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Local search is typically an approximation or incomplete algorithm because the search may stop even if the current best solution found is not optimal. This can happen even if termination happens because the current best solution could not be improved, as the optimal solution can lie far from the neighborhood of the solutions crossed by the ...
Variable Neighborhood Formulation Space Search [21] FSS is a method which is very useful because, one problem could be defined in addition formulations and moving through formulations is legitimate. It is proved that local search works within formulations, implying a final solution when started from some initial solution in first formulation.
Hill climbing finds optimal solutions for convex problems – for other problems it will find only local optima (solutions that cannot be improved upon by any neighboring configurations), which are not necessarily the best possible solution (the global optimum) out of all possible solutions (the search space).
The new assignment is close to the previous one in the space of assignment, hence the name local search. All local search algorithms use a function that evaluates the quality of assignment, for example the number of constraints violated by the assignment. This amount is called the cost of the assignment. The aim of local search is that of ...
Continuous local search (CLS) is a class of search problems designed to model the process of finding a local optima of a continuous function over a continuous domain. It is defined as the class of problems that are polynomial-time reducible to the Continuous Localpoint problem:
The problem Real-Local-Opt (finding the ɛ local optimum of a λ-Lipschitz continuous objective function : [,] [,] and a neighborhood function : [,] [,]) is PLS-complete. [ 8 ] Finding a local fitness peak in a biological fitness landscapes specified by the NK-model /Point-mutation with K ≥ 2 was proven to be PLS-complete via a tight PLS ...
Iterated local search kicks a solution out from a local optimum. Iterated Local Search [1] [2] (ILS) is a term in applied mathematics and computer science defining a modification of local search or hill climbing methods for solving discrete optimization problems. Local search methods can get stuck in a local minimum, where no improving ...
Tabu search (TS) is a metaheuristic search method employing local search methods used for mathematical optimization. It was created by Fred W. Glover in 1986 [ 1 ] and formalized in 1989. [ 2 ] [ 3 ]