# Cuckoo Search #

## Name #

Cuckoo Search, CS

## Taxonomy #

Cuckoo Search is a nature-inspired metaheuristic optimization algorithm that falls under the broad category of Swarm Intelligence. It is closely related to other biologically inspired algorithms such as Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC).

- Computational Intelligence
- Biologically Inspired Computation
- Swarm Intelligence
- Cuckoo Search

- Swarm Intelligence

- Biologically Inspired Computation

## Strategy #

Cuckoo Search is inspired by the brood parasitism behavior of certain cuckoo species, which lay their eggs in the nests of other birds. The algorithm mimics this behavior by maintaining a population of candidate solutions (eggs) that are placed in different locations (nests) within the search space. Each candidate solution represents a potential solution to the optimization problem at hand.

The algorithm progresses through iterations, where in each iteration, a new candidate solution is generated using a Lévy flight mechanism. This new solution is then evaluated against a randomly selected existing solution in the population. If the new solution is found to be better, it replaces the existing solution in the nest. Additionally, to maintain diversity and prevent premature convergence, a fraction of the worst solutions are abandoned, and new solutions are randomly generated to replace them.

As the iterations continue, the population of candidate solutions gradually evolves towards the optimal solution. The process is terminated when a predefined stopping criterion is met, such as reaching a maximum number of iterations or achieving a satisfactory solution quality.

## Procedure #

Data Structures:

- Population: An array of candidate solutions (eggs)
- Nests: An array of locations where the candidate solutions are placed

Parameters:

`population_size`

: The number of candidate solutions in the population`abandonment_rate`

: The fraction of worst solutions to be abandoned in each iteration`max_iterations`

: The maximum number of iterations before termination

Cuckoo Search Algorithm:

- Initialize the population of candidate solutions (eggs) randomly within the search space.
- While the stopping criterion is not met, do:
- Generate a new candidate solution (cuckoo) using Lévy flights.
- Evaluate the fitness of the new solution.
- Randomly select a nest (existing solution) from the population.
- If the new solution is better than the selected existing solution:
- Replace the existing solution with the new solution.

- Abandon a fraction (abandonment_rate) of the worst solutions.
- Generate new solutions randomly to replace the abandoned solutions.
- Keep the best solutions (or nests with high-quality solutions).
- Rank the solutions and find the current best.

- Return the best solution found.

## Considerations #

Advantages:

- Simple and easy to implement, with few parameters to tune
- Exhibits good exploration and exploitation capabilities
- Can escape local optima due to the Lévy flight mechanism
- Demonstrates good performance on a wide range of optimization problems

Disadvantages:

- The algorithm’s performance is sensitive to the choice of parameters
- May require a large number of iterations to converge for high-dimensional problems
- The Lévy flight mechanism can be computationally expensive
- May not be suitable for problems with many local optima or highly complex search spaces

## Heuristics #

Parameter Selection:

- The
`population_size`

should be chosen based on the complexity of the problem. A larger population size can improve exploration but increases computational cost. - The
`abandonment_rate`

is typically set between 0.1 and 0.5. Higher values promote exploration, while lower values focus on exploitation. - The
`max_iterations`

should be set based on the desired solution quality and available computational resources.

Initialization:

- Initialize the population randomly within the search space to ensure diversity.
- If problem-specific knowledge is available, incorporate it into the initialization process.

Lévy Flights:

- Lévy flights are used to generate new candidate solutions. The step size should be adjusted based on the problem’s scale and desired exploration range.
- Lévy flights with a larger step size promote exploration, while smaller step sizes focus on exploitation.

Abandonment and Replacement:

- The abandonment rate determines the fraction of worst solutions to be discarded in each iteration. Higher values can help escape local optima but may lead to premature convergence if set too high.
- When replacing abandoned solutions, generate new solutions randomly within the search space to maintain diversity.

Termination Criteria:

- The algorithm can be terminated based on a maximum number of iterations, a target solution quality, or a combination of both.
- If the improvement in solution quality becomes negligible over a certain number of iterations, consider terminating the algorithm to avoid unnecessary computations.