Chapter 7
Introduction to Optimisation
Annalisa Riccardi, Edmondo Minisci, Kerem Akartunali, Cristian Greco,
Naomi Rutledge, Alexander Kershaw, and Aymen Hashim
Abstract This chapter gives a brief introduction to the formulation of optimisation problems and solving algorithms. After mentioning the different classes of
problems, such as continuous/discrete, local/global and single-/multi-objective, and
introducing some of the useful terminology, the chapter is split in two main parts:
(1) formulations and algorithms for continuous problems, including optimal control,
and (2) formulations and algorithms for integer and mixed-integer problems. Both
sections first consider standard deterministic methods that have been derived starting
by optimality criteria, then more recent heuristics derived by experience and
sometimes inspired by nature. This gives the basis to better read and understand
some of the following chapters on more advanced topics.
Keywords Optimisation · Optimal control · Network optimisation ·
Multi-objective · Continuous variables · Combinatorial variables
7.1 Introduction
Optimisation, derived from the Latin word optimus meaning ‘the best’, is the general
name used to characterise the process of finding the best possible solution for a
problem given a measure of ‘goodness’. This is, for example, the problem of finding
the shortest or fastest route between two points or the best investment in the stock
market that minimises risk and maximises return.
People have been optimising since the beginning of the humankind era, but the
roots for modern-day mathematical and engineering optimisation can be traced to
the Second World War, where optimisation processes were formalised, implemented
and applied to practical operational problems. The term operational research (OR)
A. Riccardi () · E. Minisci · K. Akartunali · C. Greco · N. Rutledge · A. Kershaw · A. Hashim
University of Strathclyde, Glasgow, UK
e-mail: annalisa.riccardi@strath.ac.uk; edmondo.minisci@strath.ac.uk;
kerem.akartunali@strath.ac.uk; c.greco@strath.ac.uk; naomi.rutledge.2013@uni.strath.ac.uk;
alexander.kershaw.2013@uni.strath.ac.uk; aymen.hashim.2013@uni.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_7
223
Introduction to Optimisation
Annalisa Riccardi, Edmondo Minisci, Kerem Akartunali, Cristian Greco,
Naomi Rutledge, Alexander Kershaw, and Aymen Hashim
Abstract This chapter gives a brief introduction to the formulation of optimisation problems and solving algorithms. After mentioning the different classes of
problems, such as continuous/discrete, local/global and single-/multi-objective, and
introducing some of the useful terminology, the chapter is split in two main parts:
(1) formulations and algorithms for continuous problems, including optimal control,
and (2) formulations and algorithms for integer and mixed-integer problems. Both
sections first consider standard deterministic methods that have been derived starting
by optimality criteria, then more recent heuristics derived by experience and
sometimes inspired by nature. This gives the basis to better read and understand
some of the following chapters on more advanced topics.
Keywords Optimisation · Optimal control · Network optimisation ·
Multi-objective · Continuous variables · Combinatorial variables
7.1 Introduction
Optimisation, derived from the Latin word optimus meaning ‘the best’, is the general
name used to characterise the process of finding the best possible solution for a
problem given a measure of ‘goodness’. This is, for example, the problem of finding
the shortest or fastest route between two points or the best investment in the stock
market that minimises risk and maximises return.
People have been optimising since the beginning of the humankind era, but the
roots for modern-day mathematical and engineering optimisation can be traced to
the Second World War, where optimisation processes were formalised, implemented
and applied to practical operational problems. The term operational research (OR)
A. Riccardi () · E. Minisci · K. Akartunali · C. Greco · N. Rutledge · A. Kershaw · A. Hashim
University of Strathclyde, Glasgow, UK
e-mail: annalisa.riccardi@strath.ac.uk; edmondo.minisci@strath.ac.uk;
kerem.akartunali@strath.ac.uk; c.greco@strath.ac.uk; naomi.rutledge.2013@uni.strath.ac.uk;
alexander.kershaw.2013@uni.strath.ac.uk; aymen.hashim.2013@uni.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_7
223