Reliable Path Problem Research Articles

A novel reliable path planning approach for multimodal networks based on a two-factor bound convergence algorithm

Due to the influence of diverse factors, travel time is highly uncertain. Travelers are eager to find the most reliable path in multimodal networks to reduce the penalty caused by late arrival. However, the research considering the traveler preferences in multimodal transportation networks to solve the reliable path problem with given budgets is limited. Thus, we propose two multimodal reliable path models to find personalized and reliable paths. First, we build a multimodal network based on smart card data to incorporate the multimodal transfers between public and private transportation and solve corresponding parking issues effectively. Next, we build a multimodal time-reliable path model to find time-reliable paths. Further, considering traveler preferences, we design a multimodal utility-reliable path model to find personalized and reliable paths. A novel two-factor reliability bound convergence algorithm is developed to solve the proposed models and proved for its theoretical feasibility. Finally, a real-world case study is used to verify the effectiveness and efficiency of the proposed models and algorithm.

On the shortest $$\alpha$$-reliable path problem

In this variant of the constrained shortest path problem, the time of traversing an arc is given by a non-negative continuous random variable. The problem is to find a minimum cost path from an origin to a destination, ensuring that the probability of reaching the destination within a time limit meets a certain reliability threshold. To solve this problem, we extend the pulse algorithm, a solution framework for shortest path problems with side constraints. To allow arbitrary non-negative continuous travel-time distributions, we model the random variables of the travel times using Phase-type distributions and Monte Carlo simulation. We conducted a set of experiments over small- and medium-size stochastic transportation networks with and without spatially-correlated travel times. As an alternative to handling correlations, we present a scenario-based approach in which the distributions of the arc travel times are conditioned to a given scenario (e.g., variable weather conditions). Our methodology and experiments highlight the relevance of considering on-time arrival probabilities and correlations when solving shortest path problems over stochastic transportation networks.

Lagrangian Relaxation for the Multiple Constrained Robust Shortest Path Problem

The study focuses on a multiple constrained reliable path problem in which travel time reliability and resource constraints are collectively considered. Nonlinear optimization model is developed to model constrained robust shortest path problem. The dual nature of the proposed problem is deduced based on the Lagrangian duality theory. An efficient algorithm based on Lagrangian dual relaxation is designed to solve constrained robust shortest path problem. An extension problem that considers multiple constraints is discussed. Numerical studies indicate that the proposed algorithm is efficient in terms of obtaining the close-to-optimal solutions within reasonable computational times.

Most reliable path-finding algorithm for maximizing on-time arrival probability

ABSTRACTFinding the most reliable path that maximizes the probability of on-time arrival is commonly encountered by travelers facing travel time uncertainties. However, few exact solution algorithms have been proposed in the literature to efficiently determine the most reliable path in large-scale road networks. In this study, a two-stage solution algorithm is proposed to exactly solve the most reliable path problem. In the first stage, the upper and lower bounds of on-time arrival probability are estimated. Dominance conditions and the monotonic property of the most reliable path problem are then established. In the second stage, the multi-criteria label-setting approach is utilized to efficiently determine the most reliable path. To illustrate the applicability of the proposed solution algorithm, a comprehensive case study is carried out using a real road network with stochastic travel times. The results of case study show that the proposed solution algorithm has a remarkable computational advantage over the existing multi-criteria label-correcting algorithm.

An exact algorithm for the mean–standard deviation shortest path problem

This paper studies the reliable path problem in the form of minimizing the sum of mean and standard deviation of path travel time. For the case of independent link travel times, we show that the problem can be solved exactly by repeatedly solving a subproblem minimizing the sum of mean and variance of path travel time. The latter is an additive shortest path problem, and can be solved using a standard labeling algorithm. While these subproblems are similar in form to those obtained from Lagrangian relaxation, this formulation admits proof of finite convergence to the optimal solution. An iterative labeling algorithm is developed that solves the non-additive reliable path problem from a single origin to all destinations. Moreover, a labeling technique is employed to further reduce the computational time of the proposed algorithm by partially updating the network in each iteration. As an alternative, a bisection-type search algorithm is developed that solves the problem for the single-origin and single-destination case. Numerical tests are presented, indicating that the proposed algorithm outperform others recently proposed in the literature: unlike Lagrangian relaxation, two of the proposed algorithms find solutions exactly, and the computation time is an order of magnitude faster than outer approximation methods.

Optimal Reliability Path Problem on Networks with Random and Correlated Link Travel Times

This study addressed the most reliable path problem on stochastic networks with correlated link travel times from general multivariate distributions. Both evaluation and optimization of this problem are difficult because of the absence of closed-form distribution at the path level. For tractability in reliability evaluation, the path reliability objective function was substituted by the standard-score objective with the same mean and variance as the given distribution. However, this simplified proxy objective was difficult to optimize because it was nonlinear in path mean and variance. These difficulties were circumvented by reformulating the problem as a bilevel minimization model, in which the master problem corresponded to the proxy reliability objective, and the subproblem corresponded to the solution of a related minimum robust-cost path problem. The subproblem was easier to solve because it minimized a linear combination of path travel time mean and standard deviation. An effi-cient algorithm was proposed to solve this bilevel model, whose exact and monotonic convergence was established for the proxy objective function. Computational experiments on various test networks demonstrated the robustness of the algorithm under various travel time distributions. The algorithm identified the optimal path in 96% to 99% of the cases with a maximum error of less than 0.5%. The algorithm was also applied with real-world data from an intelligent transportation systems test bed in Chennai, India. The results showed that the most reliable paths varied within the day and from day to day; this result showed potential applications of the algorithm with advanced traveler information systems.

Graphs and matroids weighted in a bounded incline algebra.

Firstly, for a graph weighted in a bounded incline algebra (or called a dioid), a longest path problem (LPP, for short) is presented, which can be considered the uniform approach to the famous shortest path problem, the widest path problem, and the most reliable path problem. The solutions for LPP and related algorithms are given. Secondly, for a matroid weighted in a linear matroid, the maximum independent set problem is studied.

3차원 격자지도 기반 생존성 극대화를 위한 다수 무인 항공기 임무경로 계획

An Unmanned Aerial Vehicle (UAV) is a powered pilotless aircraft, which is controlled remotely or autonomously. UAVs are an attractive alternative for many scientific and military organizations. UAVs can perform operations that are considered to be risky or uninhabitable for humans. UAVs are currently employed in many military missions and a number of civilian applications. For accomplishing the UAV's missions, guarantee of survivability should be preceded. The main objective of this study is to suggest a mathematical programming model and a <TEX>$A^*PS$</TEX>_PGA (A-star with Post Smoothing_Parallel Genetic Algorithm) for Multiple UAVs's path planning to maximize survivability. A mathematical programming model is composed by using MRPP (Most Reliable Path Problem) and MTSP (Multiple Traveling Salesman Problem). After transforming MRPP into Shortest Path Problem (SPP),<TEX>$A^*PS$</TEX>_PGA applies a path planning for multiple UAVs.

3차원 환경 기반 무인 항공기 생존성 극대화를 위한 이동 경로 계획

An Unmanned Aerial Vehicle(UAV) is a powered pilotless aircraft, which is controlled remotely or autonomously. UAVs are currently employed in many military missions(surveillance, reconnaissance, communication relay, targeting, strike etc.) and a number of civilian applications(communication service, broadcast service, traffic control support, monitoring, measurement etc.). For accomplishing the UAV's missions, guarantee of survivability should be preceded. The main objective of this study is the path planning to maximize survivability for UAV based on 3-dimensional environment. A mathematical programming model is suggested by using MRPP(Most Reliable Path Problem) and solved by transforming MRPP into SPP(Shortest Path Problem). This study also suggests a <TEX>$A^*PS$</TEX> algorithm based on 3-dimensional environment to UAV's path planning. According to comparison result of the suggested algorithm and SPP algorithms (Dijkstra, <TEX>$A^*$</TEX> algorithm), the suggested algorithm gives better solution than SPP algorithms.

COMPETITIVE ANALYSIS FOR THE MOST RELIABLE PATH PROBLEM WITH ONLINE AND FUZZY UNCERTAINTIES

Based on some results of the fuzzy network computation and competitive analysis, the Online Fuzzy Most Reliable Path Problem (OFRP), which is one of the most important problems in network optimization with uncertainty, has been originally proposed by our team. In this paper, the preliminaries about fuzzy and the most reliable path and competitive analysis are given first. Following that, the mathematical model of OFRP, in which two kinds of uncertainties, namely online and fuzzy, are combined to be considered at the same time, is established. Then some online fuzzy algorithms are developed to address the OFRP and the rigorous proofs of the competitive analysis are given in detail. Finally, some possible research directions of the OFRP are discussed and the conclusions are drawn.

End-to-end data paths: quickest or most reliable?

Let N=(V,E,c,l,p) be a network where V is the set of n vertices, E is the set of m edges, c(u,v)/spl ges/0 is the capacity of edge {u,v}, l(u,v)/spl ges/0 is the delay of edge {u,v}, p(u,v)/spl isin/[0,1] is the operational probability of edge {u,v}. In this letter, we present O(rm+rnlog n) time algorithms for the most reliable quickest path problem and the quickest most reliable path problem, where r is the number of different capacity values in the network.