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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.
Most problems can be formulated in terms of a search space and target in several different ways. For example, for the traveling salesman problem a solution can be a route visiting all cities and the goal is to find the shortest route. But a solution can also be a path, and being a cycle is part of the target.
Examples of simplices include a line segment in one-dimensional space, a triangle in two-dimensional space, a tetrahedron in three-dimensional space, and so forth. The method approximates a local optimum of a problem with n variables when the objective function varies smoothly and is unimodal .
Simulated annealing searching for a maximum. The objective here is to get to the highest point. In this example, it is not enough to use a simple hill climb algorithm, as there are many local maxima. By cooling the temperature slowly the global maximum is found.
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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."
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