Tab. 2: Significance test results for D1 **over all 100 test instances.**

| γ   | 1-BSH   | 2-BSH   | 3-BSH   | 1-FSH   | 2-FSH   | 3-FSH   | 1-EX   | 2-EX   | 3-EX   |
|-----|---------|---------|---------|---------|---------|---------|--------|--------|--------|
| γ1  | 0       | 0       | 0       | 37      | 0       | 0       | 15     | 0      | 0      |
| γ2  | 20      | 0       | 0       | 9       | 0       | 0       | 10     | 0      | 0      |
| γ3  | 11      | 0       | 0       | 9       | 0       | 0       | 16     | 0      | 0      |
| γ4  | 2       | 0       | 0       | 30      | 0       | 0       | 13     | 0      | 0      |
| γ5  | 1       | 0       | 0       | 39      | 0       | 0       | 15     | 0      | 0      |
| γ6  | 32      | 0       | 0       | 1       | 0       | 0       | 15     | 0      | 0      |
| γ7  | 2       | 0       | 0       | 44      | 0       | 0       | 19     | 0      | 0      |
| γ8  | 3       | 0       | 0       | 48      | 0       | 0       | 18     | 0      | 0      |
| γ9  | 20      | 0       | 0       | 17      | 0       | 0       | 17     | 0      | 0      |
| γ10 | 6       | 0       | 0       | 29      | 0       | 0       | 15     | 0      | 0      |
| γ11 | 8       | 0       | 0       | 47      | 0       | 0       | 18     | 0      | 0      |
| γ12 | 5       | 0       | 0       | 42      | 0       | 0       | 37     | 0      | 0      |

Tab. 3: Significance test results for D2 **over all 100 test instances.**

## 3 Multi Objective Variable Neighbourhood Search 3.1 Description Of The Approach

| γ   | 1-BSH   | 2-BSH   | 3-BSH   | 1-FSH   | 2-FSH   | 3-FSH   | 1-EX   | 2-EX   | 3-EX   |
|-----|---------|---------|---------|---------|---------|---------|--------|--------|--------|
| γ1  | 0       | 0       | 0       | 53      | 1       | 0       | 23     | 0      | 0      |
| γ2  | 22      | 0       | 0       | 14      | 0       | 0       | 12     | 0      | 0      |
| γ3  | 13      | 0       | 0       | 15      | 0       | 0       | 24     | 0      | 0      |
| γ4  | 3       | 0       | 0       | 41      | 0       | 0       | 20     | 0      | 0      |
| γ5  | 4       | 0       | 0       | 49      | 1       | 0       | 24     | 0      | 0      |
| γ6  | 30      | 0       | 0       | 2       | 0       | 0       | 19     | 0      | 0      |
| γ7  | 2       | 0       | 0       | 49      | 2       | 0       | 24     | 0      | 0      |
| γ8  | 5       | 1       | 0       | 56      | 0       | 0       | 19     | 0      | 0      |
| γ9  | 20      | 0       | 0       | 23      | 0       | 0       | 23     | 0      | 0      |
| γ10 | 14      | 1       | 0       | 34      | 0       | 0       | 27     | 0      | 0      |
| γ11 | 10      | 2       | 0       | 51      | 1       | 0       | 21     | 0      | 0      |
| γ12 | 10      | 1       | 0       | 32      | 0       | 0       | 53     | 0      | 0      |

Based on the investigation presented in section 2, an improved local **search approach has been proposed, described** in algorithm 3.1. Its main idea is the randomised application of a set of neighbourhood operators to increase the overall identification probability of every Pareto optimal alternative. Compared with existing concepts of variable neighbourhood search [16], the applied operator is randomly chosen **at every step of the algorithm from a predefined**
set of neighbourhoods. Also, only a single neighbourhood is generated, even if it is not possible to achieve further improvements with the selected operator. The computational complexity of this approach is therefore identical with the multi objective local search framework in section 2.

The MOVNS heuristic has been applied to the 100 test instances regarding the twelve optimality criteria definitions in 100 test runs each. Two different configurations have been considered:
1. MOVNS/3, applying a neighbourhood from the set {**1-BSH, 1-FSH, 1-EX**}.

2. MOVNS/9, selecting in each step from all nine neighbourhood definitions as given in section 2.