Chapter 8
An Introduction to Many-Objective
Evolutionary Optimization
Dani Irawan and Boris Naujoks
Abstract This chapter describes the differences between single-objective, multiobjective, and many-objective optimization problems. In multi- and many-objective
optimization, often the objectives are conflicting; hence there is no single best
point, and a trade-off between the objectives must be considered. Many-objective
optimization problems can be more difficult than multi-objective problems mainly
because of the curse of dimensionality and because it is also difficult to visualize the
trade-off between the objectives. To solve many-objective optimization problems,
some algorithms are designed with the challenges in consideration. These algorithms are also described in this chapter, including surrogate-assisted algorithms.
Furthermore, several benchmark problems to test and compare the algorithms are
discussed.
Keywords Many-objective optimization · Evolutionary algorithms ·
Benchmarking · Surrogate model · High-dimension visualization
8.1 Introduction
Optimization is the process to bring some things (referred to as objectives) to its best
state, i.e., maximum or minimum [2]. Mankind has been optimizing since antiquity.
The oldest known record of optimization dates back to 300 BC on works made by
Euclid [31].
In this chapter we will consider minimization problems. A maximization problem can be transformed into minimization simply by taking its negative. Often the
system is limited by some conditions, known as constraints. The general form of a
regular optimization problem is
D. Irawan () · B. Naujoks
Institute for Data Science, Engineering, and Analytics, TH Köln, Köln, Germany
e-mail: irawan_dani@yahoo.com
© 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_8
269
An Introduction to Many-Objective
Evolutionary Optimization
Dani Irawan and Boris Naujoks
Abstract This chapter describes the differences between single-objective, multiobjective, and many-objective optimization problems. In multi- and many-objective
optimization, often the objectives are conflicting; hence there is no single best
point, and a trade-off between the objectives must be considered. Many-objective
optimization problems can be more difficult than multi-objective problems mainly
because of the curse of dimensionality and because it is also difficult to visualize the
trade-off between the objectives. To solve many-objective optimization problems,
some algorithms are designed with the challenges in consideration. These algorithms are also described in this chapter, including surrogate-assisted algorithms.
Furthermore, several benchmark problems to test and compare the algorithms are
discussed.
Keywords Many-objective optimization · Evolutionary algorithms ·
Benchmarking · Surrogate model · High-dimension visualization
8.1 Introduction
Optimization is the process to bring some things (referred to as objectives) to its best
state, i.e., maximum or minimum [2]. Mankind has been optimizing since antiquity.
The oldest known record of optimization dates back to 300 BC on works made by
Euclid [31].
In this chapter we will consider minimization problems. A maximization problem can be transformed into minimization simply by taking its negative. Often the
system is limited by some conditions, known as constraints. The general form of a
regular optimization problem is
D. Irawan () · B. Naujoks
Institute for Data Science, Engineering, and Analytics, TH Köln, Köln, Germany
e-mail: irawan_dani@yahoo.com
© 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_8
269