Ricerc@Sapienza

As the title indicates, the proposed research activity aims to study and define new methodologies and algorithms for solving particular classes of difficult optimization problems. In particular, the considered problems belong to the classes of black box and large scale optimization problems.

Difficult Black Box Optimization Problem.

These complex problems are characterized by the fact that there exists only a ¿black box¿ (a simulation tool or an approximation technique) which is able to provide sufficiently good approximations of the relationships between the control variables and the values of the objective functions /constraints.In particular, the aim of the research activity will be the definition of efficient methods for solving particular black box optimization problems which arise in fields of optimal design in engineering and management of services in healthcare. These problems present one or more of the following challenging features: some of the variables are restricted to take integer values, the values of the objective function and constraints can be computed with different precision (fidelity) and different computational times, the values of the objective function and constraints are affected by random noise following an unknown probability distribution.

Difficult Large Scale Optimization Problems.

The distinguishing characteristic of these problems is the large number of variables and constraints .The recent developments in the field of data mining and machine learning need to deal with large scale problems in which the objective functions have particular structures that make them very difficult to minimize. In particular, these functions are very expensive from the computational point of view and have surfaces with large regions where their gradients(or parts of them) are vanishingly small.The proposed activity will try to identify possible methodological approaches to tackle the previous computational difficulties.