Stochastic Routing Research Articles

Efficient Stochastic Routing in Path-Centric Uncertain Road Networks

The availability of massive vehicle trajectory data enables the modeling of road-network constrained movement as travel-cost distributions rather than just single-valued costs, thereby capturing the inherent uncertainty of movement and enabling improved routing quality. Thus, stochastic routing has been studied extensively in the edge-centric model, where such costs are assigned to the edges in a graph representation of a road network. However, as this model still disregards important information in trajectories and fails to capture dependencies among cost distributions, a path-centric model, where costs are assigned to paths, has been proposed that captures dependencies better and provides an improved foundation for routing. Unfortunately, when applied in this model, existing routing algorithms are inefficient due to two shortcomings that we eliminate. First, when exploring candidate paths, existing algorithms only consider the costs of candidate paths from the source to intermediate vertices, while disregarding the costs of travel from the intermediate vertices to the destination, causing many noncompetitive paths to be explored. We propose two heuristics for estimating the cost from an intermediate vertex to the destination, thus improving routing efficiency. Second, the edge-centric model relies on stochastic dominance-based pruning to improve efficiency. This pruning assumes that costs are independent and is therefore inapplicable in the path-centric model that takes dependencies into account. We introduce a notion of virtual path that effectively enables stochastic dominance-based pruning in the path-based model, thus further improving efficiency. Empirical studies using two real-world trajectory sets offer insight into the properties of the proposed solution, indicating that it enables efficient stochastic routing in the path-centric model.

A Routing Model for the Distribution of Perishable Food in a Green Cold Chain

In this research, we develop an extension of the stochastic routing model with a fixed capacity for the distribution of perishable products with a time window. We use theoretical probability distributions to model the life of transported products and travel times in the network. Our main objective is to maximize the probability of delivering products within the established deadline with a certain level of customer service. Our project is justified from the perspective of reducing the pollution caused by greenhouse gases generated in the process. To optimize the proposed model, we use a Generic Random Search Algorithm. Finally, we apply the idea to a real problem of designing strategies for the optimal management of perishable food distribution routes that involve a time window, the objective being to maximize the probability of meeting the time limit assigned to the route problem by reducing, in this way, the pollution generated by refrigerated transport.

Comparative Evaluation of Road Pricing Schemes: A Simulation Approach (Australian Perspective)

Road network pricing and congestion charging continue to be debated as efficient instruments to address traffic congestion and emissions. For cities where the schemes have not been implemented yet, the impacts of these schemes are typically evaluated using transport simulation models to understand the impacts and design effective solutions before the schemes are deployed. This paper considers a simulation approach for the city of Melbourne in Australia to investigate the potential impacts of road network pricing on reducing private vehicle travel, road congestion, and vehicle emissions. The study uses a dynamic traffic simulation model developed for Melbourne using the AIMSUN modeling tool, which was extended for modeling road user pricing and congestion charging, including considerations and formulations of distance-based, delay-based, joint-distance-and-delay-based, and cordon-based schemes under low-cost, medium-cost, and high-cost regimes. The study’s contributions also include an extension of the modeling framework to include public transport options to allow for providing travelers with the option of choosing an alternative mode of transport if they do not wish to pay. A mesoscopic stochastic route choice modeling approach was adopted to examine the impact of road pricing inside a nominated charging zone within the network. The results showed it would be possible to achieve a reduction of 11% in vehicle count, a 20% reduction in travel time, a 13% reduction in emissions, and a 3% increase in travel speed within the proposed pricing zone under a high-cost pricing scenario. The results also showed a significant reduction in emissions resulting from shifting drivers who are not willing to pay the congestion charge to public transport. When 20% of car drivers shifted to public transport, carbon emissions were reduced by up to 30% and network performance improved by 45%, compared to the baseline scenario without pricing. The findings of this research provide important directions for policymakers in deciding on the type and scope of charging schemes to use and how these could reshape transportation taxation systems by moving away from taxes on vehicles through registration fees and towards user-pay taxations where travelers pay for the amount of travel they do or the pollution and emissions they are responsible for.

Stochastic Routing with Arrival Windows

Arriving at a destination within a specific time window is important in many transportation settings. For example, trucks may be penalized for early or late arrivals at compact terminals, and early and late arrivals at general practitioners, dentists, and so on, are also discouraged, in part due to COVID. We propose foundations for routing with arrival-window constraints. In a setting where the travel time of a road segment is modeled by a probability distribution, we define two problems where the aim is to find a route from a source to a destination that optimizes or yields a high probability of arriving within a time window while departing as late as possible. In this setting, a core challenge is to enable comparison between paths that may potentially be part of a result path with the goal of determining whether a path is uninteresting and can be disregarded given the existence of another path. We show that existing solutions cannot be applied in this problem setting and instead propose novel comparison methods. Additionally, we introduce the notion of Stochastic Arrival-Window Contraction Hierarchies that enable accelerated query processing in the article’s setting. Next, we present routing algorithms that exploit the above comparison methods in combination with so-called pivot paths and contraction hierarchies to enable efficient processing of the two types of queries. Finally, a detailed experimental study provides empirical insights that justify the need for the two types of routing and also offers insight into key characteristics of the problem solutions.

Modeling two-stage failure mechanism of cascading in cyber-physical power systems

Interdependency in cyber-physical power systems enables efficient monitor and control, but also brings out many threats, leading to catastrophic blackouts. To address this problem, the propagation mechanism of cascading failure in systems is analyzed. In this paper, we propose the partial random coupling systems model, and detail the interactive mechanism between physical power grid and communication network. Then, the modified failure mechanism is present, including two-stage redistribution types of traffic loads in physical power grid, and stochastic routing strategies in communication network. In simulation, the impact of attack scenes and topology structure on systems robustness is studied. Compared with random attack, high degree/betweenness attack results in first-order transition of cascading failure at a critical point, and causes more serious damage on systems. Besides, we have proved the positive correlation between clustering coefficient and robustness. To random attack, the systems consisted of double-star network behave more robust than systems consisted of mesh network, and also indicate the misproportion of increase between average dependent degree and systems robustness.

Branch-and-price for routing with probabilistic customers

We study the Vehicle Routing Problem with Probabilistic Customers (VRP-PC), a two-stage optimization model, which is a fundamental building block within the broad family of stochastic routing problems. This problem is mainly motivated by logistics distribution networks in which customers receive frequent delivery services, and by the last mile problem faced by companies such as UPS and FedEx. In a first stage before customer service requests realize, a dispatcher determines a set of vehicle routes serving all potential customer locations. In a second stage occurring after observing all customer requests, vehicles execute planned routes skipping all locations of customers not requiring service. The objective is to minimize the expected vehicle travel cost assuming known customer realization probabilities. We propose a column generation framework to solve the VRP-PC to a given optimality tolerance. Specifically, we present two novel algorithms, one that under-approximates a solution’s expected cost, and another that uses its exact expected cost. Each algorithm is equipped with a route pricing mechanism that iteratively improves the approximation precision of a route’s reduced cost; this produces fast route insertions at the start of the algorithm and reaches termination conditions at the end of the execution. Compared to branch-and-cut algorithms for arc-based formulations, our framework can more readily incorporate sequence-dependent constraints, which are typically required in routing problems. We provide a priori and a posteriori performance guarantees for these algorithms, and demonstrate their effectiveness via a computational study on instances with realization probabilities ranging from 0.5 to 0.9.

Learning Heuristics With Different Representations for Stochastic Routing.

Uncertainty is ubiquitous in real-world routing applications. The automated design of the routing policy by hyperheuristic methods is an effective technique to handle the uncertainty and to achieve online routing for dynamic or stochastic routing problems. Currently, the tree representation routing policy evolved by genetic programming is commonly adopted because of the remarkable flexibility. However, numeric representations have never been used. Considering the practicability of the numeric representations and the capability of the numeric optimization methods, in this article, we investigate two numeric representations on a representative stochastic routing problem and uncertain capacitated arc routing problem. Specifically, a linear representation and an artificial neural-network (ANN) representation are implemented and compared with the tree representation to reveal the potential of the numeric representations and the characteristics of their optimization. Experimental results show that the tree representation is the best choice, but on a majority of the test instances, the numeric representations, especially the ANN representation, can provide competitive performance. Further analyses also show that training a good ANN representation policy requires more training data than the tree representation. Finally, a guideline of representation selection is given.

The first AI4TSP competition: Learning to solve stochastic routing problems

This paper reports on the first international competition on AI for the traveling salesman problem (TSP) at the International Joint Conference on Artificial Intelligence 2021 (IJCAI-21). The TSP is one of the classical combinatorial optimization problems, with many variants inspired by real-world applications. This first competition asked the participants to develop algorithms to solve an orienteering problem with stochastic weights and time windows (OPSWTW). It focused on two learning approaches: surrogate-based optimization and deep reinforcement learning. In this paper, we describe the problem, the competition setup, and the winning methods, and give an overview of the results. The winning methods described in this work have advanced the state-of-the-art in using AI for stochastic routing problems. Overall, by organizing this competition we have introduced routing problems as an interesting problem setting for AI researchers. The simulator of the problem has been made open-source and can be used by other researchers as a benchmark for new learning-based methods. The instances and code for the competition are available at https://github.com/paulorocosta/ai-for-tsp-competition.

Double Q‐learning‐based adaptive trajectory selection for energy‐efficient data collection in wireless sensor networks

SummaryThis paper proposes a novel distributed stochastic routing strategy using mobile sink based on double Q‐learning algorithm to improve the network performance in wireless sensor network with uncertain communication links. Furthermore, in order to extend network lifetime, a modified leach‐based clustering technique is proposed. To balance the energy dissipation between nodes, the selected cluster head nodes are then rotated based on the newly suggested threshold energy value. The simulation results demonstrate that the proposed algorithms outperform the QWRP, QLMS, ESRP and HACDC in terms of network lifetime by 18.33%, 35.1%, 39.7% and 44.7%, respectively. Moreover, the proposed algorithms considerably enhances the learning rate and hence reduces the data collection latency.

Toward Robust Histology-Prior Embedding for Endomicroscopy Image Classification.

Representation learning is the critical task for medical image analysis in computer-aided diagnosis. However, it is challenging to learn discriminative features due to the limited size of the dataset and the lack of labels. In this paper, we propose a stochastic routing normalization and neighborhood embedding framework with application to breast tissue classification by learning discriminative features of probe-based confocal laser endomicroscopy. In order to align the low-level and mid-level of pCLE and histology domain, we firstly build the domain-specific normalization module with stochastic activation strategy considering both depth-wise and feature-wise criterion. For high-level features, the latent centers are learned from the histology domain as the template for feature matching. The proposed method is evaluated on a clinical database with 700 pCLE mosaics. The accuracy of image classification with limited training samples demonstrates that the proposed method can outperform previous works on domain alignment.

Potential assessment of an increased exchange of core information for remanufacturing in automotive reverse supply chains

An increasing awareness of sustainability and scarcity of resources requires to enhance a product’s lifetime. Within the context of a circular economy, remanufacturing therefore can be applied. Used products (so-called ‘cores’) are returned to at least their original performance. An efficient planning and management of reverse supply chains (RSC) is a prerequisite for successful remanufacturing. Besides the required material flow from the customer via service centers, collection stations, and core brokers to the remanufacturing plants, the reverse flow of core information is essential. The multi-tier exchange of core information potentially facilitates reducing existent uncertainties in RSC, i.e. regarding timing, quantity, and quality of returned products. Yet, current approaches neither consider the multi-tier information flow nor the differentiation of core information for different downstream tasks in detail. Specifically, information flow in the automotive RSC remains to be researched in detail. Therefore, the potential of an increased exchange of core information for remanufacturing in RSC is explored in this paper. A literature review and expert interviews with the stakeholders in the automotive RSC are conducted to assess the status quo of information exchange. Based on this, relevant core-specific information, and their impact on increasing the efficiency of different downstream planning processes are identified. To quantify the potential of an increased information exchange, both a model for the categorical use of information and a receptor model are developed. It can be concluded that an increase in the exchange of information in remanufacturing goes along with a multitude of facilitations, e.g. regarding logistics optimization, material requirement planning and stochastic routing of cores. Moreover, due to the prioritization of core information, a sequence model for core information retrieval can be derived.

Anonymous Stochastic Routing

We propose and analyze a recipient-anonymous stochastic routing model to study a fundamental trade-off between anonymity and routing delay. An agent wants to quickly reach a goal vertex in a network through a sequence of routing actions, whereas an overseeing adversary observes the agent’s entire trajectory and tries to identify the agent’s goal among those vertices traversed. We are interested in understanding the probability that the adversary can correctly identify the agent’s goal (anonymity) as a function of the time it takes the agent to reach it (delay). A key feature of our model is the presence of intrinsic uncertainty in the environment, so that each of the agent’s intended steps is subject to random perturbation and thus may not materialize as planned. Using large-network asymptotics, our main results provide near-optimal characterization of the anonymity–delay trade-off under a number of network topologies. Our main technical contributions are centered on a new class of “noise-harnessing” routing strategies that adaptively combine intrinsic uncertainty from the environment with additional artificial randomization to achieve provably efficient obfuscation.

Smart stochastic routing for 6G-enabled massive Internet of Things

Faster and energy-efficient data transmission is desired for massive Internet of Things (IoT) applications in sixth-generation networks. In such high speed networks, providing reliable data delivery with low delay, while maintaining energy-efficiency, is a challenging task. In this paper, a deep learning-based stochastic routing approach, called smart stochastic routing (SSR), is presented to address this challenge. SSR takes into account reliability, delays due to transmission, reception and processing of the neighbors’ information, and energy consumption and remaining energy of IoT devices. Through our proposed mathematical model, a dataset is generated to train a deep neural network, which predicts the best routing path from source to destination and achieves substantial accuracy over the mathematically generated dataset. Through simulations, we show the efficacy of SSR over conventional stochastic routing in terms of reduced energy consumption and expected delivery delay.

Comparing Dynamic User Equilibrium and Noniterative Stochastic Route Choice in a Simulation-Based Dynamic Traffic Assignment Model: Practical Considerations for Large-Scale Networks

Simulation-based dynamic traffic assignment (DTA) models play a vital role in transportation planning and operations. While the widely studied equilibrium-seeking DTA including dynamic user equilibrium (DUE) often provides robust and consistent outcomes, their expensive computational cost for large-scale network applications has been a burden in practice. The noniterative stochastic route choice (SRC) model, as a nonequilibrium seeking DTA model, provides an alternative for specific transportation operations applications that may not require equilibrium results after all (e.g., evacuation and major network disruptions) and thus tend to be computationally less expensive, yet may suffer from inconsistent outcomes. While DUE is a widely accepted approach for many strategic planning applications, SRC has been increasingly used in practice for traffic operations purposes. This paper aims to provide a comparative and quantitative analysis of the two modeling approaches. Specifically, a comparison has been made at two levels: link-level flows and network-level congestion patterns. Results suggest that adaptive driving improves the quality of the SRC solution, but its difference from DUE still remains significant at the link level. Results have practical implications for the application of large-scale simulation-based DTA models for planning and operations purposes.

Exploring Route Choice Behaviours Accommodating Stochastic Choice Set Generations

Modelling route choice behaviours are essential in traffic operation and transportation planning. Many studies have focused on route choice behaviour using the stochastic model, and they have tried to construct the heterogeneous route choice model with various types of data. This study aims to develop the route choice model incorporating travellers’ heterogeneity according to the stochastic route choice set. The model is evaluated from the empirical travel data based on a radio frequency identification device (RFID) called dedicated short-range communication (DSRC). The reliability level is defined to explore the travellers’ heterogeneity in the choice set generation model. The heterogeneous K-reliable shortest path- (HKαRSP-) based route choice model is established to incorporate travellers’ heterogeneity in route choice behaviour. The model parameters are estimated for the mixed path-size correction logit (MPSCL) model, considering the overlapping paths and the heterogeneous behaviour in the route choice model. The different behaviours concerning the chosen routes are analysed to interpret the route choice behaviour from revealed preference data by comparing the different coefficients’ magnitude. There are model validation processes to confirm the prediction accuracy according to travel distance. This study discusses the policy implication to introduce the traveller specified route travel guidance system.

A wireless weak-connected network routing algorithm inspired by Physarum polycephalum

Wireless weak-connected network (WWN) is a special self-organizing network, which can self-organize in an unstructured style and communicate with each other without infrastructure support. In this network, the link connection is weak and the topology is dynamic, which limits the performance of routing tasks. In order to address this issue, a novel Physarum-inspired routing algorithm (P-iRA) is proposed based on the intelligence and adaptability of Physarum polycephalum. Firstly, we construct a link capacity model for WWN via mapping the Physarum polycephalum network. Then, we design a next-hop selection strategy to obtain an optimal forwarding node in candidate set. Finally, we present a stochastic route strategy to achieve data transmission by virtue of finding the best routing path. Simulation results demonstrate that P-iRA improves approximately 47%, 34%, 56%, 20%, and 8% compared with Direct Delivery, Epidemic, First Contact, MaxProp, and Spray And Wait, respectively.

Coordinated operation of coupled transportation and power distribution systems considering stochastic routing behaviour of electric vehicles and prediction error of travel demand

The popularisation of electric vehicles (EVs) and the development of dynamic wireless charging technology have created an emerging trend of transportation electrification, which strengthens the coupling between electrified transportation network (ETN) and power distribution network (PDN). Meanwhile, the stochastic routing behaviour of EVs and prediction error of traffic demand pose a severe challenge to the coordinated ETN-PDN operation problem. This paper proposes a new hybrid optimisation method using stochastic user equilibrium (SUE)/information gap decision theory (IGDT) to study the impact of the unavoidable uncertainties on the coordinated ETN-PDN operation, which consists of the following two stages. In the first stage, a collaborative optimisation model based on SUE and Dist-Flow equations is established to deal with the stochastic EV routing behaviour. Built upon this model, the second stage continues to consider the traffic demand prediction error and establish a risk decision model using IGDT. The proposed model can provide proper road congestion tolls and local generator production schedules to lead to a minimum expected socio-economic cost. Also, two different coordinated operation strategies, that is, risk-seeker and risk-averse strategies, are provided to deal with the uncertainties. Case studies are carried out to demonstrate the effectiveness of the hybrid SUE/IGDT optimisation method.

Topology Optimization of Interactive Visual Communication Networks Based on the Non-Line-of-Sight Congestion Control Algorithm

In this paper, an in-depth study of interactive visual communication of network topology through non-line-of-sight congestion control algorithms is conducted to address the real-time routing problem of adapting to dynamic topologies, and a delay-constrained stochastic routing algorithm is proposed to enable packets to reach GB within the delay threshold in the absence of end-to-end delay information while improving network throughput and reducing network resource consumption. The algorithm requires each sending node to select an available relay set based on the location of its neighbor nodes and channel state and computes transfer probabilities for each node in the relay set combining the remaining delay of the packet with the distance from the relay node to GB. Based on the obtained transfer probability and local channel state, the sending node passes the packet to the relay node. The convergence of the algorithm is proved and its performance is verified by simulation. The first part of the algorithm is based on the greedy algorithm to deploy and locate the network flying platform nodes with the goal of efficient coverage of the network flying platform nodes, considering the ground base station services. As the delay on each link varies due to the change of channel state, the source and relay nodes asynchronously update the data generation rate and the pairwise parameters based on the received local information and use the obtained optimal values to pass the packets to GB.

Fuzzy Programming Approach to a Multi-Objective Fuzzy Stochastic Routing and Siting Hazardous Wastes

The aim of the research article is not only to propose a solution procedure to solve multi-objective fuzzy stochastic programming problem by using genetic-algorithm-based fuzzy programming method, but also to apply the computational techniques for transportation of the hazardous waste materials. In this article, routing and siting problems for nuclear hazardous waste material are studied and solved. The amount of waste materials generated in the nuclear reactors follows normal distribution. The two considered objective functions are about route selection which includes minimum travel time and minimum number of houses along the way, taking the safety measures into consideration. A multi-objective fuzzy stochastic mathematical model is formulated with the above mentioned objective functions and the route selection as the constraints. The proposed solution procedure is illustrated by a numerical example and a case study.

Designing Large-Scale Disaster Response Routes Network in Mitigating Earthquake Risk Using a Multi-Objective Stochastic Approach

The disaster response routes play a crucial role in transporting injured people and goods during the 72 golden hours after disaster. These routes connect the major disaster relief centers. Prior identification of the disaster response routes for a city enables the response teams to reach the disaster locations quickly and conduct relief and rescue operations without being obstructed by the outbound flow of evacuees from the city. These routes should not generally be used by the public unlike the evacuation routes. In this paper, a multi-objective stochastic disaster response routes design problem is presented. In this study, with the goal of reducing vulnerability, the disaster response routes network can be protected against disaster scenarios to maintain its connectivity using more independent routes. An exact approach including a bounded objective function method for considering the multi-objective functions, including the network factors (OD connectivity, vulnerability, and management) and an exact method (branch-and-cut) for solving the proposed model are suggested. The results for Sioux-Falls and Tehran networks show the effectiveness of the model.