Titolo della tesi: Variable space transformation techniques and new algorithms for global optimization
Solving a global optimization problem is a hard task.
In the chapters of this thesis variable space transformation techniques and new algorithmic
approaches are proposed to deal with such hard problems.
In the first research investigation some variable space transformation techniques
are defined as a tool that can be helpfully integrated in (almost) all algorithm
frameworks. In particular the focus will be on piecewise linear and non-linear transformations
that allow to tackle the problem advantageously. After introducing the
theory, preliminary numerical experiments are reported exploiting the transformations
in a simple multi-start framework. The idea is to gather the information
obtained during a multi-start approach and to apply a sequence of transformations
in the variable space that makes the exploration easier. The aim is to expand the
attraction basins of global minimizers shrinking those of the local minima already
found. Preliminary considerations are made about the possibility to use these transformations
as derivative-free preconditioner.
The second research investigation concerns the definition of an efficient algorithm
on a wide spectrum of global optimization problems. In particular will be discussed
how to do an accurate exploratory geometry and a space search reduction strategy,
recently renamed in literature as zoom-in strategy, in a probabilistic algorithm that
can speed up significantly the convergence towards better solutions. After introducing
the algorithm framework named GABRLS, presented as the winner of the
Generalization-based Contest in Global Optimization (GENOPT 2017, [62]), the
approach is extended to handle also non-continuous variables. The resulting algorithm
has been tested in a real case study of design optimization of electric motor.
The case study provides evidences about the promising exploratory geometry of
the approach in quickly finding feasible and optimal solutions of a mixed integer
constrained problem.
In the last research investigation, a new black-box approach is proposed to tackle a
real case study of the spare part management problem of a fleet of aircraft. In particular,
for this specific type of inventory problem, a black-box model and a tailored
global optimization algorithm is defined. The aim is to address the non-linearity
of the problem as is, without any decomposition in sub-problem and without any
approximation or necessity to check ex post the feasibility of the solution. The
main contribution consists of advancing the existing literature for multi-item inventory
systems through an enhanced time-effective optimization algorithm tested in
a single-echelon system.