# Local Search Strategy

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### Overview

We provide you a heuristic search algorithm that explores the solution space by iteratively moving from one solution to another in the vicinity, hoping to find an optimal or satisfactory solution. These strategies are commonly used in optimization problems where the goal is to find the best solution among a set of feasible solutions. Unlike global search algorithms, which explore the entire solution space, local search focuses on improving solutions through incremental changes.

###### Here are some key concepts related to local search strategies which we provide:

Current State: Local search starts with an initial solution, known as the current state. This solution is iteratively modified to improve its quality.

Neighbours: The neighbourhood of a solution consists of all possible solutions that can be reached from the current solution by making small changes. These small changes are called moves or transformations.

Objective Function: The objective function evaluates the quality of a solution. It is used to compare different solutions and determine their fitness or optimality. The goal of the local search is to find a solution with the best possible objective function value.

Local Minimum/Maximum: A local minimum is a solution that is better than its neighbours but may not be the overall best solution. Similarly, a local maximum is a solution that is worse than its neighbours but may not be the worst overall.

Exploration and Exploitation: Local search involves a trade-off between exploration and exploitation. Exploration explores new solutions by moving to neighbouring states, while exploitation exploits known good solutions to make incremental improvements.

Termination Condition: The algorithm stops when a termination condition is met. This condition could be a specific number of iterations, reaching a satisfactory solution, or other criteria.

Hill Climbing: Hill climbing is a basic local search algorithm that always moves towards the direction of increasing improvement. It continues to move to the neighbouring solution with the highest improvement until it reaches a local minimum.

Simulated Annealing: Simulated annealing is a probabilistic optimization algorithm that allows the search process to accept worse solutions with a certain probability. This helps in escaping local minima and exploring the solution space more effectively.

Genetic Algorithms: While not strictly a local search algorithm, genetic algorithms involve a form of local search when exploring the solution space through mutation and crossover operations.

These search strategies are widely used in various domains such as operations research, artificial intelligence, and combinatorial optimization problems. These are particularly useful when the solution space is large and it is impractical to explore all possible solutions exhaustively.

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