The main aims of the proposed research activity are the study and the definition of new methodologies and algorithms for tackling optimization problems that present one or both of the following features:
- there are different objective functions which are in conflict with each other.
- the relationships between the variables and the values of the objective functions and some constraints are extremely complex and cannot be described analytically; in practice there exists only a ¿black box¿ (a simulation or approximation technique) which is able to provide sufficiently good approximations of the behaviors of the objective functions and constraints to vary the variables of the problems.
As regards the optimization problems showing the first feature (called Multiobjective Optimization Problems) the research activity will try to define new efficient and globally convergent minimization methods by drawing inspiration from the methodological approaches proposed for the single objective optimization problems.
The research activity concerning the Black Box Optimization Problems will be carried on along the definition of new algorithms which, using only function evaluations, are able to tackle difficult classes of black box optimization such as constrained global optimization problems, mixed optimization problems, nonsmooth optimization problems, bilevel optimization problems.
Furthermore the research group will face the very difficult challenge of giving methodological contributions for problems that are at the same time both Multiobjective and Black Box Optimization Problems
Finally, the new algorithms developed by the research activities will be used for solving difficult real problems deriving from optimal designs of electrical motors /electrical magnetic apparatus, optimal ship design problems, managements of healthcare services.
As institutional activity, the group carries out extensive research and study on many different fields of nonlinear optimization methods. At the same time, it strongly works in using the studied methods and algorithms to tackle new difficult real world problems. Usually such real problems are the motivation of the research activity on particular new methodologies.
These particular skills of the research group should play a fundamental role for the achievement of the objectives of the project which need both new methodological contributions and an important applicative experiences.
In particular, for every objective of the project, the activities of the group will be carried out along the following approaches:
Multiobjective Optimization Problems
The group's extensive experience on methods for single objective optimization problems (some examples are [1] and [2]) can be combined with the recent results described in [3] (concerning a new algorithm approach for multiobjective optimization problems) to define new classes of efficient methods which are globally converging towards a large set of Pareto stationary points of a multiobjective optimization problem
Black Box Optimization Problems
The numerous recent methodological contributions proposed by the research group in the field of free optimization derivatives (see for example [3]-[9]) can be an excellent bases for dealing with increasingly complex problems in this field such as constrained global optimization problems, mixed optimization problems, nonsmooth optimization problems, bilevel optimization problems.
Multiobjective and Black Box Optimization Problems
For this very difficult class of problems, the methodologies proposed in [3] and [10] can be significantly improved by using the approaches proposed in [5]-[7]. The aim is to obtain new algorithms that allow to obtain the Pareto front of a multiobjective optimization problem
Optimal Design Problems
The research group has already produced important and significant applicative contributions in fields of optimal design problems (some examples are [4], [10]-[12]).
The union of this experience gained with the new methodological tools produced in the proposed project will allow the group to deal efficiently with the difficult real problems that are recently emerging in particular fields of optimal design.
Management of Healthcare Services
The ambitious objective is to provide an effective decision support system in the management of hospital services. (in particular the emergency departments) of two big and very crowed hospitals of Rome. In this difficult challenge, the research group can count on the experience gained on the discrete event simulation model in [13] and [14], and, also in this case, on the new methodological tools developed in the project
[1] De Santis, Di Pillo, Lucidi (2012). An active set feasible method for large-scale minimization problems with bound constraints. COAP, 53
[2] Cristofari, De Santis, Lucidi, Rinaldi (2017). A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization, JOTA, 172
[3] Liuzzi, Lucidi, Rinaldi (2016). A derivative-free approach to constrained multiobjective nonsmooth optimization. SIAM on Optim., 26,
[4] Latorre, Habal, Graeb, Lucidi (2018). Derivative free methodologies for circuit worst case analysis. Optim. Lett.
[5] Di Pillo, Liuzzi, Lucidi, Piccialli, Rinaldi (2016). A DIRECT-type approach for derivative-free constrained global optimization. COAP, 65
[6] Liuzzi, Lucidi, Piccialli (2016). Exploiting derivative-free local searches in DIRECT-type algorithms for global optimization. COAP, 65
[7] Di Pillo, Lucidi, Rinaldi (2015). A Derivative-Free Algorithm For Constrained Global Optimization Based On Exact Penalty Functions. JOTA, 164
[8] Liuzzi, Lucidi, Rinaldi (2015). Derivative-Free Methods For Mixed-Integer Constrained Optimization Problems. JOTA, 164,
[9] Fasano, Liuzzi, Lucidi, Rinaldi (2014). A Linesearch-Based Derivative-Free Approach For Nonsmooth Constrained Optimization. SIAM on Optim., 24
[10] Campana, Diez, Liuzzi, Lucidi, Pellegrini, Piccialli, Rinaldi, Serani (2018). A multi-objective DIRECT algorithm for ship hull optimization. COAP 71
[11] Parasiliti, Villani, Lucidi, Rinaldi (2012). Finite-Element-Based Multiobjective Design Optimization Procedure of Interior Permanent Magnet Synchronous Motors For Wide Constant-Power Region Operation. IEEE Trans. on Industrial Electronics, 59
[12] Campana, Diez, Iemma, Liuzzi, Lucidi, Rinaldi,, Serani, (2016). Derivative-free global ship design optimization using global/local hybridization of the DIRECT algorithm. Optim. and Eng., 17
[13] Lucidi, Maurici, Paulon, Rinaldi, Roma, (2016). A Derivative-Free Approach For A Simulation-Based Optimization Problem In Healthcare. Optim. Lett.,10
[14] Lucidi, Maurici, Paulon, Rinaldi, Roma, (2016). A Simulation-Based Multiobjective Optimization Approach For Health Care Service Management. IEEE Trans. on Automation Science and Engineering, 13