Introduction

Abstract

In multiobjective optimization or multiple criteria decision making (MCDM)¹ decision problems are analyzed for which several objectives or objective functions shall be optimized at the same time. Formally, such a problem can be defined as follows: Let A ≠ Ø be a set of alternatives (also called actions, strategies or feasible solutions) of a decision problem. Let

$$ f\;:\;A\; \to \;{R^q} $$

(1.1)

be a multicriteria evaluation function. A proper DCDM problem is given only for q ≥ 2. The case of an ordinary scalar optimization problem with q = 1 will be considered as a special case of a DCDM problem during this work for simplifying analysis. Each function f _k : A → R with f _k (a) = z _k (k ∈ {1,…,q}, a ∈ A) with f(a) = (z ₁,…,z _q ) is called a criterion or objective function or attribute. We assume each criterion has to be maximized, thus that a higher value is prefered to a smaller value.² (A, f) is called a multiple criteria decision making (DCDM) problem.

“Every art and every investigation, and likewise every practical pursuit or undertaking, seems to aim at some good ‖ But as there are numerous pursuits and arts and sciences, it follows that their ends are correspondingly numerous ‖”;

—Aristotle, Nicomachean Ethics

It is also common to use the acronym ‘MCDA’ where ‘A’ stands for ‘Aid’ or ‘analysis’. Along with these terminological delicacies there is a methodological dispute which will be critically discussed in Chapter 2.