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In numerical analysis, hill climbing is a mathematical optimization technique which belongs to the family of local search. It is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to find a better solution by making an incremental change to the solution.
One such algorithm is min-conflicts hill-climbing. [1] Given an initial assignment of values to all the variables of a constraint satisfaction problem (with one or more constraints not satisfied), select a variable from the set of variables with conflicts violating one or more of its constraints.
Hill climbing algorithms can only escape a plateau by doing changes that do not change the quality of the assignment. As a result, they can be stuck in a plateau where the quality of assignment has a local maxima. GSAT (greedy sat) was the first local search algorithm for satisfiability, and is a form of hill climbing.
When the choice of the neighbor solution is done by taking the one locally maximizing the criterion, i.e.: a greedy search, the metaheuristic takes the name hill climbing. When no improving neighbors are present, local search is stuck at a locally optimal point.
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 neighbors are available.
Conversely, a beam width of 1 corresponds to a hill-climbing algorithm. [3] The beam width bounds the memory required to perform the search. Since a goal state could potentially be pruned, beam search sacrifices completeness (the guarantee that an algorithm will terminate with a solution, if one exists).
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When applicable, a common approach is to iteratively improve a parameter guess by local hill-climbing in the objective function landscape. Derivative-based algorithms use derivative information of to find a good search direction, since for example the gradient gives the direction of steepest ascent. Derivative-based optimization is efficient at ...
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