An Ant-Based Algorithm for the Minimum Vertex Cover Problem

4 Experimental Results 24Figure 4.1. Solution Quality Comparison.The results of running AB–MVC on these graphs are shown in Tables A.1, A.2,and A.3. To compare our results, we tested it against the COVER algorithmof Richter, Helmert, and Gretton [21] and the ant colony optimization algorithm(ACS) of Gilmour and Dras [10].AB–MVC was able to identify solutions that were within the range of 1% tothe optimal solutions. The quality of the solutions generated were much betterwhen compared to the results of ACS. COVER was able to identify the optimalsolution in most cases, however the running time of COVER was much largerwhen compared to that of AB–MVC. The standard deviation from the optimalvertex cover for all the three algorithms, for the eight different groups of graphs ispresented in Figure 4.1. Figure 4.2, that compares the running time of AB–MVCwith COVER proves that we had a fair balance between the quality of solutionsand running time, unlike the VCOVER algorithm.4.2 The DIMACS Benchmark InstancesThe DIMACS benchmark instances are taken from the Second DIMACS ImplementationChallenge (1992–1993) [13], a competition targeting the maximum clique,