Combining Lagrangian decomposition with an evolutionary algorithm for the knapsack constrained maximum spanning tree problem

Authors:
Sandro Pirkwieser;Günther R. Raidl;Jakob Puchinger
Affiliations:
Institute of Computer Graphics and Algorithms, Vienna University of Technology, Vienna, Austria;Institute of Computer Graphics and Algorithms, Vienna University of Technology, Vienna, Austria;National ICT Australia, Victoria Laboratory, Dep. of Comp. Sci. & Softw. Eng., The University of Melbourne, Australia
Venue:
EvoCOP'07 Proceedings of the 7th European conference on Evolutionary computation in combinatorial optimization
Year:
2007

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Abstract

We present a Lagrangian decomposition approach for the Knapsack Constrained Maximum Spanning Tree problem yielding upper bounds as well as heuristic solutions. This method is further combined with an evolutionary algorithm to a sequential hybrid approach. Experimental investigations, including a comparison to a previously suggested simpler Lagrangian relaxation based method, document the advantages of the new approach. Most of the upper bounds derived by Lagrangian decomposition are optimal, and together with the evolutionary algorithm, large instances with up to 12000 nodes can be either solved to provable optimality or with a very small remaining gap in reasonable time.