Approximating the Pareto front of a bi-objective problem in telecommunication networks using a co-evolutionary algorithm

  • José-Fernando Camacho-Vallejo
  • Cristóbal Garcia-Reyes


This paper studies a telecommunication network design problem. In this network, users must be connected to capacitated hubs. Then, hubs that concentrate users must be connected to each other and possibly to other hubs with no users. The connections in the network must lead to a tree topology. Hence, connection between hubs can be considered as looking for forming a Steiner tree. This problem is modeled as a bi-objective mathematical programming problem. One objective function minimizes user’s latency with respect to the information packages flowing through the capacitated hubs, and the other objective function aims the minimization of the total network’s connection cost. To approximate the Pareto front of this bi-objective problem, a co-evolutionary algorithm is developed. In the proposed algorithm, two populations are considered. Each population is associated with one objective function. The co-evolutionary operator consists of an information exchange between both populations that occurs after the genetic operators have been applied. As a result of this co-evolutionary operator, the non-dominated solutions are identified. Computational experimentation shows that the approximated Pareto fronts are representative despite their non-convexity, and they contain a sufficient number of non-dominated solutions over the tested instances. Also, the kth distance among non-dominated solutions is relatively small, which indicates that the approximated Pareto fronts are dense. Furthermore, the required computational time is very small for a problem with the characteristics herein considered.


Bi-objective programming Telecommunication networks Steiner problems Pareto front Co-evolutionary algorithms 



The research of the first author has been partially supported by the program of professional development of professors with the Grant PRODEP/511-6/17/7425 for research stays during his sabbatical year.


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Authors and Affiliations

  1. 1.Facultad de Ciencias Físico-MatemáticasUniversidad Autónoma de Nuevo LeónSan NicolásMexico
  2. 2.Centro de Investigación en Matemáticas A.C.GuanajuatoMexico

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