Abstract:
When designing a complex industrial product, the designer often has to
optimise simultaneously multiple conflicting criteria. Such a problem does not usually
have a unique solution, but a set of non-dominated solutions known as Pareto
solutions. In this context, the progress made in the development of more powerful but
more computationally demanding numerical methods has led to the emergence of
multi-disciplinary optimisation (MDO). However, running computationally expensive
multi-objective optimisation procedures to obtain a comprehensive description of the
set of Pareto solutions might not always be possible.
The aim of this research is to develop a methodology to assist the designer in
the multi-objective optimisation process. As a result, an approach to enhance the
understanding of the optimisation problem and to gain some insight into the set of
Pareto solutions is proposed. This approach includes two main components. First,
global sensitivity analysis is used prior to the optimisation procedure to identify non-
significant inputs, aiming to reduce the dimensionality of the problem. Second, once a
candidate Pareto solution is obtained, the local sensitivity is computed to understand
the trade-offs between objectives. Exact linear and quadratic approximations of the
Pareto surface have been derived in the general case and are shown to be more
accurate than the ones found in literature. In addition, sufficient conditions to identify
non-differentiable Pareto points have been proposed. Ultimately, this approach
enables the designer to gain more knowledge about the multi-objective optimisation
problem with the main concern of minimising the computational cost.
A number of test cases have been considered to evaluate the approach. These
include algebraic examples, for direct analytical validation, and more representative
test cases to evaluate its usefulness. In particular, an airfoil design problem has been
developed and implemented to assess the approach on a typical engineering problem.
The results demonstrate the potential of the methodology to achieve a
reduction of computational time by concentrating the optimisation effort on the most
significant variables. The results also show that the Pareto approximations provide the
designer with essential information about trade-offs at reduced computational cost.