# Fast Ant System #

## Name #

Fast Ant System (FANT)

## Taxonomy #

Fast Ant System is a variant of the Ant Colony Optimization (ACO) algorithm, which belongs to the field of Swarm Intelligence, a sub-field of Computational Intelligence. It is closely related to other ACO variants such as Ant System (AS), Max-Min Ant System (MMAS), and Ant Colony System (ACS).

- Computational Intelligence
- Swarm Intelligence
- Ant Colony Optimization (ACO)
- Ant System (AS)
- Ant Colony System (ACS)
- Max-Min Ant System (MMAS)
- Fast Ant System (FANT)

- Ant Colony Optimization (ACO)

- Swarm Intelligence

## Strategy #

### Pheromone Update #

In Fast Ant System, the pheromone update process is modified to accelerate the convergence of the algorithm. Instead of updating the pheromone trails after all ants have constructed their solutions, FANT updates the pheromone trails immediately after each ant has completed its solution. This allows the algorithm to quickly identify and exploit promising solutions, leading to faster convergence.

### Pheromone Evaporation #

To balance the exploration and exploitation aspects of the algorithm, FANT incorporates a pheromone evaporation mechanism. After each iteration, the pheromone trails are evaporated by a fixed factor, allowing the algorithm to gradually forget older solutions and explore new areas of the search space.

### Candidate List #

To further improve the efficiency of the algorithm, FANT employs a candidate list strategy. For each node, a list of the most promising neighboring nodes is maintained based on the pheromone trails and heuristic information. During the solution construction phase, ants prioritize the nodes in the candidate list, reducing the computational overhead of exploring all possible options.

## Procedure #

### Data Structures #

`pheromone_matrix`

: A matrix storing the pheromone levels between each pair of nodes.`candidate_list`

: A list of the most promising neighboring nodes for each node.`solutions`

: A list to store the solutions constructed by the ants.

### Parameters #

`num_ants`

: The number of ants in the colony.`alpha`

: The weight of the pheromone trails in the probabilistic decision rule.`beta`

: The weight of the heuristic information in the probabilistic decision rule.`evaporation_rate`

: The rate at which pheromone trails evaporate.`num_iterations`

: The number of iterations to run the algorithm.

### Algorithm Steps #

- Initialize the pheromone matrix with a small positive value.
- Generate the candidate list for each node based on heuristic information.
- For each iteration:
- For each ant:
- Select a starting node randomly.
- While the solution is not complete:
- Choose the next node based on the probabilistic decision rule, favoring nodes in the candidate list.
- Update the pheromone trail between the current node and the chosen node.

- Add the ant’s solution to the
`solutions`

list.

- Evaporate the pheromone trails by multiplying them with
`(1 - evaporation_rate)`

. - Update the candidate list based on the updated pheromone trails.

- For each ant:
- Return the best solution found across all iterations.

## Considerations #

### Advantages #

- Fast convergence: The immediate pheromone update mechanism allows FANT to quickly identify and exploit promising solutions, leading to faster convergence compared to other ACO variants.
- Efficient exploration: The candidate list strategy reduces the computational overhead of exploring all possible options, enabling FANT to efficiently navigate the search space.
- Adaptability: FANT can be easily adapted to various optimization problems by defining appropriate heuristic information and candidate list generation strategies.

### Disadvantages #

- Premature convergence: The rapid convergence of FANT may lead to premature convergence, where the algorithm gets stuck in suboptimal solutions.
- Parameter sensitivity: The performance of FANT is sensitive to the choice of parameters, such as the evaporation rate and the weights of pheromone trails and heuristic information.
- Limited exploration: The focus on exploiting promising solutions may limit the algorithm’s ability to explore diverse regions of the search space, potentially missing high-quality solutions.

## Heuristics #

### Parameter Settings #

- Set the number of ants (
`num_ants`

) to be proportional to the problem size. A common heuristic is to use a number of ants equal to the number of nodes in the problem. - Choose the values of
`alpha`

and`beta`

based on the relative importance of pheromone trails and heuristic information. Typically,`alpha`

is set higher than`beta`

to give more weight to the pheromone trails. - Set the evaporation rate (
`evaporation_rate`

) to a value between 0 and 1. Higher values lead to faster forgetting of older solutions, while lower values maintain a stronger influence of past solutions. - Determine the number of iterations (
`num_iterations`

) based on the problem complexity and available computational resources. Increase the number of iterations for more difficult problems or when higher-quality solutions are desired.

### Candidate List Generation #

- Generate the candidate list for each node based on a combination of pheromone trails and heuristic information. Include the top-k most promising neighboring nodes, where k is a user-defined parameter.
- Regularly update the candidate list based on the updated pheromone trails to reflect the changing solution landscape.

### Heuristic Information #

- Define appropriate heuristic information based on the specific problem being solved. The heuristic information should provide a measure of the desirability of moving from one node to another.
- Incorporate problem-specific knowledge into the heuristic information to guide the ants towards promising solutions.

### Parallelization #

- Exploit the inherent parallelism of Fast Ant System by implementing a parallel version of the algorithm. Assign each ant to a separate processing unit to construct solutions independently.
- Synchronize the pheromone updates and candidate list generation steps to ensure consistent information sharing among the ants.