Re-Aggregation Heuristics for the Large Location Problems with Lexicographic Minimax Objective Insertion Method for Multiple Me

4 42 Matej Cebecauer - Lubos Buzna Lydia Gabrisova - Jaroslav Janacek RE-AGGREGATION HEURISTICS DESIGN OF CAPACITATED EMERGENCY FOR THE LARGE LOCATION PROBLEMS SERVICE SYSTEM WITH LEXICOGRAPHIC MINIMAX OBJECTIVE 49 Sanjin Milinkovic - Slavko Veskovic - Biljana Mitrovic Zivota Dordevic - Peter Marton 11 A SITE SELECTION MODEL Jan Fabry FOR WAYSIDE TRAIN MONITORING INSERTION METHOD FOR MULTIPLE SYSTEMS AT SERBIAN RAILWAYS MESSENGER PROBLEM WITH MULTIPLE DEPOTS 55 Vladimir Medvid TWO EFFICIENT ALGORITHMS 15 FOR WEIGHTED p-MEDIAN PROBLEM Jaroslav Janacek - Marek Kvet MIN-MAX OPTIMIZATION OF EMERGENCY 60 SERVICE SYSTEM BY EXPOSING Tomas Javorik - Lukas Tyfa CONSTRAINTS ASSESSMENT OF RAILWAY STATION MODERNISATION COMBINING RISK ANALYSIS WITH MULTI-CRITERIA 23 ANALYSIS Matyas Koniorczyk - Borbala Talas - Ferenc Gedeon PRECONDITIONING IN THE 66 BACKTRACKING DUTY GENERATION Maria Durisova - Beata Holkova - Michal Lekyr OF PASSENGER RAIL CREW TAX EVASION IN SALES CUTS SCHEDULING: A CASE STUDY REGISTERED BY ELECTRONIC CASH REGISTER 30 Ludmila Janosikova - Martin Slavik 73 Lubica Konusikova - Alzbeta Kucharcikova MODELLING PASSENGERS’ ARRIVALS APPROACHES TO ACTIVE LABOUR AT PUBLIC TRANSPORT STOPS MARKET POLICY IN THE SLOVAK REPUBLIC, CZECH REPUBLIC 35 AND IN FINLAND Vojtech Graf - Dusan Teichmann - Michal Dorda AN EXPERIMENTAL STUDY 80 Reiner Keil - Dirk Krone - Iveta Kremenova ON DEPENDENCE OF TIME INTERVALS Radovan Madlenak FOR CONNECTIONS ON OPTIMIZATION COMMUNICATION NETWORKS AS BASE COMPUTATIONS FOR TASK OF AIRCRAFT FOR MOBILITY – TREND DEVELOPMENT SCHEDULING OF NETWORK ARCHITECTURES 86 103 Ivana Zidek - Jana Musinska - Jozef Zivcak Michal Valco - Roman Kralik - Lee Barrett THE METHODOLOGY MORAL IMPLICATIONS OF AUGUSTINE’S OF THE BIOMECHANICAL MOVEMENTS PHILOSOPHICAL AND SPIRITUAL FOR THE DISABLED BASED ON ART JOURNEY IN HIS CONFESSIONES THERAPY 109 92 Pavel Danihelka - Martie Van Tongeren Milos Poliak - Stefania Semanova - Salvador Hernandez Lucie Sikorova - Tana Brzicova Eliska Pastuszkova NANOTECHNOLOGY SAFETY AS A NEW IMPACT OF ROAD INFRASTRUCTURE CHALLENGE FOR OCCUPATIONAL PRICING ON TRANSPORT PLANNING HEALTH AND SAFETY 98 Ladislav Janosik - Marek Cochlar - Pavel Polednak OPERATIONAL RELIABILITY OF FIRE APPLIANCES ON MERCEDES-BENZ CHASSIS WITH BRIGADES OF FIRE RESCUE SERVICE OF THE MORAVIAN-SILESIAN REGION Dear Readers, You have got in your hands this volume of the university scientific letters, which is the fifth time devoted to informatics and its applications to a broad spectrum of scientific and professional branches as sophisticated decision support tools, information systems, transport, logistics, economics and others. Nowadays, various forms of informatics penetrate almost into every human activity and the current issue tries to reflect this phenomenon. Inside this volume we attempt to submit papers written by authors not only from the University of Zilina, but we appealed to professionals from other cooperating universi- ties and scientific institutions to contribute to the topic mentioned above. In the frame of this issue you can find works dealing with optimization techniques supported by means of informatics rather than pure problems of informatics. It is no surprise that most of the works are devoted to applications of informatics to transport and related professional fields. This issue continues with topics concerning intelligent transportation systems and various sorts of scheduling problems. But, the attention is also paid to design or reengineering of public service systems, which provide rescue service to population in urgent situations and also to fair public service system design and other non-transport problems of applied informatics, where users’ equity in access to the provided service is accented. I would like to express my opinion that this issue would attract your attention and ignite your inte- rest in some future cooperation in the area of informatics and its applications. Jaroslav Janacek COMMUNICATIONS 2/2015 ● 3 Matej Cebecauer - Lubos Buzna * RE-AGGREGATIONRE-AGGREGATION HEURISTICSHEURISTICS FORFOR THETHE LARGELARGE LOCATIONLOCATION PROBLEMSPROBLEMS WITHWITH LEXICOGRAPHICLEXICOGRAPHIC MINIMAXMINIMAX OBJECTIVEOBJECTIVE We propose a new heuristic algorithm that provides solutions to the discrete lexicographic minimax location problem. The algorithm is applicable to large instances of the problem. The lexicographic minimax location problem is known to be NP-hard. Therefore, the large instances of the problem are not computable in reasonable time. An aggregation is a valuable tool that allows to adjust the size of the problem and approximate the problem by another one that can be solved. An inevitable consequence of aggregation is the loss of the precision. Typically, an aggregation method is used only once, in the initial phase of the solving process. Here, we propose iterative re-aggregating approach which adapts aggregated problem to achieve more precise location of facilities. To test the efficiency of the proposed method, we compute large location problems reaching 67 000 aggregated customers. The proposed approach is versatile and can be used for large range of location problems. Keywords: Location problem, heuristics, aggregation, lexicographic minimax. 1. Introduction achieved by the exact method, when solving aggregated problem [8 and 9]. Often, aggregation is used only in the initial phase of the A location problem consists of finding a suitable set of facility solving process, to match the problem size with the performance locations from where services could be efficiently distributed to of the used solving method. In this paper, we propose simple customers [1, 2 and 3]. Many location problems are known to be re-aggregation heuristics, where the solved problem is modified NP-hard. Consequently, the ability of algorithms to compute the to minimise the aggregation error in the following iterations. The optimal solution quickly decreases as the problem size is growing. aim of this article is to assess whether re-aggregation approach There are two basic approaches how to deal with this difficulty. can be used for solving large location problem with lexicographic First approach is to use a heuristic method, which, however, does minimax objective. Our results show that the re-aggregation may not guarantee that we find the optimal solution. Second approach provide better solutions than the solution obtained by the exact or is to use the aggregation that lowers the number of customers heuristic method, when the aggregation is used only once on the and candidate locations. The aggregated location problem (ALP) large location problems. can be solved by exact methods or by heuristics. Aggregation, The paper is organised as follows: section 2 briefly introduces however, induces various types of errors. There is a strong stream the data processing procedure. In section 3 we summarise the of literature studying aggregation methods and corresponding lexicographic minimax problem. The re-aggregation heuristics errors [4 and 5]. Various sources of aggregation errors and is explained in section 4. Results of numerical experiments are approaches to minimise them are discussed by [4, 6 and 7]. reported in section 5. We conclude in section 6. Here, we are specifically interested in finding the fair design of a public service system that is serving spatially large geographical area with many customers. Customers are modelled by a set 2. Data model of demand points (DP) representing their spatial locations [5]. To include all possible locations of customers as DPs is The OpenStreetMap (OSM) provides all necessary data often impossible and also unnecessary. In similar situations the to generate DP locations and to extract the road network. To aggregation is a valuable tool to obtain ALP of computable size. estimate the position of demand points we use OSM layers It is well known that the solution provided by a heuristic describing positions of buildings, roads, residential, industrial and method using more detailed data is often better than a solution commercial areas. To generate DPs we use a simple procedure. * Matej Cebecauer, Lubos Buzna Department of Mathematical Methods and Operations Research, Faculty of Management Science and Informatics, University of Zilina, Slovakia E-mail: [email protected] 4 ● COMMUNICATIONS 2/2015 First, we generate a spatial grid which consists of uniform square and the assigned facility is exactly Dk. The component Bk is a value cells with a size of 100 meters. For each cell, we extract elements defined as Bbkj= , which denotes the number of individual / jJ! k from the OSM layers that are situated inside each cell. Second, customers situated in the subset Jk. If a set is empty, then the DPs are located as centroids of the cells with a non-empty content. associated value Bk is zero. Third, generated DPs are connected to the road network and we The lexicographically minimal solution in the set is a solution compute the shortest paths distances between them. Finally, we that corresponds to the lexicographically minimal vector [B1, B2, calculate Voronoi diagrams, while using DP as generating points, ..., B ] [12]. kmax and we associate with each DP a demand by intersecting Voronoi To solve this problem we use the algorithm A-LEX [13] which polygons with residential population grids produced by [10]. similarly to the algorithm [11] solves optimisation problems in stages corresponding to individual distance values. Correctness and finiteness of the algorithm A-LEX,

Load more