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The Bounded Diameter (a.k.a Diameter Constraint) Minimum Spanning Tree (BDMST/DCMST) is a well-known combinatorial optimization problem. In this paper, we recast a few well-known heuristics, which are evolved for BDMST problem to a Bi-Objective Minimum Spanning Tree (BOMST) problem and then obtain Pareto fronts. After examining Pareto fronts, it is concluded that none of the heuristics provides the superior solution across the complete range of the diameter. We have used a Multi-Objective Evolutionary Algorithm (MOEA) approach, Pareto Converging Genetic Algorithm (PCGA), to improve the Pareto front for BOMST, which in turn provides better solution for BDMST instances. We have considered edge-set encoding to represent MST and then applied recombination operators having strong heritability and mutation operators having negligible complexity to improve the solutions. Analysis of MOEA solutions confirms the improvement of Pareto front solutions across the complete range of the diameter over Pareto front solutions generated from individual heuristics. We have considered multi-island scheme using Inter-Island rank histogram and performed multiple run of the algorithm to avoid from trapping into local-optimal solutionset.

Bounded-Diameter MST Instances with Hybridization of Multi-Objective EA