Improved Quality of Solutions for Multiobjective Spanning Tree Problem Using Distributed Evolutionary Algorithm

Abstract

The problem of computing spanning trees along with specific constraints has been studied in many forms. Most of the problem instances are NP-hard, and many approximation and stochastic algorithms which yield a single solution, have been proposed. Essentially, such problems are multi-objective in nature, and a major challenge to solving the problems is to capture possibly all the (representative) equivalent and diverse solutions at convergence. In this paper, we attempt to solve the generic multi-objective spanning tree (MOST) problem, in a novel way, using an evolutionary algorithm (EA). We consider, without loss of generality, edge-cost and diameter as the two objectives, and use a multiobjective evolutionary algorithm (MOEA) that produces diverse solutions without needing a priori knowledge of the solution space. We employ a distributed version of the algorithm and generate solutions from multiple tribes. We use this approach for generating (near-) optimal spanning trees from benchmark data of different sizes. Since no experimental results are available for MOST, we consider two well known diameter-constrained spanning tree algorithms and modify them to generate a Pareto-front for comparison. Interestingly, we observe that none of the existing algorithms could provide good solutions in the entire range of the Pareto-front.