# Cellular Genetic Algorithms #

## Name #

Cellular Genetic Algorithms (cGAs)

## Taxonomy #

Cellular Genetic Algorithms are a subclass of Genetic Algorithms that incorporate spatial locality, inspired by cellular automata. They are closely related to Parallel Genetic Algorithms and Diffusion Genetic Algorithms.

- Computational Intelligence
- Biologically Inspired Computation
- Evolutionary Computation
- Evolutionary Algorithms
- Genetic Algorithms
- Cellular Genetic Algorithms

- Genetic Algorithms

- Evolutionary Algorithms

- Evolutionary Computation

- Biologically Inspired Computation

## Strategy #

In Cellular Genetic Algorithms, individuals are arranged in a spatial grid, typically a 2D lattice, where each individual interacts only with its immediate neighbors. This localized interaction allows for the formation of niches and the preservation of genetic diversity, as promising solutions can emerge and spread gradually through the population.

The overlapping neighborhoods promote exploration while limiting the propagation of genetic material, striking a balance between local optimization and global search. This structured population approach can help prevent premature convergence and escape local optima.

The selection and reproduction operators are applied within each individual’s neighborhood, leading to the emergence of high-quality solutions that can diffuse across the grid over time. This process of diffusion enables the algorithm to exploit good solutions while still maintaining a level of diversity throughout the search.

## Procedure #

### Data Structures #

- Population: A 2D grid of individuals, where each individual represents a potential solution to the problem.
- Individual: Encodes a solution to the problem, typically as a fixed-length string (e.g., binary, integer, or real-valued).
- Neighborhood: A set of individuals that interact with a central individual, often defined as the immediately adjacent cells (e.g., von Neumann or Moore neighborhoods).

### Parameters #

- Population Size: The number of individuals in the grid.
- Grid Topology: The shape and connectivity of the grid (e.g., square, hexagonal, toroidal).
- Neighborhood Size: The number of individuals in each neighborhood.
- Selection Method: The algorithm used to select parents for reproduction within each neighborhood.
- Crossover Rate: The probability of applying the crossover operator to generate offspring.
- Mutation Rate: The probability of applying the mutation operator to introduce random changes.

### Steps #

Initialize the population:

- Create a 2D grid of individuals with random initial solutions.
- Evaluate the fitness of each individual in the population.

While the termination criteria are not met, repeat:

- For each individual in the population:
- Define the neighborhood of the current individual.
- Select parents from the neighborhood using the specified selection method.
- Apply the crossover operator to the selected parents to generate offspring, according to the crossover rate.
- Apply the mutation operator to the offspring, according to the mutation rate.
- Evaluate the fitness of the offspring.
- Replace the current individual with the best offspring if it has higher fitness.

- Update the termination criteria (e.g., number of generations, fitness threshold).

- For each individual in the population:
Return the best solution found in the population.

## Considerations #

### Advantages #

- Promotes diversity and reduces premature convergence by maintaining localized interactions and niches.
- Allows for parallel implementation, as each individual’s reproduction process is independent of others.
- Can effectively solve problems with complex fitness landscapes and multiple local optima.

### Disadvantages #

- May require more computational resources due to the larger population size and localized interactions.
- The choice of grid topology and neighborhood size can significantly impact performance and must be carefully tuned.
- The diffusion of good solutions across the grid may be slower compared to traditional Genetic Algorithms.

## Heuristics #

### Population Initialization #

- Use problem-specific heuristics or domain knowledge to generate initial solutions that are diverse and cover promising regions of the search space.
- If no prior knowledge is available, ensure that the initial population is randomly generated to maximize diversity.

### Grid Topology and Neighborhood Size #

- For most problems, a square grid with von Neumann or Moore neighborhoods (4 or 8 adjacent cells) works well.
- Consider using a toroidal grid to eliminate edge effects and ensure uniform neighborhood sizes for all individuals.
- Larger neighborhood sizes can promote faster diffusion of good solutions but may reduce diversity.

### Selection Method #

- Tournament selection with small tournament sizes (e.g., 2-4) is often effective for maintaining selection pressure while preserving diversity.
- Fitness-proportionate selection can be used but may lead to premature convergence if the fitness landscape is highly skewed.

### Crossover and Mutation Rates #

- Start with a high crossover rate (e.g., 0.8-0.9) to promote the exploration of new solutions.
- Use a low mutation rate (e.g., 1/L, where L is the length of the solution encoding) to introduce small variations without disrupting good solutions.
- Adaptively adjust the crossover and mutation rates based on the population’s diversity and convergence rate.

### Termination Criteria #

- Set a maximum number of generations based on the problem complexity and available computational resources.
- Use a fitness threshold to stop the algorithm when a satisfactory solution is found.
- Consider a convergence criterion based on the population’s diversity or the rate of fitness improvement.

### Parallelization #

- Exploit the inherently parallel nature of Cellular Genetic Algorithms by assigning each individual’s reproduction process to a separate processor or thread.
- Synchronize the updates of the population grid to ensure consistency and avoid race conditions.