL, ABC, ACO, Bat, Blackhole, Cuckoo, Firefly, Harmony
• --problem <function> - Test function (required)
  • Options: Camelback, Goldsteinprice, Pshubert1, Pshubert2, Shubert, Quartic
• --verbose <0|1> - Print optimization logs (default: 1)
• --iterations <int> - Number of iterations (default: 100)
• --population <int> - Population size (default: 30)
• --plottype <2d|3d> - Plot type (default: 2d)
• --traces <all|none|smooth> - Trace visualization mode (default: none)
• --fps <int> - Video frame rate (default: 10)

Algorithm-Specific Parameters:

AFSA (Artificial Fish Swarm Algorithm):

--parameter-afsa-visualdistancepercentage <float>  # Visual distance (default: 0.2)
--parameter-afsa-velocitypercentage <float>        # Velocity (default: 0.3)
--parameter-afsa-npointstochoose <int>            # Points to choose (default: 5)
--parameter-afsa-crowdedpercentage <float>        # Crowded threshold (default: 0.8)
--parameter-afsa-itsstagnation <int>              # Stagnation iterations (default: 7)
--parameter-afsa-leappercentage <float>           # Leap distance (default: 0.2)
--parameter-afsa-stagnationvariation <float>      # Variation threshold (default: 0.4)

PSO (Particle Swarm Optimization):

--parameter-pso-omega <float>   # Inertia weight (default: 0.5)
--parameter-pso-phig <float>    # Global coefficient (default: 1.0)
--parameter-pso-phip <float>    # Personal coefficient (default: 2.0)

PSOWL (PSO with Leap):

--parameter-psowl-omega <float>                # Inertia weight (default: 0.5)
--parameter-psowl-phig <float>                 # Global coefficient (default: 1.0)
--parameter-psowl-phip <float>                 # Personal coefficient (default: 2.0)
--parameter-psowl-stagnationvariation <float>  # Variation threshold (default: 0.4)
--parameter-psowl-itsstagnation <int>          # Stagnation iterations (default: 5)
--parameter-psowl-leappercentage <float>       # Leap distance (default: 0.8)

GreedWL (Greedy with Leap):

--parameter-greedwl-stagnationvariation <float>  # Variation threshold (default: 0.4)
--parameter-greedwl-itsstagnation <int>          # Stagnation iterations (default: 5)
--parameter-greedwl-leappercentage <float>       # Leap distance (default: 0.8)

ABC (Artificial Bee Colony):

--parameter-abc-limit <int>  # Abandonment limit (default: 20)

ACO (Ant Colony Optimization):

--parameter-aco-evaporationrate <float>  # Pheromone evaporation (default: 0.1)
--parameter-aco-alpha <float>            # Pheromone importance (default: 1.0)
--parameter-aco-beta <float>             # Heuristic importance (default: 2.0)

BAT Algorithm:

--parameter-bat-fmin <float>  # Minimum frequency (default: 0.0)
--parameter-bat-fmax <float>  # Maximum frequency (default: 2.0)
--parameter-bat-a <float>     # Loudness (default: 0.9)
--parameter-bat-r0 <float>    # Pulse rate (default: 0.9)

CUCKOO Search:

--parameter-cuckoo-pa <float>  # Abandonment probability (default: 0.25)

FIREFLY Algorithm:

--parameter-firefly-alpha <float>  # Randomness (default: 0.5)
--parameter-firefly-beta0 <float>  # Attractiveness (default: 1.0)
--parameter-firefly-gamma <float>  # Absorption coefficient (default: 1.0)

HARMONY Search:

--parameter-harmony-hmcr <float>  # Harmony Memory Considering Rate (default: 0.9)
--parameter-harmony-par <float>   # Pitch Adjustment Rate (default: 0.3)
--parameter-harmony-bw <float>    # Bandwidth (default: 0.2)

Examples:

# 2D visualization with ABC algorithm
anmetal mh_graph_each_it --mh ABC --problem Camelback --iterations 20 --population 30

# 3D visualization with custom parameters
anmetal mh_graph_each_it --mh Firefly --problem Goldsteinprice --iterations 15 --plottype 3d --fps 30 --parameter-firefly-alpha 0.6

# PSO with traces and custom parameters
anmetal mh_graph_each_it --mh PSO --problem Quartic --traces all --parameter-pso-omega 0.7 --parameter-pso-phig 1.5

# Custom output folder
anmetal mh_graph_each_it --mh ABC --problem Shubert --folder ./my_results --iterations 50

2. Genetic Algorithm Visualization (genetic_categorical_plot)

Visualize genetic algorithms on categorical problems like Knapsack and Sudoku.

Basic Usage:

anmetal genetic_categorical_plot --problem <problem> [options]

Arguments:

• --folder <path> - Output folder for plots and videos (default: mh_graphs)
• --seed <int> - Random seed (default: 0)
• --iterations <int> - Number of generations (default: 50)
• --population <int> - Population size (default: 20)
• --elitist <float> - Elitist percentage (default: 0.3)
• --mutability <float> - Mutation rate (default: 0.1)
• --fidelity <0|1> - Enable fidelity (default: 1)
• --parents_mutation <0|1> - Enable parent mutation (default: 1)
• --leap <0|1> - Use leap variant (default: 0)
• --categorytype <type> - Visualization type (default: character)
  • Options: character, color, icon, number, value, colorvalue
• --fps <int> - Video frame rate (default: 5)
• --problem <problem> - Problem to solve (required)
  • Options: knapsack, sudoku, sudoku_opt
• --dims <int> - Problem dimensions (for Knapsack, default: 20)

Examples:

# Knapsack with color visualization
anmetal genetic_categorical_plot --problem knapsack --dims 30 --categorytype color --iterations 100

# Sudoku with optimized version
anmetal genetic_categorical_plot --problem sudoku_opt --categorytype colorvalue --iterations 200 --population 50

# With leap variant
anmetal genetic_categorical_plot --problem knapsack --leap 1 --mutability 0.2 --elitist 0.4

3. NP-Complete Trajectory Plotting (trajectory_plot_npcomp)

Plot fitness trajectories of metaheuristics on NP-complete problems (Partition and Subset Sum).

Basic Usage:

anmetal trajectory_plot_npcomp --algorithms <alg1> <alg2> ... [options]

Arguments:

• --folder <path> - Output folder for plots (default: current directory)
• --algorithms <list> - Algorithms to run (space-separated, required)
  • Options: AFSA, Greedy, GreedyWL, PSO, PSOWL, ABC, ACO, BAT, BH, CUCKOO, FIREFLY, HS
  • Default: PSO ABC ACO BAT FIREFLY HS
• --problem <problem> - Problem type (default: partition sum)
  • Options: partition sum, subset sum
• --verbose <0|1|2> - Verbosity level (default: 0)
  • 0=quiet, 1=normal, 2=debug
• --max-iterations <int> - Maximum iterations (default: 50)
• --population-size <int> - Population size (default: 20)
• --seed <int> - Random seed (default: 115)
• --ndims <int> - Problem dimensions (default: 500)

Algorithm-Specific Parameters: All algorithm parameters from mh_graph_each_it are supported with the same names.

Examples:

# Compare PSO and ABC on partition problem
anmetal trajectory_plot_npcomp --algorithms PSO ABC --problem "partition sum" --max-iterations 100

# Run AFSA with custom parameters
anmetal trajectory_plot_npcomp --algorithms AFSA --parameter-afsa-visualdistancepercentage 0.6 --ndims 1000

# Multiple algorithms with custom settings
anmetal trajectory_plot_npcomp --algorithms PSO ABC ACO --folder ./results --ndims 1000 --seed 42 --verbose 1

4. Nonlinear Function Optimization (nonlinear_mh_optimization)

Run metaheuristics on various nonlinear benchmark functions. This is a Python script for testing and comparison - no CLI arguments.

5. Basic Optimization Scripts

The following commands are available for testing but don't require specific arguments (they use hardcoded test cases):

• basic_mh_optimization_npcomp - Test metaheuristics on Partition/Subset Sum problems
• basic_math_it_optimization - Test Newton and Euler iterative methods
• categorical_mh_optimization - Test genetic algorithms on categorical problems

Usage:

anmetal basic_mh_optimization_npcomp
anmetal basic_math_it_optimization
anmetal categorical_mh_optimization

---

🎛️ 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