Dynamic Shortest Path Problem Research Articles

Multi-Objective Decision-Making Meets Dynamic Shortest Path: Challenges and Prospects

The Shortest Path (SP) problem resembles a variety of real-world situations where one needs to find paths between origins and destinations. A generalization of the SP is the Dynamic Shortest Path (DSP) problem, which also models changes in the graph at any time. When a graph changes, DSP algorithms partially recompute the paths while taking advantage of the previous computations. Although the DSP problem represents many real situations, it leaves out some fundamental aspects of decision-making. One of these aspects is the existence of multiple, potentially conflicting objectives that must be optimized simultaneously. Recently, we performed a first incursion on the so-called Multi-Objective Dynamic Shortest Path (MODSP), presenting the first algorithm able to take the MODM perspective into account when solving a DSP problem. In this paper, we go beyond and formally define the MODSP problem, thus establishing and clarifying it with respect to its simpler counterparts. In particular, we start with a brief overview of the related literature and then present a complete formalization of the MODSP problem class, highlighting its distinguishing features as compared to similar problems and representing their relationship through a novel taxonomy. This work also motivates the relevance of the MODSP problem by enumerating real-world scenarios that involve all its ingredients, such as multiple objectives and dynamically updated graph topologies. Finally, we discuss the challenges and open questions for this new class of shortest path problems, aiming at future work directions. We hope this work sheds light on the theme and contributes to leveraging relevant research on the topic.

Data-Driven Optimization for Dynamic Shortest Path Problem Considering Traffic Safety

Traffic congestion is an inescapable problem that frustrates drivers in megacities. Although there is hardly a way to eliminate the congestion, it is possible to mitigate the impact through predictive methods. This paper develops a data-driven optimization approach for the dynamic shortest path problems (DSPP), considering traffic safety for urban navigations. The dynamic risk scores and travel times at different times and locations are estimated by the Safe Route Mapping (SRM) methodology and Long Short-Term Memory (LSTM) with Autoencoder, respectively, where possible variations in the future are considered. The DSPP is formulated as a mixed-integer linear programming problem under risk constraints to minimize the total travel cost, defined as the weighted sum of distance and travel time. To improve the efficiency of the DSPP, we design an improved tabu search with alternative initial-solution algorithms to accommodate various problem scales. Moreover, subgraph and self-adaptive insertion techniques are adopted as acceleration strategies to enhance computational efficiency further. Numerical experiments investigate the computational performance and the solution quality of our algorithm. The result shows satisfactory solution quality and computational efficiency with the proposed acceleration strategies compared to the CPLEX solver, a label-setting algorithm, and a state-of-the-art algorithm. Our algorithm can also compete with Google Maps regarding the travel cost in a real network in Manhattan, NY, USA, which is promising for Urban Navigations.

A Retroactive Approach for Dynamic Shortest Path Problem

Dynamic shortest path algorithms modify the existing shortest path tree or graph, taking into account changes in the underlying graph configuration. In the premise of this paper, the dynamic Dijkstra algorithm is specifically considered which is used for the solution of single source shortest path problem in dynamic graphs. Dynamic Single Source Shortest Path (DSSSP) problem is considered from a completely different perspective. For incorporating the dynamic changes into the solution, the retroactive data structure has been used. Dynamics of retroactive data structures provide a natural order for propagating the desired changes in the underlying graph configuration. DSSSP has been solved in efficient way with worst case complexity O(m log n) and also proved the correctness of our proposed algorithm.

Dispatch approaches for scheduling radio telescope observations

Radio telescopes are a scarce resource designed to provide experimental data for astrophysical research, and various studies have focused on the design of observing schedules that make optimal use of available telescope time. We consider strategies for minimising the time required to observe a fixed set of pulsars, which provides an excellent example of scheduling in an unpredictable environment. First, owing to scintillation, the intensity of a pulsar signal is variable and random; therefore, the decision to abort or prolong an observation can be made only after some fraction of the scheduled observation has been completed. Second, observations may be interrupted by radio frequency interference or when the source sets below the horizon. Some sources are visible for more or less time depending on their declination and the latitude of the observing telescope. Formulating the problem in these terms leads to a highly dynamic shortest path problem with uncertainty. Unlike other documented telescope scheduling approaches, we demonstrate how a simple earliest setting policy achieves sets of pulsar observations in a rather short timespan. The policy is fast to apply due to a novel algorithm that pre-calculates the subset of next candidates before the end of the current integration. Our simulation also clarifies that the uncertainty arising from the scintillation (signal strength) encountered on arrival adds significantly to the variation in overall durations and that different hourly start times can favour or hamper the progress of a set of observations.

The dynamic shortest path problem with time-dependent stochastic disruptions

The dynamic shortest path problem with time-dependent stochastic disruptions consists of finding a route with a minimum expected travel time from an origin to a destination using both historical and real-time information. The problem is formulated as a discrete time finite horizon Markov decision process and it is solved by a hybrid Approximate Dynamic Programming (ADP) algorithm with a clustering approach using a deterministic lookahead policy and value function approximation. The algorithm is tested on a number of network configurations which represent different network sizes and disruption levels. Computational results reveal that the proposed hybrid ADP algorithm provides high quality solutions with a reduced computational effort.

A decremental approach with the A∗ algorithm for speeding-up the optimization process in dynamic shortest path problems

Dynamic (time-dependent) network routing has become important due to the deployment of advanced traveler information systems in navigation systems. We study the problem of speeding-up the shortest path in continuous-time dynamic networks without a priori knowledge of the link travel times. We apply the A∗ algorithm using the decremental approach to reduce the network size and speed-up the optimization process in dynamic shortest path problems. We utilize the weighted metric multidimensional scaling technique to define the potential function in the A∗ algorithm by converting the link travel costs (times) into distances. Moreover, we evaluate the performance of the decremental approach with respect to the CPU times and optimal costs by applying the A∗ algorithm and Dijkstra’s algorithm to different networks.

Dynamic shortest path problems: Hybrid routing policies considering network disruptions

Traffic network disruptions lead to significant increases in transportation costs. We consider networks in which a number of links are vulnerable to these disruptions leading to a significantly higher travel time on these links. For these vulnerable links, we consider known link disruption probabilities and knowledge of transition probabilities for recovering from or getting into a disruption. We develop a framework based on dynamic programming in which we formulate and evaluate different known online and offline routing policies. Next to this, we develop computation-time-efficient hybrid routing policies. To test the efficiency of the different routing policies, we develop a test bed of networks based on a number of characteristics and analyze the results in terms of routes, cost performance and calculation times. Our results show that a significant part of the cost reduction can be obtained by considering only a limited part of the network in detail. The performance of our proposed hybrid policy is only slightly worse than the optimal policy.

Dynamic shortest path problems with time-varying costs

This paper concerns the problem of finding shortest paths from one node to all other nodes in networks for which arc costs can vary with time, each arc has a transit time, and parking with a corresponding time-varying cost is allowed at the nodes. The transit times can also take negative values. A general labeling method, as well as several implementations, are presented for finding shortest paths and detecting negative cycles under the assumption that arc traversal costs are piecewise linear and node parking costs are piecewise constant.

The dynamic shortest path problem with anticipation

Mobile communication technologies enable truck drivers to keep abreast of changing traffic conditions in real-time. We assume that such communication capability exists for a single vehicle traveling from a known origin to a known destination where certain arcs en route are congested, perhaps as the result of an accident. Further, we know the likelihood, as a function of congestion duration, that congested arcs will become uncongested and thus less costly to traverse. Using a Markov decision process, we then model and analyze the problem of constructing a minimum expected total cost route from an origin to a destination that anticipates and then responds to changes in congestion, if they occur, while the vehicle is en route. We provide structural results and illustrate the behavior of an optimal policy with several numerical examples and demonstrate the superiority of an optimal anticipatory policy, relative to a route design approach that reflects the reactive nature of current routing procedures.

Bitwise Algorithm for Fastest Paths in Time-Dependent Networks

An algorithm operating on a new and compact representation of link exit times to solve the one-to-all fastest path problem in dynamic networks is presented. The new space-efficient representation that exploits the first-in, first-out property of link travel times in dynamic networks is developed. The algorithm is described, and its working on a simple network is presented. The algorithm directly operates on bit streams of data representing time-dependent link travel times and performs logical operations on 0 and 1 bits only. Computational results are presented for large dynamic networks. The ideas behind the development of this algorithm are extendable to the development of algorithms operating at the bit level to solve other variants of dynamic shortest path problems and other dynamic network flow problems. These developments then open new research possibilities in the development of solution algorithms for dynamic network problems.

Design and Implementation of Parallel Dynamic Shortest Path Algorithms for Intelligent Transportation Systems Applications

The problem of computing shortest paths in time-dependent networks is considered. This computational problem is at the heart of solution methods to a variety of dynamic network models that arise in the context of intelligent transportation systems applications. The design, implementation, and computational testing are reported for parallel algorithms that exploit possibilities offered by low-cost, commonly available, parallel, and distributed computing platforms to solve many-to-many shortest path problems in time-dependent networks. Five shared-memory implementations and five message-passing implementations are developed. The parallel implementations adopt three decomposition strategies based on the sets of destination nodes, origin nodes, and departure times at origin nodes. The algorithms are coded with two types of parallel computing environments: a message-passing environment based on the parallel virtual machine library and a multithreading environment based on the Sun Microsystems Multi-Threads library. Numerical results are obtained with large-sized dynamic networks and two types of parallel computing platforms: a distributed network of Unix workstations and a Sun shared-memory machine containing eight processors. Satisfactory speedups of sequential algorithms are achieved. Numerical results obtained indicate that, overall, shared-memory platforms appear to be the most appropriate type of parallel computing platforms to solve dynamic shortest path problems that arise in the context of intelligent transportation systems applications.

Iterative methods for dynamic stochastic shortest path problems

Iterative methods for dynamic stochastic shortest path problems

Iterative methods for dynamic stochastic shortest path problems

Iterative methods for dynamic stochastic shortest path problems

An Incremental Algorithm for a Generalization of the Shortest-Path Problem

Thegrammar problem, a generalization of the single-source shortest-path problem introduced by D. E. Knuth (Inform. Process. Lett.6(1) (1977), 1–5) is to compute the minimum-cost derivation of a terminal string from each nonterminal of a given context-free grammar, with the cost of a derivation being suitably defined. This problem also subsumes the problem of finding optimal hyperpaths in directed hypergraphs (under varying optimization criteria) that has received attention recently. In this paper we present an incremental algorithm for a version of the grammar problem. As a special case of this algorithm we obtain an efficient incremental algorithm for the single-source shortest-path problem with positive edge lengths. The aspect of our work that distinguishes it from other work on the dynamic shortest-path problem is its ability to handle “multiple heterogeneous modifications”: between updates, the input graph is allowed to be restructured by an arbitrary mixture of edge insertions, edge deletions, and edge-length changes.

On the dynamic shortest path problem

On the dynamic shortest path problem