An Ant-Based Algorithm for the Minimum Vertex Cover Problem

2 PRELIMINARIES 6interacting locally with one another and with their environment. Ant algorithmswere inspired by the observation of real ant colonies. Ants are social insects, thatis, insects that live in colonies and whose behavior is directed more to the survivalof the colony as a whole than to that of a single individual component of the colony.An important feature of ant colonies is their nature to find shortest pathsbetween their nest and the food source. While travelling from their nest to thefood source and on the way back, ants deposit a substance called pheromone onthe ground. It is nothing but a volatile chemical substance which can be detectedby other ants. So, when the next ant sets about in search of food from its nest,it is more inclined to choose paths marked by strong pheromone concentrations.These ants in turn will increase the pheromone concentration on that path evenmore. This will soon lead to the typical line of ants all following the same path.However, it should be noted that the pheromone evaporates as time goes by and apath that has been deserted for a while tends to vanish. This phenomenon helpsthe ants to explore and identify paths leading to different food sources.Ant algorithms can be broadly classified into two types: Ant colony optimization(ACO) and Ant-Based systems (AB). In ACO algorithms, a colony of artificialants collectively searches for good solutions to the optimization problem under consideration.Each ant builds a complete solution on its own. While building thesolution it collects information, both on the problem characteristics and on itsown performance. It then uses this information to modify the representation ofthe problem, as seen by the other ants. Travelling Salesman problem (TSP) wasthe first problem to which the ACO technique was applied because of its obvioususe of the ants’ ability to find the shortest path [6]. Other problems that havebeen the focus of ACO work include the quadratic assignment, network routing,vehicle routing and frequency assignment problems [17].In an ant-based system, each ant does not construct a complete solution butrather confines itself to a part of the problem space. It coordinates with otherants to identify a promising configuration that is later used for constructing thesolution. The distinct advantage of AB systems over ACO is the fact that the antsneed not possess knowledge of the problem space from a global perspective. Thismakes them more amenable to an implementation in a distributed environment.AB systems have been used to solve problems such as the k-cardinality tree [4] and