
| γ   | 1-BSH   | 1-FSH   | 1-EX   | MOVNS/3   | MOVNS/9   |
|-----|---------|---------|--------|-----------|-----------|
| γ1  | 0       | 1       | 1      | 53        | 0         |
| γ2  | 3       | 3       | 0      | 47        | 0         |
| γ3  | 0       | 2       | 0      | 53        | 0         |
| γ4  | 0       | 4       | 0      | 35        | 0         |
| γ5  | 0       | 8       | 0      | 46        | 0         |
| γ6  | 3       | 0       | 1      | 30        | 0         |
| γ7  | 0       | 7       | 0      | 63        | 0         |
| γ8  | 0       | 8       | 0      | 65        | 0         |
| γ9  | 0       | 8       | 0      | 65        | 0         |
| γ10 | 1       | 6       | 0      | 54        | 0         |
| γ11 | 0       | 19      | 0      | 64        | 0         |
| γ12 | 0       | 9       | 3      | 79        | 0         |

Tab. 4: Significance test results for D1 **over all 100 test instances.**
Tab. 5: Significance test results for D2 **over all 100 test instances.**

| γ   | 1-BSH   | 1-FSH   | 1-EX   | MOVNS/3   | MOVNS/9   |
|-----|---------|---------|--------|-----------|-----------|
| γ1  | 0       | 10      | 2      | 58        | 0         |
| γ2  | 5       | 5       | 0      | 58        | 0         |
| γ3  | 1       | 6       | 0      | 64        | 0         |
| γ4  | 1       | 12      | 1      | 46        | 0         |
| γ5  | 0       | 14      | 0      | 48        | 0         |
| γ6  | 5       | 0       | 2      | 42        | 0         |
| γ7  | 0       | 18      | 1      | 66        | 1         |
| γ8  | 0       | 20      | 0      | 64        | 1         |
| γ9  | 4       | 9       | 1      | 66        | 0         |
| γ10 | 2       | 10      | 2      | 68        | 0         |
| γ11 | 1       | 21      | 1      | 67        | 1         |
| γ12 | 3       | 15      | 17     | 60        | 1         |

all considered problem instance. Furthermore, it has been possible **to show that the identification probability of a**
specific Pareto optimal alternative depends on the choice of the neighbourhood in the local search procedure.

Improvements have been obtained in a significantly large number of test cases by applying a concept of randomised variable neighbourhood search. While the in average superior behaviour of the MOVNS approach is independent from the choice of the optimality criteria, a restriction **to favourable neighbourhood definitions is** necessary as weaker operators do not contribute to the quality of the obtained results.

The study demonstrates the advantages of hybridising traditional local search techniques with multi neighbourhood strategies. This is especially of importance as in the proposed setting of alternatively selecting operators the computational complexity of the approach is not increased while superior results are obtained.

## Acknowledgements

The author wants to thank two anonymous referees for their helpful comments.