Computing the metric dimension of graphs by genetic algorithms

Kratica, Jozef; Kovačevíc-Vujčić, Vera; Čangalović, Mirjana

doi:10.1007/s10589-007-9154-5

Cited by 41 publications

(29 citation statements)

References 33 publications

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“…Computing the metric dimension of a graph is an NP-hard problem: it is one of the examples given in the book by Garey and Johnson [57, Appendix A1, GT61], while a proof of this is given by Khuller et al [71]. Indeed, the problem is one of the computationally hard problems that have had genetic algorithms applied to them; see Kratica et al [73] for details.…”

Section: Metric Dimensionmentioning

confidence: 99%

Base size, metric dimension and other invariants of groups and graphs

Bailey¹,

Cameron²

2011

Bulletin of the London Mathematical Society

225

297

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The base size of a permutation group, and the metric dimension of a graph, are two of a number of related parameters of groups, graphs, coherent configurations and association schemes. They have been repeatedly redefined with different terminology in various different areas, including computational group theory and the graph isomorphism problem. We survey results on these parameters in their many incarnations, and propose a consistent terminology for them. We also present some new results, including on the base sizes of wreath products in the product action, and on the metric dimension of Johnson and Kneser graphs.

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Section: Metric Dimensionmentioning

confidence: 99%

Base size, metric dimension and other invariants of groups and graphs

Bailey¹,

Cameron²

2011

Bulletin of the London Mathematical Society

225

297

View full text Add to dashboard Cite

show abstract

“…Detailed description of GA is out of this paper's scope and it can be found in [26]. Extensive computational experience on various optimization problems shows that GA often produces high quality solutions in a reasonable time, as can be seen from the following recent applications [8,19,20,21,27,32].…”

Section: Proposed Ga Methodsmentioning

confidence: 99%

A genetic algorithm for the minimum hitting set

Cendic-Lazovic¹

2014

Sci Publ State Univ Novi Pazar Ser A

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In this paper the Minimum Hitting Set (MHS) problem is considered. The problem is solved by a genetic algorithms (GA) that uses binary encoding and standard genetics operators adapted to the problem. In proposed implementation all individuals are feasibility by default, so search is directed into the promising regions. The overall performance of the GA implementation is improved by caching technique. Local search optimization is used to refine the solutions explored by GAs. The algorithm is tested on standard instances from the literature. The obtained results are also compared with the results of existing methods for solving MHS in order to assess their merits.

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“…Gademann and van de Velde [6] introduced a straightforward 0-1 optimization model for the OBP whose columns consist of all feasible batches [7] (see Fig. 2).…”

Section: Minimizing the Order Picking Timesmentioning

confidence: 99%

Tackling the storage problem through genetic algorithms

Chirici

Wang

2014

Adv. Manuf.

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The capability of a company to implement an automated warehouse in an optimized way might be nowadays a crucial leverage in order to gain competitive advantage to satisfy the demand. The order picking is a warehouse function that needs to deal with the retrieval of articles from their storage locations. Merging several single customer orders into one, a picking order can increase efficiency of warehouse operations. The aim of this paper is to define throughout the use of ad-hoc genetic algorithm (GA) how better a warehouse can be set up. The paper deals with order batching, which has a major effect on efficiency of warehouse operations to avoid wastes of resources in terms of processes and to control possibility of unexpected costs in advance.

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Computing the metric dimension of graphs by genetic algorithms

Abstract: Graph theory, Metric dimension, Evolutionary approach,

Cited by 41 publications

References 33 publications

Base size, metric dimension and other invariants of groups and graphs

Base size, metric dimension and other invariants of groups and graphs

A genetic algorithm for the minimum hitting set

Tackling the storage problem through genetic algorithms

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