# Guided Local Search #

## Name #

Guided Local Search (GLS)

## Taxonomy #

Guided Local Search is a metaheuristic optimization technique that extends local search methods to escape local optima and improve solution quality. It is closely related to other local search-based metaheuristics such as Iterated Local Search and Variable Neighborhood Search.

- Optimization
- Metaheuristics
- Local Search Methods
- Guided Local Search

- Local Search Methods

- Metaheuristics

## Strategy #

Guided Local Search enhances the performance of local search algorithms by guiding the search process towards promising regions of the solution space. It achieves this by augmenting the objective function with penalty terms that encourage the exploration of new solutions and penalize features associated with recently visited local optima.

The core idea behind GLS is to identify solution features that are likely to be present in local optima and to penalize them, effectively modifying the search landscape to favor the exploration of new regions. The penalties are dynamically adjusted based on the search history, allowing the algorithm to adapt to the problem structure and avoid revisiting previously explored areas.

### Feature Identification #

GLS relies on the concept of solution features, which are problem-specific attributes or characteristics that can be used to describe and differentiate solutions. These features are typically defined by the problem domain and can capture relevant aspects of the solution structure.

### Penalty Calculation #

Each solution feature is associated with a penalty term that reflects its contribution to the objective function. The penalties are initialized to zero and are dynamically updated during the search process based on the frequency and impact of the features in the visited solutions.

### Augmented Objective Function #

GLS modifies the original objective function by adding the weighted sum of the penalty terms associated with the solution features. This augmented objective function guides the local search towards solutions that minimize both the original objective and the penalties, encouraging the exploration of new regions and the escape from local optima.

## Procedure #

- Initialize the solution
`s`

using a construction heuristic or random initialization. - Set the initial penalty values for all solution features to zero.
- Perform local search on the current solution
`s`

to find a local optimum`s*`

. - While the termination criteria are not met:
- Identify the solution features present in the local optimum
`s*`

. - Update the penalty values of the identified features based on their frequency and impact.
- Modify the objective function by adding the weighted sum of the penalty terms.
- Perform local search on the current solution
`s*`

using the augmented objective function. - If a new local optimum is found, update
`s*`

to the new solution. - If the termination criteria are met, return the best solution found.

- Identify the solution features present in the local optimum

### Data Structures #

- Solution: Represents a candidate solution to the problem, typically encoded as a vector or a more complex data structure depending on the problem domain.
- Feature: Represents a problem-specific attribute or characteristic of a solution, used to guide the search process.
- Penalty: Represents the penalty value associated with each solution feature, dynamically updated during the search.

### Parameters #

`lambda`

: The weight factor that determines the balance between the original objective function and the penalty terms in the augmented objective function.`alpha`

: The scaling factor that controls the rate at which penalties are updated based on the frequency and impact of the solution features.`max_iterations`

: The maximum number of iterations allowed for the GLS algorithm.

## Considerations #

### Advantages #

- Guided Local Search can effectively escape local optima and explore promising regions of the search space, leading to improved solution quality compared to basic local search methods.
- The dynamic adjustment of penalties allows GLS to adapt to the problem structure and avoid revisiting previously explored areas, enhancing search efficiency.
- GLS is a flexible framework that can be applied to a wide range of optimization problems, as long as suitable solution features can be defined.

### Disadvantages #

- The performance of GLS heavily relies on the proper definition of solution features, which can be problem-specific and may require domain knowledge or experimentation to identify.
- The effectiveness of GLS depends on the balance between the original objective function and the penalty terms, which is controlled by the
`lambda`

parameter. Tuning this parameter can be challenging and may require trial and error. - GLS introduces additional computational overhead compared to basic local search methods due to the feature identification and penalty update processes.

## Heuristics #

### Feature Definition #

- Define solution features that capture relevant aspects of the problem structure and can differentiate between good and bad solutions.
- Consider features that are likely to be present in local optima and can guide the search towards unexplored regions.
- Experiment with different feature sets and evaluate their impact on the search performance.

### Parameter Tuning #

- Start with a small value of
`lambda`

(e.g., 0.1) and gradually increase it if the search tends to get stuck in local optima. - Adjust
`alpha`

to control the rate at which penalties are updated. Higher values of`alpha`

will lead to faster penalty updates and more aggressive exploration. - Set
`max_iterations`

based on the problem size and the available computational resources. Allow sufficient iterations for the search to converge while avoiding excessive runtime.

### Local Search Integration #

- Use an efficient and effective local search algorithm as the underlying search method in GLS.
- Consider problem-specific neighborhood structures and move operators to explore the search space effectively.
- Experiment with different local search techniques (e.g., hill climbing, simulated annealing) to find the best match for the problem at hand.

### Hybridization #

- Consider combining GLS with other metaheuristics or problem-specific heuristics to further enhance its performance.
- Explore hybrid approaches that leverage the strengths of different techniques, such as using GLS to guide a population-based metaheuristic or incorporating domain-specific knowledge into the feature definition and penalty update processes.

### Termination Criteria #

- Define suitable termination criteria based on the problem requirements and available resources.
- Consider criteria such as the maximum number of iterations, the maximum number of function evaluations, or the achievement of a target solution quality.
- Implement early stopping mechanisms to terminate the search if no significant improvement is observed after a certain number of iterations.