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A Genetic Algorithm for the Bi-Level Topological Design of Local Area Networks.

Camacho-Vallejo JF, Mar-Ortiz J, López-Ramos F, Rodríguez RP - PLoS ONE (2015)

Bottom Line: Local access networks (LAN) are commonly used as communication infrastructures which meet the demand of a set of users in the local environment.Therefore, the decision of optimally assigning users to clusters will be made by the leader and the follower will make the decision of connecting all the clusters while forming a spanning tree.Our solution method considers the Stackelberg equilibrium to solve the bi-level problem.

View Article: PubMed Central - PubMed

Affiliation: Universidad Autónoma de Nuevo León, Facultad de Ciencias Físico-Matemáticas, San Nicolás de los Garza, Nuevo León, México.

ABSTRACT
Local access networks (LAN) are commonly used as communication infrastructures which meet the demand of a set of users in the local environment. Usually these networks consist of several LAN segments connected by bridges. The topological LAN design bi-level problem consists on assigning users to clusters and the union of clusters by bridges in order to obtain a minimum response time network with minimum connection cost. Therefore, the decision of optimally assigning users to clusters will be made by the leader and the follower will make the decision of connecting all the clusters while forming a spanning tree. In this paper, we propose a genetic algorithm for solving the bi-level topological design of a Local Access Network. Our solution method considers the Stackelberg equilibrium to solve the bi-level problem. The Stackelberg-Genetic algorithm procedure deals with the fact that the follower's problem cannot be optimally solved in a straightforward manner. The computational results obtained from two different sets of instances show that the performance of the developed algorithm is efficient and that it is more suitable for solving the bi-level problem than a previous Nash-Genetic approach.

No MeSH data available.


The process of the emulated Nash-Genetic algorithm is shown.
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pone.0128067.g005: The process of the emulated Nash-Genetic algorithm is shown.

Mentions: Let yk−1 be the best value found by the leader at generation k−1 and xk−1 be the best value found by the follower at generation k−1. At generation k, the leader optimizes yk while using xk−1 in order to evaluate (y / x). In the same way, the follower optimizes xk while using yk−1 in order to evaluate (y / x). After the optimization process, the leader sends the best value yk to the follower who will use it at generation k + 1; then the follower makes the same procedure. The Nash equilibrium is reached when neither the leader nor the follower can further improve their criteria without affect the other party interests. This procedure is illustrated in Fig 5.


A Genetic Algorithm for the Bi-Level Topological Design of Local Area Networks.

Camacho-Vallejo JF, Mar-Ortiz J, López-Ramos F, Rodríguez RP - PLoS ONE (2015)

The process of the emulated Nash-Genetic algorithm is shown.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4478021&req=5

pone.0128067.g005: The process of the emulated Nash-Genetic algorithm is shown.
Mentions: Let yk−1 be the best value found by the leader at generation k−1 and xk−1 be the best value found by the follower at generation k−1. At generation k, the leader optimizes yk while using xk−1 in order to evaluate (y / x). In the same way, the follower optimizes xk while using yk−1 in order to evaluate (y / x). After the optimization process, the leader sends the best value yk to the follower who will use it at generation k + 1; then the follower makes the same procedure. The Nash equilibrium is reached when neither the leader nor the follower can further improve their criteria without affect the other party interests. This procedure is illustrated in Fig 5.

Bottom Line: Local access networks (LAN) are commonly used as communication infrastructures which meet the demand of a set of users in the local environment.Therefore, the decision of optimally assigning users to clusters will be made by the leader and the follower will make the decision of connecting all the clusters while forming a spanning tree.Our solution method considers the Stackelberg equilibrium to solve the bi-level problem.

View Article: PubMed Central - PubMed

Affiliation: Universidad Autónoma de Nuevo León, Facultad de Ciencias Físico-Matemáticas, San Nicolás de los Garza, Nuevo León, México.

ABSTRACT
Local access networks (LAN) are commonly used as communication infrastructures which meet the demand of a set of users in the local environment. Usually these networks consist of several LAN segments connected by bridges. The topological LAN design bi-level problem consists on assigning users to clusters and the union of clusters by bridges in order to obtain a minimum response time network with minimum connection cost. Therefore, the decision of optimally assigning users to clusters will be made by the leader and the follower will make the decision of connecting all the clusters while forming a spanning tree. In this paper, we propose a genetic algorithm for solving the bi-level topological design of a Local Access Network. Our solution method considers the Stackelberg equilibrium to solve the bi-level problem. The Stackelberg-Genetic algorithm procedure deals with the fact that the follower's problem cannot be optimally solved in a straightforward manner. The computational results obtained from two different sets of instances show that the performance of the developed algorithm is efficient and that it is more suitable for solving the bi-level problem than a previous Nash-Genetic approach.

No MeSH data available.