### 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 |
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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 |
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Volume | 991 |

ISSN (Print) | 2194-5357 |

### Conference

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

City | Metz |

Period | 8/07/19 → 10/07/19 |

### Fingerprint

### Keywords

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

### 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

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*Optimization of Complex Systems: Theory, Models, Algorithms and Applications, 2019.*Advances in Intelligent Systems and Computing, vol. 991, Springer Verlag, pp. 611-616, 6th World Congress on Global Optimization, WCGO 2019, Metz, France, 8/07/19. https://doi.org/10.1007/978-3-030-21803-4_61

**A Numerical Study on MIP Approaches over the Efficient Set.** / Lu, Kuan; Mizuno, Shinji; Shi, Jianming.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - A Numerical Study on MIP Approaches over the Efficient Set

AU - Lu, Kuan

AU - Mizuno, Shinji

AU - Shi, Jianming

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - Efficient set

KW - Gloal optimization

KW - Linear complementarity conditions

KW - Mixed integer programming

KW - Multiobjective programming

UR - http://www.scopus.com/inward/record.url?scp=85068422816&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-21803-4_61

DO - 10.1007/978-3-030-21803-4_61

M3 - Conference contribution

AN - SCOPUS:85068422816

SN - 9783030218027

T3 - Advances in Intelligent Systems and Computing

SP - 611

EP - 616

BT - Optimization of Complex Systems

A2 - Le Thi, Hoai An

A2 - Le, Hoai Minh

A2 - Pham Dinh, Tao

PB - Springer Verlag

ER -