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Hill climbing attempts to maximize (or minimize) a target function (), where is a vector of continuous and/or discrete values. At each iteration, hill climbing will adjust a single element in and determine whether the change improves the value of ().
In fact, Constraint Satisfaction Problems that respond best to a min-conflicts solution do well where a greedy algorithm almost solves the problem. Map coloring problems do poorly with Greedy Algorithm as well as Min-Conflicts. Sub areas of the map tend to hold their colors stable and min conflicts cannot hill climb to break out of the local ...
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).
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.
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 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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Stochastic hill climbing is a variant of the basic hill climbing method. While basic hill climbing always chooses the steepest uphill move, "stochastic hill climbing chooses at random from among the uphill moves; the probability of selection can vary with the steepness of the uphill move."