Creative Problem Solving: A Simulated Annealing Search

Annealing Schedule

Exploring (divergent)

Starting temperature T₀ 2.20

Cooling rate α 0.9930

Idea step radius 1.10

Search speed 8/s

Live Readout

Temperature T

2.20

Cycle

Current quality

0.00

Best found

0.00

Steps taken

Bad-idea accept %

How it works

The landscape's height f(x, z) is a "solution-quality" surface — every point is one possible idea, and higher ground is a better solution. The search agent is a simulated-annealing algorithm (Kirkpatrick, Gelatt & Vecchi, 1983), the same optimizer used to model structured creative problem solving: divergent idea generation followed by convergent refinement.

propose:  x' = x + step·(rand-0.5)
ΔE = f(x') - f(x)
accept if ΔE ≥ 0            (better idea → always keep it)
accept if ΔE < 0 with
  probability P = exp(ΔE / T)  (worse idea → keep it anyway sometimes)
cool:     T ← T · α   each step

High T (early / divergent phase) — the acceptance probability for a worse idea stays close to 1, so the search jumps around freely, escaping local optima the way brainstorming embraces "bad" ideas to find better ones later.
Low T (late / convergent phase) — P collapses toward 0, so only genuine improvements are kept: the algorithm behaves like plain hill-climbing, mirroring the refinement stage of design thinking.
When T cools past a floor, a new idea cycle reheats T and the search keeps exploring from where it stands — an iterative "diverge again, then converge again" loop, exactly how real creative processes rarely stop after one pass.

Real-world relevance: this exact cooling schedule is used for VLSI chip layout, the travelling-salesman problem, and neural-network hyperparameter search — anywhere a "good enough" solution must be found in a landscape too large to search exhaustively.

Current idea (search agent) Best solution found

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