Hill Climbing Algorithm
Hill climbing is a heuristic search algorithm used for mathematical optimization problems. It is an iterative algorithm that starts with an arbitrary solution and then makes incremental changes to the solution, selecting the neighbor with the highest (or lowest, in minimization problems) value. The process continues until no further improvement is possible.
How It Works:
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Start with a random initial state.
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Evaluate the neighbors of the current state.
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Move to the neighbor that has the highest value.
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Repeat the process until no better neighbor is found (i.e., a peak or plateau is reached).
Types of Hill Climbing:
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Simple Hill Climbing – selects the first neighbor that improves the value.
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Steepest-Ascent Hill Climbing – evaluates all neighbors and chooses the best.
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Stochastic Hill Climbing – selects a random improving neighbor.
Problems in Hill Climbing and Solutions:
| Problem | Description | Solution |
|---|---|---|
| Local Maximum | A peak that is higher than nearby states but lower than the global maximum. | Random restarts or simulated annealing. |
| Plateau | A flat area where neighboring states have the same value. | Use sideways moves (limited number) or random walk. |
| Ridges | A narrow path to the top that cannot be climbed directly by single moves. | Modify algorithm to look in multiple directions or use bidirectional search. |
| Shoulders | A gentle slope that leads to higher peaks but may mislead the algorithm. | Add momentum or gradient-based enhancement. |
Example Illustration:
Suppose you’re climbing a hill in thick fog, taking steps only in the direction that leads you upwards. If you reach a small peak (local maximum), you might think you’ve reached the top, even if there’s a taller mountain nearby (global maximum).
Advantages:
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Simple to implement.
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Uses less memory than other search algorithms.
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Works well for continuous optimization.
Disadvantages:
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Can get stuck in local maxima, plateaus, or ridges.
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Not complete (may not find the optimal solution).
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Performance depends heavily on the shape of the search space.