An artificial immune algorithm for minimal steiner tree problems

The Minimum Steiner tree (MST) problem in the Euclidean plane is an nonlinear programming hard (NP-hard) problem, polynomial time algorithm is absent for solving the MST for a group of arbitrary terminal points, and the most difficulty is how to determine the position and number of Steiner points. A new method to solve MST problem by using an artificial immune algorithm was proposed in this paper. According to the breadth - first traversal sequence of minimum spanning tree, the terminal points can be divided into different convex hull sets, and the full Steiner tree (FST, named by Melzak) can be structured from the convex hull. The Steiner points can be vaccinated to minimum spanning tree as a vaccine, and the shortest length of the tree is the solution of MST. The average optimization effect of artificial immune algorithm is shorter 5.3% than the minimum spanning, and the performance of algorithm is remarkable and outstanding effectively with some engineering examples.