Chapter 17
Introduction to Evidence-Based Robust
Optimisation
Gianluca Filippi and Massimiliano Vasile
Abstract This chapter introduces the concept of Evidence-Based Robust Optimisation (EBRO) and a few computational methods that allow calculating a robust
solution when uncertainty is modelled with Dempster–Shafer Theory of evidence
(DST). The chapter provides the basic elements of DST and the framework in which
DST can be introduced in the robust optimisation of engineering systems. The main
interest is in using DST to quantify extreme cases of epistemic uncertainty. EBRO
inserts DST within an optimisation loop to generate a solution that maximises a
given performance index (the quantity of interest) and the belief in its value at the
same time. The chapter introduces also a decomposition approach that allows one
to calculate an approximation to Belief and Plausibility in polynomial time.
Keywords Robust optimisation · Epistemic uncertainty · Evidence theory ·
Network model · Efficient approximation
17.1 Introduction
In the early phase of the design of an engineering system, there is a degree of
uncertainty on its parts and configurations. This uncertainty is often epistemic in
nature and translates into an uncertainty in the performance of the system as a whole.
In order to account for this, it is common practice to add margins at system and
sub-system level. This way of proceeding is commonly called margin approach.
The margin approach evaluates the quantity of interest (for example, the mass)
associated to a proposed nominal design solution, called Best Estimate (BE), and
adds to it, and to each sub-system quantity of interest, a margin often called the
contingency or safety factor. The safety factor accounts for the expected variations
of all uncertain components. For example, a margin is added to the power demand
G. Filippi () · M. Vasile
University of Strathclyde, Glasgow, UK
e-mail: g.filippi@strath.ac.uk; massimiliano.vasile@strath.ac.uk
© Springer Nature Switzerland AG 2021
M. Vasile (ed.), Optimization Under Uncertainty with Applications to Aerospace
Engineering, https://doi.org/10.1007/978-3-030-60166-9_17
541
Introduction to Evidence-Based Robust
Optimisation
Gianluca Filippi and Massimiliano Vasile
Abstract This chapter introduces the concept of Evidence-Based Robust Optimisation (EBRO) and a few computational methods that allow calculating a robust
solution when uncertainty is modelled with Dempster–Shafer Theory of evidence
(DST). The chapter provides the basic elements of DST and the framework in which
DST can be introduced in the robust optimisation of engineering systems. The main
interest is in using DST to quantify extreme cases of epistemic uncertainty. EBRO
inserts DST within an optimisation loop to generate a solution that maximises a
given performance index (the quantity of interest) and the belief in its value at the
same time. The chapter introduces also a decomposition approach that allows one
to calculate an approximation to Belief and Plausibility in polynomial time.
Keywords Robust optimisation · Epistemic uncertainty · Evidence theory ·
Network model · Efficient approximation
17.1 Introduction
In the early phase of the design of an engineering system, there is a degree of
uncertainty on its parts and configurations. This uncertainty is often epistemic in
nature and translates into an uncertainty in the performance of the system as a whole.
In order to account for this, it is common practice to add margins at system and
sub-system level. This way of proceeding is commonly called margin approach.
The margin approach evaluates the quantity of interest (for example, the mass)
associated to a proposed nominal design solution, called Best Estimate (BE), and
adds to it, and to each sub-system quantity of interest, a margin often called the
contingency or safety factor. The safety factor accounts for the expected variations
of all uncertain components. For example, a margin is added to the power demand
G. Filippi () · M. Vasile
University of Strathclyde, Glasgow, UK
e-mail: g.filippi@strath.ac.uk; massimiliano.vasile@strath.ac.uk
© Springer Nature Switzerland AG 2021
M. Vasile (ed.), Optimization Under Uncertainty with Applications to Aerospace
Engineering, https://doi.org/10.1007/978-3-030-60166-9_17
541