Basin-hopping

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Basin-hopping is a global optimization method used to find the best solution in tough, high‑dimensional problems. It works by repeating three steps: (1) make a random change to the current solution, (2) quickly refine the new point with a local search to reach a nearby minimum, and (3) decide whether to keep this new point based on its quality. If the new solution has a lower value (better), it is accepted; if it’s worse, it may still be accepted sometimes to help the search escape getting stuck in a bad region. The process is repeated many times to explore different possibilities.

This approach is especially useful for complex problems like finding the lowest‑energy arrangement of atoms in a molecule. The idea comes from Monte Carlo minimization and was described in 1997 by David J. Wales and Jonathan Doye.