# Niche Radius Adaptation #

## Name #

Niche Radius Adaptation (NRA)

## Taxonomy #

Niche Radius Adaptation is a technique used in Evolutionary Algorithms, specifically in Multimodal Optimization and Niching Methods. It is closely related to other niching techniques such as Fitness Sharing and Crowding.

- Computational Intelligence
- Biologically Inspired Computation
- Evolutionary Computation
- Evolutionary Algorithms
- Niching Methods
- Niche Radius Adaptation

- Niching Methods

- Evolutionary Algorithms

- Evolutionary Computation

- Biologically Inspired Computation

## Strategy #

Niche Radius Adaptation is a dynamic niching technique that adjusts the niche radius during the evolutionary process to maintain population diversity and prevent premature convergence. The niche radius determines the extent of the neighborhood around each individual in which competition for resources occurs.

### Adaptive Niche Radius #

The core idea behind Niche Radius Adaptation is to dynamically adjust the niche radius based on the distribution of individuals in the search space. In regions with a high density of individuals, the niche radius is reduced to promote local competition and preserve diversity. Conversely, in regions with a low density of individuals, the niche radius is increased to encourage exploration and prevent stagnation.

### Fitness Sharing #

Niche Radius Adaptation is often used in conjunction with fitness sharing, a niching technique that modifies the fitness of individuals based on their proximity to other individuals in the population. Fitness sharing reduces the fitness of individuals in densely populated regions, promoting the formation of stable subpopulations around multiple optima.

### Maintaining Diversity #

By dynamically adapting the niche radius and incorporating fitness sharing, Niche Radius Adaptation helps maintain population diversity throughout the evolutionary process. This diversity is crucial for exploring multiple optima in multimodal optimization problems and preventing the population from converging prematurely to suboptimal solutions.

## Procedure #

- Initialize the population with random individuals.
- Evaluate the fitness of each individual in the population.
- Calculate the pairwise distances between all individuals in the population.
- For each individual:
- Determine the niche radius based on the distribution of individuals in the search space.
- Identify the neighbors within the niche radius.
- Calculate the shared fitness of the individual using fitness sharing.

- Apply selection, crossover, and mutation operators to create the next generation.
- Repeat steps 2-5 until the termination criterion is met.

### Data Structures #

- Population: An array or list of individuals representing potential solutions to the optimization problem.
- Individual: A data structure representing a single solution, typically encoded as a vector of decision variables.
- Fitness: A scalar value indicating the quality or fitness of an individual.
- Distance Matrix: A matrix storing the pairwise distances between individuals in the population.

### Parameters #

- Population Size: The number of individuals in the population.
- Niche Radius: The initial niche radius determining the extent of the neighborhood around each individual.
- Sharing Factor: A parameter controlling the strength of fitness sharing.
- Crossover Rate: The probability of applying the crossover operator to create offspring.
- Mutation Rate: The probability of applying the mutation operator to introduce variation.

## Considerations #

### Advantages #

- Maintains population diversity and prevents premature convergence.
- Adaptively adjusts the niche radius based on the distribution of individuals.
- Promotes the formation of stable subpopulations around multiple optima.
- Effective in multimodal optimization problems with multiple global and local optima.

### Disadvantages #

- Increases computational complexity due to the calculation of pairwise distances.
- Requires the selection of appropriate parameters, such as the initial niche radius and sharing factor.
- May struggle with high-dimensional search spaces where the distance metric becomes less meaningful.
- The effectiveness of the technique depends on the proper tuning of the niche radius adaptation mechanism.

## Heuristics #

### Niche Radius Initialization #

- Start with a relatively large niche radius to encourage initial exploration of the search space.
- Consider using a fraction of the maximum distance between individuals as the initial niche radius.

### Niche Radius Adaptation #

- Adapt the niche radius based on the local density of individuals in the search space.
- Decrease the niche radius in regions with a high density of individuals to promote local competition.
- Increase the niche radius in regions with a low density of individuals to encourage exploration.
- Experiment with different adaptation strategies, such as linear, exponential, or logarithmic scaling of the niche radius.

### Fitness Sharing #

- Use a sharing function that decreases the fitness of individuals as their distance to other individuals decreases.
- Adjust the sharing factor to control the strength of fitness sharing and the formation of stable subpopulations.
- Consider using a dynamic sharing factor that adapts based on the population diversity or the stage of the evolutionary process.

### Population Size and Diversity #

- Use a sufficiently large population size to maintain diversity and explore multiple optima.
- Monitor the population diversity during the evolutionary process and adjust the niche radius or other parameters if diversity drops below a certain threshold.
- Consider incorporating additional diversity preservation mechanisms, such as restricted mating or speciation.

### Termination Criteria #

- Define appropriate termination criteria based on the problem domain and computational resources.
- Consider using a combination of criteria, such as a maximum number of generations, a target fitness value, or a measure of population convergence.
- Allow sufficient time for the population to explore and converge to multiple optima before terminating the algorithm.