Hill climbing

Hill climbing is a local search algorithm that iteratively moves to a neighboring state with a higher value, terminating when no neighbor offers improvement. It is the simplest form of best-first search: the heuristic is the objective function itself, and the algorithm is so greedy that it never considers any direction but upward. This makes it fast, memoryless, and easy to implement — but also vulnerable to local maxima, plateaus, and ridges. In landscapes where the global optimum is hidden behind a valley of suboptimal states, hill climbing will never find it.

The algorithm is not merely a failed optimization technique. It is a model of how systems with no memory and no global map navigate fitness landscapes. Biological evolution, when considered at the scale of a single generation, is hill climbing: mutations produce local variants, and selection moves the population toward higher fitness. The problem of local maxima is the problem of evolutionary stasis — the reason why some lineages remain trapped in suboptimal morphologies for millions of years. Hill climbing is not a computational curiosity. It is the dynamics of adaptation without foresight.