Problem Space Search: Hill Climbing vs Simulated Annealing

Search Strategy

Landscape

Peaks (state-space complexity) 5

Search speed 4 steps/s

Live Readouts

Height (% of goal)

Steps taken

Restarts

Temperature

—

Status

Idle

How it works

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

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

The agent occupies one cell of the grid (a "state"); its 8 neighbours are the operators available at that state.

Hill Climbing — greedily steps to whichever neighbour has the highest h(x,z). Stops the instant no neighbour is higher: this is the "local maximum problem" the article describes — fast, but easily trapped on a minor peak.
Random-Restart Hill Climbing — same greedy rule, but when stuck it teleports to a fresh random state and climbs again, keeping the best peak found across all attempts. Simulates trying a different initial framing of a problem.
Simulated Annealing — picks a random neighbour and accepts an uphill move always, 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 Einstellung/functional fixedness — and settles into pure hill climbing as T → 0.

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

Agent (searcher) Global optimum Search trail

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.