Class Steiner trees and VLSI-design
Discrete Applied Mathematics - Special volume on VLSI
Beyond Steiner's Problem: A VLSI Oriented Generalization
WG '89 Proceedings of the 15th International Workshop on Graph-Theoretic Concepts in Computer Science
Heuristic Search for the Generalized Minimum Spanning Tree Problem
INFORMS Journal on Computing
An efficient algorithm for generalized minimum spanning tree problem
Proceedings of the 12th annual conference on Genetic and evolutionary computation
A reactive GRASP with path relinking for capacitated clustering
Journal of Heuristics
An evolutionary algorithm with solution archive for the generalized minimum spanning tree problem
EUROCAST'11 Proceedings of the 13th international conference on Computer Aided Systems Theory - Volume Part I
Hybrid Adaptive Large Neighborhood Search for the Optimal Statistic Median Problem
Computers and Operations Research
Proceedings of the 14th annual conference on Genetic and evolutionary computation
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We consider the generalized version of the classical Minimum Spanning Tree problem where the nodes of a graph are partitioned into clusters and exactly one node from each cluster must be connected. We present a Variable Neighborhood Search (VNS) approach which uses three different neighborhood types. Two of them work in complementary ways in order to maximize search effectivity. Both are large in the sense that they contain exponentially many candidate solutions, but efficient polynomial-time algorithms are used to identify best neighbors. For the third neighborhood type we apply Mixed Integer Programming to optimize local parts within candidate solution trees. Tests on Euclidean and random instances with up to 1280 nodes indicate especially on instances with many nodes per cluster significant advantages over previously published metaheuristic approaches.