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Title of Journal: Comput Optim Appl

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Abbravation: Computational Optimization and Applications

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Springer US

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DOI

10.1016/0016-0032(68)90040-9

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1573-2894

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Computing the metric dimension of graphs by geneti

Authors: Jozef Kratica Vera KovačevićVujčić Mirjana Čangalović
Publish Date: 2007/12/04
Volume: 44, Issue: 2, Pages: 343-
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Abstract

In this paper we consider the NPhard problem of determining the metric dimension of graphs We propose a genetic algorithm GA that uses the binary encoding and the standard genetic operators adapted to the problem The feasibility is enforced by repairing the individuals The overall performance of the GA implementation is improved by a caching technique Since the metric dimension problem up to now has been considered only theoretically standard test instances for this problem do not exist For that reason we present the results of the computational experience on several sets of test instances for other NPhard problems pseudo boolean crew scheduling and graph coloring Testing on instances with up to 1534 nodes shows that GA relatively quickly obtains approximate solutions For smaller instances GA solutions are compared with CPLEX results We have also modified our implementation to handle theoretically challenging largescale classes of hypercubes and Hamming graphs In this case the presented approach reaches optimal or best known solutions for hypercubes up to 131072 nodes and Hamming graphs up to 4913 nodes

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  11. On the resolution of certain discrete univariate max–min problems
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