## Abstract

Bi-level optimisation problems have gained increasing interest in the field of combinatorial optimisation in recent years. With this paper, we start the runtime analysis of evolutionary algorithms for bi-level optimisation problems. We examine the NP-hard generalised minimum spanning tree problem and analyse the two approaches presented by Hu and Raidl [7] in the context of parameterised complexity (with respect to the number of clusters) that distinguish each other by the chosen representation of possible solutions. Our results show that a (1+1) EA working with the spanning nodes representation is not a fixed-parameter evolutionary algorithm for the problem, whereas the global structure representation enables to solve the problem in fixed-parameter time. Furthermore, we present hard instances for each approach and show that the two approaches are highly complementary by proving that they solve each other's hard instances very efficiently.

Original language | English |
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Title of host publication | GECCO 2013 - Proceedings of the 2013 Genetic and Evolutionary Computation Conference |

Pages | 519-525 |

Number of pages | 7 |

DOIs | |

Publication status | Published - 2013 |

Event | 2013 15th Genetic and Evolutionary Computation Conference, GECCO 2013 - Amsterdam, Netherlands Duration: 6 Jul 2013 → 10 Jul 2013 |

### Conference

Conference | 2013 15th Genetic and Evolutionary Computation Conference, GECCO 2013 |
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Country/Territory | Netherlands |

City | Amsterdam |

Period | 6/07/13 → 10/07/13 |

## Keywords

- Bi-level optimisation
- Combinatorial optimisation
- Evolutionary algorithms

## ASJC Scopus subject areas

- Genetics
- Computational Mathematics