What are the local search algorithms explain in details?

The local search algorithm explores and evaluates different solutions (search space) by applying local changes until an optimal solution is achieved or certain iterations are calculated. Local search algorithms are widely applied to numerous complex computational problems, including problems in computer science (particularly artificial intelligence), mathematics, operations research, engineering, and bioinformatics. Some examples of local search algorithms are WalkSat, the two-option algorithm for the street vendor problem, and the Metropolis-Hastings algorithm. Local search algorithms move from one solution to another in the candidate solution space (the search space) by applying local changes, until a solution that is considered optimal is found or a deadline has elapsed.