Detour Distance Research Articles

Unmanned Aerial Vehicle Obstacle Avoidance Based Custom Elliptic Domain

The velocity obstacles (VO) method is widely employed in real-time obstacle avoidance research for UAVs due to its succinct mathematical foundation and rapid, dynamic planning abilities. Traditionally, VO assumes a circle protection domain with a fixed radius, leading to issues such as excessive conservatism of obstacle avoidance areas, longer detour paths, and unnecessary avoidance angles. To overcome these challenges, this paper firstly reviews the fundamentals and pre-existing defects of the VO methodology. Next, we explore a scenario involving UAVs in head-on conflicts and introduce an elliptic velocity obstacle method tailored to the UAV’s current flight state. This method connects the protection domain size directly to the UAV’s flight state, transitioning from the conventional circle domain to a more efficient elliptic domain. Additionally, to manage the computational demands of Minkowski sums and velocity obstacle cones, an approximation algorithm for discretizing elliptic boundary points is introduced. A strategy to mitigate unilateral velocity oscillation had is developed. Comparative validation simulations in MATLAB R2022a confirm that, based on the experimental results for the first 10 s, the apex angle of the velocity obstacle cone for the elliptical domain is, on average, reduced by 0.1733 radians compared to the circular domain per unit simulation time interval, saving an airspace area of 13,292 square meters and reducing the detour distance by 14.92 m throughout the obstacle avoidance process, facilitating navigation in crowded situations and improving airspace utilization.

Rolling optimal scheduling for urban parcel crowdsourced delivery with new order insertion

The rapid development of mobile information technology has introduced numerous new solutions for delivery companies to enhance profits. One such solution employed by some companies is crowdsourced delivery. In this paper, we focus on rolling optimal scheduling for urban parcel crowdsourced delivery by utilizing private cars that will be in passing with the incorporation of new order insertion. The bonus incentive strategy is introduced to enhance the delivery probability of private car drivers. A static model and a rolling optimization model to maximize profits and the number of parcels delivered by private cars are established. To address the NP-hard problem, a hybrid genetic algorithm and insertion algorithm are designed. Numerical experiments are carried out to verify the proposed method in different scenarios, including the scattered network, clustered network, Dalian network, and Foursquare network. The computational results demonstrate that the method enhances the matching ratio and increases profits. Utilizing private cars that will be in passing for urban parcel delivery reduces the need for dedicated vehicles, mitigating traffic growth and alleviating traffic congestion. Increasing the private car-parcel ratio improves profits and the matching ratio while reducing traffic growth. Raising the incentive coefficient for bonuses increases the matching ratio and detour distance, but profits first increase and then decrease, and delivery distance by dedicated vehicles decreases. Our research findings offer a more rational basis for green urban parcel delivery decision-making by companies.

Multi-Objective Planning of Commuter Carpooling under Time-Varying Road Network

Aiming at the problem of urban traffic congestion in morning and evening rush hours, taking commuter carpool path planning as the research object, the spatial correlation of traffic flow at adjacent intersections is mined using convolutional neural networks (CNN), and the temporal features of traffic flow are mined using long short-term memory (LSTM) model. The extracted temporal and spatial features are fused to achieve short-term prediction. Considering the travel willingness of drivers and passengers, a multi-objective optimization model with minimum driver and passenger loss time and total travel time is established under the constraints of vehicle capacity, time windows and detour distances. An Improved Non-dominated Sorted Genetic Algorithm-II (INSGA-II) is proposed to solve it. The open-loop saving algorithm is used to generate an initial population with better quality, and the 2-opt local search strategy is adopted in the mutation operation to improve search efficiency. The influence of vehicle speed on the matching scheme is analyzed. The research results show that under the same demand conditions, the total travel distance of the carpool scheme is reduced by about 56.19% and total travel time is reduced by about 65.52% compared with the non-carpool scheme. Research on carpool matching under time-varying road networks will help with urban commuting efficiency and environmental quality, and play a positive role in alleviating traffic congestion and promoting carpool services.

Modeling package delivery acceptance in Crowdshipping systems by Public Transportation Passengers: A latent class approach

The subject of this research is to model the probability of accepting package delivery tasks in Crowd-Shipping (CS) systems focusing on shipping packages by Public Transportation (PT) passengers. Real-world implementation of such a PT-based CS initiative requires a proper grasp of the behavior of crowd shippers, package receivers, and senders, among which crowdshippers are at the center of attention. Given survey data collected from 2,208PT passengers in the Sydney metropolitan area, this study constructs a model for package delivery task acceptance among PT passengers who express a willingness to participate as crowdshippers. A Latent Class (LC) choice model is developed and estimated to explore different classes of participant characteristics and preferences for accepting CS delivery tasks, under different levels of offered incentive, package weight, and required detour distance at the destination. As a key finding, the model identifies three classes, namely “leisurely”, “avid”, and “skeptical” users with class sizes of 19%, 53%, and 28%, respectively. Leisurely users tend to be majorly employed with relatively higher ages and lower PT trip frequency per month. This class shows a potential desire to take CS tasks as long as they are not logistically burdensome. Avid users, forming the largest class of the population, are mostly younger PT passengers who are less sensitive to task difficulty and might accept even CS tasks with minimum incentives (around AU$3). Skeptical users, displaying high PT trip frequency per month and high income, are unwilling to accept the CS tasks unless get compensated well.

An enhanced node segmentation and distance estimation scheme with a reduced search space boundary and improved PSO for obstacle-aware wireless sensor network localization

This paper proposes an enhanced method for localizing sensor nodes in wireless sensor networks with obstacles. Such environment settings lead to lower localization accuracy because locations are estimated based on detour distances circumventing the obstacles; we, therefore, improve the segmentation technique to address the issue as they divide the whole area into multiple smaller ones, each containing fewer or no obstacles. Nevertheless, when radio transmissions between sensor nodes are obstructed (as simulated by the radio irregularity model), the signal-strength variation tends to be high, reducing localization accuracy; thus, we provide a method for accurately approximating the distances between pairs of an anchor node (whose location is known) and an unknown node by incorporating the related error into the approximation process. Additionally, when the nodes with unknown locations are outside the polygon formed by the anchor nodes, the search area for localization is relatively large, resulting in lower accuracy and a longer search time; we then propose a method for reducing the size of approximation areas by forming boundaries based on the two intersection points between the ranges of two anchor nodes used to localize an unknown node. However, these reduced search areas could still be large; we further increase the accuracy of the PSO location estimation method by adaptively adjusting the number of particles. In addition, with PSO, the accuracy of unknown node location estimation depends on having a properly selected fitness function; therefore, we incorporate appropriate variables to reflect the distance approximation accuracy between each anchor-unknown node pair. In experiments, we measure performance in sensor node deployment areas of three different shapes: C-shaped, with 1 hole, and with 2 rectangular holes. The results show that our method provides higher localization accuracy than others in small-, medium-, and large-scaled WSNs. Specifically, our proposed method is 27.46%, 49.28%, 50.33%, and 74.62% more accurate on average than IDE-NSL, PSO–C, min-max PSO, and niching PSO, respectively.

Square Distance in Graphs

In this paper, we consider a simple connected graph having no loops and multiple edges. The order and size of are denoted by and respectively in graphs is a wide branch of graph theory having many scientific and real-life applications. There are various types of distances studied in the literature.The distance is the length of the shortest path between the vertices and in [2]. The detour distance is the length of the longest path between the vertices and in [3]. The concept of centrality widely applied in social network analysis. Degree centrality is the simplest centrality measure to compute centre. Betweenness centrality measures used for analyzed cancer network.

Detour Polynomial of Theta Graph

Let be any connected graph with vertices set and edges set . For any two distinct vertices and , the detour distance between and which is denoted by is a longest path between and in a graph . The detour polynomial of a connected graph is denoted by ; and is defined by . In this paper, the detour polynomial of the theta graph and the uniform theta graph will be computed.

Detour distance Laplacian matrices for signed networks

A signed network [Formula: see text] with the underlying graph [Formula: see text], used as a mathematical model for analyzing social networks, has each edge in [Formula: see text] with a weight [Formula: see text] or [Formula: see text] assigned by the signature function [Formula: see text]. In this paper, we deal with two types of Detour Distance Laplacian (DDL) matrices for signed networks. We characterize balance in signed social networks using these matrices and we compute the DDL spectrum of certain unbalanced signed networks, as balanced signed networks behave like unsigned ones.

NCG-TSM: A Noncooperative Game for the Taxi Sharing Model in Urban Road Networks

Taxi sharing is a promising method to save resource consumption and alleviate traffic congestion while satisfying people’s commuting needs. Existing research methods include taxi dispatching methods based on intelligent algorithms, single vehicle route recommendation algorithms, and route recommendation algorithms based on vehicle traffic history. However, these studies either focus on how to efficiently dispatch satisfactory vehicles for passengers, ignoring the effect of efficient routes on vehicle travel efficiency, or let vehicles follow the shortest detour distance recommended by the system, ignoring the traffic congestion caused by the influx of vehicles into the same road. To address the abovementioned problems, a noncooperative game for a taxi sharing model (NCG-TSM) in urban road networks is proposed in this paper combined with the traffic conditions of the optional routes, and a distribution estimation algorithm for the shared taxi game is designed to make multivehicle route selections reach Nash equilibrium. The effectiveness of NCG-TSM is verified through simulation experiments. When the number of vehicles reaches the congestion capacity of the road segment, compared to the three common frameworks, the travel time cost and fuel consumption cost can be reduced by 5.8% to 9.1% and 3.5% to 8.9%, respectively. Besides, the occupancy rate has been improved, especially compared to the BMP framework, by 5.5% to 40%.

Operational Impacts of On-Demand Ride-Pooling Service Options in Birmingham, AL

Transportation Network Companies (TNCs) use online-enabled apps to provide on-demand transportation services. TNCs facilitate travelers to connect with drivers that can offer them rides for compensation using driver-owned vehicles. The ride requests can be for (a) individual or (b) shared rides. The latter, also known as ride-pooling services, accommodates requests of unrelated parties with origins and destinations along the same route who agree to share the same vehicle, usually at a discounted fare. Uber and Lyft offer ride-pooling services in select markets. Compared to individual ride requests, ride-pooling services hold better promise toward easing urban congestion by reducing the number of automobiles on the road. However, their impact on traffic operations is still not fully understood. Using Birmingham, AL as a case study, this research evaluated the impact that ride-pooling services have on traffic operations using a Multi-Agent Transport Simulation (MATSim) model of the Birmingham metro area. Scenarios were developed to simulate baseline conditions (no TNC service) and ride-pooling availability with two types of ride-pooling services, namely door-to-door (d2d) and stop-based (sB) service and three fleet sizes (200, 400, and 800 vehicles). The results indicate that when TNC vehicles are added to the network, the Vehicle Kilometers Traveled (VKT) decrease by up to 5.78% for the door-to-door (d2d) service, and up to 2.71% for stop-based (sB) services, as compared to the baseline scenario (no TNC service). The findings also suggest that an increase in the size of the ride-pooling fleet results in a rise in total ride-pooling service VKT, network-wide total VKT, and detour distance. However, increasing the size of the ride-pooling fleet also results in a decrease in the ride request rejection rates, thus benefiting the customers and decreasing the vehicle empty ratio which, in turn, benefits the TNC drivers. The results further suggest that a fleet of 200 ride-pooling vehicles can meet the current demand for service in the Birmingham region at all times, thus it is the optimal ride-pooling TNC fleet size for a medium-sized city such as Birmingham.

On the utilization of dedicated bus lanes for pooled ride-hailing services

Ride-sourcing platforms, among other solution services, offer convenience and flexibility when it comes to pick-up/drop-off time and location. Similarly, ride-splitting renders itself as an extension of ride-sourcing where platform users agree to share their rides in return for a reduced fare yet possibly a longer travel time. Despite the numerous advantages that sharing introduced to the platform operator by reducing the fleet size necessary to serve demand levels, e-hailing is still overall negatively impacting traffic performance in urban spaces. This is partially due to the current tendency of users to favor solo over shared rides. This paper aims to use aggregate traffic flow models to put forward a network space redistribution policy that has the potential to reduce total delays of the different mode users in the network. Accordingly, we investigate the solo-pool demand split that minimizes the total Passenger Hours Traveled for all network commuters in the event where shared rides are allowed to use underutilized bus lanes. As a result, the choice to share is associated with an inevitable additional detour distance but with a lower-than-expected trip time compared to standard scenarios where the whole fleet utilizes the same network space. In this paper, we present an analytical macroscopic modeling approach to evaluate equilibrium solutions between network supply and multi-modal demand. By resorting to a numerical example of the model, we show that the optimal strategy that minimizes delays for multi-modal transport users occurs when only a fraction of the pooling vehicles uses the dedicated bus lanes. This fraction is dependent on the distribution of space and the value of demand for private vehicles, buses, and ride-hailing services.

Solutions of Detour Distance Graph Equations.

Graph theory is a useful mathematical structure used to model pairwise relations between sensor nodes in wireless sensor networks. Graph equations are nothing but equations in which the unknown factors are graphs. Many problems and results in graph theory can be formulated in terms of graph equations. In this paper, we solved some graph equations of detour two-distance graphs, detour three-distance graphs, detour antipodal graphs involving with the line graphs.

Weak edge triangle free detour number of a graph

For any two vertices u and v in a connected graph G = ( V , E ), a u − v path P is called a u − v triangle free path if no three vertices of P induce a triangle. The triangle free detour distance D △ f ( u , v ) is the length of a longest u − v triangle free path in G . A u − v path of length D △ f ( u , v ) is called a u − v triangle free detour . A set S ⊆ V is called a weak edge triangle free detour set of G if every edge of G has both ends in S or it lies on a triangle free detour joining a pair of vertices of S . The weak edge triangle free detour number w d n △ f ( G ) of G is the minimum order of its weak edge triangle free detour sets and any weak edge triangle free detour set of order w d n △ f ( G ) is a weak edge triangle free detour basis of G . Certain properties of these concepts are studied. The weak edge triangle free detour numbers of certain classes of graphs are determined. Its relationship with the triangle free detour diameter is discussed and it is proved that for any three positive integers a , b and n of integers with 3 ≤ b ≤ n − a + 1 and a ≥ 4, there exists a connected graph G of order n with triangle free detour diameter D △ f = a and w d n △ f ( G )= b . It is also proved that for any three positive integers a , b and c with 3 ≤ a ≤ b and c ≥ b + 2, there exists a connected graph G such that R △ f = a , D △ f = b and w d n △ f ( G )= c .

Travel time optimization on multi-AGV routing by reverse annealing

Quantum annealing has been actively researched since D-Wave Systems produced the first commercial machine in 2011. Controlling a large fleet of automated guided vehicles is one of the real-world applications utilizing quantum annealing. In this study, we propose a formulation to control the traveling routes to minimize the travel time. We validate our formulation through simulation in a virtual plant and authenticate the effectiveness for faster distribution compared to a greedy algorithm that does not consider the overall detour distance. Furthermore, we utilize reverse annealing to maximize the advantage of the D-Wave’s quantum annealer. Starting from relatively good solutions obtained by a fast greedy algorithm, reverse annealing searches for better solutions around them. Our reverse annealing method improves the performance compared to standard quantum annealing alone and performs up to 10 times faster than a commercial classical solver, Gurobi. This study extends a use of optimization with general problem solvers in the application of multi-AGV systems and reveals the potential of reverse annealing as an optimizer.

The Two Echelon Open Vehicle Routing Problem: Optimization of Crowdshipping Based Parcel Delivery

Crowdshipping is a revolutionary concept of the sharing economy. In this study, two carriers are used to perform the following expedition: the truck starts from the depot to complete part of the deliveries, shares part of the load with the crowdshipper at the relay point, and the private driver selected as the crowdshipper continues from that point onward. This study proposes the two-echelon open vehicle routing problem with crowdshipping (2EOVRP-CS) and formulates a mathematical model to determine the crowdshipper, parcel relay location, truck route, and crowdsource route. A tangible nested genetic algorithm (NGA) is proposed, and its efficiency is demonstrated by comparison with CPLEX and genetic algorithm (GA). A real case study is investigated in Xi'an city to test the applicability of the proposed model. The results show that using crowdshipping instead of truck delivery alone can save approximately 14% of the total cost and 26% of truck vehicle miles traveled (VMT). Moreover, several sensitivity analyses are performed. The results show that crowdshipping is sensitive to the detour limit and the time value of carriers. For the detour limit, after the acceptable detour distance increases by 8%, the total cost can be reduced by up to 5.94%.

Mining Urban Sustainability: Vehicle Emission Changes on Traffic Corridor by One-Way Traffic Conversion

A one-way traffic strategy is widely used in densely populated urban areas to improve traffic efficiency, but its environmental impacts remain largely unclear. This study investigated the effects of a one-way traffic strategy on vehicle emissions along a busy traffic corridor in Xi’an, China. This was done by integrating the traffic flow model calibrated by onsite traffic data and the emission model. The detour distance estimation method was proposed so that the emission trade-offs between increased vehicle miles traveled (VMTs) and improved traffic efficiency on one-way traffic corridors could be uncovered. Empirical results showed that one-way traffic cut down the total CO2 emissions by 11.8%, and reduced the CO, hydrocarbon (HC), and NOx emissions by 4.7%–25.0%. However, such emission reduction capacity gradually weakened and even completely dissipated with the increase of traffic demand on the corridor. When the road volume-to-capacity ratio (V/C > 0.87), one-way traffic was no longer a greener traffic organization. With the promotion of mitigation policies and technologies, one-way traffic is expected to further reduce CO2 emissions by 4.7%–10.9% and CO, HC, and NOx emissions by 8.4%–41.1%. In addition, there was a total of 456 vehicles detours with an overall detour distance of 316.8 km, which resulted in a doubling of the emissions of detour vehicles. Although the implementation of one-way traffic brings environmental benefits, the detour problem should also be taken seriously. This study provides convincing evidence for understanding the emission changes on traffic corridors caused by one-way traffic conversion to support the promotion of eco-friendly traffic organization for realizing the goal of carbon peaking.

What if Air Quality Dictates Road Pricing? Simulation of an Air Pollution-based Road Charging Scheme

Road tolls serve various purposes, such as to refinance the road infrastructure or to regulate traffic. They are typically levied for the use of a freeway or the entire road network of a region or country. Toll charges may depend on the duration of use, the vehicle's emission class, the time of the day, the distance travelled, or the traffic volume. The primary objective of a few recent toll system deployments is to internalize externalities with respect to vehicle-caused air pollution. However, the air quality along the toll roads has so far not been considered to directly influence road usage prices. This article investigated by simulation the expected monetary expenditure for drivers and the traffic impact of applying a new distance and air pollution-based charging scheme in the metropolitan region of Berlin. The road usage charges were determined on a per-trip basis by taking the vehicle's emission class, the distance travelled, and the air pollution levels along the route into consideration. The simulation results indicate that it is beneficial for drivers to avoid areas of high air pollution in order to reduce the trip's total road usage charges. The average additional detour distance is thereby short in comparison to the route's length and the resulting additional emissions do not increase to the same extent as the number of detours, since detours are partly even shorter in terms of distance. The explorative analysis gives initial insights into the traffic effects of a charging scheme in which air pollution dictates road pricing.

Time-optimal and privacy preserving route planning for carpool policy

To alleviate the traffic congestion caused by the sharp increase in the number of private cars and save commuting costs, taxi carpooling service has become the choice of many people. Current research on taxi carpooling services has focused on shortening the detour distances. While with the development of intelligent cities, efficiently match passengers and vehicles and planning routes become urgent. And the privacy between passengers in the taxi carpooling service also needs to be considered. In this paper, we propose a time-optimal and privacy-preserving carpool route planning system via deep reinforcement learning. This system uses the traffic information around the carpooling vehicle to optimize passengers’ travel time, not only to efficiently match passengers and vehicles but also to generate detailed route planning for carpooling vehicles. We conducted experiments on an Internet of Vehicles simulator CARLA, and the results demonstrate that our method is better than other advanced methods and has better performance in complex environments.

Detour polynomials of some cog-special graphs

The detour distance is the length of a longest path between two distinct vertices u and υ in a connected graph G and denoted by D(u, υ), the detour distance is an important type of distances types in graph theory because of its importance in chemical applications and other sciences. We find detour polynomial, detour index and study some properties for some cog-special graphs in this paper.

Social balance - a signed detour distance analysis

ABSTRACT In this paper, by defining two types of signed detour distances and corresponding detour distance matrices, we introduce the notion of detour distance compatibility for signed graphs and later applying these concepts, we give yet another characterization of balance in signed graphs. Further, we discuss signed detour spectra of certain classes of unbalanced signed graphs.