Dynamic strategy based parallel ant colony optimization on GPUs for TSPs

In computational complexity theory, the TSP is an NP-hard problem. It plays a prominent role in research as well as in a number of application areas [1]. The objective of this problem is to find a minimum-weight Hamilton cycle in a complete weighted directed graph G = (V,A, d), where V = 1, 2, ..., n is a set of vertices (cities), E = {(i, j)|(i, j) V × V } is a set of edges (paths), and d : E → N is a function assigning a weight or distance (positive integer) dij to every edge (i, j). Dorigo et al. [2] proposed a basic ACO algorithm named the ant system (AS) to solve the TSP. It involves using many artificial ants to perform parallel searches on a graph. Each ant moves independently on the graph until it has traveled to all of the vertices on the graph. Because each ant constructively builds a route, this process is referred to as the tour construction, which is the first stage. The second stage is the pheromone update. To obtain a better solution, each ant strengthens the pheromone on its path to guide other ants. The ants stochastically move to the next city based on the heuristic information obtained from the pheromone trail and inter-city distances. However, a pheromone-evaporation process is also applied to avoid falling into local optimum solutions. In the tour-construction stage, each ant independently selects a route for traveling to all cities. Take ant k, for example; when this ant is placed at city i, the probability of visiting city j is calculated by (A1):