Many interesting and challenging real world problems can be modelled as optimization problems where the relationships between the variables and the values of the objective functions and some constraints are extremely complex and cannot be described analytically. Such class of problems need the use of efficient simulation techniques able to provide sufficiently good approximations of the behaviors of the objective functions and constraints to vary the variables of the problems.
The research activity will be devoted to the study and the description of new methodologies and algorithms for solving the previous simulation based optimization problems. This activity will be carried on along two main themes.
The first one is the definition of new algorithms and strategies for tackling difficult classes of simulation based optimization problems such as constrained global multiobjective optimization problems, nonlinear mixed optimization problems, nonsmooth optimization problems, problems where the objective function and the constraints can be approximated with different precisions, bilevel optimization problems, stochastic optimization problems.
The second theme focuses on the need of defining new optimization methods for the realization of new approximation/simulation tools. This need follows from the fact that, recently, particularly complex problems must be considered. The available simulation codes are not able to describe these problems. This difficulty could be overcome by using data mining tools efficiently trained by new and more efficient optimization techniques.
From the practical point of view, the new algorithms developed by the two research activities will be used for tackling difficult real problems deriving from optimal designs of electrical motors, optimal designs of electrical magnetic apparatus, optimal ship design problems, managements of healthcare services, workforce management, definitions of optimal trading strategies.
The research group has produced important methodological and applicative contributions in field of nonlinear optimization methods. The results obtained and the methods proposed in the field of derivative free algorithms and in the field of large-scale optimization methods can play a fundamental role for the achievement of the objectives of the project
As regards the area of derivative free algorithms, the research activity will be carried out along the following approaches:
-derivative-free methods for constrained global multiobjective optimization problems:
new methods for getting global Pareto points could be obtained by combining the global strategies proposed in [Di Pillo, Liuzzi, Lucidi, Piccialli, Rinaldi, COAP (2016)] e [Liuzzi, Lucidi, Piccialli, COAP (2016)] with the local strategy proposed in [Liuzzi, Lucidi, Rinaldi, SOPT (2016)]. These new methods should exploit the good features of two approaches and should guarantee good theoretical and practical properties;
- derivative-free methods for nonlinear mixed optimization problems:
the aim is to improve the methods proposed in [Liuzzi, Lucidi, Rinaldi, COAP (2012)] and [Liuzzi, Lucidi, Rinaldi, JOTA (2015)] both in term of efficiency and in term of quality of the produced points. The idea is to enforce a quick convergence towards ¿good solutions¿ by using new efficient search directions and nonmonotone line search techniques;
- derivative-free methods for nonsmooth optimization problems:
the idea is to compute search directions by minimizing suitable local model of the nonsmooth objective function. Such directions e should guarantee a better efficiency with respect the previous derivative free algorithm for nonsmooth problems;
- derivative-free methods for variable precision optimization problems:
some recent results obtained by the research group could be the to define a globally convergent derivative free algorithm for problems where both the objective functions and the nonlinear constraints can be approximated with a variable precision;
- bilevel optimization problems:
The approach [Ciccazzo, Latorre, Liuzzi, Lucidi, Rinaldi, JOTA 2015] could be extended to tackle bilevel optimization problems.
- medium/large dimension problems:
a possible approach to solve bigger derivative free problems could be to combine the algorithms proposed by the research group with some efficient modelling technique for the objective function and the constraints.
The research activity concerning optimization methods for machine learning techniques will follows these lines:
- unconstrained or simply constrained problems where the number of variables can be very large or where the objective functions can be the sum of huge number of the terms:
New efficient algorithms for such classes of difficult optimization problems can be defined by taking into account the following results:
the new preconditioned truncated Newton method proposed in [Fasano, Roma, COAP (2016)] which are able to solve efficiently large scale highly ill-conditioned unconstrained problem;
the use of negative curvature directions described in [Fasano, Lucidi, Opt.Letters 2009];
the efficient active set strategy studied in [De Santis, Lucidi, Rinaldi, SIOP (2016)];
- Nonlinear optimization methods for large scale nonlinear constrained optimization problems:
the research activity will study new algorithms based on the approach of transforming the original nonlinear constrained problem into an equivalent box constrained minimization problem. Then this simpler problem will be tackled by combining the approach prosed in [De Santis, Di Pillo, Lucidi, COAP (2012)] with the use of efficient Newto-type directions..
The more application-oriented research activity will consider difficult real world problems deriving from the of the following fields:
- optimal designs of electrical motors and electrical magnetic apparatus;
- optimal ship design problems;
- circuit worst case analysis
- managements of healthcare services;
- optimal trading strategies;
- workforce management;
- optimal design of satellite control parameters;
-machine learning techniques;
- data mining problems.
In this contest, the common approach could be to study in depth the considered real problem, to model it as a suitable optimization problem.
The use of efficient optimization methods in the above described could produce a significant impact.
For example, we can consider the problem of increasing of electric motors efficiency would lead
- to reduce expenses resulting from the use of electric motors from the industry (according to 2016 data of Terna, using more efficient electricmotors could lead to savings of up to 2,3-3 billion euro per year):
- to save energy consumption, and, consequently, a decrease of the demand for electricity and less emissions related to power generation, in agreement with EU directives.