# Bees Algorithm #

## Name #

Bees Algorithm, BA

## Taxonomy #

The Bees Algorithm is a swarm intelligence optimization algorithm inspired by the foraging behavior of honey bees. It belongs to the family of biologically inspired computation and is closely related to other swarm intelligence algorithms such as Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO).

- Computational Intelligence
- Biologically Inspired Computation
- Swarm Intelligence
- Bees Algorithm

- Swarm Intelligence

- Biologically Inspired Computation

## Strategy #

The Bees Algorithm is based on the idea that a colony of bees can efficiently explore a large search space and locate the most promising regions containing high-quality solutions. The algorithm maintains a population of bees, each representing a potential solution to the optimization problem.

The search process is divided into two main phases: global search and local search. During the global search phase, scout bees are sent out to randomly explore the search space and identify promising regions. These regions are then exploited during the local search phase, where worker bees are recruited to intensify the search around the best solutions found so far.

The algorithm employs a combination of exploration and exploitation to balance the search process. Exploration is achieved through the random search performed by scout bees, while exploitation is carried out by worker bees focusing on the most promising regions. This balance allows the algorithm to avoid getting trapped in local optima and effectively navigate the search space.

### Selection and Recruitment #

The Bees Algorithm uses a selection mechanism to determine which solutions are considered promising and worthy of further exploration. The fitness of each solution is evaluated based on the objective function of the optimization problem. The solutions with higher fitness values are selected as elite solutions and are given more importance during the recruitment process.

The recruitment process involves assigning a larger number of worker bees to the elite solutions, allowing for a more thorough exploration of the promising regions. The number of worker bees assigned to each selected solution is proportional to its fitness value, with better solutions receiving more bees.

### Local Search #

During the local search phase, worker bees explore the neighborhood of the selected solutions. They perform a localized search by making small perturbations to the current solution, seeking to find better solutions within the same region. The size of the neighborhood and the magnitude of the perturbations are controlled by algorithm parameters.

The local search process allows the algorithm to refine and improve the solutions within the promising regions identified during the global search phase. By focusing the search effort on these regions, the algorithm can efficiently converge towards high-quality solutions.

### Convergence and Termination #

The Bees Algorithm iteratively performs global search and local search until a termination criterion is met. This criterion can be based on a maximum number of iterations, a target fitness value, or a predefined computational budget.

As the algorithm progresses, the population of bees converges towards the most promising regions of the search space. The best solution found during the search process is considered the optimal or near-optimal solution to the optimization problem.

## Procedure #

Data Structures:

- Population: A collection of bees, each representing a potential solution.
- Elite Sites: A subset of the population containing the best solutions found so far.
- Selected Sites: A subset of the population selected for local search.

Parameters:

- Population Size: The number of bees in the population.
- Number of Elite Sites: The number of elite solutions selected for exploitation.
- Number of Selected Sites: The number of solutions selected for local search.
- Number of Bees for Elite Sites: The number of worker bees assigned to each elite site.
- Number of Bees for Selected Sites: The number of worker bees assigned to each selected site.
- Neighborhood Size: The size of the neighborhood around a solution for local search.
- Max Iterations: The maximum number of iterations or a termination criterion.

Pseudocode:

- Initialize the population of bees randomly.
- Evaluate the fitness of each bee in the population.
- While termination criterion is not met:
- Select the elite sites based on fitness values.
- Select the selected sites based on fitness values.
- For each elite site:
- Assign a fixed number of worker bees to the site.
- Perform local search around the elite site using the assigned bees.
- Evaluate the fitness of the new solutions generated.
- Update the elite site if a better solution is found.

- For each selected site:
- Assign a fixed number of worker bees to the site.
- Perform local search around the selected site using the assigned bees.
- Evaluate the fitness of the new solutions generated.
- Update the selected site if a better solution is found.

- Send scout bees to randomly explore the search space.
- Evaluate the fitness of the scout bees.
- Update the population with the best solutions found.

- Return the best solution found.

## Considerations #

Advantages:

- Effective in solving complex optimization problems with multiple local optima.
- Balances exploration and exploitation to avoid premature convergence.
- Can be parallelized to improve computational efficiency.

Disadvantages:

- Requires careful tuning of algorithm parameters for optimal performance.
- May be computationally expensive for high-dimensional problems.
- Convergence speed can be slower compared to some other optimization algorithms.

## Heuristics #

### Parameter Selection #

- Population Size: Choose a population size that provides a good balance between exploration and computational efficiency. A larger population size can improve exploration but increases computational cost.
- Number of Elite Sites: Select a small number of elite sites (e.g., 5-10% of the population) to focus the search on the most promising regions.
- Number of Selected Sites: Choose a larger number of selected sites compared to elite sites to maintain diversity in the search.
- Number of Bees for Elite Sites: Assign a larger number of bees to elite sites to intensify the search in promising regions.
- Number of Bees for Selected Sites: Assign a smaller number of bees to selected sites compared to elite sites to balance exploration and exploitation.
- Neighborhood Size: Determine the neighborhood size based on the characteristics of the problem. A larger neighborhood size allows for more extensive local search but may increase computational cost.

### Initialization and Search #

- Initialize the population randomly to cover a wide range of the search space.
- Use problem-specific knowledge, if available, to generate initial solutions that are more likely to be promising.
- Adjust the balance between global search and local search based on the problem characteristics. More global search may be beneficial for highly multimodal problems, while more local search can be effective for problems with fewer local optima.

### Termination Criteria #

- Set a maximum number of iterations or a computational budget based on the available resources and the problem complexity.
- Use a target fitness value as a termination criterion if the optimal solution or a desired level of performance is known.
- Employ a convergence measure, such as the improvement in the best solution over a certain number of iterations, to determine when to stop the algorithm.

### Parallelization #

- Parallelize the Bees Algorithm by distributing the search process across multiple computing nodes or cores.
- Assign each node or core a subset of the population and perform local search independently.
- Synchronize the best solutions found by each node or core periodically to update the global best solution.