𐰆𐰺𐰴𐰣

Neuroevolution Maze Solver

This simulation develops agents that learn to solve mazes using artificial neural networks and genetic algorithms.

Mathematical Model and Technical Details

Artificial Neural Network Architecture

• Input Layer: 8 neurons - Detects wall presence in 8 directions around the agent (north, northeast, east, southeast, south, southwest, west, northwest)
• Hidden Layer: 4-8 neurons - For processing and pattern recognition
• Output Layer: 4 neurons - Represents the agent's movement directions (up, down, left, right)

Achieving flawless neural evolution in its current structure takes between 3,000 and 50,000+ generations, depending on the complexity of the maze and the population size. However, if sufficiently trained, the system will train an increasing number of agents from the initial population to reach the target.

Mathematical Operations

Each neuron applies weighted sum and activation function:

Z = W·X + B

A = σ(Z)

Where W is the weight matrix, X is the input vector, B is the bias term, and σ is the activation function (typically ReLU or sigmoid).

Genetic Algorithm Process

1. Initial Population: Start with neural networks having random weights
2. Evaluation: Each agent is tested in the maze, fitness score is calculated:
   • Fitness = Proximity to target - Collision count × penalty
3. Selection: Agents with highest fitness scores are selected based on elitism rate
4. Crossover: Neural network weights of selected agents are mixed to create new generation
5. Mutation: Random changes are applied to weights in the new generation

Optimization Parameters

• Elitism Rate: Percentage of best agents directly transferred to next generation
• Mutation Rate: How frequently new weights are altered
• Mutation Range: Magnitude of weight changes
• Random Behavior: Probability of random movement for exploration-exploitation balance

Application Areas

• Autonomous navigation systems
• Robotic path planning
• Game AI development
• Solving optimization problems
• Decision-making mechanisms in real-world scenarios