Beyond Classical Search: Local Search

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Local search is a type of search algorithm that is used for solving optimization problems, where the goal is to find the best solution among a set of possible solutions. Unlike classical search algorithms, which systematically explore the search space, local search algorithms focus on a single candidate solution and iteratively improve it by making small local modifications.

The basic idea of local search is to start with an initial solution, evaluate its quality using an objective function, and then repeatedly modify the current solution by making small changes, until a better solution is found or a stopping criterion is met.

Some common local search algorithms include:

  1. Hill climbing: This is a simple local search algorithm that starts with an initial solution and repeatedly makes small changes to it, keeping the changes that improve the objective function value. The algorithm terminates when no further improvements can be made.

  2. Simulated annealing: This is a stochastic local search algorithm that allows for occasional moves to worse solutions to avoid getting trapped in local optima. The algorithm starts with a high temperature, allowing for more random moves, and gradually decreases the temperature, leading to a more greedy search.

  3. Tabu search: This is a meta-heuristic that uses a memory structure to prevent revisiting previously visited solutions. The algorithm maintains a list of "tabu" moves that are temporarily disallowed, allowing for more diverse exploration of the search space.

Local search algorithms can be very effective for solving optimization problems, especially when the search space is large or complex, and finding a global optimum is difficult. However, they are not guaranteed to find the optimal solution, and the quality of the solution obtained depends heavily on the choice of initial solution and the search strategy used

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