Multiobjective EA approach for improved quality of solutions for spanning tree problem

Abstract

The problem of computing spanning trees along with specific constraints is mostly NP-hard. Many approximation and stochastic algorithms which yield a single solution, have been proposed. In this paper, we formulate the generic multi-objective spanning tree (MOST) problem and consider edge-cost and diameter as the two objectives. Since the problem is hard, and the Pareto-front is unknown, the main issue in such problem-instances is how to assess the convergence. We use a multiobjective evolutionary algorithm (MOEA) that produces diverse solutions without needing a priori knowledge of the solution space, and generate solutions from multiple tribes in order to assess movement of the solution front. Since no experimental results are available for MOST, we consider three well known diameter-constrained minimum spanning tree (dc-MST) algorithms including randomized greedy heuristics (RGH) which represents the current state of the art on the dc-MST, and modify them to yield a (near-) optimal solution-fronts. We quantify the obtained solution fronts for comparison. We observe that MOEA provides superior solutions in the entire-range of the Pareto-front, which none of the existing algorithms could individually do.