Simulated Annealing — Probabilistic Optimization

The geometric schedule T ← α·T with α between 0.90 and 0.99 is the most common starting point. A practical approach is to set the initial temperature high enough that roughly 80% of moves are accepted at the start, then reduce it until fewer than 1% of uphill moves are accepted. If the final solution quality is poor, slow the cooling rate (increase α); if runtime is too long, speed it up. Always run the algorithm several times from different starting solutions to assess robustness.

Simulated annealing maintains a single solution and explores the neighbourhood through random perturbations, accepting worse solutions probabilistically. Genetic algorithms and particle swarm optimisation maintain a population of solutions and use crossover, mutation, or swarm movement to evolve the population. Simulated annealing is generally simpler to implement for problems with a natural neighbourhood structure, while population-based methods can be more effective for high-dimensional continuous problems.

Theoretically yes, under the condition that the temperature decreases sufficiently slowly (logarithmic cooling). In practice, such cooling is computationally infeasible, so the algorithm finds a near-optimal solution. The quality of the result improves with slower cooling and more iterations, but there is no finite-time guarantee. Running multiple restarts and keeping the best solution found is a practical way to increase confidence.

Choose tabu search when you need a deterministic, memory-guided search that avoids revisiting recent solutions and can exploit problem structure efficiently in a shorter run. Choose a genetic algorithm or particle swarm optimisation when the problem is high-dimensional and continuous, or when a population of diverse solutions is needed to map the optimum landscape. Simulated annealing is a strong default for combinatorial problems with a clear neighbourhood structure and when implementation simplicity matters.