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 with 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 Brute Force Optimizer (BFO) package firstly introduced in [Porcelli and Toint 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.

This article shows how to use performance and data profile benchmarking tools to improve the performance of algorithms. We propose to achieve this goal by defining and approximately solving suitable optimization problems involving the parameters of the algorithm under consideration. Because these problems do not have derivatives and may involve integer variables, we suggest using a mixed-integer derivative-free optimizer for this task. A numerical illustration is presented (using the BFO package), which indicates that the obtained gains are potentially significant.

A direct-search derivative-free Matlab optimizer for bound-constrained problems is described, whose remarkable features are its ability to handle a mix of continuous and discrete variables, a versatile interface as well as a novel self-training option. Its performance compares favorably with that of NOMAD (Nonsmooth Optimization by Mesh Adaptive Direct Search), a well-known derivative-free optimization package. It is also applicable to multilevel equilibrium- or constrained-type problems. Its easy-to-use interface provides a number of user-oriented features, such as checkpointing and restart, variable scaling, and early termination tools.