Problem Space Search: Hill Climbing vs Simulated Annealing (2D)

Landscape

Peaks (state-space complexity) 5

Search speed 4 steps/s

Hill Climbing (greedy)

Height (% of goal)

Steps taken

Status

Idle

Simulated Annealing

Height (% of goal)

Steps taken

Temperature

1.00

Status

Idle

How it works

The landscape is a real height field — a sum of Gaussian "peaks" over the plane, exactly the kind of state-space Newell & Simon (1972) used to model problem solving:

h(x,y) = Σ A_i · exp( -((x-cx_i)² + (y-cy_i)²) / (2σ_i²) )

Both agents start from the same cell (a "state"); their 8 neighbours are the operators available there.

Hill Climbing — greedily steps to whichever neighbour has the highest h. Stops the instant no neighbour is higher: the "local maximum problem" — fast, but easily trapped on a minor peak.
Simulated Annealing — picks a random neighbour and always accepts an uphill move, but also accepts a downhill move with probability P = exp(Δh / T). T cools every step: T_k = max(0.02, T₀ − k·rate). Early on the agent tolerates temporarily "worse" states — the computational analogue of incubation and escaping functional fixedness — and settles into pure hill climbing as T → 0.

"Reached global optimum" means the agent's cell exactly matches the highest cell measured over the whole rendered landscape — not an approximation.

Hill climbing Simulated annealing Global optimum