# Local search

> Start with a full, imperfect board and improve it by moves: destroy-and-repair, annealing and tempering, evolutionary recombination. The most reliable polishers here, and the cleanest demonstrations of the rigidity wall, where every one of them stops at the same height.

- Canonical page (with interactive figures/demos): https://eternity2.dev/research/build/local-search/
- Updated: 2026-07-13

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Start with a full, imperfect board and improve it by moves: destroy-and-repair, annealing and tempering, evolutionary recombination. The most reliable polishers here, and the cleanest demonstrations of the rigidity wall, where every one of them stops at the same height.

The pages below go technique by technique: what each is in a line, what it
actually reached on the real 16×16 board, where it stops, and the labs and
measurements to back it. For the whole territory at once, start with
[a map of every known approach](/research/build/approaches-map).

## Pages in this section

- [Local search and ALNS](https://eternity2.dev/research/build/local-search/local-search-alns) — Destroy part of a board, rebuild it better, and let the algorithm learn which demolitions pay. Adaptive large-neighborhood search is the most reliable polisher this project has, and the cleanest demonstration of the wall where polishing ends.
- [Simulated annealing and parallel tempering](https://eternity2.dev/research/build/local-search/parallel-tempering) — Treat mismatches as energy and temperature as tolerance for making things worse. Annealing holds the puzzle's longest-standing record; parallel tempering crosses barriers annealing can't. Both stop at the same wall.
- [Evolutionary and genetic approaches](https://eternity2.dev/research/build/local-search/evolutionary) — Breed a population of boards, keep the fittest, recombine the survivors. The most natural metaphor in the toolbox, and the one method whose central operator, crossover, fights the structure of Eternity II head-on. The complete record of what the community bred, measured, and abandoned.

## Related

- [A map of every known approach](https://eternity2.dev/research/build/approaches-map) — The survey the community keeps asking for and never finds: every family of attack tried on Eternity II, what each one actually reached, where it walls out, and a link to the deep page. One organising insight runs through all of them.
- [The techniques](https://eternity2.dev/research/build/techniques) — The technique shelf: the algorithms and pruning ideas that recur in every serious Eternity II solver, each with what it is, what it costs, and what it actually bought when measured on this puzzle.