Resumen
The cutwidth minimization problem consists of finding a linear arrangement of the vertices of a graph where the maximum number of cuts between the edges of the graph and a line separating consecutive vertices is minimized. We first review previous approaches for special classes of graphs, followed by lower bounds and then a linear integer formulation for the general problem. We then propose a branch-and-bound algorithm based on different lower bounds on the cutwidth of partial solutions. Additionally, we introduce a Greedy Randomized Adaptive Search Procedure (GRASP) heuristic to obtain good initial solutions. The combination of the branch-and-bound and GRASP methods results in optimal solutions or a reduced relative gap (difference between upper and lower bounds) on the instances tested. Empirical results with a collection of previously reported instances indicate that the proposed algorithm is able to solve all the small instances (up to 32 vertices) as well as some of the large instances tested (up to 158 vertices) using less than 30 minutes of CPU time. We compare the results of our method with previous lower bounds, and with the best previous linear integer formulation solved using Cplex. Both comparisons favor the proposed procedure.
Abraham Duarte
Catedrático de Universidad
Mi carrera investigadora se ha centrado en el desarrollo de nuevos algoritmos y técnicas de Inteligencia Computacional (metaheurísticas) y su aplicación a diferentes problemas en Ciencia e Ingeniería desde que me incorporé a la Universidad Rey Juan Carlos (URJC) en el octubre del año 2000.
Eduardo García Pardo
Catedrático de Universidad
Miembro fundador del grupo de investigación GRAFO, cuya línea de investigación principal es el desarrollo de algoritmos para abordar problemas de optimización, temática sobre la que versa la Tesis Doctoral del investigador y en la que se enmarcan sus publicaciones más destacadas.