Global Procedures for Solving Black-Box Optimization Problems

Sometimes it is not possible to define either the objective function or the feasible set of an Optimization Problem by means of an algebraic model. It may happen, usually if dealing with real world applications,that there is a lack of reliable analytic models for describing the system process. This can be due either to the high complexity within the system or to the fact that any kind of simplification is not allowed. In this case, the objective function (and sometimes even the feasible set) is described through a simulation process and the related Problem relies in the Simulation-Optimization framework. The term Simulation-Optimization (SO) includes a very wide range of problems and in particular it refers to all the techniques used for optimizing stochastic simulations. This dissertation focuses on this kind of Optimization Problems. In particular, the main topic of the whole work is Black-Box Optimization, namely the area of optimization which studies problems whose objective function is defined purely by means of an input-output model. When solving such problems, many information used by the optimization algorithms, as first order information, is not available. For this reason, over time many different optimization algorithms have been developed to tackle all the difficulties relying behind these problems structure. In the first Chapter of this dissertation are reported the main characteristics of both Simulation-Optimization Problems and Algorithms. One of the features that differentiates between this kind of problems is the presence or not of uncertainty within the simulation model used. As exposed in Chapter \ref{BBOI}, a stochastic or deterministic simulation implies a different implementation in the structure of the algorithm to solve the related Simulation-Optimization problem. After Chapter 1, the whole dissertation is focused on the development and the numerical experimentation of global optimization procedures able to solve Black-Box Optimization Problems starting from real world applications. In particular, Chapters 2, 3 and 4 focus on solving BB Optimization Problems with a deterministic simulation model, while in 5 a stochastic simulation model is introduced. For each of these Chapters it has been defined the same structure: first of all, an introduction of the application is reported, including a description of the state of the art of the literature. Then, the features of the defined optimization problem are explained. Starting from these, it is possible to define an ad-hoc Optimization algorithm, able to solve the modelled problem. It follows, then, a description of the Optimization procedure design and at last some numerical results are reported. Each of them is compared with different alternative optimization algorithms, in order to define the best setting for a particular problem. Moreover, whenever it is possible, the proposed approach is compared with other proposed for a similar problem in previous works. Since we are dealing with real-world applications all the conducted analysis of the numerical results focus on both the efficiency and the effectiveness aspects for the proposed algorithms.