A study of Ant Colony Algorithms and a potential application in Graph Drawing

Context: Emergence is a term used to describe complex patterns or systems which are formed from very basic rules or agents. Once such example which has intrigued scientists across several fields has been ant colonies. Computer scientists are particularly interested in ant colonies as although each individual ant acts in a very simple manor, the ant colony as a whole is able to find shortest paths between the nest and food sources. Modelling this can provide approximate solutions to many NP–Hard problems. Aims: The purpose of this research is firstly to compare various ant colony optimization algorithms against each other, as well as against other well know heuristics, including Simulated Annealing and Genetic Algorithms on the Travelling Salesman problem which is a typical graph based problem. Secondly, to look at applying an ant colony algorithm in graph drawing. The force–directed graph drawing algorithms are a class of algorithms which are commonly used, however, they only perform a local search so the results on large graphs can be poor. This research looks at using a force–directed graph drawing algorithm as a local search with a modified ant–colony algorithm to achieve better results. Method: Several ant colony algorithms; Ant System,MAX −MIN Ant System and Ant Colony System; Simulated Annealing and the Genetic Algorithm were implemented, tuned and tested on the Travelling Salesman problem. This was done to determine how the various parameters effected performance on different problems and how the algorithms compared against each other. Each algorithm outputs its performance in csv format, as well as optionally as a series of svg images. A force–directed graph drawing algorithm, a basic ant colony algorithm and an ant colony algorithm using a force–directed local search method were implemented. The ant colony algorithms were modified to work with the graph drawing problem and tests were done to determine the best set of parameters and to see how the ant colony algorithms compared against the well known force–directed graph drawing algorithm. Results: The ant colony algorithms were tested and optimal parameters were found as the influence parameter β = 3.0 and the decay constant ρ = 0.15 for Ant System; the decay constants ρ = χ = 0.11 and the probability of exploitation q0 = 0.65 for Ant Colony System and the lower pheromone limit τmin = 0.05 forMAX −MIN Ant System. The well known 2-opt, 2.5-opt and 3-opt local search methods were tested with the best results coming from 2.5-opt with theMMAS. The algorithms were then tested against Simulated Annealing and the basic genetic algorithm. Overall MMAS with 2.5-opt was the closest to Simulated Annealing which gave the best final results. When taking into account time considerations, Ant System provided good results very quickly so was best for very large graphs or situations with very tight time constraints. Given moderate time constraintsMMAS with 2.5-opt provided the best results with Simulated Annealing coming out best with reasonable time. The graph drawing tests showed that an ant colony algorithm could be paired with a force–directed graph drawing algorithm to achieve better results with the ant colony algorithm’s solutions being 11% better on average. This advantage was lost, however, on very small graphs and came with a severe time penalty with the ant colony algorithm being over 200 times slower, although of comparable time complexity. Conclusion: Three variations on the ant colony algorithm have been implemented and compared along with Simulated Annealing and a genetic algorithm. We have investigated the family and proposed a new hybrid algorithm which combines the force–directed graph drawing algorithm with an ant colony algorithm and in doing so produces better results than the force–directed graph algorithm alone.