Derivative-free optimization methods

The efficient solution of optimization problems arising in real applications increasingly calls for the development of efficient and easy-to-use implementations of derivative-free algorithms. In applications such as engineering design and design of algorithms (amongst many others), optimization problems are often defined by functions computed by costly simulation. A single simulation performed to evaluate the costly function may, for instance, require the solution of large systems of partial differential equations or even a costly measurement procedure, and hence, may take from a few minutes to many hours or days depending on the particular application. Functions have therefore to be treated as expensive black-boxes. Moreover, optimization variables can be of different nature: continuous (e.g. geometrical parameters), integer (e.g. on/off element of a structure) or more generally categorical variables, which are discrete variables which identify an element of an unordered set (e.g. colors, shapes, or materials). For such general class of optimization problems, derivative-free optimization algorithms have been developed with the aim of producing reasonably good solutions within a limited number of function evaluations.


Margherita Porcelli

Associate Professor