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# What is Local Search

Local search methods are usually deterministic. They can find a local optimum very quickly, but will get stuck there.
Published in Chapter:
Stochastic Optimization Algorithms
P. Collet (Université du Littoral Côte d’Opale, France) and J. Rennard (Grenoble Graduate School of Business, France)
DOI: 10.4018/978-1-59140-984-7.ch003
Abstract
When looking for a solution, deterministic methods have the enormous advantage that they do find global optima. Unfortunately, they are very CPU intensive, and are useless on untractable NP-hard problems that would require thousands of years for cutting-edge computers to explore. In order to get a result, one needs to revert to stochastic algorithms that sample the search space without exploring it thoroughly. Such algorithms can find very good results, without any guarantee that the global optimum has been reached; but there is often no other choice than using them. This chapter is a short introduction to the main methods used in stochastic optimization.
More Results
A search algorithm to carry out exploitation.
A type of search method that starts at some point in search space and iteratively moves from position to neighbouring position using heuristics.
Given a set of solutions S , every solution has an associated set of neighbors, expressed by , each of them is called the neighborhood of s . All the neighborhood of s , namely , can be reached directly from s by one move (or transition) to . Local search is performed in such a way to find a local optimal solution. It should be noted that this search is achieved by defining a neighborhood structure.
A search algorithm to carry out exploitation. Pure local search algorithms are prone to getting trapped in local optima, without converging to good solutions.
Method that starts with an initial solution then applies a sequence of local changes in attempt to improve the value of the objective function and obtain the local optima.