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

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.

A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications

“…Bilevel optimization is quite commonly used in network design problems. Instead of going through specific problems, we refer the readers to a variety of applications of bilevel optimization to the area of network design [100], [21], [115], [184], [188], [43], [183], [45], [74], [69], [120], [181], [134], [39]. 2) Environmental Economics: Bilevel optimization commonly appears in environmental economics, where an authority wants to tax an organization or individual that is polluting the environment as a result of its operations.…”

Golden Grain: Building a Secure and Decentralized Model Marketplace for MLaaS

“…Additionally, we employ genetic algorithm [62] to solve the defined bi-level programming problem which is a provably NP-hard problem [61]. The reason to choose genetic algorithm is that it has been proved solving bi-level problem efficiently [63], [64], [65], [66]. Then, the solutions guide the BM-Contract to decide a price for a model with given performance.…”

“…Solving the bi-level programming problem is not easy due to the need of solving the low-level problem at each step of an algorithm that finds solutions for the uplevel problem. Specifically, the decision maker deciding y i in the up-level should interact with the decision maker deciding x i,j of the low-level to obtain the best solution [63], [69] .…”

“…Lastly, we use genetic algorithm to approximately solve the above problem in finite time steps, following the works [63], [69]. Genetic algorithm is a stochastic search technique derived from natural selection and natural genetics mechanisms, consisting of the procedures of initialization, fitness evaluation, selection, crossover and mutation, in which the latter four procedures repeat successively [62].…”

Analyzing the Performance of a Hybrid Heuristic for Solving a Bilevel Location Problem under Different Approaches to Tackle the Lower Level

“…In order to avoid finding the optimal solution for the follower, a local approach was designed for getting the follower's response. Then, in [18], a topological design of Local Area Networks bilevel problem is considered. The lower level must construct a capacitated spanning tree and it is solved by a greedy constructive algorithm similar to Kruskal's algorithm.…”