Update the benchmark state (optimum position and radius). Should be called at the start of each optimization iteration to update the

Get a property value for this soil type.

Initialize the population of particles.

Perform one optimization step. Args: iteration: Current iteration number (for adaptive exploration) max_itera

Clamp position within bounds.

Gaussian walk operator for local search.

Record current state of algorithm for visualization.

Assign streams to rivers or sea using roulette wheel selection.

Levy flight operator for exploration.

Run algorithm and create animation. Args: iterations: Number of iterations to run

Get a property value for this liquid type.

Initialize the population of water drops.

Initialize the population of water bodies.

Perform one optimization step.

Perform one optimization step.

Calculate knowledge gain at a given position. Higher knowledge gain indicates unexplored regions with potential for discoveri

Clamp position within bounds.

Dance party selection - the best dancer wins!

Check if evaporation should occur (water is close to target). Boiling point affects the distance threshold - liquids with lower

Move water body toward target based on flow rate and liquid properties.

Get effective evaporation rate for a water body based on liquid type.

Generate new water bodies through rain (random positions). Rain can have different liquid types based on distribution.

Update a reactive particle using standard PSO.

Update sub-population groupings.

Example creating interactive HTML visualization for browser.

Default benchmark function (global minimum at 0).

Run the optimization algorithm for specified iterations.

Convenience function to create CA visualization. Args: bounds: Search space bounds (must be 2D) population_size: Population size

Select individuals to influence the belief space.

Assign operators to sub-populations in a round-robin fashion.

Calculate attractiveness based on distance. β(r) = β₀ * exp(-γ * r²) Args: distance: Euclidean

Crossover operator between current and another eagle.

Perform crossover between two parents.

Determine the current optimization phase.

Calculate Euclidean distance between two positions.

Exploration phase update.

Gaussian Process-inspired knowledge gain.

Generate HTML content with embedded visualization using Plotly.

Generate new position influenced by belief space.

Initialize the belief space with initial knowledge.

Inverse distance-based knowledge gain.

Local optimization phase update.

Move the water drop based on its velocity and update position.

Move particle and apply bounds.

Apply mutation to a position.

Perturbation operator for exploration.

Render the animation from recorded history.

Select target position for the water drop. Combines attraction to best solution with exploration based on soil.

Update belief space based on accepted individuals.

Update normative knowledge from accepted individuals.

Update a proactive particle using knowledge gain.

Update situational knowledge with best individuals.

Update soil content based on fitness improvement and material properties. Drops pick up soil from worse positions and deposit it at b

Update velocity based on soil content, target position, and material properties. Velocity increases when moving toward areas with les

Create an interactive HTML visualization that can be opened in a browser. Args: iterations: Number of iterations to run

Example with custom algorithm configuration.

Simple example using the convenience function.

Example with a custom 2D objective function.

Demonstrate a hybrid approach: use different algorithms in sequence. Strategy: 1. Start with PPSO for exploration (proactive particl

Initialize the firefly population.

Initialize the population and divide into sub-populations.

Initialize population and belief space.

Example usage.

Example usage of the PPSO algorithm.

Example usage of the Firefly Algorithm.

Example usage of the Philippine Eagle Optimization algorithm.

Example usage of the IWD-CO algorithm.

Example usage of the Water Cycle Algorithm.

Example usage of the Cultural Algorithm.

Main comparison example.

Plot convergence curves for all three algorithms.

Print a summary comparison of the algorithms.

Run the optimization algorithm for specified iterations.

Run the Firefly Algorithm optimization. Args: iterations: Number of iterations to run Returns:

Run the optimization algorithm for specified iterations.

Run the optimization algorithm for specified iterations.

Run the optimization algorithm for specified iterations.

Compare PPSO, IWD-CO, and Water Cycle Algorithm on the same problem.

Perform one iteration of the Firefly Algorithm.

Perform one optimization step.

Perform one iteration of the Cultural Algorithm.