Two hybrid evolutionary algorithms for the rectilinear Steiner arborescence problem

Authors:
Bryant A. Julstrom;Athos Antoniades
Affiliations:
St. Cloud State University, St. Cloud, MN;University of Cyprus, Nicosia, Cyprus
Venue:
Proceedings of the 2004 ACM symposium on Applied computing
Year:
2004

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Abstract

Given a collection of points in the first quadrant, a rectilinear Steiner arborescence is a tree made up of horizontal and vertical line segments on the points and the origin in which every path from the origin leads only up and to the right. The minimum rectilinear Steiner arborescence problem seeks such a tree of minimum total length.A greedy heuristic due to Rao et al. [13] builds short arborescences and can be implemented to require time that is O(n log n). Two evolutionary encodings of rectilinear Steiner arborescences represent them as permutations of points and as strings of perturbations of point locations. A decoder in the style of Prim's algorithm identifies the arborescence that a permutation represents; the heuristic of Rao et al. identifies the arborescence corresponding to a string of perturbations.In tests on twenty instances of the problem of 50 to 250 points, a genetic algorithm using the permutation coding is unable to compete with the greedy heuristic, but a GA using the perturbation coding almost always improves on the heuristic's results, though in general the improvement is small.