Set Of Optimal Paths Research Articles

System survivability in the context of interdiction networks

We define the concept of network survivability in the context of defense/attack strategies. We assume that a network is threatened by attackers. The attacker is referred to as a leader that targets selected links. Typically, the overall attack is considered as successful if the network is disabled. The follower is interested in preserving the functionality of the network and may restrict the network operation to limited paths. His/her problem is to determine which optimal set of paths to operate with the highest probability to survive an attack; while the leader seeks to determine which links to target to maximize the chance of a successful attack. In case of absence of knowledge, we distinguish two types of network survivability related to the follower and to the leader of the network, respectively. The latter has to do with partitioning the network. Both types are compared against each other as well as against network reliability. We derive a number of results both under the cases of full and absence of knowledge. We model the problem as a game and investigate the best strategy of each player as well as the cases of occurrence of equilibrium in a variety of settings.

PACE: a PAth-CEntric paradigm for stochastic path finding

With the growing volumes of vehicle trajectory data, it becomes increasingly possible to capture time-varying and uncertain travel costs, e.g., travel time, in a road network. The current paradigm for doing so is edge-centric: it represents a road network as a weighted graph and splits trajectories into small fragments that fit the underlying edges to assign time-varying and uncertain weights to edges. It then applies path finding algorithms to the resulting, weighted graph. We propose a new PAth-CEntric paradigm, PACE, that targets more accurate and more efficient path cost estimation and path finding. By assigning weights to paths, PACE avoids splitting trajectories into small fragments. We solve two fundamental problems to establish the PACE paradigm: (i) how to compute accurately the travel cost distribution of a path and (ii) how to conduct path finding for a source–destination pair. To solve the first problem, given a departure time and a query path, we show how to select an optimal set of paths that cover the query path and such that the weights of the paths enable the most accurate joint cost distribution estimation for the query path. The joint cost distribution models well the travel cost dependencies among the edges in the query path, which in turn enables accurate estimation of the cost distribution of the query path. We solve the second problem by showing that the resulting path cost distribution estimation method satisfies an incremental property that enables the method to be integrated seamlessly into existing stochastic path finding algorithms. Further, we propose a new stochastic path finding algorithm that fully explores the improved accuracy and efficiency provided by PACE. Empirical studies with trajectory data from two different cities offer insight into the design properties of the PACE paradigm and offer evidence that PACE is accurate, efficient, and effective in real-world settings.

An integrated inverse model-experimental approach to determine soft tissue three-dimensional constitutive parameters: application to post-infarcted myocardium.

Knowledge of the complete three-dimensional (3D) mechanical behavior of soft tissues is essential in understanding their pathophysiology and in developing novel therapies. Despite significant progress made in experimentation and modeling, a complete approach for the full characterization of soft tissue 3D behavior remains elusive. A major challenge is the complex architecture of soft tissues, such as myocardium, which endows them with strongly anisotropic and heterogeneous mechanical properties. Available experimental approaches for quantifying the 3D mechanical behavior of myocardium are limited to preselected planar biaxial and 3D cuboidal shear tests. These approaches fall short in pursuing a model-driven approach that operates over the full kinematic space. To address these limitations, we took the following approach. First, based on a kinematical analysis and using a given strain energy density function (SEDF), we obtained an optimal set of displacement paths based on the full 3D deformation gradient tensor. We then applied this optimal set to obtain novel experimental data from a 1-cm cube of post-infarcted left ventricular myocardium. Next, we developed an inverse finite element (FE) simulation of the experimental configuration embedded in a parameter optimization scheme for estimation of the SEDF parameters. Notable features of this approach include: (i) enhanced determinability and predictive capability of the estimated parameters following an optimal design of experiments, (ii) accurate simulation of the experimental setup and transmural variation of local fiber directions in the FE environment, and (iii) application of all displacement paths to a single specimen to minimize testing time so that tissue viability could be maintained. Our results indicated that, in contrast to the common approach of conducting preselected tests and choosing an SEDF a posteriori, the optimal design of experiments, integrated with a chosen SEDF and full 3D kinematics, leads to a more robust characterization of the mechanical behavior of myocardium and higher predictive capabilities of the SEDF. The methodology proposed and demonstrated herein will ultimately provide a means to reliably predict tissue-level behaviors, thus facilitating organ-level simulations for efficient diagnosis and evaluation of potential treatments. While applied to myocardium, such developments are also applicable to characterization of other types of soft tissues.

Path Planning for GEO-UAV Bistatic SAR Using Constrained Adaptive Multiobjective Differential Evolution

With the geosynchronous synthetic aperture radar (SAR) satellite as the transmitter, the unmanned aerial vehicle (UAV) can passively receive the echo within the illuminated ground area and achieve 2-D imaging of the interested target. This SAR system, known as GEO-UAV bistatic SAR, is capable of autonomously accomplishing the bistatic SAR mission in rough terrain environments by prespecifying a path for the UAV receiver. In this paper, the GEO-UAV bistatic SAR system is first investigated. The practical advantages and spatial resolution are then analyzed in detail. The spatial resolution of GEO-UAV bistatic SAR is dependent on the observation geometry, which is determined by the UAV path. Therefore, the path planning for GEO-UAV bistatic SAR aims at identifying a set of optimal paths for the UAV receiver to travel through a 3-D terrain environment that simultaneously guarantees the safety of the UAV and achieves SAR imaging with optimized performance during the flight. The path planning is modeled as a constrained multiobjective optimization problem (MOP), which accurately represents the two main aspects for the path planning problem, i.e., UAV navigation and bistatic SAR imaging. Then, a path planning method based on a constrained-adaptive-multiobjective-differential-evolution algorithm is proposed to solve the MOP and generate multiple feasible paths for the UAV receiver with different tradeoffs between navigation for UAV and bistatic SAR imaging performance. The GEO-UAV bistatic SAR mission designer can choose a path from the solution set according to the application requirements, which makes the method more pragmatic.

An approximate method to compute a sparse graph for traveling salesman problem

It is well known that traveling salesman problem has the exp(Ω(n)) time complexity in most cases. The exponential base will be reduced with the bounded degree graphs. The number of Hamiltonian cycles is approximately computed as e×(Davg/2)n for a n-vertex graph of average degree Davg, where e is the base of natural logarithm. It is much smaller than the total number of Hamiltonian cycles (n−1)!/2 in a complete undirected graph. An approximate method to compute a sparse graph is introduced to decrease the search space of the optimal solution. Firstly, a set of optimal k-vertex paths are computed with a weighted graph. Secondly, a frequency graph is computed with the set of optimal k-vertex paths. The frequency graph maintains the topological structure of the weighted graph whereas the numbers on the edges represent the frequencies of edges enumerated form the set of optimal k-vertex paths. Thirdly, a frequency threshold is deduced to remove the edges with frequencies below it and the sparse graph is generated. The bounded degree of the sparse graph is much smaller than n−1 and the complexity of traveling salesman problem is reduced. The approximate method is verified with tens of Euclidean TSP instances.

Statistical analysis of frequency graph for traveling salesman problem

Traveling salesman problem TSP is a typical of combinatorial optimization problem. Its objective is to find an optimal Hamiltonian circuit OHC. It has been proven to be NP-complete. The frequency graph for TSP has been introduced in a previous paper. This article is the progressive research of the frequency graph for TSP. The probability of the edges is computed based on a frequency graph which is computed with a set of local optimal Hamiltonian paths. The bigger the probability of an edge, the more possible the edge belongs to the OHC. The value span of the probability of an edge in the OHC is derived and used to select the candidate edges to form the OHC. A variable m is noted as the number of the local optimal Hamiltonian paths with each edge. These optimal Hamiltonian paths are used to compute a frequency graph. The probability function of the edges in the OHC is derived and it is a geometric progression according to variable m. The general term formula of the probability of the edges in the OHC is simulated based on the experiments with the Euclidean TSP instances. It is used to evaluate the rightness of the generated OHC composed of the candidate edges.

A Method to Select the Edges in the Minimum Hamiltonian Cycle

To find the minimum Hamiltonian cycle is the objective of traveling salesman problem (TSP) whereas it has been proven to be NP-complete. To select the right edges in the minimum Hamiltonian cycle, the frequency graph is computed with a set of optimal i-vertex paths. The number of optimal i-vertex paths is formulated according to i. In these frequency graphs, the frequencies of the edges in the minimum Hamiltonian cycle are generally bigger than the average frequency and those of most of the other edges. Before i ≤ n/2+1 for even number n and i ≤ (n ± 1)/2+1 for odd number n, the frequencies of the edges in the minimum Hamiltonian cycle increase faster than the average frequency does according to i. The frequencies on the edges and their change can be taken as the heuristic information to select the edges in the minimum Hamiltonian cycle. Two simple examples are given to show the change of the frequencies of the edges in the minimum Hamiltonian cycle. The results show that they are different from those of the other edges according to i. The results can be used as the basis to design algorithms for TSP

Energy-Aware Multipath Routing Scheme Based on Particle Swarm Optimization in Mobile Ad Hoc Networks.

Mobile ad hoc network (MANET) is a collection of autonomous mobile nodes forming an ad hoc network without fixed infrastructure. Dynamic topology property of MANET may degrade the performance of the network. However, multipath selection is a great challenging task to improve the network lifetime. We proposed an energy-aware multipath routing scheme based on particle swarm optimization (EMPSO) that uses continuous time recurrent neural network (CTRNN) to solve optimization problems. CTRNN finds the optimal loop-free paths to solve link disjoint paths in a MANET. The CTRNN is used as an optimum path selection technique that produces a set of optimal paths between source and destination. In CTRNN, particle swarm optimization (PSO) method is primly used for training the RNN. The proposed scheme uses the reliability measures such as transmission cost, energy factor, and the optimal traffic ratio between source and destination to increase routing performance. In this scheme, optimal loop-free paths can be found using PSO to seek better link quality nodes in route discovery phase. PSO optimizes a problem by iteratively trying to get a better solution with regard to a measure of quality. The proposed scheme discovers multiple loop-free paths by using PSO technique.

Optimal shortest path set problem in undirected graphs

This paper proposes the optimal shortest path set problem in an undirected graph $$G=(V,E)$$ G = ( V , E ) , in which some vehicles have to go from a source node $$s$$ s to a destination node $$t$$...

Research on Vehicle Path Planning Based on the BDD in the Uncertain Environment

Aimed at the high dynamics and uncertainty of road traffic, we propose a method combine BDD (binary decision diagram)-Based heuristic algorithm which used to do the initial path planning with BDD-Based incremental to solve the route replanning problem. In order to get the optimal path set, BDD-Based heuristic Search is firstly used for global planning. BDD is a compact data structure, the BDD-Based heuristic Search use this characteristic to represent state space and compress the search space through heuristic information at the same time; when the road network information changes, incremental replanning was used in difference type of congestion and the optimum path set again. The simulation results show that the BDD-Based heuristic Search and incremental replanning method has high efficiency and practicability in solving vehicle routing problem under dynamic and uncertain environment.

Order statistics for correlated random variables and its application to at-speed testing

Although order statistics have been studied for several decades, most of the results are based on the assumption of independent and identically distributed (i.i.d.) random variables. In the literature, how to compute the m th order statistics of n correlated random variables is still a problem. This article proposes a recursive algorithm based on statistical min/max operations to compute order statistics for general correlated and not necessarily identically distributed random variables. The algorithm has an O( mn ) time complexity and O( m + n ) space complexity. A binary tree-based data structure is further developed to allow selective update of the order statistics with O( nm 2 ) time. As a vehicle to demonstrate the algorithm, we apply it to the path selection algorithm in at-speed testing. A novel metric multilayer process space coverage metric is proposed to quantitatively gauge the quality of path selection. We then show that such a metric is directly linked to the order statistics, and our recursive algorithm can thus be applied. By employing a branch-and-bound path selection algorithm with these techniques, this article shows that selecting an optimal set of paths for a multimillion-gate design can be performed efficiently. Compared to the state of the art, experimental results show both the efficiency of our algorithms and better quality of our path selection.

Speeding up Martins’ algorithm for multiple objective shortest path problems

The latest transportation systems require the best routes in a large network with respect to multiple objectives simultaneously to be calculated in a very short time. The label setting algorithm of Martins efficiently finds this set of Pareto optimal paths, but sometimes tends to be slow, especially for large networks such as transportation networks. In this article we investigate a number of speedup measures, resulting in new algorithms. It is shown that the calculation time to find the Pareto optimal set can be reduced considerably. Moreover, it is mathematically proven that these algorithms still produce the Pareto optimal set of paths.

Simulation Analysis of the Market Diffusion Effects of Risk-averse Route Guidance on Network Traffic

Though the development of real-time traffic information and vehicle navigation has contributed to the increase in drivers’ satisfaction, the market diffusion of these technologies may not lead to the reduction of traffic congestion mainly due to the concentration of traffic into particular paths or links in the traffic networks. The hyperpath-based route recommendation would have the potential of reducing the congestion of the entire network because it recommends a potential optimal set of paths instead of the shortest (single) path and lead to the dispersion of traffic in an appropriate way. This study analyses the market diffusion effects of hyperpath-based route recommendation on the whole network traffic by employing agent-based traffic simulation mid dynamic traffic assignment. Some comparison studies reveal that indeed the hyperpath-based route recommendation would contribute to the mitigation of traffic congestion in some aspects.

The cost optimal solution of the multi-constrained multicast routing problem

In this paper, we define the cost optimal solution of the multi-constrained multicast routing problem. This problem consists in finding a multicast structure that spans a source node and a set of destinations with respect to a set of constraints, while minimizing a cost function. This optimization is particularly interesting for multicast network communications that require Quality of Service (QoS) guarantees. Finding such a structure that satisfies the set of constraints is an NP-hard problem. To solve the addressed routing problem, most of the proposed algorithms focus on multicast trees. In some cases, the optimal spanning structure (i.e. the optimal multicast route) is neither a tree nor a set of trees nor a set of optimal QoS paths. The main result of our study is the exact identification of this optimal solution. We demonstrate that the optimal connected partial spanning structure that solves the multi-constrained multicast routing problem always corresponds to a hierarchy, a recently proposed generalization of the tree concept. We define the directed partial minimum spanning hierarchies as optimal solutions for the multi-constrained multicast routing problem and analyze their relevant properties. To our knowledge, our paper is the first study that exactly describes the cost optimal solution of this NP-hard problem.

High reliable disjoint path set selection in mobile ad-hoc network using Hopfield neural network

Mobile ad-hoc network (MANET) is a collection of wireless mobile computers forming a temporary network without any fixed infrastructure or wired backbone. Topological changes in MANET frequently render routing paths unusable. A suitable technique for addressing this problem is to enhance the diversity of paths between the source and destination. However, multipath routing is a challenging task. In particular, the correlation between the failures of the paths in a path set should be as small as possible. Shared nodes and links between the paths are usual failure points. Disjointed path sets require the multiple paths to be link-disjoint or node-disjoint. However, selecting an optimal path set is an NP-complete problem. Artificial neural networks have been proposed as computational tools to solve constrained optimisation problems. The use of Hopfield neural network as a path set selection algorithm is explored. Since this algorithm produces a set of backup paths with much higher reliability, it is beneficial for MANETs. We use link expiration time (LET) between two nodes to estimate link reliability. In this approach, node-disjoint and link-disjoint path sets can be found simultaneously with route discovery algorithm. So, if someone wants to find both node-disjoint and link-disjoint path sets, there is no need to submit extra control messages, as overhead, to the MANET. Simulation results show that the proposed protocol can find path sets with higher reliability in comparison to the other recent proposed algorithms.

Sequential Optimization of Paths in Directed Graphs Relative to Different Cost Functions

Abstract This paper is devoted to the consideration of an algorithm for sequential optimization of paths in directed graphs relative to di_erent cost functions. The considered algorithm is based on an extension of dynamic programming which allows to represent the initial set of paths and the set of optimal paths after each application of optimization procedure in the form of a directed acyclic graph.

ORGANIZING PROCESSES OF INFORMATION TRANSMISSION IN MOBILE AD HOC NETWORKS

The work contains: 1. Analysis of known shared methods of sets with the purpose to choose the most efficient method of constructing of maximally durable infrastructure of a mobile computer set according to districtions of a cells’ diameter and available values of the sum intensity of channels in each cell. 2. Analysis of existing me-thods and algorithms of routing with the purpose to choose the most efficient algorithm by the criteria of re-routing time and the volume of control information. 3. The method of increasing of the security level by means of choosing the optimal set of paths. 4. The theoretical proof of the organization of data transmitting in mobile nets.

Optimal Kinematic Control of an Autonomous Underwater Vehicle

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SE</i> (3) , where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the maximum principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.

Minimum Wheel-Rotation Paths for Differential-Drive Mobile Robots

The shortest paths for a mobile robot are a fundamental property of the mechanism, and may also be used as a family of primitives for motion planning in the presence of obstacles. This paper characterizes shortest paths for differential-drive mobile robots, with the goal of classifying solutions in the spirit of Dubins curves and Reeds—Shepp curves for car-like robots. To obtain a well-defined notion of shortest, the total amount of wheel-rotation is optimized. Using the Pontryagin Maximum Principle and other tools, we derive the set of optimal paths, and we give a representation of the extremals in the form of finite automata. It turns out that minimum time for the Reeds—Shepp car is equal to minimum wheel-rotation for the differential-drive, and minimum time curves for the convexified Reeds—Shepp car are exactly the same as minimum wheel-rotation paths for the differential-drive. It is currently unknown whether there is a simpler proof for this fact.

Adaptive state-based multi-radio multi-channel multi-path routing in Wireless Mesh Networks

Wireless Mesh Networks (WMNs) are envisioned to seamlessly extend the network connectivity to end users by forming a wireless backbone that requires minimal infrastructure. Unfortunately for WMNs, frequent link quality fluctuations, excessive load on selective links, congestion, and limited capacity due to the half-duplex nature of radios are some key limiting factors that hinder their deployment. To address these problems, we propose a novel Adaptive State-based Multi-path Routing Protocol (ASMRP), which constructs Directed Acyclic Graphs (DAGs) from each Mesh Router (MR) to Internet Gateways (IGWs) and effectively discovers multiple optimal path set between any given MR-IGW pair. A congestion aware traffic splitting algorithm to balance traffic over these multiple paths is presented which synergistically improves the overall performance of the WMNs. We design a novel Neighbor State Maintenance module that innovatively employs a state machine at each MR to monitor the quality of links connecting its neighbors in order to cope with unreliable wireless links. We also employ a 4-radio architecture for MRs, which allows them to communicate over multiple radios tuned to non-overlapping channels and better utilize the available spectrum. Through extensive simulations using ns-2, we observe that ASMRP substantially improves the achieved throughput (∼5 times gain in comparison to AODV), and significantly minimizes end-to-end latencies. We also show that ASMRP ensures fairness in the network under varying traffic load conditions.