Evolutionary Approach to Find Kernel and Shell Structure of a Connection Graph

The theory of logistic transportation systems deals with models of phenomena connected with movement of goods and persons. The developed model of the transportation system is expected to simulate a real system, but also should help us to solve given transportation tasks. In order to describe transportation system (rail, bus or air), as a routine a connection graphwould be used. Vertices of the graph can be train stations, bus stops etc.. The edges show direct connections between vertices. Its direct application can be difficult and computational problems can occur while one would try to organize or optimize such a transportation system. Therefore, amethod of aggregation of such graphwas introduced, using the general kernel and shell structure and its particular instances: hub-and-spoke and α-clique structured graphs of connections. These structures enable to concentrate and order the transport of goods/persons among vertices. To obtain these desired structures an evolutionary algorithm (EA) was applied. This method enables to reduce the number of analyzed vertices as well as arcs/edges of the graph.