Chapter 10
Sequential Parameter Optimization for
Mixed-Discrete Problems
Lorenzo Gentile, Thomas Bartz-Beielstein, and Martin Zaefferer
Abstract Mixed-discrete optimization deals with mathematical optimization problems with multiple types of variables: discrete (nominal) taking values from a
not-sortable set of possible elements, integer variables and variables taking values
in a continuous domain. Mixed-discrete problems appear naturally in many contexts
such as in the real world in the engineering domain, bioinformatics and data
sciences, and this has led to an increased interest in the design of strong algorithms
for different variants of the problem. Much effort has been spent over the last
decades in studying and developing new methodologies, but unfortunately mixeddiscrete optimization problems are much less understood then their “non-mixed”
counterparts. In this chapter we will focus on the rather new approaches to handle
mixed-discrete problems by means of surrogate methods.
Keywords Optimization · Mixed-discrete optimization · Sequential parameter
optimisation
10.1 Introduction
Many real-world optimization problems consider the optimization of ordinal integers, categorical integers, binary variables, permutations, strings, trees or graphs
structures in general. These real-world problems pose complex search spaces which
require a deep understanding of the underlying solution representations. Some of
them, for example, integers, are more suitable to be treated by classic optimization
algorithms. Others, such as trees, have to be handled by specifically developed
optimization algorithms. In general, solving these kinds of problems usually
necessitates a significant number of objective function evaluations. However, in
many engineering problems, a single evaluation is based either on experimental or
L. Gentile () · T. Bartz-Beielstein · M. Zaefferer
Institute for Data Science, Engineering, and Analytics, TH Köln, Köln, Germany
e-mail: lorenzo.gentile@th-koeln.de; thomas.bartz-beielstein@th-koeln.de;
martin.zaefferer@th-koeln.de
© 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_10
333
Sequential Parameter Optimization for
Mixed-Discrete Problems
Lorenzo Gentile, Thomas Bartz-Beielstein, and Martin Zaefferer
Abstract Mixed-discrete optimization deals with mathematical optimization problems with multiple types of variables: discrete (nominal) taking values from a
not-sortable set of possible elements, integer variables and variables taking values
in a continuous domain. Mixed-discrete problems appear naturally in many contexts
such as in the real world in the engineering domain, bioinformatics and data
sciences, and this has led to an increased interest in the design of strong algorithms
for different variants of the problem. Much effort has been spent over the last
decades in studying and developing new methodologies, but unfortunately mixeddiscrete optimization problems are much less understood then their “non-mixed”
counterparts. In this chapter we will focus on the rather new approaches to handle
mixed-discrete problems by means of surrogate methods.
Keywords Optimization · Mixed-discrete optimization · Sequential parameter
optimisation
10.1 Introduction
Many real-world optimization problems consider the optimization of ordinal integers, categorical integers, binary variables, permutations, strings, trees or graphs
structures in general. These real-world problems pose complex search spaces which
require a deep understanding of the underlying solution representations. Some of
them, for example, integers, are more suitable to be treated by classic optimization
algorithms. Others, such as trees, have to be handled by specifically developed
optimization algorithms. In general, solving these kinds of problems usually
necessitates a significant number of objective function evaluations. However, in
many engineering problems, a single evaluation is based either on experimental or
L. Gentile () · T. Bartz-Beielstein · M. Zaefferer
Institute for Data Science, Engineering, and Analytics, TH Köln, Köln, Germany
e-mail: lorenzo.gentile@th-koeln.de; thomas.bartz-beielstein@th-koeln.de;
martin.zaefferer@th-koeln.de
© 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_10
333