Nature-Inspired Optimisation

My goal with this project is to celebrate optimization strategies from our blue planet. I see our collective documentation of strategies from nature as a heritage we can all observe, document, and celebrate together. My hope is we can use these algorithms as a meeting ground for refining our collective understanding.

Links to original papers introducing (or meta-analysis overviews of) the following algorithms/heuristics/methods:

• Genetic Algorithms (GA)
• Particle Swarm Optimization (PSO)
• Artificial immune systems (AIS)
• Boids
• Memetic Algorithm (MA)
• Ant Colony Optimization (ACO)
• Cultural Algorithms (CA)
• Particle Swarm Optimization (PSO)
• Self-propelled Particles
• Differential Evolution (DE)
• Bacterial Foraging Optimization
• Marriage in Honey Bees (MHB)
• Artificial Fish School
• Bacteria Chemotaxis (BC)
• Social Cognitive Optimization (SCO)
• Artificial Bee Colony
• Glowworm Swarm Optimization (GSO)
• Honey-Bees Mating Optimization (HBMO)
• Invasive Weed Optimization (IWO)
• Shuffled Frog Leaping Algorithm (SFLA)
• Intelligent Water Drops - Continuous Optimization(IWD-CO)
• River Formation Dynamics
• Biogeography-based Optimization (BBO)
• Roach Infestation Optimization (RIO)
• Bacterial Evolutionary Algorithm (BEA)
• Cuckoo Search (CS)
• Firefly Algorithm (FA)
• Gravitational Search Algorithm (GSA)
• Bat Algorithm
• Phillippine Eagle Optimization Algorithm
• Fireworks algorithm
• Altruistic Population Algorithm
• Spiral Dynamic Algorithm (SDA)
• Strawberry Algorithm
• Artificial Algae Algorithm (AAA)
• Bacterial Colony Optimization
• Flower pollination algorithm (FPA)
• Krill Herd
• Water Cycle Algorithm
• Proactive Particle Swarm Optimization (PPSO)
• Dragonfly Algorithm (DA)
• Black Holes Algorithm
• Cuttlefish Algorithm
• Gases Brownian Motion Optimization
• Mine blast algorithm
• Plant Propagation Algorithm
• Social Spider Optimization (SSO)
• Spider Monkey Optimization (SMO)
• Animal Migration Optimization (AMO)
• Artificial Ecosystem Algorithm (AEA)
• Bird Mating Optimizer
• Forest Optimization Algorithm (FOA)
• Grey Wolf Optimizer
• Lion Optimization Algorithm (LOA)
• Optics Inspired Optimization (OIO)
• The Raven Roosting Optimisation Algorithm
• Water Wave Optimization
• Collective animal behavior (CAB)
• Aritificial Chemical Process Algorithm
• Bull optimization algorithm
• Elephent herding optimization (EHO)

Publications

• Algorithms
• Journal of Algorithms
• Swarm and Evolutionary Computation
• International Journal of Swarm Intelligence and Evolutionary Computation
• Swarm Intelligence
• Evolutionary Intelligence

Conferences

• GECCO

Research teams

• Tübingen

Getting Started

Install the package locally. Once installed you can import nio from anywhere on your system.

EXAMPLE: Using the IWD-CO Algorithm

The Intelligent Water Drops - Continuous Optimization (IWD-CO) algorithm simulates water drops flowing through a landscape, where drops move toward areas with less soil (better solutions). The implementation includes multiple liquid and soil types, each with distinct physical properties that affect optimization behavior.

Basic usage:

from nio import IWDCO

optimizer = IWDCO(bounds=[(-5.12, 5.12)] * 5, population_size=40, seed=42)
best_position, best_value = optimizer.run(iterations=200)
print(best_value)

Using specific material types:

The algorithm supports 6 liquid types (H2O, OIL, ALCOHOL, GLYCEROL, MERCURY, HONEY) and 6 soil types (SAND, CLAY, SILT, GRAVEL, LOAM, PEAT), each with different properties affecting velocity, soil pickup, and deposition:

from nio import IWDCO, LiquidType, SoilType

# Use specific liquid and soil types
optimizer = IWDCO(
    bounds=[(-5.12, 5.12)] * 5,
    population_size=40,
    liquid_types=[LiquidType.OIL, LiquidType.ALCOHOL, LiquidType.HONEY],
    soil_types=[SoilType.SAND, SoilType.CLAY, SoilType.LOAM],
    liquid_distribution="uniform",  # or "random"
    seed=42
)
best_position, best_value = optimizer.run(iterations=200)

Material properties:

• Liquid types affect velocity (viscosity, velocity multiplier) and soil carrying capacity
• Soil types affect movement resistance, pickup difficulty, deposition rate, and erosion rate
• Different combinations create diverse optimization behaviors

EXAMPLE: Using the Water Cycle Algorithm

The Water Cycle Algorithm (WCA) simulates the natural water cycle process, where streams flow toward rivers, rivers flow toward the sea, and evaporation/raining processes provide exploration.

Basic usage:

from nio import WaterCycleAlgorithm

optimizer = WaterCycleAlgorithm(
    bounds=[(-5.12, 5.12)] * 5,
    population_size=40,
    num_rivers=4,
    seed=42
)
best_position, best_value = optimizer.run(iterations=200)

Algorithm features:

• Sea: Best solution (global best)
• Rivers: Better solutions that streams flow toward
• Streams: Population members that flow toward rivers or sea
• Flow process: Streams and rivers move toward better solutions
• Evaporation: When streams/rivers get close to sea, they evaporate
• Raining: Evaporated water creates new random solutions for exploration

Parameters:

• num_rivers: Number of rivers (better solutions), typically 3-5
• evaporation_rate: Base probability of evaporation (controls exploration)
• max_evaporation_distance: Maximum distance for evaporation to occur
• flow_rate: Base rate at which water bodies move toward targets

Using specific liquid types:

The algorithm supports 7 liquid types (FRESH_WATER, SALTWATER, DISTILLED_WATER, HOT_WATER, COLD_WATER, HEAVY_WATER, STEAM), each with different properties affecting flow speed, evaporation rate, and boiling point:

from nio import WaterCycleAlgorithm, WCA_LiquidType

# Use specific liquid types
optimizer = WaterCycleAlgorithm(
    bounds=[(-5.12, 5.12)] * 5,
    population_size=40,
    num_rivers=4,
    liquid_types=[WCA_LiquidType.HOT_WATER, WCA_LiquidType.STEAM, WCA_LiquidType.FRESH_WATER],
    liquid_distribution="uniform",  # or "random"
    seed=42
)
best_position, best_value = optimizer.run(iterations=200)

Liquid properties:

• Flow speed: Affects how fast water bodies move toward targets (STEAM is fastest, HEAVY_WATER is slowest)
• Evaporation rate: Affects probability of evaporation (HOT_WATER/STEAM evaporate faster, COLD_WATER slower)
• Boiling point: Affects distance threshold for evaporation (lower = evaporates at greater distances)
• Density: Affects flow behavior

Different liquid types create diverse optimization behaviors - fast-flowing liquids like STEAM explore quickly, while slower liquids like HEAVY_WATER provide more controlled convergence.

Contributing

Contributions are welcome across algorithms, benchmarks, documentation, and examples.

• Open an issue first for substantial feature work to align on scope.
• Fork the repo and create a focused branch per change.
• Add or update tests and examples where practical.
• Keep algorithm references (paper links/citations) in the README or module docstrings.
• Open a pull request with a clear summary of motivation, approach, and validation steps.

License

This project is licensed under the MIT License.

Copyright (c) 2018-present Nature-Inspired Optimisation contributors.