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EN
The paper is devoted to the analysis of a graph transformation, pertinent for the transport and logistic systems and their planning and management. Namely, we consider, for a given graph, representing some existing transport or logistic system, its transformation to a (non-equivalent) so-called ”hub-and-spoke” structure, known from both literature and practice of transportation and logistics. This structure is supposed to bring benefits in terms of functioning and economic performance of the respective systems. The transformation into the ”hub-and-spoke” is not only non-equivalent (regarding the original graph of the system), but is also, in general, non unique. The structure sought is composed of two kinds of elements - nodes of the graph (stations, airports, havens, etc.), namely: the subgraph of hubs, which, in principle, ought to constitute a complete sub-graph (a clique), and the ”spokes”, i.e. the subsets of nodes, each of which is connected in the ultimate structure only with one of the hubs. The paper proposes a relaxation of the hub-and-spoke structure by allowing the hub subgraph not to be complete, but at least connected, with a definite ”degree of completeness” (alpha), from where the name of ”alpha-clique”. It is shown how such structures can be obtained and what are the resulting benefits for various assumptions, regarding such structures. The benefits are measured here with travel times. The desired structures are sought with an evolutionary algorithm. It is shown on an academic example how the results vary and how the conclusions, relevant for practical purposes, can be drawn from such analyses, done with the methods here presented.
EN
In this paper we consider the well known Hub and Spoke problem, analyzed in the context of Warsaw Public Transport System. Our method was designed for data preprocessing so as to allow using a timetable obtained from the public transport web site after conversion into the required data format. A dedicated evolutionary algorithm method that detects the hubs of almost all available transport means was also developed. The hubs identified are well connected to the center of the city and to other identified hubs (characterized by high capacity or short travel time). These hubs may become the skeleton of the public transport system and, in particular, good points for locating Park and Ride facilities.
EN
A model of a transportation system is expected to be useful in simulations of a real system to solve given transportation tasks. A connection graph is routinely used to describe a transportation system. Vertices can be train stations, bus stops, airports etc. The edges show direct connections between vertices. A direct approach can be difficult and computational problems can arise in attempts to organize or optimize such a transportation system. Therefore, a method for aggregating such graphs was introduced, using a general kernel and shell structure and its particular instances: α-clique structured graphs of connections and a hub and spoke transformation of the source graph. These structures enable the concentration and ordering of transport between vertices and reduction of the analyzed graph. To obtain the desired structures, several versions of a specialized evolutionary algorithm were developed and applied.
EN
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.
EN
This article describes two evolutionary methods for dividing a graph into densely connected structures. The first method deals with the clustering problem, where the element order plays an important role. This formulation is very useful for a wide range of Decision Support System (DSS) applications. The proposed clustering method consists of two stages. The first is the stage of data matrix reorganization, using a specialized evolutionary algorithm. The second stage is the final clustering step and is performed using a simple clustering method (SCM). The second described method deals with a completely new partitioning algorithm, based on the subgraph structure we call α-clique. The α-clique is a generalization of the clique concept with the introduction of parameter α, which imposes for all vertices of the subgraph the minimal percentage (α*100%) of vertices of this subgraph that must be connected with vertices of this α-clique. Traditional clique is an instance of α-clique with α = 1. Application of this parameter makes it possible to control the degree (or strength) of connections among vertices (nodes) of this subgraph structure. The evolutionary approach is proposed as a method that enables finding separate α-cliques that cover the set of graph vertices.
EN
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.
PL
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).
7
Content available remote Evolutionary approach to find kernel and shell structure of a connection graph
EN
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 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.
PL
Reguły gospodarki rynkowej i coraz ostrzejsza konkurencja zmuszają przedsiębiorstwa do poszukiwania sposobów obniżenia kosztów działalnosci gospodarczej. Konieczność redukcji kosztów dotyczy m.in. gospodarki transportowej. Znaczenie optymalizacji rozwiązań w sferze transportu w aspekcie kosztowym jest szczegolnie istotne, jeżeli weźmie się pod uwagę znaczny udział kosztów transportu w kosztach logistycznych przedsiebiorstwa. Oczywisty staje się fakt, iż nie jest możliwe funkcjonowanie firm działających na współczesnych globalnych rynkach bez transportu. Zdecydowana większość przedsiębiorstw znajduje się w pewnej odległości od swoich źrodeł zaopatrzenia, co sprawia, że są one zależne od transportu łączącego źrodlo zaopatrzenia z miejscem konsumpcji. Specjalizacja pracy, masowa konsumpcja i ekonomia skali produkcji powodują, że miejsca wytwarzania produktów nie pokrywają się z miejscem, gdzie zgłaszany jest na nie popyt. Stąd też transport staje się niezbędnym narzędziem łączącym nabywców i sprzedawców. W niniejszym artykule przedstawiono narzędzie wspomagające modelowanie systemu transportowego. Jak wiadomo, dokładny model systemu transportowego przedsiębiorstwa trudno jest analizować czy też optymalizować jego działanie. Dlatego jako model sieci transportowej proponujemy strukturę kernel and shell i jej szczególne przypadki: strukturę hub and spoke oraz strukturę α-klikową. Struktury te umożliwiają koncentrację i zarządzanie transportem pomiędzy węzłami. W celu uzyskania tych struktur z wejściowego grafu połączeń stosujemy opracowane przez nas specjalizowane algorytmy ewolucyjne (EA).
EN
In the paper we present the notion of alpha-clique and some of its properties. Covering with alpha-cliques is a preprocessing method for an air network, described as a graph, in which vertices correspond to airports and edges correspond to air connections. Using the alpha-clique cover we obtain a hypergraph, in which we find the minimum transversal. The set of vertices thus obtained is the sought-for set of transits nodes, called hubs. Using the alpha-clique concept instead of proper cliques we can obtain the solution to the graph covering problem easier.
PL
W niniejszej pracy prezentujemy pojęcie alfa-kliki i pewne jej własności. Znalezienie pokrycia alfa-klikami traktujemy jako metodę preprocessingu dla sieci lotniczych opisanych jako graf, w którym węzły odpowiadają lotniskom, a krawędzie odpowiadają połączeniom lotniczym. Znajdując pokrycie alfa-klikami, uzyskujemy hipergraf, dla którego otrzymujemy minimalną transwersalę. W ten sposób uzyskujemy zbiór wierzchołków będących węzłami tranzytowymi czyli hubami. Stosując alfa-kliki zamiast odpowiednich klik, możemy uzyskać lepsze pokrycie grafu.
EN
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.
PL
Rozważając problemy kombinatoryczne, zwłaszcza pod kątem praktycznego zastosowania należy wziąć pod uwagę złożoność algorytmów. W niniejszej pracy omówiono algorytm dokładny backtrackingowy, a także przedstawiono algorytmy aproksymacyjne: Lovasza-Johnsona-Chvatala oraz SBT (suboptymalnej drogi w drzewie bactrackingowym) i jego modyfikacje. Przeprowadzono analizę porównawczą zaprezentowanych algorytmów oraz przedstawiono praktyczne ich zastosowanie.
EN
Considering combinatorial problems, especially the practical use, the algorithm complexity should be taken into account. In this paper author describes Precise Backtracking Algorithm, Lovdsza-Johnsona-Chvatala Approximational Algorithm and Algorithm SBT (Sub-optimal Track in Backtracking tree) with it's modifications. Presented algorithms were comparatively analyzed and the practical implementation was shown.
PL
W referacie rozwiązujemy problem wyboru minimalnego w sensie inkluzji zbioru węzłów w sieci logistycznej. Problem sprowadzamy do poszukiwania minimalnej bazy wierzchołkowej w hipergrafie, a następnie stosujemy algorytm MSBT w celu znalezienia minimalnej w sensie inkluzji transwersali czyli bazy wierzchołkowej co interpretujemy jako minimalny zbiór usługowych centrów logistycznych.
EN
The article describes a new evolutionary based method to divide graph into strongly connected structures we called α-cliques. The α-clique is a generalization of a clique concept with the introduction of parameter a. Using this parameter it is possible to control the degree (or strength) of connections among vertices (nodes) of this sub-graph structure. The evolutionary approach is proposed as a method that enables to find separate a-cliques that cover the set of graph vertices.
PL
W celu zapewnienia optymalnej eksploatacji KWB "Bełchatów" niezbędne jest funkcjonowanie sprawnego systemu odwadniającego w obrębie prowadzonych prac górniczych. System ten musi zapewniać obniżenie poziomu wód z odpowiednim wyprzedzeniem. Podstawowym systemem odwadniania odkrywki jest system studzienny, oparty na wielkośrednicowych studniach odwadniających, rozmieszczonych w odpowiednich barierach o odmiennych funkcjach i zadaniach. Bieżące odwodnienie zapewnia kilkaset studni. Aby zabezpieczyć sprawne i bieżące odwodnienie konieczne jest wykonywanie coraz to nowych studni i utrzymywanie w sprawności już eksploatowanych.
EN
To ensure an optimal mining operation of the Belchatow" LM it is indispensable that the dewatering system within the mine operation zone function efficiently. The system must ensure well in advance the lovering of water level. The basic dewatering system of the opencast mine is a water well system based on large-diameter dewatering wells placed within relevant barriers differing in function and performance. To ensure current and efficient dewatering it is necessary to provide ever newer and newer wells and maintain the efficiency level of those in operation.
PL
Morze Bałtyckie to jedno z najbardziej zdegradowanych mórz na świecie. Eksploracja podmorskich złóż ropy i gazu oraz ich eksploatacja stanowią poważne czynniki oddziaływania na środowisko. Autorzy artykułu, na przykładzie prac wiertniczych i eksploatacyjnych "Pertobalticu" dowodzą, że działalność ta może być prowadzona w sposób bezpieczny zarówno dla środowiska morskiego jak i dla ludzi.
EN
The Baltic Sea in one of the most degraded seas in the world. The exploration and submarine mining operations in oil and gas depostis present the factors of serious impact on the environment. On the basis of an example of drilling and mining operation works of "PETROBALTIC", the authors of this article prove that the activity can be conducted in a manner that is safe both for the marine environment and for people.
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