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Unit 1 — Hill Climbing — Artificial Intelligence Notes

Hill Climbing

Hill climbing is generate-and-test augmented with a heuristic: at each step, move to the neighbouring state that most improves the heuristic value — like climbing a hill by always stepping uphill.

Algorithm (Simple Hill Climbing)

1. Evaluate the initial state. If it is the goal, stop.
   Otherwise, let current = initial state.
2. Loop:
   a. Generate a successor of current that has not yet been tested.
   b. Evaluate the successor's heuristic value.
   c. If successor is the goal, stop and return it.
   d. If successor is better than current, set current = successor.
   e. If no new successor remains to try and current isn't the goal, fail.

Steepest-Ascent Hill Climbing

Instead of moving to the first better neighbour, generate all neighbours, evaluate each, and move to the best one.

The Problems With Hill Climbing

Problem	Description	Illustration
Local maximum	A state better than all its neighbours, but not the best overall — climbing stops here even though a higher peak exists elsewhere	Small hill next to a mountain
Plateau	A flat region where all neighbouring states have the same heuristic value — no direction looks better	A flat area with no slope
Ridge	A sequence of local maxima that requires moving sideways or even downhill briefly to cross, but the algorithm only evaluates single moves at a time	Diagonal ridge, direct single-step moves fall off it

Fixes / Escapes

Technique	How it helps
Random restart	On getting stuck, restart from a new random state; repeat and keep the best result found
Sideways moves	Allow a bounded number of moves to states with equal heuristic value, to escape plateaus
Backtracking	Keep more than one path so the algorithm can retreat and try a different branch
Simulated annealing	Occasionally accept a worse move (with a probability that decreases over time), allowing escape from local maxima while still generally climbing

Strengths and Weaknesses

Strengths	Weaknesses
Low memory (only needs to track the current state)	Not complete — can get stuck and never find a solution that exists
Fast when the landscape is "smooth" toward the goal	Not optimal — the local maximum found may not be the best solution
Simple to implement	Highly sensitive to the choice of heuristic function