Journal of Computer Science 3 (9): 717-722, 2007 ISSN 1549-3636 © 2007 Science Publications 717 Experimental Comparison Between Evolutionary Algorithm and Barycenter Heuristic for the Bipartite Drawing Problem Zoheir Ezziane Faculty of Information Technology, Higher Colleges of Technology, Al-Ain, P.O. Box. 17258, UAE Abstract: This research investigates the use of intelligent techniques for the bipartite drawing problem (BDP). Due to the combinatorial nature of the solution space, the use of traditional search methods lead to exponential time. Hence, the aim of this paper is to speed up the search time when solving the BDP through the use of Evolutionary Algorithms (EAs) and Barycenter Heuristic (BC). EA is applied on the BDP wherein genetic operators such as crossover and mutation are employed while searching for the best possible solution. The results show that the EA approach guides the search towards optimal solutions and in many instances it outperforms the BC. Key words: Evolutionary algorithm, edge crossing, bipartite graph, barycenter heuristic, NP-complete problems INTRODUCTION The Evolutionary Algorithm (EA) offers the promise of a widely applicable, robust global search strategy. Good EA-performance is a matter of finding a proper balance between exploitation and exploration. This in turn is affected by EA-parameters such as the selection strategy, the genetic operators and their corresponding rates. Directed graphs are used to represent aspects of systems in a wide variety of disciplines, including software, networking, information engineering and management. The usefulness of these representations depends on the layout of the graph. Thus there has been considerable interest in algorithms for drawing directed graphs so they are easy to understand and remember [1,2] . One of the most important constraints, which should be respected, is that there are as few edge crossings as possible in drawing a bipartite graph. The number of crossings in a drawing of a bipartite graph does not depend on the precise position of vertices but only on the ordering of the vertices within each subset. Therefore, the problem of reducing edge crossing is the combinatorial one of choosing an appropriate ordering for each subset. Even though this combinatorial status simplifies the problem, it was shown that the problem of minimizing edge crossing for the bipartite graph is NP-complete [3] . Most of the known heuristics for the bipartite graph problem produce acceptable drawings. However, obtaining better drawings has always attracted many researchers [4,5,6] in finding fewer edge crossings than it is possible to get with heuristics. May and Szkatula [7] have applied simulated annealing to BDP and Lee et al. [8] proposed a neural network model for this problem. Genetic algorithms (GAs) and EAs were used in solving NP-complete problems [9,10] . Background: Let G = (V, E) be a bipartite graph such as V = P∪Q, P∩Q = ∅. The barycenter heuristic (BC) orders the vertices according to the average of the positions of the vertices incident with them. The x- coordinate of each vertex u∈L 1 is chosen as the barycenter (average) of the x-coordinates of its neighbors. That is, x 1 (u) is selected to be avg(u) for all u ∈ L 1 . Where         ∈ =  u v u N v x d u avg ) ( 1 ) ( 0 The number of crossings output by the barycenter heuristic is defined by avg (G,x 0 ). In the median heuristic, the x-coordinate of each u ∈ L 1 is chosen to be a median of the x-coordinate of the neighbors of u. The BC heuristic and the median heuristic were investigated and compared [11] . Tests have shown that the BC heuristic performs slightly better than the median heuristic. The density of bipartite graphs is a very important factor. The density of a bipartite graph G is defined by the ratio between the number of edges in G and in the corresponding complete bipartite graph K m,n . Note this latter graph has density of 100%. In this research, the BC heuristic is compared with the EA model.