Local Search

Picks a random neighbor each step. Uphill moves are always taken; downhill moves are sometimes taken anyway, with a chance that shrinks as the temperature cools — letting it escape local hills early on, then settle down. Once the temperature freezes, the search finishes with a quick greedy climb to the nearest peak, so it never stops beside an obviously better cell it simply hadn't sampled yet.

multiplier applied to T every step (closer to 1 = slower cooling)

Keeps k candidate states at once. Each step, every state generates its own top-k neighboring moves; all of those are pooled and the overall best k become the next generation. If two states would land on the same cell, the later one is nudged to a free neighboring cell so the beam always holds k distinct points.

Runs k independent hill-climbing searches from k different starting points, with no communication between them. Each one climbs to its own nearest peak on its own schedule and stops there — even if a sibling search finds a taller one. This is the contrast to beam search: no pruning, no sharing, no competition, just k separate hill climbs running side by side.

Like Hill Climbing, but instead of always taking the single best neighbor, it evaluates all neighbors and picks uniformly at random among those that are strictly better than the current cell. This adds randomness to the path it takes uphill. With random restarts on, reaching a local maximum doesn't end the run — it jumps to a new random cell and tries again, always keeping track of the best point found across every attempt.

total moves + restarts across the whole run, not per climb

If the current position is already the best one found, the ring won't be visible — it's sitting directly on top of the orange marker.