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An ACO-RFD hybrid method to solve NP-complete problems

Frontiers of Computer Science 2013年第5期7卷 729-744页

作者： pablo rabanal ismael rodriguez fernando rubio Dept. Sistemas Inforrnaiticos y Computacion Facultad de Informatica Universidad Complutense de Madrid Madrid 28040 Spain

In this paper we hybridize ant colony optimiza- tion （ACt） and river formation dynamics （RFD）, two related swarm intelligence methods. In ACt, ants form paths （prob- lem solutions） by following each other＇s pheromone trails and reinforcing trails at best paths until eventually a single path is followed. On the other hand, RFD is based on copy- ing how drops form rivers by eroding the ground and de- positing sediments. In a rough sense, RFD can be seen as a gradient-oriented version of ACt. Several previous experi- ments have shown that the gradient orientation of RFD makes this method solve problems in a different way as ACt. In particular, RFD typically performs deeper searches, which in turn makes it find worse solutions than ACt in the first exe- cution steps in general, though RFD solutions surpass ACt solutions after some more time passes. In this paper we try to get the best features of both worlds by hybridizing RFD and ACt. We use a kind of ant-drop hybrid and consider both pheromone trails and altitudes in the environment. We apply the hybrid method, as well as ACt and RFD, to solve two NP-hard problems where ACt and RFD fit in a different manner： the traveling salesman problem （TSP） and the prob- lem of the minimum distances tree in a variable-cost graph （MDV）. We compare the results of each method and we an- alyze the advantages of using the hybrid approach in each case.

关键词： river formation dynamics ant colony optimization heuristic algorithms NP-hard problems

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Alliance Free and Alliance Cover Sets

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Acta Mathematica Sinica,English Series 2011年第3期27卷 497-504页

作者： Juan Alberto rodriguez-VELAZQUEZ Jose Maria SIGARRETA ismael GONZALEZ YERO Sergio BERMUDO Departament d'Enginyeria Informdtica i Matematiques Universitat Rovira i Virgili Av. Paisos Catalans 26 43007 Tarragona Spain Faculty of Mathematics Autonomous University of Guerrero Carlos E. Adame 5 Col. La Garita Acapuleo Guerrero Mexico Departament d'Enginyeria Informatica i Matematiques Universitat Rovira i Virgili Av. Pai'sos Catalans 26 43007 Tarragona Spain Department of Economy Quantitative Methods and Economic History Pablo de Olavide University Carretera de Utrera Kin. 1 41013 Sevilla Spain

A defensive （offensive） k-alliance in F = （V, E） is a set S C V such that every v in S （in the boundary of S） has at least k more neighbors in S than it has in V ／ S. A set X C_ V is defensive （offensive） k-alliance free, if for all defensive （offensive） k-alliance S, S／ X ≠ 0, i.e., X does not contain any defensive （offensive） k-alliance as a subset. A set Y C V is a defensive （offensive） k-alliance cover, if for all defensive （offensive） k-alliance S, S ∩ Y ≠ 0, i.e., Y contains at least one vertex from each defensive （offensive） k-alliance of F. In this paper we show several mathematical properties of defensive （offensive） k-alliance free sets and defensive （offensive） k-alliance cover sets, including tight bounds on their cardinality.

关键词： Defensive alliance offensive alliance alliance free set alliance cover set

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Partitioning a Graph into Defensive k-Alliances

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Acta Mathematica Sinica,English Series 2011年第1期27卷 73-82页

作者： ismael G.YERO Sergio BERMUDO Juan A.rodriguez-VELAZQUEZ Jose M.SIGARRETA Department of Computer Engineering and Mathematics Rovira i Virgili UniversityAv.Pai'sos Catalans 2643007 TarragonaSpain Department of Economy Quantitative Methods and Economic HistoryPablo de Olavide UniversityCarretera de Utrera Kin.141013-SevillaSpain Department of Computer Engineering and Mathematics Rovira i Virgili UniversityAv.Paisos Catalans 2643007 TarragonaSpain Faculty of Mathematics Autonomous University of GuerreroCarlos E.Adame 5Co1.La GaritaAcapulcoGuerreroMexico

A defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating Set. In this paper we study the problem of partitioning the vertex set of a graph into （global） defensive k-alliances. The （global） defensive k-alliance partition number of a graph Г = （V, E）, ψkgd（F）） ψkd（F）, is defined to be the maximum number of sets in a partition of V such that each set is a （global） defensive k-alliance. We obtain tight bounds on ψkd（F） and ψkgd（F） in terms of several parameters of the graph including the order, size, maximum and minimum degree, the algebraic connectivity and the isoperimetric number. Moreover, we study the close relationships that exist among partitions of F1 × F2 into （global） defensive （kl ＋ k2）-alliances and partitions of Fi into （global） defensive ki-alliances, i ∈ {1, 2}.

关键词： Defensive alliances dominating sets domination isoperimetric number

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