Descent methods

Contenus

Descent methods

As the explicit name indicates, the methods of descent, or local search, consist in "sliding" along the objective function until a local optimum is found, that is to say where the descent is no longer possible. There are several kinds of descent method which we will describe here.

Simple descent

From an initial solution, the simple descent algorithm chooses a neighboring solution better than the current solution, until it cannot make such a choice.

The algorithm is as follows:

```S_O
to do
S(i + 1) = neighbor (Si)
if f (S(i + 1)) <f (Si) accept S(i + 1)
end if
as long as f (S(i + 1)) <f (Si), whatever S(i + 1) = neighbor (Si)
return Rnot```

Greatest descent

The algorithm is mainly the same as for the simple descent, only a selection criterion of a neighboring solution is modified:

`choose s' neighbor of s / f (s') <f (s' ') or f (s') = f (s'') qq is s' 'neighbor of s`

We therefore choose the neighboring solution offering the best improvement of the current solution.

Multi-start descent

Multi-start descent performs multiple instances of the single descent or greater descent problem. The algorithm is as follows:

```iter = 1 f (Best) = infinity
to do
Choose a starting solution sO at random s 0)
if f (s) <f(Best) alors Best tant que iter < iterMax
return Bes```
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