### Abstract

This paper concerns an optimization problem over the efficient set of a multiobjective linear programming problem. We propose an equivalent mixed integer programming (MIP) problem and compute an optimal solution by solving the MIP problem. Compared with the previous MIP approach by Sun, the proposed approach relaxes an assumption which lets a more general class of problem can be solved and reduces the size of the MIP problem. By conducting the experiments on a well-known application of the OE problem, the minimum maximal flow problem, we find that the proposed approach is more accurate and faster. The MIP problem can be efficiently solved by current state-of-the-art MIP solvers when the objective function is convex or linear.

Original language | English |
---|---|

Title of host publication | Optimization of Complex Systems |

Subtitle of host publication | Theory, Models, Algorithms and Applications, 2019 |

Editors | Hoai An Le Thi, Hoai Minh Le, Tao Pham Dinh |

Publisher | Springer Verlag |

Pages | 611-616 |

Number of pages | 6 |

ISBN (Print) | 9783030218027 |

DOIs | |

Publication status | Published - 1 Jan 2020 |

Event | 6th World Congress on Global Optimization, WCGO 2019 - Metz, France Duration: 8 Jul 2019 → 10 Jul 2019 |

### Publication series

Name | Advances in Intelligent Systems and Computing |
---|---|

Volume | 991 |

ISSN (Print) | 2194-5357 |

ISSN (Electronic) | 2194-5365 |

### Conference

Conference | 6th World Congress on Global Optimization, WCGO 2019 |
---|---|

Country | France |

City | Metz |

Period | 8/07/19 → 10/07/19 |

### Keywords

- Efficient set
- Gloal optimization
- Linear complementarity conditions
- Mixed integer programming
- Multiobjective programming

## Fingerprint Dive into the research topics of 'A Numerical Study on MIP Approaches over the Efficient Set'. Together they form a unique fingerprint.

## Cite this

*Optimization of Complex Systems: Theory, Models, Algorithms and Applications, 2019*(pp. 611-616). (Advances in Intelligent Systems and Computing; Vol. 991). Springer Verlag. https://doi.org/10.1007/978-3-030-21803-4_61