In EA, there are two classic ways of dealing with the constrains of a problem: whether correct them, or penalize their value in the objective function [6]. After some trial and error, we choose the second one, through a pre-process that consists in determining the **shortest** **path** between any two nodes in the network using the Dijkstra algorithm, and saving this values to posterior use. This values are not used anywhere in DE, except in the evaluation function, as a penalty factor for the invalid paths, and are calculated previously to speed up the algorithm. We also use the values to have the optimum value to compare to the one obtained in DE.

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Bellman-Ford successive approximation algorithm (Lawler, 1976). These algorithms have major shortcomings such as they search only for the **shortest** route and they exhibit high computational complexity for real-time communications. Artificial Neural Networks (ANN) has been examined to solve the **shortest** **path** problem relying on their parallel architecture to provide a fast solution (Araujo et al., 2001). However, the ANN approach has several limitations. These include the complexity of the hardware which increases considerably with increasing number of network nodes; at the same time, the reliability of the solution decreases. Secondly, they are less adaptable to topological changes in the network graph. Evolutionary algorithms such as Genetic Algorithm (GA) (Ahn and Ramakrishna, 2002) and Particle Swarm Optimization (PSO) (Mohemmed et al., 2008) have been used. However, the approaches are meant to find single-objective optimization of either cost or delay, mostly cost only. It is apparent that there is a need for more efficient algorithm which gives multi-objective trade-off solutions involving cost, delay and bandwidth.

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One of the most important and challenging problems in biomedicine and genomics is how to identify the disease genes. In this study, we developed a computational method to identify colorectal cancer-related genes based on (i) the gene expression profiles, and (ii) the **shortest** **path** analysis of functional protein association networks. The former has been used to select differentially expressed genes as disease genes for quite a long time, while the latter has been widely used to study the mechanism of diseases. With the existing protein-protein interaction data from STRING (Search Tool for the Retrieval of Interacting Genes), a weighted functional protein association network was constructed. By means of the mRMR (Maximum Relevance Minimum Redundancy) approach, six genes were identified that can distinguish the colorectal tumors and normal adjacent colonic tissues from their gene expression profiles. Meanwhile, according to the **shortest** **path** approach, we further found an additional 35 genes, of which some have been reported to be relevant to colorectal cancer and some are very likely to be relevant to it. Interestingly, the genes we identified from both the gene expression profiles and the functional protein association network have more cancer genes than the genes identified from the gene expression profiles alone. Besides, these genes also had greater functional similarity with the reported colorectal cancer genes than the genes identified from the gene expression profiles alone. All these indicate that our method as presented in this paper is quite promising. The method may become a useful tool, or at least plays a complementary role to the existing method, for identifying colorectal cancer genes. It has not escaped our notice that the method can be applied to identify the genes of other diseases as well.

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This paper proposed a coarse grained parallel genetic algorithm for solving the **shortest** **path** routing with the primary goal of achieving faster computation speed. The experiment is based on MPI cluster environment. The accuracy and computation time of the algorithm is dependent on population size and the number of computing nodes. The accuracy decreases linearly with larger number of computing nodes whereas the computation time decreases exponentially. The accuracy and execution time are higher when population size is more. Due to increase in population the computation time increases and this can be reduced by using larger number of computing nodes. When compared to non-parallel version of the same algorithm, the developed parallel algorithm is observed to have a greatly reduced computation time.

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In this section, the results obtained in chapter three are presented with their Performance Analysis of Enhance Interior Gateway Routing Protocol over Open **Shortest** **Path** First protocol. In all a model of three networks were designed and simulated, with configuration parameters and simulated based on 1st scenario with OSPF alone, 2nd scenario with EIGRP alone and 3rd scenario was a combination of both EIGRP and OSPF concurrently. A failure link established between Sub-E and Sub-D has been configured to occur at 300 seconds and to recover at 500 seconds tentatively.

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In this paper we investigated an algorithm for solving **shortest** **path** problem on a network with fuzzy arc lengths. The algorithm can be useful to decision makers. We have developed an example with the help of a minimum Euclidean distance. From the above computations we can observe that **Path** W 4 : U has W Y Z the **shortest** Euclidean distance for membership and non-membership. Hence the **shortest** **path** from source node U to destination node Z is W 4 : U W Y Z .

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For the purpose of **shortest** **path** routing on MOT, we address each node of the MOT by two-index binary labels as shown in Fig. 2 for a 7×7 mesh of trees. In this binary labelling, the root of a row-tree or column-tree is labelled with 1; if any internal node is labelled with u then its left child and right child are labelled with 2u and 2u+1 respectively. Let (x, y) and (u, v) denote the source and destination nodes respectively in a MOT and (x b , y b ) and (u b ,

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This study is based on finding the fuel optimal trajectories of the climb, cruise and descent phases of the flight, but ignores the takeoff and landing phases of the flight. In this work, several steps were made in order to achieve a complete trajectory from a 4D waypoint network that optimizes the fuel consumption. This study uses Dijkstra’s **shortest** **path** algorithm that finds a fuel optimal trajectory from a given 4D waypoints network, this technique was used to compare different length (short and medium-haul) flights.

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The analysis results show promising potential for reduction of consumed fuel and travel time in different flights via using the Dijkstra’s **shortest** **path** algorithm, across a range of common aircraft and routes. The results suggest that by flying fuel and time optimal trajectory for short haul flight, it is possible to save 2.4−4.1% on fuel burn, which is equivalent to 105.9 – 181.3 kilograms of fuel and 2.7−3.7 minutes or 2.4 - 3.2 % of total travel time. In medium haul flight by flying the fuel optimal trajectory can potentially save 2.1−2.3% fuel, reducing fuel burn by 579.2 – 637.4 kilograms and by flying the time optimal trajectory the travel time was reduced by 4.2−5.5 minutes or 1.9 – 2.6% of total travel time. For long haul flight it is possible to save 2.8−2.9% on fuel burn, which is equivalent to 1322.7 – 1354.1 kilogram of fuel by flying the fuel optimal trajectory, and 9.9−10.8 minutes or 2.7 -2.9% of total travel time was saved by flying the time optimal trajectory. In general the savings of the fuel and time are proportional to the trip lengths, and depends on the aircraft types.

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Objective of the project is to find the **shortest** **path** and avoid the obstacles which are either moving or stationary. For achieving this objective the function of algorithm is divided into three sub functions. Function should be consist short **path** between goals and start point, and some clearance in between robot and obstacle to avoid hitting, and the Bezier curve is used to recover the sharp turning as a smoothness function [2,3]

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In this survey, starting from the origin till the current state of the art, two different kinds of **shortest** **path** problem on dynamic networks have been analyzed: reoptimization of **shortest** paths and time-dependent SPP. The onset of these problems can be traced back respectively to the works of Gallo [32] and Cooke & Halsey [13], both inspired by the seminal algorithm of Dijkstra [21] and Ford Jr [28] for the **shortest** **path** problem. In Tables 1, 2, and 3 the most relevant works are listed, respectively surveyed in this paper for root change, arc cost change and time dependent **shortest** **path**. More specifically, each table reports the problem in question, the reference, the computational complexity of the proposed algorithm (if specified), and the year of publication. For the three main problem categories, {P2P, SPT and APSP}, the following notations have been adopted: a + and a − are respectively used to indicate cost increase and decrease for a single arc, while A + and A − are similarly used for batch updates, addressing respectively cost increase and decrease for a whole a set of arcs.

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IPv6 Low Wireless Personal Area Networks (6LoWPAN) is the most promising tech- nology for implementing the so called Internet of Things. In order for this technology to become a reality, routing protocols need to be resilient to variations in the links quality, due the constantly changes in the channels. The most promising of these protocols is the IPv6 Routing Protocol for Low-Power and Lossy Networks (RPL). In this work, the RPL routing protocol was extended to consider the uncertainty in the link quality. The RPL routing problem is modeled as a Robust Optimization problem derived from the **Shortest** **Path** Tree problem, denominated Robust **Shortest** **Path** Tree problem (RSPT). A new heuristics for the RSPT is developed, besides a mathematical formulation and an exact algorithm based in the proposed formulation. Besides that, a heuristic and three aproximative algorithms from literature of Robust Optimization were extend for the RSPT, and a proof of its approximation ratio is developed. The proposed algorithms are compared with the algorithms from the lit- erature. Computational experiments shown that the proposed exact algorithm solved all the proposed instances with 100 vertices at optimality. However, it could not solve instances with 200 vertices at optimality within 24 hours. The proposed heuristics presented better results that the approximative algorithms extended from literature, such that it achieves a relatively gap close to the gap of the proposed exact algorithm with a smaller computational time. The proposed heuristic can be easily extended to other robust optimization problems.

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Finally, the third component is a traffic monitoring and distribution adjustment algorithm, which dynamically changes the flow traffic rates used by the previous component in order to reach optimality. The optimality criteria for this algorithm can be loosely defined by stating that, in an optimal distribution, no more network traffic can be routed by the **shortest** **path** with- out causing congestion. As a result, this criteria leads to the minimisation of end-to-end delay while simultaneously avoiding packet loss. The component relies on a distributed optimisation algorithm, known as the gradient projection algorithm, in order to optimise the traffic distribu- tion for the said criteria. Furthermore, this algorithm requires that each ingress node is aware of network traffic on the paths used by its flows. Such load awareness is granted by end-to-end signaling messages.

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We close the discussion with two remarks, the first being of interest for experimentalists. Our findings also shed light on a network construction technique that relies on significance testing in order to decide upon defining a link or not [21]. For this purpose, a null distribution of a chosen estimator of signal interdependence (r m ) is generated for each pair of time series and a link is established if the null hypothesis of independent processes generating the time series can be rejected at a predefined significance level. It was suggested in Ref. [21] to use a limited subset of time series in order to minimize computational burden when generating null distributions. Our findings indicate that networks constructed this way will yield an artificially increased number of false positive or of false negative links which will depend on the frequency contents of time series being part or not part of the subset. Our second remark is related to network modeling. By choosing some threshold and generating time series that satisfy the relation between the size of the moving average and the length of time series, networks can be generated which differ in their degree distributions but approximately equal in their clustering coefficient and average **shortest** **path** length. This property could be of value for future modeling studies.

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For a FiWi access mesh network N , with R routers and G gateway routers, let us consider only the links that belong to the shortest path between each router and its nearest gateway route[r]

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As described in section 2, agents live on the nodes of a network, which we call the influence network, since a ’newborn’ agent is influenced by his neighbor- hood on this network, in his decision concerning education. When team effects are considered (see eq. (8)), the output of ideas is enhanced if the ’distance’ between pairs of skilled workers is small. This distance may be the euclidean one on a regular lattice or the **shortest** **path** along links of a random network. One may even consider a collaboration network among senior skilled agents, distinct from the underlying influence network. Take for example a situation where education is decided on a family/local neighbors basis, whereas intellec- tual workers collaborate with colleagues from a distant town by e-mailing or indirectly through mutual acquaintances. This case can be modeled by taking a square lattice (with a neighborhood of size z = 4 or z = 8) as influence network, plus a small-world for the collaboration network.

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MANET is a self-organizing and self-configuring multihop wireless network, which has a wide usage nowadays. MANETs are an wide area for research with lots of practical applications. However, MANETs are vulnerable to attacks due to their dynamic topology, open medium etc. Thus security issue is becoming a main concern in the applications of MANET. According to the model It can be seen that after passing through the various steps of GA the information regarding the **shortest** **path** is optimized and provides the best and optimal **path** which will consider the problem of finding optimum **path** with least cost and least delay by using Genetic algorithm. It is hypothesized that the resultant **path** is more optimal and reliable with minimum of the malicious or misbehaving node in the system.

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Analyzing the system’s output paints a more nuanced picture, however. In some cases, the system would ﬁnd the correct justiﬁcation article for the correct answer, but would pick as its putative answer another (incorrect) item, because it had a shorter **path**. Other times, it would not be capable of deciding between two (or more) answer items, as they all had a **shortest** **path** of the same distance. The following exam question is a sample case where this statistical approach to question answering is defective:

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