  A structured version of derivative-free random pattern search optimization
algorithms is introduced which is able to exploit coordinate partially
separable structure (typically associated with sparsity) often present in
unconstrained and bound-constrained optimization problems. This technique
improves performance by orders of magnitude and makes it possible to solve
large problems that otherwise are totally intractable by other derivative-free
methods. A library of interpolation-based modelling tools is also described,
which can be associated to the structured or unstructured versions of the
initial pattern search algorithm. The use of the library further enhances
performance, especially when associated with structure. The significant gains
in performance associated with these two techniques are illustrated using a new
freely-available release of the BFO (Brute Force Optimizer) package firstly
introduced in [Porcelli,Toint, ACM TOMS, 2017], which incorporates them. An
interesting conclusion of the numerical results presented is that providing
global structural information on a problem can result in significantly less
evaluations of the objective function than attempting to building local
Taylor-like models.
