 Olivier C. Martin

Olivier C. Martin coauthored the 2001 survey Iterated Local Search by Helena R. Lourenço and others with Helena Ramalhinho Dias Lourenço and Thomas Stützle. Its title page identifies him with Université Paris-Sud, Orsay. The survey describes searching over outputs of an embedded optimizer, rather than treating every feasible solution as an equally likely search state.^[ref]

An original finite example distinguishes uniformly chosen starting states from uniformly chosen local minima. Let a deterministic local search operator $\mathcal{L}$ map six possible starts as follows:Here $a,b,c$ are its three possible locally optimized outputs. A uniform random start reaches them with probabilities $1/2$, $1/3$ and $1/6$, not $1/3$ each. This follows simply by counting the starts mapped to each output. It is a chosen abstract optimizer map, not a claim about a particular benchmark landscape.

In iterated local search, a local-search perturbation followed by $\mathcal{L}$ induces another transition mechanism on those outputs. Its probabilities depend on both components. Consequently a chain of locally optimized candidates is not automatically a uniform sample of local minima, nor does it automatically have a prescribed equilibrium distribution. The optimizer and transition rule must be specified before making such sampling claims.