in this first approach on problem independent working operators.

Among the best studied crossover operators for permutation based encodings are the "partially mapped crossover" (PMX) [16], the "order based **crossover"**
(OBX) [33] and the "uniform order based crossover" (UOBX) [9]. We **apply**
them with a crossover probability of p cross **= 1.**
Crossover operators introduce implicit mutations to the offspring. **To distinguish between the true results obtained by crossover, no mutation operator**
is used in the basic test runs. However, for comparison reason a simple "swap mutation" exchanging two randomly picked genes is examined in a separate test run in combination with the UOBX as this crossover operator is being described as the best among the problem independent operators for the considered problem type. In this configuration (UOBX∧**2EX) , it is applied with**
a probability of p mut = 0.**1 for the whole individual. Thus, the probability of**
an exchange of a single gene is 2pmut N.

## 3.4 Elitism

It has been shown, that elitism plays in general an important role in genetic algorithms and in particular in multi-objective GAs, see e.g. [41]. Various approaches exist to implement an elitist strategy, ranging from preserving the k **best individuals in the population to storing the best individuals in an**
external set. We use a simple, but effective strategy to obtain an elitist genetic algorithm by using overlapping populations. This principle has been introduced as the so called "steady state" genetic algorithm. From each generation to the next, the population is preserved and new individuals are only inserted if they improve the average quality of the population. Duplicates are not allowed, including duplicates of encoded strings as well as duplicates of the corresponding solutions in the decision space. The improvement of the population is in our case measured by the ξi**-values. This means that the complexity of** the necessary calculations to obtain the ξi**-values by pairwise comparison is**
2n pop.

## 3.5 Termination Criterion

The algorithm can terminate after a defined time, a given number of calculations or after the algorithm has converged to a given goal and does not produce any improvements for a defined time or number of calculations. It is certainly interesting to perform calculations until a convergence to a local or global optimal front is reached. The termination criterion is chosen **according** to this goal. The genetic algorithm stops after 10,000 iterations with **no found**
new individual i having a ξi = 0.