Olivier C. Martin
= Olivier C. Martin
{c}
<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.<Iterated Local Search by Helena R. Lourenço and others>[Title page; §1, reduced search space; §2.1, general framework]{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:
$$
\mathcal L(1)=\mathcal L(2)=\mathcal L(3)=a,\qquad
\mathcal L(4)=\mathcal L(5)=b,\qquad
\mathcal L(6)=c.
$$
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.