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Random-restart hill climbing is a surprisingly effective algorithm in many cases. It turns out that it is often better to spend CPU time exploring the space, than carefully optimizing from an initial condition.
Only one of them is the global maximum. If a hill-climber begins in a poor location, it may converge to the lower maximum. Hill climbing will not necessarily find the global maximum, but may instead converge on a local maximum.
This problem does not occur if the heuristic is convex.
However, as many functions are not convex hill climbing may often fail to reach a global maximum. Other local search algorithms try to overcome this problem such as stochastic hill climbingrandom walks and simulated annealing.
Despite the many local maxima in this graph, the global maximum can still be found using simulated annealing. Unfortunately, the applicability of simulated annealing is problem-specific because it relies on finding lucky jumps that improve the position.
In such extreme examples, hill climbing will most probably produce a local maximum. Ridges and alleys[ edit ] A ridge Ridges are a challenging problem for hill climbers that optimize in continuous spaces.
Because hill climbers only adjust one element in the vector at a time, each step will move in an axis-aligned direction. If the target function creates a narrow ridge that ascends in a non-axis-aligned direction or if the goal is to minimize, a narrow alley that descends in a non-axis-aligned directionthen the hill climber can only ascend the ridge or descend the alley by zig-zagging.
If the sides of the ridge or alley are very steep, then the hill climber may be forced to take very tiny steps as it zig-zags toward a better position. Thus, it may take an unreasonable length of time for it to ascend the ridge or descend the alley.
By contrast, gradient descent methods can move in any direction that the ridge or alley may ascend or descend. Hence, gradient descent or the conjugate gradient method is generally preferred over hill climbing when the target function is differentiable. Hill climbers, however, have the advantage of not requiring the target function to be differentiable, so hill climbers may be preferred when the target function is complex.
Plateau[ edit ] Another problem that sometimes occurs with hill climbing is that of a plateau. A plateau is encountered when the search space is flat, or sufficiently flat that the value returned by the target function is indistinguishable from the value returned for nearby regions due to the precision used by the machine to represent its value.
In such cases, the hill climber may not be able to determine in which direction it should step, and may wander in a direction that never leads to improvement.The International Data Encryption Algorithm (IDEA) is a symmetric-key, block cipher.
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