# A New Bi-Level Mathematical Model And Algorithm For Vons Mapping Problem

IEEE ACCESS（2020）

Abstract

Elastic optical networks (EONs) virtualization can allow the virtual optical networks (VONs) to utilize all the physical resources of EONs, and can attain a high performance of the networks. However, the optimal scheme for VONs mapping should be determined. To tackle these challenges, a bi-level mathematical model is established. leader's and follower's objectives are to minimize energy consumption and the maximum index of used frequency slots, respectively. The bi-level mathematical model can determine the optimal schemes of VONs mapping. To solve the mathematical model effectively, a uniform design method is applied to generate initial population for the lower level problem. In addition, To solve the whole model effectively, a tailor-made encoding, population initialization, genetic operators and local search operator are designed. An efficient genetic algorithm with local search operator is proposed for the bi-level mathematical model. To evaluate the mathematical model and the designed algorithm, a large number of experiments are performed on three kinds of the widely used networks, and the experimental results indicate that the effectiveness of the proposed bi-level mathematical model and designed algorithms.

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Key words

Bi-level optimization, VONs mapping, spectrum assignment, VONs, local search

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