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

### BibTeX

@MISC{Saha_bounded-diametermst,

author = {Soma Saha and Rajeev Kumar},

title = {Bounded-Diameter MST Instances with Hybridization of Multi-Objective EA},

year = {}

}

### OpenURL

### Abstract

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.

### Citations

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Citation Context ...rate new improved solutions in successive generations across the complete range of diameter bound. Along with easily visualizable Pareto front plots, we have considered convergence metric [6], spread =-=[5]-=-, C-measure [27] and hypervolume/S-metric [13] to assess the performance of MOEA. The reference set is considered as the Pareto front obtained from all EA solutions. 5.3.1 Avoiding Local Optimal We ha... |

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Citation Context ...roved solutions for each heuristic by MOEA and genetic operators. Wellknown MOEAs that do not require problem specific knowledge to the extent are Non-dominated Sorting Genetic algorithm II (NSGA-II) =-=[7]-=-, Pareto Converging Genetic Algorithm (PCGA) [16], Strength Pareto Evolutionary Algorithm 2 (SPEA-2) [26], PAES [12] etc. Researchers revealed that in this particular case, the variations of solution ... |

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Citation Context ... try to generate new improved solutions in successive generations across the complete range of diameter bound. Along with easily visualizable Pareto front plots, we have considered convergence metric =-=[6]-=-, spread [5], C-measure [27] and hypervolume/S-metric [13] to assess the performance of MOEA. The reference set is considered as the Pareto front obtained from all EA solutions. 5.3.1 Avoiding Local O... |

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Citation Context ...atorial optimization, multi-objective optimization, heuristics, MST, BDMST problem, evolutionary algorithm, Pareto front, edge list encoding. 1. INTRODUCTION BDMST has many applications in real-world =-=[2, 4, 22]-=-; it is an NP-hard problem within diameter bound (D) ranges 4 ≤ D < |V| - 1 [9], where diameter bound (D) is a constraint, the maximum feasible longest path between two vertices of a connected, undire... |

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Citation Context ...atorial optimization, multi-objective optimization, heuristics, MST, BDMST problem, evolutionary algorithm, Pareto front, edge list encoding. 1. INTRODUCTION BDMST has many applications in real-world =-=[2, 4, 22]-=-; it is an NP-hard problem within diameter bound (D) ranges 4 ≤ D < |V| - 1 [9], where diameter bound (D) is a constraint, the maximum feasible longest path between two vertices of a connected, undire... |

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Citation Context ...-node of the spanning tree is the center of the sub-graph. These sub-graphs are composed of nodes in the sub-tree rooted at that in-node. The inspiration of introducing CBRC came from the observation =-=[1, 21]-=- that good solutions for BDMST problem have “star-like structures“. In most of the previous work, Euclidean data sets have been considered and little efforts have been done with nonEuclidean instances... |

1 |
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(Show Context)
Citation Context ...omplexity of this algorithm is O(n 3 ), where n is the number of vertices in the graph. There are number of research papers for BDMST problem using OTTC for both Euclidean and non-Euclidean instances =-=[3, 8, 10, 20, 21, 25]-=-; all those works generalize MST problem with particular diameter constraint. But, for biobjective MST problem using OTTC heuristics very little work has been done [14]. 3.2 Iterative Refinement Itera... |