Local search (optimization)

In computer science, local search is a heuristic method for solving computationally hard optimization problems. Local search can be used on problems that can be formulated as finding a solution maximizing a criterion among a number of candidate solutions. Local search algorithms move from solution to solution in the space of candidate solutions (the search space) by applying local changes, until a solution deemed optimal is found or a time bound is elapsed. Local search algorithms are widely applied to numerous hard computational problems, including problems from computer science (particularly artificial intelligence), mathematics, operations research, engineering, and bioinformatics. Examples of local search algorithms are WalkSAT, the 2-opt algorithm for the Traveling Salesman Problem and the Metropolis–Hastings algorithm. While it is sometimes possible to substitute gradient descent for a local search algorithm, gradient descent is not in the same family: although it is an iterative method for local optimization, it relies on an objective function’s gradient rather than an explicit exploration of the solution space. Some problems where local search has been applied are: The vertex cover problem, in which a solution is a vertex cover of a graph, and the target is to find a solution with a minimal number of nodes The traveling salesman problem, in which a solution is a cycle containing all nodes of the graph and the target is to minimize the total length of the cycle The boolean satisfiability problem, in which a candidate solution is a truth assignment, and the target is to maximize the number of clauses satisfied by the assignment; in this case, the final solution is of use only if it satisfies all clauses The nurse scheduling problem where a solution is an assignment of nurses to shifts which satisfies all established constraints The k-medoid clustering problem and other related facility location problems for which local search offers the best known approximation ratios from a worst-case perspective The Hopfield Neural Networks problem for which finding stable configurations in Hopfield network.