Zastosowanie metod ewolucyjnych do wyznaczania struktur kernel and shell w grafie połączeń

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 graph would 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, a method of aggregation of such graph was introduced, using the general kernel and shell structure and its particular instance the α-clique structured graphs of connections. In the present approach, we use a predetermined number of communication hubs with the possibility of direct determining which nodes should become hubs or selecting them by the solving method. This structure allows to concentrate and order the transport of goods/persons among vertices and enables to reduce the number of analyzed vertices as well as arcs/edges of the graph. To obtain the desired structure, an evolutionary algorithm (EA) was applied.Teoria logistycznych systemów transportowych zajmuje się zagadnieniem połączeń w przewozach ludzi i towarów. Od modelu systemu transportowego oczekuje się symulowania rzeczywistego systemu w celu rozwiązywania problemów transportowych. Do opisania systemów transportowych (kolejowych, drogowych czy lotniczych) przydatne mogą się okazać grafy. Wierzchołki grafu mogą odpowiadać węzłom logistycznym, takim jak: stacje kolejowe, przystanki autobusowe, lotniska itd., a krawędzie - bezpośrednim połączeniom pomiędzy węzłami. Dokładny model trudno byłoby analizować lub optymalizować, dlatego jako przydatny model proponujemy strukturę kernel and shell oraz jej szczególny przypadek - strukturę α-klikową jako graf odwzorowujący strukturę połączeń. Struktury te umożliwiają koncentrację i zarządzanie transportem pomiędzy węzłami. W celu uzyskania tej struktury stosujemy specjalizowany algorytm ewolucyjny (EA)

Evolutionary approach for obtaining the hub and spoke structure in the logistic network

In order to describe transportation system, as a routine a connection graph would be used. Vertices of the graph can be train stations, bus stop, airports etc. The edges show direct connections between vertices. A direct application of such graph 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 graph was introduced, using the general kernel and shell structure and a hub and spoke transformation method of the source graph. These structures allow to concentrate and order the transport of goods/persons among vertices and enable to reduce the number of analyzed vertices as well as edges of the graph. In the presented paper we continue our work on kernel and shell and its instance hub and spoke methods of connection graph transformation. In this paper we develop model of the transportation system using the hub and spoke method with predetermined, minimum and indirectly described numbers of hub nodes. To obtain the desired structures, several versions of specialized evolutionary algorithm (EA) were developed and applied