The role of multiobjective optimization in industrial design of
electromagnetic devices is remarkable and is more and more
increasing. The availability of powerful and flexible FEM codes
for field analysis and the increasing power of computers gives the
designer the chance of building complex parametric models to be
considered for an automatic optimization procedures. As in almost
all design problems, objectives in an electromagnetic devices
design are numerous and often in contrast each other. The
classical, and still widely used, approach to such a situation is
to transform the multiobjective problem into a single-objective
one using some extra knowledge, and to solve it with classical
techniques for single-objective optimization.
Under such a perspective the multi-objective problem is considered
as a special case of the single-objective one.
This approach has three main drawbacks:
1)the variety of solution of a multiobjective problem is reduced
to one with a significant reduction of information,
2)the choice of one solution using some extra knowledge is done
a-priori with no complete information about all possible
solutions,
3)in some (frequent) multiobjective problems (non-convex problems)
the true multiobjective approach gives solutions that would be
mathematically impossible to obtain via the classical approach.
On the other hand, when Pareto optima theory is considered, no
a-priori choice of preferences is required and the perspective is
inverted, that is the single-objective problem becomes a special
case of the multi-objective one. The aim of the optimization
process is the approximation of the infinite Pareto-optimal
solution throughout a convergent and equally spaced sampling of
the Pareto optimal front.
The mathematical theory of multiobjective optimization is mature
and gives useful theorems for existence and uniqueness of
solutions both when classical scalar formulations are considered
and when the problem is tackled via Pareto optima theory. A wide
variety of evolutionary and non evolutionary methods being
specially devoted to Pareto multiobjective optimization
(Multiobjective Evolutionary Algorithms MOEAs) have been
developing and are being developed in the scientific community. In
order to do this huge amount of different strategies univocally a
debate is in progress about test functions, specific convergence
criteria and approximation errors because the extension to Pareto
Optimal Front (POF) approximation of such concepts is non at all
straightforward. This is why, for instance, a special section of
the first congress on Evolutionary Multiobjective Optimization
(EMO2001, Zurich) was devoted to performance measurements.
On the other hand real-life application of MOEAs is often hard and
unpractical due to the complexity of methods and the computational
cost deriving from the required huge number of objective functions
calls. This is particularly true when shape design in
electromagnetic industrial devices is concerned, where the
evaluation of objective functions often requires FEM computations
(sometimes 3D or non-linear or coupled). A special section of
EMO2001 was devoted to real-life applications.
The effort of this thesis is to link true multiobjective
optimization mathematical theory and algorithms with automated
optimal design of electromagnetic devices in order to build
effective methodologies to be practical in industrial environment.
The following key-point will be tackled:
1)Build cost effective strategies requiring a small number of
objectives function calls at a given accuracy of Pareto Optimal
Front approximation.
2)In order to do this consider the world of Evolutionary
multiobjective Optimization methods and try to modify strategies
in order them to be practical in electromagnetic shape design.
3)Consider classical non-evolutionary strategies (based of
preference function) as well, in a critical way and link them to
hybrid stochastic-deterministic search tools.
4)Try to extend neural network based single objective response
surface methods to POF approximation.
5)Link developed strategies to commercial FEM field analysis
tools.
6)Apply developed strategies to industrial design problem in
cooperation with industrial designers.