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

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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

T2 - 12th Pacific Rim International Conference on Artificial Intelligence, PRICAI 2012

Y2 - 3 September 2012 through 7 September 2012

ER -