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### Evolutionary approach to solve hub-and-spoke problem using α-cliques

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Evolutionary Computation and Global Optimization 2008 / National Conference (11 ; 2-4.06.2008 ; Szymbark, Poland)
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EN
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The theory of transportation systems deals with models of phenomena connected with movement of goods and persons. The model of the transportation system should simulate a real system, but should also be a tool that enables to solve given transportation tasks. In order to describe transportation system (rail, bus or air), as a routine a connection graph would be used. Vertices of the graph can be train stations, bus stops or in case of air transport - airports. The edges of the graph show direct connections between vertices. It can be noticed that such a graph can have many vertices as well as many edges. Its direct application can be difficult and computational problems can occur while one would try to organize or optimize such a transportation system. Therefore, a method of aggregation of such a graph was introduced, using the hub-and-spoke structured graph of connections. This structure enables to concentrate and order the transport of goods/persons among vertices. To obtain the hub-and-spoke structure an evolutionary algorithm (EA) was applied. EA divides the connection graph into α-cliques (a generalization of the notion of a clique, which groups into sub-graphs highly connected vertices) and then in each α-clique a vertex with a maximum degree in this sub-graph and a maximal number of connections among other selected hubs is chosen. The α-clique with chosen vertex constitutes a "hub" with point-to-point connections - "spokes". This method enables reducing the number of analyzed vertices as well as arcs of the graph. Examples visualizing functioning of the described algorithms are presented later in this paper.
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Tom
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121--130
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Bibliogr. 16 poz., tab., rys.
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Bibliografia
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• [11] Potrzebowski H., Stańczak J., Sęp K. (2006) Evolutionary Algorithm to Find Graph Covering Subsets Using α-Cliques, Evolutionary Computation and Global Optimization, Prace naukowe PW, Warszawa, pp. 351-358.
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Bibliografia