### Abstract

Multilevel optimization problems deals with mathematical programming problems whose feasible set is implicitly determined by a sequence of nested optimization problems. These kind of problems are common in different applications where there is a hierarchy of decision makers exists. Solving such problems has been a challenge especially when they are non linear and non convex. In this paper we introduce a new algorithm, inspired by natural adaptation, using (1+1)-evolutionary strategy iteratively. Suppose there are k level optimization problem. First, the leader's level will be solved alone for all the variables under all the constraint set. Then that solution will adapt itself according to the objective function in each level going through all the levels down. When a particular level's optimization problem is solved the solution will be adapted the level's variable while the other variables remain being a fixed parameter. This updating process of the solution continues until a stopping criterion is met. Bilevel and trilevel optimization problems are used to show how the algorithm works. From the simulation result on the two problems, it is shown that it is promising to uses the proposed metaheuristic algorithm in solving multilevel optimization problems.

Original language | English |
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Title of host publication | PRICAI 2012 |

Subtitle of host publication | Trends in Artificial Intelligence - 12th Pacific Rim International Conference on Artificial Intelligence, Proceedings |

Pages | 577-588 |

Number of pages | 12 |

DOIs | |

Publication status | Published - Oct 25 2012 |

Event | 12th Pacific Rim International Conference on Artificial Intelligence, PRICAI 2012 - Kuching, Malaysia Duration: Sep 3 2012 → Sep 7 2012 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7458 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 12th Pacific Rim International Conference on Artificial Intelligence, PRICAI 2012 |
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Country | Malaysia |

City | Kuching |

Period | 9/3/12 → 9/7/12 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*PRICAI 2012: Trends in Artificial Intelligence - 12th Pacific Rim International Conference on Artificial Intelligence, Proceedings*(pp. 577-588). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7458 LNAI). https://doi.org/10.1007/978-3-642-32695-0_51

}

*PRICAI 2012: Trends in Artificial Intelligence - 12th Pacific Rim International Conference on Artificial Intelligence, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7458 LNAI, pp. 577-588, 12th Pacific Rim International Conference on Artificial Intelligence, PRICAI 2012, Kuching, Malaysia, 9/3/12. https://doi.org/10.1007/978-3-642-32695-0_51

**A new algorithm for multilevel optimization problems using evolutionary strategy, inspired by natural adaptation.** / Tilahun, Surafel Luleseged; Kassa, Semu Mitiku; Ong, Hong Choon.

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

TY - GEN

T1 - A new algorithm for multilevel optimization problems using evolutionary strategy, inspired by natural adaptation

AU - Tilahun, Surafel Luleseged

AU - Kassa, Semu Mitiku

AU - Ong, Hong Choon

PY - 2012/10/25

Y1 - 2012/10/25

N2 - Multilevel optimization problems deals with mathematical programming problems whose feasible set is implicitly determined by a sequence of nested optimization problems. These kind of problems are common in different applications where there is a hierarchy of decision makers exists. Solving such problems has been a challenge especially when they are non linear and non convex. In this paper we introduce a new algorithm, inspired by natural adaptation, using (1+1)-evolutionary strategy iteratively. Suppose there are k level optimization problem. First, the leader's level will be solved alone for all the variables under all the constraint set. Then that solution will adapt itself according to the objective function in each level going through all the levels down. When a particular level's optimization problem is solved the solution will be adapted the level's variable while the other variables remain being a fixed parameter. This updating process of the solution continues until a stopping criterion is met. Bilevel and trilevel optimization problems are used to show how the algorithm works. From the simulation result on the two problems, it is shown that it is promising to uses the proposed metaheuristic algorithm in solving multilevel optimization problems.

AB - Multilevel optimization problems deals with mathematical programming problems whose feasible set is implicitly determined by a sequence of nested optimization problems. These kind of problems are common in different applications where there is a hierarchy of decision makers exists. Solving such problems has been a challenge especially when they are non linear and non convex. In this paper we introduce a new algorithm, inspired by natural adaptation, using (1+1)-evolutionary strategy iteratively. Suppose there are k level optimization problem. First, the leader's level will be solved alone for all the variables under all the constraint set. Then that solution will adapt itself according to the objective function in each level going through all the levels down. When a particular level's optimization problem is solved the solution will be adapted the level's variable while the other variables remain being a fixed parameter. This updating process of the solution continues until a stopping criterion is met. Bilevel and trilevel optimization problems are used to show how the algorithm works. From the simulation result on the two problems, it is shown that it is promising to uses the proposed metaheuristic algorithm in solving multilevel optimization problems.

UR - http://www.scopus.com/inward/record.url?scp=84867669755&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867669755&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-32695-0_51

DO - 10.1007/978-3-642-32695-0_51

M3 - Conference contribution

AN - SCOPUS:84867669755

SN - 9783642326943

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 577

EP - 588

BT - PRICAI 2012

ER -