An optimization algorithm never searches in a void.
It searches in an already partitioned space. Variables. Constraints. Encoding. Objective function. Stopping criterion. Each point corresponds to a possible solution. Each value indicates performance according to the chosen measure. The algorithm does not create this space. It traverses it.
Holland gave artificial form to this logic of adaptation. Genetic algorithms recombine, mutate, select. They can produce configurations no one has designed. But they do not produce the problem that receives them. This already existed in the function that decides what deserves to survive.
Mutation is random. Survival is not.
A fitness landscape is not hidden nature. It is a geometry produced by problem formulation. Change the representation, change the objective function, change the constraints, change the penalties, and the terrain changes. A peak is not an absolute summit. It is a summit in a constructed space.
Optimization therefore discovers less a solution than it reveals the form of the framework that made it findable.
Artificial selection exposes the same limit. The breeder chooses a trait. Size. Yield. Speed. Docility. Color. Resistance. This choice does not create all possible forms. It modifies the pressure exerted on available variation. Selection does not overflow what heredity, development, physiological cost and reproduction can sustain.
To formulate what one seeks is already to construct what one can recognize as progress.
This is why no algorithm possesses general superiority over all problems. A performant method is so because it exploits a particular structure: continuity, gradients, useful recombinations, modularity, regularities, neighborhoods. Where these structures are absent, its advantage disappears. The algorithm is not intelligent in itself. It is adapted to a terrain.
Convergence does not prove the solution was waiting. It proves the problem had an exploitable form.
The decisive act is therefore not only in the search. It is in formulation. The fitness function precedes the discovery it makes possible. It does not only say which solution wins. It says which world can produce a winner.
Doctrine
Optimization does not reveal the best in general. It reveals the best according to an already formulated world.
The solution is not independent of the space that renders it visible. Algorithmic invention is not only in the search. It is in choosing what will count as improvement. What one calls optimum is a property of the problem as much as a property of the solution.
Open vector
A model trained on a benchmark, a factory optimized for yield, a city piloted by an indicator, a platform tuned to engagement: each system learns the terrain it is given.
When a machine perfectly attains its objective, what do we still know of the objective itself?
