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Edge-based blockchain enabled anomaly detection for insider attack prevention in Internet of ThingsTukur, Yusuf M., Thakker, Dhaval, Awan, Irfan U. 31 March 2022 (has links)
Yes / Internet of Things (IoT) platforms are responsible for overall data processing in the IoT System. This ranges from analytics and big data processing to gathering all sensor data over time to analyze and produce long-term trends. However, this comes with prohibitively high demand for resources such as memory, computing power and bandwidth, which the highly resource constrained IoT devices lack to send data to the platforms to achieve efficient operations. This results in poor availability and risk of data loss due to single point of failure should the cloud platforms suffer attacks. The integrity of the data can also be compromised by an insider, such as a malicious system administrator, without leaving traces of their actions. To address these issues, we propose in this work an edge-based blockchain enabled anomaly detection technique to prevent insider attacks in IoT. The technique first employs the power of edge computing to reduce the latency and bandwidth requirements by taking processing closer to the IoT nodes, hence improving availability, and avoiding single point of failure. It then leverages some aspect of sequence-based anomaly detection, while integrating distributed edge with blockchain that offers smart contracts to perform detection and correction of abnormalities in incoming sensor data. Evaluation of our technique using real IoT system datasets showed that the technique remarkably achieved the intended purpose, while ensuring integrity and availability of the data which is critical to IoT success. / Petroleum Technology Development Fund(PTDF) Nigeria, Grant/Award Number:PTDF/ED/PHD/TYM/858/16
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Forest edges in boreal landscapes - factors affecting edge influenceJansson, Ulrika January 2009 (has links)
The boreal forest in Fennoscandia has been subjected to major loss and fragmentation of natural forests due to intensive forestry. This has resulted in that forest edges are now abundant and important landscape features. Edges have documented effects on the structure, function and biodiversity in forests. Edge influence on biodiversity is complex and depends on interactions between many local and regional factors. This thesis focuses on sharp forest edges and their potential to influence biodiversity at the landscape-level. I have developed a method for quantification and characterization of sharp forest edges by interpretation of colour infrared (CIR) aerial photographs in combination with line intersect sampling (LIS) and sample plots. The method was used to estimate density of forest edge in 28 landscapes (each 1600 ha) in northern Sweden, differing in management intensity, landscape composition and geographical location. Forest edges were described in detail using edge, canopy and neighbourhood attributes. By combining these attributes it was possible to classify edges with respect to levels of exposure. A field experiment was conducted to examine the effect of edge contrast on growth of the old forest lichen Usnea longissima. The edge quantification method is accurate and efficient for estimating the length of sharp forest edges on an area basis (edge density, m ha-1) and for collecting detailed attributes of edges and their surroundings. In northern Sweden, the forest edge density is high (54 m ha-1) but varies extensively (12-102 m ha-1) between landscapes. Edge density is strongly correlated with the level of human disturbance and increases towards the southern part of the study area, at lower altitudes were management intensity is highest. Edge orientation, contrast and neighbourhood size shows an immense variation between edges and also varies between edge types. Regenerating edges are generally of higher contrast and face larger neighbourhoods than natural edges. Maintained edges had high contrast but small neighbourhoods. A larger proportion of edges in mature forests are highly exposed to microclimatic edge influence than edges in general. The field experiment revealed that growth of U. longissima was highest near edges where the vegetation on the adjacent area was sheltering, but not shading, the lichen. In the present thesis, I have provided a valuable tool for estimating density of forest edges with potential to yield information on important factors determining edge influence at landscape-level. The large variability in edge density, edge and neighbourhood attributes imply large differences in microclimate anf thus in the potential for ede influence. Management and conservation strategies must incorporate these factors to realistically address edge influence on biota at the landscape-level.
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Rauheitsuntersuchungen an Glaskanten mittels konfokalem Laserscanning-MikroskopBukieda, Paulina, Weller, Bernhard 22 February 2024 (has links)
Untersuchungen zur Kantenfestigkeit von Gläsern zeigen, dass diese in Abhängigkeit des Herstellers und der Kantenbearbeitungsart nach DIN 1249-11 stark variiert. Insbesondere der Bearbeitungsprozess des Schleifens weist eine Vielzahl von Parametern auf, welche die resultierende Oberflächenbeschaffenheit der Glaskante beeinflussen, allerdings noch unzureichend untersucht sind. Eine objektive Erfassung der Oberflächenbeschaffenheit über Kennwerte der Rauheit könnte helfen, Prozessparameter bewertbar zu machen und eine Korrelation zwischen dem Bearbeitungsprozess und der Kantenfestigkeit zu schaffen. Im Rahmen einer ersten Vorstudie wurden Rauheitskennwerte geschliffener und polierter Kantenoberflächen von drei Herstellern mittels konfokalem Laserscanning-Mikroskop ermittelt und hinsichtlich ihrer Eignung zur Bewertung der Bearbeitungsprozesse geprüft. / Roughness examination of processed glass edges under a confocal laser scanning microscope. Findings on the edge strength show that, it varies depending on the manufacturer and the type of edge finishing. In particular the grinding process has a large number of parameters that influence the surface quality of the glass edge, which have not yet been fully investigated. The determination of objective roughness parameters could help to evaluate the grinding processes and further correlate the surface quality with the edge strength. Within the scope of a preliminary study, roughness parameters were calculated for ground and polished glass edges of three manufacturers using a confocal laser scanning microscope. Finally the method was tested regarding to its suitability for a determination of characteristic roughness parameters that could be used to evaluate the grinding processes.
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Kan jag låta sådär? : En observationsstudie med fokus på "edge" i sångmetoden "komplett sångteknik" / Can I sound like that? : An observation study with focus on "edge" in the vocal method "complete vocal tecnique"Adamsson, Sophie January 2015 (has links)
Syftet med denna studie är att få större insikt i vad det innebär att utveckla en ny sångteknik. För att undersöka detta har jag under en fyraveckorsperiod övat edge tio minuter per dag, fem dagar i veckan. Tre av dessa övningstillfällen har videofilmats. Jag har också använt mig av loggbok för att dokumentera mina olika upplevelser under processens gång. Som teoretisk utgångspunkt har jag utgått utifrån ett sociokulturellt perspektiv. I resultatet redovisas vilka redskap som användes och hur dessa hanterades samt hur processen gällande lärandet har utvecklats. Resultatet visar att de mest centrala redskap som användes var kroppen, metodboken, pianostol, vägg och en låt. Flera av redskapen användes för att få bättre luftkontroll. I diskussionen beskriver jag utifrån det sociokulturella perspektivet vilka förutsättningar som har funnits samt vilka redskap som användes vid lärandet. / The purpose of the study is to get a deeper insight of what it means to develop a new singing technique. To study this I have practiced edge ten minutes per day during a period of four weeks, five times a week. Three of these exercices have been videotaped. I have also used a logbook to document new experiences during the process. I have a socio-cultural perspective as a theoretical base in this study. In the result the different tools that were selected show how these were handled and how the process in learning has developed. The results show that the most central tools that were used were the body, the method book, the piano chair, the wall and a song. In the discussion I describe, from a socio-cultural perspective, what the conditions have been, and which tools I have used.
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Edge criticality in secure graph dominationDe Villiers, Anton Pierre 12 1900 (has links)
Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: The domination number of a graph is the cardinality of a smallest subset of its vertex set with
the property that each vertex of the graph is in the subset or adjacent to a vertex in the subset.
This graph parameter has been studied extensively since its introduction during the early 1960s
and finds application in the generic setting where the vertices of the graph denote physical
entities that are typically geographically dispersed and have to be monitored efficiently, while
the graph edges model links between these entities which enable guards, stationed at the vertices,
to monitor adjacent entities.
In the above application, the guards remain stationary at the entities. In 2005, this constraint
was, however, relaxed by the introduction of a new domination-related parameter, called the
secure domination number. In this relaxed, dynamic setting, each unoccupied entity is defended
by a guard stationed at an adjacent entity who can travel along an edge to the unoccupied entity
in order to resolve a security threat that may occur there, after which the resulting configuration
of guards at the entities is again required to be a dominating set of the graph. The secure
domination number of a graph is the smallest number of guards that can be placed on its
vertices so as to satisfy these requirements.
In this generalised setting, the notion of edge removal is important, because one might seek the
cost, in terms of the additional number of guards required, of protecting the complex of entities
modelled by the graph if a number of edges in the graph were to fail (i.e. a number of links
were to be eliminated form the complex, thereby disqualifying guards from moving along such
disabled links).
A comprehensive survey of the literature on secure graph domination is conducted in this dissertation.
Descriptions of related, generalised graph protection parameters are also given. The
classes of graphs with secure domination number 1, 2 or 3 are characterised and a result on
the number of defenders in any minimum secure dominating set of a graph without end-vertices
is presented, after which it is shown that the decision problem associated with computing the
secure domination number of an arbitrary graph is NP-complete.
Two exponential-time algorithms and a binary programming problem formulation are presented
for computing the secure domination number of an arbitrary graph, while a linear algorithm is
put forward for computing the secure domination number of an arbitrary tree. The practical
efficiencies of these algorithms are compared in the context of small graphs.
The smallest and largest increase in the secure domination number of a graph are also considered
when a fixed number of edges are removed from the graph. Two novel cost functions are
introduced for this purpose. General bounds on these two cost functions are established, and
exact values of or tighter bounds on the cost functions are determined for various infinite classes
of special graphs. Threshold information is finally established in respect of the number of possible edge removals
from a graph before increasing its secure domination number. The notions of criticality and
stability are introduced and studied in this respect, focussing on the smallest number of arbitrary
edges whose deletion necessarily increases the secure domination number of the resulting graph,
and the largest number of arbitrary edges whose deletion necessarily does not increase the secure
domination number of the resulting graph. / AFRIKAANSE OPSOMMING: Die dominasiegetal van ’n grafiek is die kardinaalgetal van ’n kleinste deelversameling van die
grafiek se puntversameling met die eienskap dat elke punt van die grafiek in die deelversameling
is of naasliggend is aan ’n punt in die deelversameling. Hierdie grafiekparameter is sedert die
vroeë 1960s uitvoerig bestudeer en vind toepassing in die generiese situasie waar die punte van
die grafiek fisiese entiteite voorstel wat tipies geografies verspreid is en doeltreffend gemonitor
moet word, terwyl die lyne van die grafiek skakels tussen hierdie entiteite voorstel waarlangs
wagte, wat by die entiteite gebaseer is, naasliggende entiteite kan monitor.
In die bogenoemde toepassing, bly die wagte bewegingloos by die fisiese entiteite waar hulle
geplaas word. In 2005 is hierdie beperking egter verslap met die daarstelling van ’n nuwe
dominasie-verwante grafiekparameter, bekend as die sekure dominasiegetal. In hierdie verslapte,
dinamiese situasie word elke punt sonder ’n wag deur ’n wag verdedig wat by ’n naasliggende
punt geplaas is en wat langs die verbindingslyn na die leë punt kan beweeg om daar ’n bedreiging
te neutraliseer, waarna die gevolglike plasing van wagte weer ’n dominasieversameling van die
grafiek moet vorm. Die sekure dominasiegetal van ’n grafiek is die kleinste getal wagte wat op
die punte van die grafiek geplaas kan word om aan hierdie vereistes te voldoen.
Die beginsel van lynverwydering speel ’n belangrike rol in hierdie veralgemeende situasie, omdat
daar gevra mag word na die koste, in terme van die addisionele getal wagte wat vereis word, om
die kompleks van entiteite wat deur die grafiek gemodelleer word, te beveilig indien ’n aantal
lynfalings in die grafiek plaasvind (m.a.w. indien ’n aantal skakels uit die kompleks van entiteite
verwyder word, en wagte dus nie meer langs sulke skakels mag beweeg nie).
’n Omvattende literatuurstudie oor sekure dominasie van grafieke word in hierdie verhandeling
gedoen. Beskrywings van verwante, veralgemeende verdedigingsparameters in grafiekteorie word
ook gegee. Die klasse van grafieke met sekure dominasiegetal 1, 2 of 3 word gekarakteriseer
en ’n resultaat oor die getal verdedigers in enige kleinste sekure dominasieversameling van ’n
grafiek sonder endpunte word daargestel, waarna daar getoon word dat die beslissingsprobleem
onderliggend aan die berekening van die sekure dominasiegetal van ’n arbitrêre grafiek NP-
volledig is.
Twee eksponensiële-tyd algoritmes en ’n binêre programmeringsformulering word vir die bepaling
van die sekure dominasiegetal van ’n arbitrêre grafiek daargestel, terwyl ’n lineêre algoritme vir
die berekening van die sekure dominasiegetal van ’n arbitrêre boom ontwerp word. Die praktiese
doeltreffendhede van hierdie algoritmes word vir klein grafieke met mekaar vergelyk. Die kleinste en groostste toename in die sekure dominasiegetal van ’n grafiek word ook oorweeg
wanneer ’n vaste getal lyne uit die grafiek verwyder word. Twee nuwe kostefunksies word vir
hierdie doel daargestel en algemene grense word op hierdie kostefunksies vir arbitrêre grafieke
bepaal, terwyl eksakte waardes van of verbeterde grense op hierdie kostefunksies vir verskeie
oneindige klasse van spesiale grafieke bereken word.
Drempelinligting word uiteindelik bepaal in terme van die moontlike getal lynverwyderings uit
’n grafiek voordat die sekure dominasiegetal daarvan toeneem. Die konsepte van kritiekheid en
stabiliteit word in hierdie konteks bestudeer, met ’n fokus op die kleinste getal arbitrêre lynfalings
wat noodwendig die sekure dominasiegetal van die gevolglike grafiek laat toeneem, of die grootste
getal arbitrêre lynfalings wat noodwendig die sekure dominasiegetal van die gevolglike grafiek
onveranderd laat.
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Distribution des communautés végétales sous l'influence des lisières forestières dans des bois fragmentés / Distribution of vegetation communities under forest edge influence in fragmented forestsAlignier, Audrey 05 November 2010 (has links)
Les lisières forestières constituent un enjeu pour la gestion des territoires, par la biodiversité qu’elles abritent, les processus écologiques qu’elles régulent et les services environnementaux qu’elles rendent à l’agriculture et à la foresterie. C’est pourquoi il est nécessaire de connaitre et quantifier précisément leurs influences sur la végétation pour proposer des mesures de gestion adaptées à la variabilité des situations de lisière. En référence aux hypothèses de la littérature, ce travail vise à comprendre comment varie la répartition des communautés végétales forestières en réponse à la diversité des types de lisières, dans un paysage agriforestier. Les espèces vasculaires de la strate basse de la végétation forestière ont été recensées le long de 28 transects, représentatifs de sept types de lisières des coteaux de Gascogne. Ces transects, perpendiculaires à la bordure et dirigés vers l’intérieur du bois, comportent 20 quadrats contigus de 2 m × 2 m. J’ai cherché à mesurer la profondeur d’influence des effets de lisières sur la végétation par la méthode de régression à deux phases. Face à l’hétérogénéité observée, j’ai caractérisé les patrons de distribution des communautés végétales par cinq modèles continus pour les comparer. Les lisières structurent la répartition des communautés végétales suivant un gradient, de la bordure vers l’intérieur du bois, mais les patrons sont plus variables qu’attendus et remettent en cause la généricité du modèle théorique à deux phases largement admis dans la littérature. Néanmoins, un patron de distribution de la végétation commun à l’ensemble des lisières a été identifié au moyen de la méthode STATIS d’analyse à k-tableaux. L’analyse des effets de lisière sur un sous-échantillon d’espèces a été affinée par la prise en compte des caractéristiques biologiques et écologiques des espèces d’une part, et des variables environnementales, à différentes échelles spatio-temporelles d’autre part. Les traits biologiques et écologiques des espèces répondent davantage à l’âge et l’histoire des lisières qu’à la distance à la bordure. La hiérarchie des facteurs environnementaux, paysagers et historiques confirment le rôle prépondérant de la qualité locale de l’habitat dans la structure des communautés. La variabilité temporelle des effets de lisière a été abordée par un suivi horaire des variations microclimatiques au cours d’une année. Les faibles écarts microclimatiques entre la lisière et l’intérieur du bois au cours des saisons suggèrent un rôle faible du microclimat sur la structure des assemblages d’espèces. Enfin, la variabilité spatiale des lisières dans un paysage de large étendue a été évaluée par la mise au point d’une méthode originale afin de caractériser et cartographier la diversité des segments de lisières. Les résultats remettent en cause les modèles théoriques antérieurs et ouvrent des perspectives pour une meilleure compréhension des principes d’organisation des communautés végétales en lisières de forêt. La complexité des patrons de réponse aux effets de lisière justifie de porter une attention plus soutenue à la diversité des lisières dans la perspective de mieux les gérer. / Forest edges are a challenge for land management. They contain high biodiversity, regulate ecological processes and provide environmental services to agriculture and forestry. Therefore, it is necessary to evaluate and quantify precisely edge influence on vegetation to propose management measures adapted to edge diversity. Referring to the literature asusmptions, this paper focuses on understanding the variation in the distribution patterns of forest plant communities in response to contrasted edge types in rural landscape. All vascular plant species of the understorey forest vegetation have been identified along 28 transects, pertaining to seven edge types of “coteaux de Gascogne”. Transects were perpendicular to the forest border and included 20 contiguous quadrats of 2 m × 2 m, towards forest interior. I tried to measure the depth of edge influence on vegetation using the two-phase linear regression method. Facing to high heterogeneity, I characterized the distribution patterns of plant communities by five continuous models for comparison. Edge effect structure the distribution of plant communities along a gradient from the border toward the forest interior. Response patterns to edge influence were more variable than expected and challenge the hypothetical response model pattern widely accepted in the literature. However, a common pattern of vegetation for all transects was identified using the k-tables STATIS method. Analysis of edge effects on a sub-sample of species was refined using on the one hand biological and ecological species traits and environmental variables at different spatio-temporal scales, on the other. The functional response of plant species better suited to the age and history of the edges than the distance from the border. Nevertheless, the hierarchy of environmental, landscape and historical context confirm the role of habitat quality on distribution patterns of forest vegetation. Temporal variability of edge effects has been addressed by monitoring hourly microclimatic variations over one year. The small differences in microclimate between edge and forest interior over seasons suggest a weak role of microclimate on the structure of plant species assemblages. Finally, the spatial variability of edges at the landscape level has been evaluated. An original method, Cartolis, has been developed to characterize and map the diversity of forest edge segments. Our results, calling into question the earlier theoretical models, provide opportunities for a better understanding of plant distribution patterns in forest edges. The complexity of responses obtained warrants to bring more attention to edge diversity for better management and conservation of plant species.
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Variation des biomarqueurs dans le spectre visible non résolu de la TerreNaud, Marie-Eve 12 1900 (has links)
L’évolution rapide des technologies de détection et de caractérisation des exoplanètes depuis le début des années 1990 permet de croire que de nouveaux instruments du type Terrestrial Planet Finder (TPF) pourront prendre les premiers spectres d’exoplanètes semblables à la Terre d’ici une ou deux décennies. Dans ce contexte, l’étude du spectre de la seule planète habitée connue, la Terre, est essentielle pour concevoir ces instruments et analyser leurs résultats. Cette recherche présente les spectres de la Terre dans le visible (390-900 nm), acquis lors de 8 nuits d’observation étalées sur plus d’un an. Ces spectres ont été obtenus en observant la lumière cendrée de la Lune avec le télescope de 1.6 m de l’Observatoire du Mont-Mégantic (OMM). La surface de la Lune réfléchissant de manière diffuse la lumière provenant d’une portion de la Terre, ces spectres sont non résolus spatialement. L’évolution de ces spectres en fonction de la lumière réfléchie à différentes phases de Terre est analogue à celle du spectre d’une exoplanète, dont la phase change selon sa position autour de l’étoile.
L'eau, l'oxygène et l'ozone de l’atmosphère, détectés dans tous nos spectres, sont des biomarqueurs dont la présence suggère l’habitabilité de la planète et/ou la présence d’une activité biologique. Le Vegetation Red Edge (VRE), une autre biosignature spectrale, dû aux organismes photosynthétiques à la surface, est caractérisé par l’augmentation de la réflectivité autour de 700 nm. Pour les spectres de 5 nuits, cette augmentation a été évaluée entre -5 et 15% ±~5%, après que les contributions de la diffusion de Rayleigh, des aérosols et d’une large bande moléculaire de l’ozone aient été enlevées. Les valeurs mesurées sont cohérentes avec la présence de végétation dans la phase de la Terre contribuant au spectre, mais s’étendent sur une plage de variations plus large que celles trouvées dans la littérature (0-10%). Cela pourrait s’expliquer par des choix faits lors de la réduction des données et du calcul du VRE, ou encore par la présence d’autres éléments de surface ou de l’atmosphère dont la contribution spectrale autour de 700 nm serait variable. / The rapid evolution of the detection and characterization of exoplanets since the nineties is such that instruments like the Terrestrial Planet Finder (TPF) will surely take the first spectra of exoplanets similar to the Earth in the next decades. The study of the spectrum of the only inhabited planet we know, the Earth, is thus essential to conceive these instruments and to complete pertinent analyses of their results. This research presents the optical spectra (390-900 nm) of the Earth that were secured on 8 observing nights covering more than a year. These spectra were obtained by observing the Earthshine with the 1.6 m telescope at the Observatoire du Mont-Mégantic (OMM). Because the surface of the Moon reflects diffusely the light coming from a portion of the Earth, the observation of Earthshine allow us to get spatially unresolved spectra, like those that will likely be obtained for exoplanets with the first generation of instruments. The variation of the Earth’s spectrum with the changing contributing phase of the Earth is also similar to that of an exoplanet spectrum, which changes with its position around the star.
Water, oxygen and ozone of the Earth’s atmosphere, detected in all of our spectra, are biomarkers. They give clues about the habitability and the possible presence of life on a planet. The Vegetation Red Edge (VRE), another spectral biomarker, caused by photosynthetic organisms, is characterized by an increase in reflectivity around 700 nm. For the spectra of 5 nights, this increase was evaluated to be between -5 and 15% ±~5%, after the contributions of Rayleigh and aerosol scattering, as well as of a wide ozone absorption band were removed. These values are consistent with the presence of vegetation in the phase of the Earth contributing to the spectra. However, they cover a larger range than that usually found in the literature (0-10%). A possible explanation could be the few arbitrary choices that were made during data processing and VRE computation or the presence of other surface and atmospheric elements with a spectral signature varying around 700 nm.
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關於邊連通數和邊度數的問題 / Some topics on edge connectivity and edge degrees陳玫芳 Unknown Date (has links)
在這篇論文中,我們根據局部連通和局部補連通性質將圖分類,計算在 Harary 圖裡大小為 2k - 1 和 2k 邊切集的個數,和證明當圖形有最大的最小邊度數和最小點度數差,一些關於度數為 1 的點個數性質。 / In this thesis, we classify some graphs into locally coconnected graphs or locally connected graphs, compute the number of its edge cuts of size 2k - 1 and 2k in a Harary graph, and show some properties of the number of vertices of degree 1 when the graph has the maximum difference of minimum edge degree and minimum vertex degree.
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Towards Efficient Delivery of Dynamic Web ContentRamaswamy, Lakshmish Macheeri 26 August 2005 (has links)
Advantages of cache cooperation on edge cache networks serving dynamic web content were studied. Design of cooperative edge cache grid a large-scale cooperative edge cache network for delivering highly dynamic web content with varying server update frequencies was presented. A cache clouds-based architecture was proposed to promote low-cost cache cooperation in cooperative edge cache grid. An Internet landmarks-based scheme, called selective landmarks-based server-distance sensitive clustering scheme, for grouping edge caches into cooperative clouds was presented. Dynamic hashing technique for efficient, load-balanced, and reliable documents lookups and updates was presented. Utility-based scheme for cooperative document placement in cache clouds was proposed. The proposed architecture and techniques were evaluated through trace-based simulations using both real-world and synthetic traces. Results showed that the proposed techniques provide significant performance benefits.
A framework for automatically detecting cache-effective fragments in dynamic web pages was presented. Two types of fragments in web pages, namely, shared fragments and lifetime-personalization fragments were identified and formally defined. A hierarchical fragment-aware web page model called the augmented-fragment tree model was proposed. An efficient algorithm to detect maximal fragments that are shared among multiple documents was proposed. A practical algorithm for detecting fragments based on their lifetime and personalization characteristics was designed. The proposed framework and algorithms were evaluated through experiments on real web sites. The effect of adopting the detected fragments on web-caches and origin-servers is experimentally studied.
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Hibridinis genetinis algoritmas komivojažieriaus uždaviniui / Hybrid Genetic Algorithm for the Traveling Salesman ProblemKatkus, Kęstutis 06 June 2006 (has links)
In this work, the Traveling Salesman Problem (TSP) is discussed. The Hybrid Genetic Algorithm for solving the TSP is presented. The traveling salesman problem is formulated as follows: given matrix D=(dij)nxn of distances between n objects and the set P of permutations of the integers from 1 to n, find a permutation p=(p(1), p(2), ..., p(n)) P that minimizes. Many heuristic algorithms can be applied for the TSP. Recently, genetic algorithms (GAs) are among the advanced heuristic techniques for the combinatorial problems, like the TSP. genetic algorithms are based on the biological process of natural selection. The original concepts of GAs were developed in 1970s. Many simulations have demonstrated the efficiency of GAs on different optimization problems, among them, bin–packing, generalized assignment problem, graph partitioning, job–shop scheduling problem, set covering problem, vehicle routing. One of the main operators in GAs is the crossover (i.e. solution recombination). This operator plays a very important role by constructing competitive GAs. In this work, we investigate several crossover operators for the TSP, among them, CX (cycle crossover), PMX (partialy mapped crossover), POS (position based crossover), ER (edge recombination crossover), edge-NN (edge recombination crossover, nearest neighbour) and AP (alternating-positions crossover). Comparison of these crossover operators was performed. The results show high efficiency of the edge-NN, ER and PMX crossovers.
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