Simulated Annealing

Cooling toward a good look

Simulated annealing borrows from metallurgy: heat a metal and cool it slowly and it settles into a low-energy, well-ordered state. As an algorithm it explores by making random changes, accepting worse ones freely at first (high "temperature") and less as it cools, so it can escape dead-ends before settling. It is a workhorse of real optimisation.

Here the "energy" it minimises is purely cosmetic — balanced even/odd and low/high, a typical sum, no clustering — so it converges on a pleasingly balanced-looking set.

A cosmetic objective, honestly

Like the Genetic method, annealing can only optimise the objective you give it. Ours is a look, not "likelihood of winning" — which is impossible to optimise because the draw is uniform and memoryless. The result is a balanced set, no more likely to win than any other.

How we borrow its shape

The Simulated Annealing method draws from genuine quantum entropy, then anneals a set toward a cosmetic balance-and-spread objective. Real randomness; the annealed balance is the shape.

• —Starts random, swaps numbers, and “cools” over time
• —Accepts worse moves early, settles late (Metropolis rule)
• —Optimises a cosmetic objective — balance and spread

Sources & further reading

1. An exhaustive review of the metaheuristic algorithms (PMC) — Taxonomy of simulated annealing, PSO, ant-colony and other metaheuristics.
2. Simulated annealing — Wikipedia — The cooling schedule and Metropolis acceptance criterion.
3. World Lotteries Association — random chance is the essence of the lottery — Draws are random and independent; no objective can optimise a uniform draw.