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A vehicle routing problem arising in unmanned aerial monitoring

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Abstract

Unmanned aerial vehicles (UAVs) are widely used to perform monitoring tasks both in the military and civilian areas, and the planning of their routes is critical. This study investigates a routing problem in which UAVs monitor a set of areas with different accuracy requirements. This problem is a variant of the classical vehicle routing problem (VRP), where one must determine not only the order in which to visit a set of nodes located in the plane, but also the height at which to visit them, which impacts the accuracy level and the service time. An integer programming model is formulated to optimize flight routes and minimize the total time needed to complete the monitoring tasks. A tabu search metaheuristic is developed for the problem. Extensive numerical experiments are conducted to assess the efficiency of the heuristic.

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... With the increasing focus on environmental protection, electric vehicle distribution has also gradually become a mainstream research topic. Relevant research can be found in [49,72,81,89,116]. Single-objective models still occupy a certain research space, where the objective value setting is still largely based on cost metrics (e.g., cost, distance, and 2 emission). ...
... This trend is closely related to the concept of the "to C" distribution, where customers focus on service satisfaction. There have been various extensions of the VRP, including the VRPTW and time-dependent problems such as those discussed in [17,24,41,75,89]. Additional research has focused on heterogeneous vehicle problems that are closely related to real-life vehicle applications. ...
... With the increasing focus on environmental protection, electric vehicle distribution has also gradually become a mainstream research topic. Relevant research can be found in [49,72,81,89,116]. Single-objective models still occupy a certain research space, where the objective value setting is still largely based on cost metrics (e.g., cost, distance, and CO 2 emission). ...
Article
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Transportation planning has been established as a key topic in the literature and social production practices. An increasing number of researchers are studying vehicle routing problems (VRPs) and their variants considering real-life applications and scenarios. Furthermore, with the rapid growth in the processing speed and memory capacity of computers, various algorithms can be used to solve increasingly complex instances of VRPs. In this study, we analyzed recent literature published between 2019 and August of 2021 using a taxonomic framework. We reviewed recent research according to models and solutions, and divided models into three categories of customer-related, vehicle-related, and depot-related models. We classified solution algorithms into exact, heuristic, and meta-heuristic algorithms. The main contribution of our study is a classification table that is available online as Appendix. This classification table should enable future researchers to find relevant literature easily and provide readers with recent trends and solution methodologies in the field of VRPs and some well-known variants.
... a certain quality (e.g., low, medium, and high) using the drones. The drones can conduct these observations from points or arcs at any multiple altitudes [8], [9]. When the drones fly at a relatively low altitude, they can capture highquality photos but can only perform observations within a small range. ...
... An integer linear and mixed integer nonlinear optimization models were formulated, and some centralized and localized heuristics were presented. Zhen et al. [9] studied an observation problem using multiple drones at more than one altitude. Zhen et al. [9] performed observations for the square area. ...
... Zhen et al. [9] studied an observation problem using multiple drones at more than one altitude. Zhen et al. [9] performed observations for the square area. The proposed method might be unfit when a high-quality observation is required for a long target arc because the arc might be excluded in the defined area. ...
Article
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Our study introduces a drone routing problem in which drones fly to capture photos for surveillance purposes after a disaster. The drones perform observations on nodes and edges representing populated areas and road segments of a network from multiple altitudes. Each target node and edge requires observation at least once with a certain required quality. When the drones fly at a relatively high altitude, they can simultaneously capture low-quality photos and a large number of observed target nodes and edges. However, high-quality photos and narrow observation areas can be captured from a relatively low altitude. Each drone has a limited battery capacity and thus must return to the depot for battery replacement. This study routes the drones to satisfy the required photo quality of all target nodes and edges while minimizing the makespan of the surveillance by all drones. Our study is the first to examine a multiple-drone routing problem while considering flight altitude-dependent observation quality, battery replacement, node and edge combination, and minimizing the makespan. Our problem is formulated as a mixed-integer linear programming (MILP) model. Firefly and adaptive–reactive tabu search algorithms are proposed. The latter outperforms the former and obtains better solutions than those in the MILP model for small-sized instances within a given short computation time. Index terms: adaptive–reactive tabu search, altitude, battery replacement, drone routing, firefly algorithm, photo quality, surveillance
... Thus, authors developed an SA method. Zhen et al. [20] developed a kind of classical VRP which routes and determines flight height for UAVs. They concluded that as the flight height increases the monitoring area increases. ...
... Constraint (18) limit that each sortie (arrival -departure) time cannot be greater than maximum flight time. Constraints (19)(20) force that if there is no departure or arrival from/to any target in a sortie, "Departure Time" and "Arrival Time" must be zero at that sortie. Constraints (21-25) identify the decision variable types. ...
Article
The aim of this research is to detect the post-disaster damage by drones as soon as possible so that decision makers can assign search and rescue teams effectively and efficiently. The main differences of this research from the others, which use drones in literature, are as: First, the regions are divided into grids and different importance values are assigned according to the number of buildings that are likely to be damaged and are vital for the response stage, such as hospitals, schools, and fire stations. Second, these importance levels are updated based on the day and time, which helps ordering the grids in a more realistic manner. Third, the depots are selected among the predetermined candidate locations in accordance with the purpose of objective function. Fourth, detection times at grids are considered as uncertain. Fifth, two versions of Ant Colony Optimization (ACO) are developed as alternatives to exact solution tools. Last, sensitivity analyzes are performed by reducing the number of sorties, reducing the number of drones, and comparing day and night importance values for each instance. According to the results, only for very small-scale instances, exact solution tool was able to reach the optimal while both versions of ACO reached to similar results within a very less CPU times. Additionally, these ACO algorithms also found good results for the larger scaled problems. Then the performance of these ACO algorithms and the exact solution method are compared based on the CPU time and solution quality.
... The time spent by vehicles traveling in specific areas needs to be optimized because of their limitations in sensory range and delivery capability. Route planning is one of the most challenging issues in UAVs research [1,2,8]. In general, we can solve this problem through a traveling salesman problem (TSP), which is a special type of vehicle routing problem (VRP). ...
... (7) The required operating time of the unmanned vehicle must be smaller than the maximum operating time. (8) The unmanned vehicle will depart from the current customer to the next customer to avoid looping. (9) There is a penalty cost of the unmanned vehicle missing the time window. ...
Article
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In recent years, consumers have come to expect faster and better delivery services. Logistics companies, therefore, must implement innovative technologies or services in their logistics processes. It is critical to adopt unmanned aerial vehicles (UAV) in last mile delivery and urban logistics. The service provider applies the characteristics of UAVs to complete more requests, benefiting more revenue. However, it may not be a satisfactory solution, because the customers will be dissatisfied if the actual delivery time does not align with their expectations. This study constructs a revenue maximization model subject to time windows and customer satisfaction. Instead of addressing the traveling salesmen problem, this model takes new customer requests during the delivery process into account. We solved the problem using a genetic algorithm. The results show: (1) the model found an approximate and effective solution in the real-time delivery environment; (2) customer satisfaction is inversely proportional to the total delivery distance; (3) regarding the result of the sensitivity analysis of this study, investment in UAV has no influence on total profit and customer satisfaction. Moreover, the customer is a key factor in the logistics decision-making platform, not the provider’s investment in UAVs.
... In [30], Abeywickrama et al. recorded and analyzed the energy consumption of hovering, horizontal movement, and vertical movement by measuring the voltage and current of the UAV through experiments; however, the authors did not study the energy consumption in oblique flight. In [46], Zhen et al. did not specifically calculate the propulsion energy consumption of the UAV, but by taking the lift forces of the UAV in upward, downward, oblique upward, oblique downward, and level flight as the weights in the flight path planning. Through the force analysis, it can be seen that the energy consumption of the UAV in each direction is different due to the different lift forces. ...
... As shown in Figure 2, the energy consumption of a UAV flying from x i to z l can be subdivided based on the flying directions [30,46,48]. Let α (J/m), β (J/m), γ (J/m) correspond to the energy consumption of a level flight, vertical upward flight, vertical downward flight, respectively. ...
Article
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According to different mission scenarios, the UAV swarm needs to form specific topology shapes to achieve more robust system capability. The topology shaping, which will guide the UAVs autonomously to form the desired topology shape, is considered one of the most basic procedures in the UAV swarm field operations. The traditional optimization model of UAV swarm topology shaping proposed in most studies roughly represents the energy consumption by the squared Euclidean distances from initial positions to target positions of nodes. However, in practice, UAVs flying in different directions (vertical or horizontal) usually exhibits different energy consumption even though under the same moving distance. This paper proposes a more precise energy consumption model for UAV swarm topology shaping while taking the energy consumption for a UAV flying vertically upward, vertically downward, and horizontally into account. Simulation results show that the global energy consumption of the topology shaping modeled by the proposed energy consumption model is reduced by more than 38% on average compared with that using the traditional energy consumption model. Furthermore, to further reduce the global energy consumption, a translation vector is introduced in the optimization model to obtain the optimal topology shaping position of the UAV swarm system. Newton’s method is employed to derive the translation vector which exhibits good convergence. Simulation results show that the global energy consumption of optimal topology shaping position is reduced by 9.8% on average compared with that without translation.
... The vehicle routing network plays a key role in logistics costs. Recent research [13][14][15][16][17] underlined the fact that most convenient itineraries that a vehicle should follow in a transit line can be obtained from vehicle routing problem (VRP) approaches. ...
... Constraints (11)-(15) guarantee demand conservation. Constraint (16) ensures that variable z p is 1 when the demand of pair p goes through the public network and z p = 0 if it uses the private network. Constraint (17) guarantees that the trip demand of pair p can be routed through edge (i,j) only if such an edge belongs to the public system. ...
Article
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The achievement of some of the Sustainable Development Goals (SDGs) from the recent 2030 Agenda for Sustainable Development has drawn the attention of many countries towards urban transport networks. Mathematical modeling constitutes an analytical tool for the formal description of a transportation system whereby it facilitates the introduction of variables and the definition of objectives to be optimized. One of the stages of the methodology followed in the design of urban transit systems starts with the determination of corridors to optimize the population covered by the system whilst taking into account the mobility patterns of potential users and the time saved when the public network is used instead of private means of transport. Since the capture of users occurs at stations, it seems reasonable to consider an extensive and homogeneous set of candidate sites evaluated according to the parameters considered (such as pedestrian population captured and destination preferences) and to select subsets of stations so that alignments can take place. The application of optimization procedures that decide the sequence of nodes composing the alignment can produce zigzagging corridors, which are less appropriate for the design of a single line. The main aim of this work is to include a new criterion to avoid the zigzag effect when the alignment is about to be determined. For this purpose, a curvature concept for polygonal lines is introduced, and its performance is analyzed when criteria of maximizing coverage and minimizing curvature are combined in the same design algorithm. The results show the application of the mathematical model presented for a real case in the city of Seville in Spain.
... UAV fleet mission planning problems are by their nature an extension of the well-known Vehicle Routing Problem (VRP). However, these problems have the added complexity of combining routing and scheduling, three-dimensional operations, and nonlinear fuel consumption [3,4,7]. The classical VRP is well-studied and the methods and approaches found within this domain are still very much applicable for the advancement of new technology in the area of UAV operations. ...
... However, mission planning for UAV fleets must consider a number of constraints and operating conditions rarely seen in the traditional VRP and operating conditions and limitations not found in other transportation means [3]. Some central examples of this are the constraints on UAV range that depend on weather conditions, airspace regulations and restrictions, as well as congestion in terms of collision avoidance and safety distance, and the UAV characteristics such as airspeed, maximum payload, energy capacity, physical dimensions, etc. [3,4,7,8]. In UAV mission planning, it is necessary to address weather conditions [9,10] and changes to these weather conditions can potentially strongly influence the solution strategy for the UAV mission planning, especially wind direction and speed as they directly impact energy consumption and flight characteristics [3,11]. ...
Article
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Fleet mission planning for Unmanned Aerial Vehicles (UAVs) is the process of creating flight plans for a specific set of objectives and typically over a time period. Due to the increasing focus on the usage of large UAVs, a key challenge is to conduct mission planning addressing changing weather conditions, collision avoidance, and energy constraints specific to these types of UAVs. This paper presents a declarative approach for solving the complex mission planning resistant to weather uncertainty. The approach has been tested on several examples, analyzing how customer satisfaction is influenced by different values of the mission parameters, such as the fleet size, travel distance, wind direction, and wind speed. Computational experiments show the results that allow assessing alternative strategies of UAV mission planning.
... In a planning context, Coutinho et al. [25] proposed a complex variant of the VRP that involves the use of dronesnamely, a routing problem that considers the flight dynamics of UAVs known as the UAV routing and trajectory optimization problem (UAVRTOP). To make UAV routing applicable in a three-dimensional (3-D) space, another complex variant of VRP is discussed in [26], in which the authors state that area coverage planning and UAV routing are the major optimization problems in the field of UAV monitoring. ...
... The literature has extensively addressed the use of MILP to model variants of the VRP. Examples that involve UAVs are described in [9], [11], [12], [17], [19], [22]- [24], and [26] and examples whose main devices are ground vehicles are reported in [32]- [34]. However, although the VRP literature has been extensively surveyed, to the best of our knowledge, no MILP models address the VRPSN. ...
Article
Recent technological breakthroughs have allowed unmanned aerial vehicles (UAVs) to be utilized in a broad range of new operations. Among these various applications, herein, we focus on the use of UAVs for search and rescue missions in emergency and postdisaster scenarios. In this context, self-charging technologies for drones create new challenges in the routing of UAVs with charging stations. We present a variant of the vehicle routing problem (VRP) to address the integrated use of UAVs and mobile charging stations and define the VRP with synchronized networks (VRPSN), a new class of VRPs involving the routing of UAVs whose recharge platforms can travel to different locations during an operation. This leads to two networks within the VRP that must be integrated and synchronized. This research develops a mixed-integer linear program model for the VRPSN that considers the use of UAVs and mobile charging stations in a synchronized manner. To overcome the computational limits of the MILP model, this research presents a construct-and-adjust heuristic method integrated with a genetic algorithm. As a numerical example, we test the proposed model on the Córrego do Feijão Mine located in Minas Gerais, Brazil, where a dam recently collapsed, killing many workers. Numerical tests show that the new methodology is an attractive planning method for providing efficient and rapid responses in search and rescue missions.
... are fixed, the UAVs have pre-defined trajectories obtained by solving the vehicle routing problem [16]. For persistent operation, the issue of docking station placement is considered in [17]. ...
... Furthermore, it follows from (15), (16) and (17) that q(t, P 1 (t + 1), . . . , P n (t + 1)) − q(t, P 1 (t), . . . ...
Article
This paper focuses on navigating a team of unmanned aerial vehicles (UAVs) equipped with cameras to monitor groups of ground pedestrians or vehicles that move along given paths with unkown, time-varying but bounded speeds. The objective is to deliver a high-quality surveillance of the pedestrians or vehicles. We formulate a surveillance problem which requires the UAVs to monitor the pedestrians or vehicles from as short as possible distances. We propose a navigation algorithm that enables each UAV to determine its movement locally with a minor participation of a central station. We prove that this algorithm is locally optimal. Simulations confirm its performance.
... Vehicles or subjects tracking, traffic management or fire detection are only some of the possible applications. Surveillance activities can occur in indoors environments (Raja and Pang, 2016;Chakrabarty et al., 2016), in large outdoor environments such as air traffic monitoring (Kim and Sivits, 2015), maritime monitoring (Jeon et al., 2019;Suteris et al., 2018), ground-traffic monitoring (Roudet et al., 2016;Sutheerakul et al., 2017;Barmpounakis and Geroliminis, 2020) or, in general, for target tracking (Zorbas et al., 2013;Zorbas et al., 2016;Di Puglia Pugliese et al., 2016;Zhen et al., 2019). ...
Article
The interest in using drones in various applications has grown significantly in recent years. The reasons are related to the continuous advances in technology, especially the advent of fast microprocessors, which support intelligent autonomous control of several systems. Photography, construction, and monitoring and surveillance are only some of the areas in which the use of drones is becoming common. Among these, last-mile delivery is one of the most promising areas. In this work we focus on routing problems with drones, mostly in the context of parcel delivery. We survey and classify the existing works and we provide perspectives for future research.
... The authors of [19] present a persistent intelligence, surveillance, and reconnaissance routing problem, which includes collecting data from a set of specified task locations and delivering those data to a control station. Zhen et al. [20] consider a vehicle routing problem in which UAVs monitor a set of areas with different accuracy requirements. The problem of how to deploy multiple UAVs most efficiently was considered in the work of [21], in an application where UAVs act as wireless base stations that provide coverage for ground users. ...
Article
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In recent years, the use of modern technology in military operations has become standard practice. Unmanned systems play an important role in operations such as reconnaissance and surveillance. This article examines a model for planning aerial reconnaissance using a fleet of mutually cooperating unmanned aerial vehicles to increase the effectiveness of the task. The model deploys a number of waypoints such that, when every waypoint is visited by any vehicle in the fleet, the area of interest is fully explored. The deployment of waypoints must meet the conditions arising from the technical parameters of the sensory systems used and tactical requirements of the task at hand. This paper proposes an improvement of the model by optimizing the number and position of waypoints deployed in the area of interest, the effect of which is to improve the trajectories of individual unmanned systems, and thus increase the efficiency of the operation. To achieve this optimization, a modified simulated annealing algorithm is proposed. The improvement of the model is verified by several experiments. Two sets of benchmark problems were designed: (a) benchmark problems for verifying the proposed algorithm for optimizing waypoints, and (b) benchmark problems based on typical reconnaissance scenarios in the real environment to prove the increased effectiveness of the reconnaissance operation. Moreover, an experiment in the SteelBeast simulation system was also conducted.
... The routing phase is considered as a fundamental issue in logistics costs. The analysis of the most convenient itineraries that a vehicle should fulfill, following a defined network (Ghannadpour and Zarrabi, 2019), can be reached by using Vehicle Routing Problem (VRP) approaches, which are broadly adopted in various research applications (Suman and Bolia, 2019;Salonen, 2019;Hymel 2019;Reihaneh and Ghoniem, 2019;Zhen and Laporte, 2019;Musolino et al., 2019). ...
Article
The paper focuses on the fuel transport optimization network for the Total Erg Oil Company to the distribution points sited in a zone near Rome, in Italy. The numerical method is based on a capacitated vehicle itinerary issue for time intervals, considering various heuristic procedures. The fixed and time-dependent travel times are considered. Compared to the standard operational costs, a multivariable objective function is developed that considers: (1) the risk associated with an incidental event involving a fuel tank; (2) that not all the roads are suitable for heavy vehicles transporting fuel products. These two additional terms permit to better quantify the costs for the operator, since it is assumed that roads with higher number of accidents or with not suitable infrastructure conditions have also higher probability of making the fuel tank experiences at least a delay during the day. Results show that a proper vehicle routes design on our multivariable objective function allows economizing about 40 km daily respect to a benchmark. The fuel company can also consider the itinerary design, modifying the weights used with the aim to comprise the additional variables with respect to the standard operational costs, thus assuring a higher safety route planning.
... Because of enormous and rapid developments in all branches of information, remote sensing, aviation and other related technologies, unmanned aerial vehicles (UAVs) are being extensively employed in various governmental, scientific or commercial applications (e.g., environmental monitoring, disaster management, border security, intelligence, and etc.). UAVs can capture target images and these images can be transmitted to the ground control station in real time via wireless data transmission systems (Zhen et al., 2019). ...
Conference Paper
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Forests have crucial importance for the sustainability of Earth and humanity and one of the biggest threats to the existence of forests are the fires. This paper proposes a conceptual model for mitigating forest fire risk by use of self-adaptive and autonomous unmanned aerial vehicles (UAVs). Memoryless property of exponential distribution is also reflected and considered in the calculations of forest fire probabilities. Stochastic and dynamic properties of the situation and the mathematical complexity of the routing problem entailed and justified a simulation study. The effectiveness of the proposed dispatching approach for routing UAVs and the validity of the proposed model are tested on a small sized realistic scenario. Experimental results encourage the development of complex models. Integrating the proposed model with advanced information technologies may lead to the development of a digital twin system.
... The reconnaissance task for short-range tactical UAVs is hardly present in the literature, although the route planning algorithms, based on VRPTW models, are described in many papers [6][7][8][9][10][11][12][13]. However, the basic issues for these algorithms are ignored, such as the method of constructing the connection network, which takes into account the sensor capabilities, the arrangement of targets to be identified, and threats to UAVs in the terrain. ...
Article
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The paper presents the concept of mission planning for a short-range tactical class Unmanned Aerial Vehicle (UAV) that recognizes targets using the sensors it has been equipped with. Tasks carried out by such systems are mainly associated with aerial reconnaissance employing Electro Optical (EO)/Near Infra-Red (NIR) heads, Synthetic Aperture Radar (SAR), and Electronic Intelligence (ELINT) systems. UAVs of this class are most often used in NATO armies to support artillery actions, etc. The key task, carried out during their activities, is to plan a reconnaissance mission in which the flight route will be determined that optimally uses the sensors’ capabilities. The paper describes the scenario of determining the mission plan and, in particular, the UAV flight routes to which the recognition targets are assigned. The problem was decomposed into several subproblems: assigning reconnaissance tasks to UAVs with choosing the reconnaissance sensors and designating an initial UAV flight plan. The last step is planning a detailed flight route taking into account the time constraints imposed on recognition and the characteristics of the reconnaissance sensors. The final step is to generate the real UAV flight trajectory based on its technical parameters. The algorithm for determining exact flight routes for the indicated reconnaissance purposes was also discussed, taking into account the presence of enemy troops and available air corridors. The task scheduling algorithm—Vehicle Route Planning with Time Window (VRPTW)—using time windows is formulated in the form of the Mixed Integer Linear Problem (MILP). The MILP formulation was used to solve the UAV flight route planning task. The algorithm can be used both when planning individual UAV missions and UAV groups cooperating together. The approach presented is a practical way of establishing mission plans implemented in real unmanned systems.
... Chen et al. (2017) designed an improved GA and a PS optimization based AC optimization algorithm to solve the TSP for UAV path planning. Finally, Zhen et al. (2019) developed a TS metaheuristic to solve a variant of the VRP. ...
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During recent years, advances in drone technologies have made them applicable in various fields of industry, and their popularity continues to grow. In this paper, the academic contributions on drones routing problems are analyzed between 2005 and 2019 to identify the main characteristics of these types of problems, as well as the research trends and recent improvements. The literature is classified according to the objectives optimized, solution methods, applications, constraints, and whether they use a complementary vehicle or not. Finally, a discussion for trends and future research is presented.
... UAV routing and trajectory optimization is a popular area of research. Zhen, Li, Laporte, and Wang (2019) takes the accuracy requirement over the area of interest into consideration in route planning. The height of the vehicle impacts the accuracy level of surveillance. ...
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In Aerial Surveillance Problem (ASP), an air platform with surveillance sensors searches a number of rectangular areas by covering the rectangles in strips and turns back to base where it starts. In this paper, we present a multiobjective extension to ASP, for which the aim is to help aerial mission planner to reach his/her most preferred solution among the set of efficient alternatives. We consider two conflicting objectives that are minimizing distance travelled and maximizing minimum probability of target detection. Each objective can be used to solve single objective ASPs. However, from mission planner’s perspective, there is a need for simultaneously optimizing both objectives. To enable mission planner reaching his/her most desirable solution under conflicting objectives, we propose exact and heuristic methods for multiobjective ASP (MASP). We also develop an interactive procedure to help mission planner choose the most satisfying solution among all Pareto optimal solutions. Computational results show that the proposed methods enable mission planner to capture the trade-offs between the conflicting objectives for large number of alternative solutions and to eliminate the undesirable solutions in small number of iterations.
... The routing phase is considered as a fundamental issue in logistics costs. The analysis of the most convenient itineraries that a vehicle should fulfill, following a defined network (Ghannadpour and Zarrabi, 2019), can be reached by using Vehicle Routing Problem (VRP) approaches, which are broadly adopted in various research applications (Hoff et al. 2010, Reihaneh and Ghoniem, 2019, Zhen et al. 2019Li et al. 2018;Breuning et al. 2019;Bruglieri et al., 2019). The literature on VRP applied to fuel distribution is rich of contributions. ...
Conference Paper
Full-text available
The paper analyses a practical case of study related to the distribution of fuels for the Total Erg Oil Company to the service stations located in the Province of Rome (Italy). The problem is formulated as a capacitated vehicle routing problem with time windows, where several heuristic procedures have been tested, considering both fixed and time-dependent travel times. With respect to the standard operational costs, a multivariable objective function is proposed which takes into account: 1) the risk associated with an incidental event involving a fuel tank; 2) that not all the roads are suitable for heavy vehicles transporting fuel products. These two additional terms permit to better quantify the costs for the operator, since it is assumed that roads with higher number of accidents or with specific infrastructure conditions have also higher probability of making the fuel tank experiences at least a delay during the day. Results demonstrate how an accurate planning of the service based on our multivariable objective function saves up to 40 km on a daily basis compared to a benchmark. Moreover, the distribution company can parameterize the configuration of the service, by varying the weights adopted in order to include the additional parameters with respect to the standard operational costs, thus assuring a higher safety route planning.
... Generally, an expected result of effectual snow plow operations would be a quicker traffic flow recovery and an appropriate algorithm would prompt snow plowing to operate more quickly. Based on such considerations, two typical algorithms, the sophisticated mathematical programming decomposition algorithms [3] and the heuristics algorithms [8], were then put forward for the solution of CARP and also other routing problems [9,10]. Among them, the exact algorithms usually apply shortest path relaxations and combine them through finding a minimum-cost subset of edges. ...
Article
Vehicle drivers usually perceive a higher risk when driving on snow covered roads. The city cleaning efficiency would directly influence the risk and mitigation of wintertime events, especially for snow covered roads. Under the risk-informed approach background, more attention is paid to the capacitated arc routing problem (CARP) of urban snow plowing operations. Current algorithms mainly relies on the topology of road network without considering snow covered pavement's negative effect on road capacity and traffic flow. This paper proposes a vulnerability-based parallel heuristic algorithms applied for the CARP by implementing risk-informed approach. First, a method is proposed to set service priorities based on the vulnerability evaluation by considering the added cost of travel demands. Second, a sub-process path-scanning approach is developed to avoid redundant path scans. Then verification and comparison between this newly proposed constructive heuristic and existing algorithms of whole-process path-scanning and sequential processing are conducted. Results show that the sub-process path-scanning approach obviously costs less service completion time than the existing algorithms for solving the CARP. However, this improved algorithm would also cause an increase of deadhead time upon dispatch. The balance between service completion time and deadhead time for more routing problems would be discussed in the near future.
... However, in this setting, it is hard to consider physical obstacles between customers because the UAV altitude cannot be manipulated. In Reference [7], Zhen et al. defined optimal routes and heights of UAVs in a three-dimensional space using vertical indices from a single depot. They can avoid obstacles by determining vertical indices, but they do not consider obstacles between two vertices. ...
Article
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A delivery service using unmanned aerial vehicles (UAVs) has potential as a future business opportunity, due to its speed, safety and low-environmental impact. To operate a UAV delivery network, a management system is required to optimize UAV delivery routes. Therefore, we create a routing algorithm to find optimal round-trip routes for UAVs, which deliver goods from depots to customers. Optimal routes per UAV are determined by minimizing delivery distances considering the maximum range and loading capacity of the UAV. In order to accomplish this, we propose an algorithm with four steps. First, we build a virtual network to describe the realistic environment that UAVs would encounter during operation. Second, we determine the optimal number of in-service UAVs per depot. Third, we eliminate subtours, which are infeasible routes, using flow variables part of the constraints. Fourth, we allocate UAVs to customers minimizing delivery distances from depots to customers. In this process, we allow multiple UAVs to deliver goods to one customer at the same time. Finally, we verify that our algorithm can determine the number of UAVs in service per depot, round-trip routes for UAVs, and allocate UAVs to customers to deliver at the minimum cost.
... This problem has effectively served as the basis for many VRP variants since, each of which considers a unique set of additional constraints. These additional constraints accommodate, for example, heterogeneous fleets (e.g., Golden et al. (1984), Gendreau et al. (1999b), Markov et al. (2016)), routes whose customers require both pickups and deliveries (e.g., Savelsbergh and Sol (1995), Berbeglia et al. (2007)), time-dependent travel times (e.g., Jabali et al. (2012)), customers whose demand can only be serviced by a particular vehicle or on a particular day (e.g., Nag et al. (1988), Vidal et al. (2012)), customers with time-windows (e.g., Savelsbergh (1985), Hiermann et al. (2016)), customers with mobile delivery locations (e.g., Reyes et al. (2017)), delivery via unmanned aerial vehicles (drones; e.g., Zhen et al. (2019)), and many other features that ultimately make the addressed problem more closely mirror actual business cases. These variants have been nicely summarized in reviews such as Laporte (2009), and in books such as Toth and Vigo (2014). ...
Thesis
This thesis details three problems and two software tools related to dynamic decision making under uncertainty in vehicle routing and logistics, with an emphasis on the challenges encountered when adopting electric vehicles. We first introduce the electric vehicle routing problem with public-private recharging strategy in which vehicles may recharge en-route at public charging infrastructure as well as at a privately-owned depot. To hedge against uncertain demand at public charging stations, we design routing policies that anticipate station queue dynamics. We leverage a decomposition to identify good routing policies, including the optimal static policy and fixed-route-based rollout policies that dynamically respond to observed queues. The decomposition also enables us to establish dual bounds, providing a measure of goodness for our routing policies. In computational experiments using real instances from industry, we show the value of our policies to be within five percent of the value of an optimal policy in the majority of instances and within eleven percent on average. Further, we demonstrate that our policies significantly outperform the industry-standard routing strategy in which vehicle recharging generally occurs at a central depot. Our proposed methods for this problem stand to reduce the operating costs associated with electric vehicles, facilitating the transition from internal-combustion engine vehicles. We then consider the problem of an operator controlling a fleet of electric vehicles for use in a ridehailing service. The operator, seeking to maximize revenue, must assign vehicles to requests as they arise and recharge and reposition vehicles in anticipation of future requests. To solve this problem, we employ deep reinforcement learning, developing policies whose decision making uses Q-value approximations learned by deep neural networks. We compare these policies against a common taxi dispatching heuristic and against dual bounds on the value of an optimal policy, including the value of an optimal policy with perfect information which we establish using a Benders-based decomposition. We assess performance on instances derived from real data for the island of Manhattan in New York City. We find that, across instances of varying size, our best policy trained with deep reinforcement learning outperforms the taxi dispatching heuristic. We also provide evidence that this policy may be effectively scaled and deployed on larger instances without retraining. We then present a new general approach to modeling research problems as Atari-like videogames to make them amenable to recent solution methods from the deep reinforcement learning community. The approach is flexible, applicable to a wide range of problems. Here, we demonstrate its application on the well-studied vehicle routing problem with stochastic service requests. Our preliminary results on this problem, though not transformative, show signs of success and suggest that Atari-fication may be a useful modeling approach for researchers studying problems involving sequential decision making under uncertainty. We then introduce frvcpy, the first of our two proposed software tools. In the routing of electric vehicles, one of the most challenging tasks is determining how to make good charging decisions for an electric vehicle traveling a given route. This is known as the fixed route vehicle charging problem. An exact and efficient algorithm for this task exists, but its implementation is sufficiently complex to deter researchers from adopting it. Our proposed tool, frvcpy, is an open-source Python package implementing this algorithm. Our aim with the package is to make it easier for researchers to solve electric vehicle routing problems, facilitating the development of optimization tools that may ultimately enable the mass adoption of electric vehicles. Finally, we introduce the second software tool, Mapper. Mapper is a simple web-based visualizer of problem instances and solutions for vehicle routing problems. It is designed to accompany the suite of tools already available to users of the vehicle routing community's website, The Vehicle Routing Problem Repository (VRP-REP).
Conference Paper
پهپادها پتانسیل بالایی برای مدیریت بحران دارند، چراکه میتوانند لحظه به لحظه بر منطقه بحران زده نظارت کنند که با جمع آوری سریع اطلاعات، به برنامه ریزی و استقرار کارامد عملیات ها ی امدادی بشردوستانه کمك مي کند. به همین دلیل، مطالعات مربوط به آ ن ها در سال های ا خیر به یک موضوع محبوب مبد ل شده است. تاکنون مطالعات کمی در کاربرد نظارتی پهپادها در شرایط اضطراری متمرکز شده اند، که یک خلا تحقیقاتی جدی است. برای پوشش این خلا، در این مطالعه به این موضوع پرداخته مي شود که علاوه بر برنامه ریزی برای پوشش منطقه با مسیریابی پهپاد، مصرف انرژی و ارتفاع آن ها را نیز در نظر می گیرد. همچنین، الزامات درجه دقت نظارت از یک منطقه به منطقه دیگر متفاوت است و زمان مورد نیاز بر ای نظارت به ارتفاع پهپاد بستگی دارد. با توجه به حداکثر زمان پرواز محدود و وجود چندین منطقه نظارت با درجه های مختلف دقت مورد نیاز، مسیریابی آنها بسیار مهم است. بنابراین یک مدل برنامه ریز ی خطی - عدد صحیح برای این مسئله ارائه می شود که بر خلاف مسئله مسیریابی کلاسیک که فقط ترتیب بازدید مجموعه ای از گر ه ها را تعیین می کند، ارتفاع بازدید از هر گره توسط یک پهپاد نیز مشخص می شود. به علاوه، به علت اینكه میزان محدودیت باتری بر زمان پرواز پهپا د تأثیر می گذارد، مصرف انرژ ی هر پهپاد را در نظر خواهد گرفت تا به واقعیت نزدیكتر باشد. هدف از این مدل به حداقل رساندن کل زمان و برآورد ه کردن الویت گره ها برای نظارت است، که در نرم افزار گمز کدنویسي شده و عملكرد ان با يك مثال عددي مورد تحليل قرار گرفته است
Chapter
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Chapter
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We study a time-constrained heterogeneous vehicle routing problem on a multigraph where parallel arcs between pairs of vertices represent different travel options based on criteria such as time, cost, and distance. We formulate the problem as a mixed-integer linear programming model and develop a tabu search heuristic that efficiently addresses computational challenges due to parallel arcs. Numerical experiments show that the heuristic is highly effective and that freight operators can achieve advantages in cost and customer service by considering alternative paths, especially when route duration limits are restrictive and/or when vehicles of smaller capacity are dispatched to serve remote customers.
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This paper addresses the mobile targets covering problem by using unmanned aerial vehicles (UAVs). It is assumed that each UAV has a limited initial energy and the energy consumption is related to the UAV’s altitude. Indeed, the higher the altitude, the larger the monitored area and the higher the energy consumption. When an UAV runs out of battery, it is replaced by a new one. The aim is to locate UAVs in order to cover the piece of plane in which the target moves by using a minimum number of UAVs. Each target has to be monitored for each instant time. The problem under consideration is mathematically represented by defining mixed integer non-linear optimization models. Heuristic procedures are defined and they are based on restricted mixed integer programming (MIP) formulation of the problem. A computational study is carried out to assess the behaviour of the proposed models and MIP-based heuristics. A comparison in terms of efficiency and effectiveness among models and heuristics is carried out.
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Once limited to the military domain, unmanned aerial vehicles are now poised to gain widespread adoption in the commercial sector. One such application is to deploy these aircraft, also known as drones, for last-mile delivery in logistics operations. While significant research efforts are underway to improve the technology required to enable delivery by drone, less attention has been focused on the operational challenges associated with leveraging this technology. This paper provides two mathematical programming models aimed at optimal routing and scheduling of unmanned aircraft, and delivery trucks, in this new paradigm of parcel delivery. In particular, a unique variant of the classical vehicle routing problem is introduced, motivated by a scenario in which an unmanned aerial vehicle works in collaboration with a traditional delivery truck to distribute parcels. We present mixed integer linear programming formulations for two delivery-by-drone problems, along with two simple, yet effective, heuristic solution approaches to solve problems of practical size. Solutions to these problems will facilitate the adoption of unmanned aircraft for last-mile delivery. Such a delivery system is expected to provide faster receipt of customer orders at less cost to the distributor and with reduced environmental impacts. A numerical analysis demonstrates the effectiveness of the heuristics and investigates the tradeoffs between using drones with faster flight speeds versus longer endurance.
Conference Paper
In this paper, the problem of planning paths for a collection of vehicles passing through a set of targets is considered. Each vehicle starts at a specified location (called a depot) and it is required that each target be on the path of at least one vehicle. Every vehicle has a motion constraint and the path of each vehicle must satisfy that constraint. In this article, we developed a method to compute lower bounds to this path planning problem by relaxing some of the constraints and posing it as a standard multiple traveling salesmen problem. For those problem instances where the distance between every pair of targets is at least 4 units, another method is developed to compute a lower bound using the convexity property of the length of such paths. The proposed bounds are numerically corroborated.
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The duration of missions that can be accomplished by a system of unmanned aerial vehicles (UAVs) is limited by the battery or fuel capacity of its constituent UAVs. However, a system of UAVs that is supported by automated refueling stations may support long term or even indefinite duration missions. We develop a mixed integer linear program (MILP) model to formalize the problem of scheduling a system of UAVs and multiple shared bases in disparate geographic locations. There are mission trajectories that must be followed by at least one UAV. A UAV may hand off the mission to another in order to return to base for fuel. To address the computational complexity of the MILP formulation, we develop a genetic algorithm to find feasible solutions when a state-of-the-art solver such as CPLEX cannot. In practice, the approach allows for a long-term mission to receive uninterrupted UAV service by successively handing off the task to replacement UAVs served by geographically distributed shared bases.
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We apply column generation with branch-and-price optimization to a multi-target, multi-task assignment problem, with precedence constraints. Column generation transforms the nonlinear program with separable costs and constraints into a linear program. This reformulation divides the original problem into a number of smaller problems, where one of these smaller problems accounts for the coupling constraints between agents and must be known by every agent. All other divisions consider local constraints affecting only one agent; these smaller problems are known by only one corresponding agent. Because of this reformulation, the assignment problem can be solved in a distributed manner. A theorem is proven which details the central analytical result of the paper, allowing a nonlinear program to be reformulated as a linear program. Simulation results for a multi-target, single-task assignment problem, as well as a multi-target, multi-task assignment problem with precedence constraints are presented. Published 2011. This article is a US Government work and is in the public domain in the USA.
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Crossdocking studies have mostly been concerned with the physical layout of a crossdock or on a single crossdock. In this work, we study a network of crossdocks taking into consideration delivery and pickup time windows, warehouse capacities and inventory-handling costs. Because of the complexity of the problem, local search techniques are developed and used with simulated annealing and tabu search heuristics. Extensive experiments were conducted and results show that the heuristics outperform CPLEX, providing solutions in realistic timescales.
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In this paper, a system that allows applying precision agriculture techniques is described. The application is based on the deployment of a team of unmanned aerial vehicles that are able to take georeferenced pictures in order to create a full map by applying mosaicking procedures for postprocessing. The main contribution of this work is practical experimentation with an integrated tool. Contributions in different fields are also reported. Among them is a new one-phase automatic task partitioning manager, which is based on negotiation among the aerial vehicles, considering their state and capabilities. Once the individual tasks are assigned, an optimal path planning algorithm is in charge of determining the best path for each vehicle to follow. Also, a robust flight control based on the use of a control law that improves the maneuverability of the quadrotors has been designed. A set of field tests was performed in order to analyze all the capabilities of the system, from task negotiations to final performance. These experiments also allowed testing control robustness under different weather conditions. © 2011 Wiley Periodicals, Inc.
Article
It has been observed by many people that a striking number of quite diverse mathematical problems can be formulated as problems in integer programming, that is, linear programming problems in which some or all of the variables are required to assume integral values. This fact is rendered quite interesting by recent research on such problems, notably by R. E. Gomory [2, 3], which gives promise of yielding efficient computational techniques for their solution. The present paper provides yet another example of the versatility of integer programming as a mathematical modeling device by representing a generalization of the well-known “Travelling Salesman Problem” in integer programming terms. The authors have developed several such models, of which the one presented here is the most efficient in terms of generality, number of variables, and number of constraints. This model is due to the second author [4] and was presented briefly at the Symposium on Combinatorial Problems held at Princeton University, April 1960, sponsored by SIAM and IBM. The problem treated is: (1) A salesman is required to visit each of n cities, indexed by 1, … , n . He leaves from a “base city” indexed by 0, visits each of the n other cities exactly once, and returns to city 0. During his travels he must return to 0 exactly t times, including his final return (here t may be allowed to vary), and he must visit no more than p cities in one tour. (By a tour we mean a succession of visits to cities without stopping at city 0.) It is required to find such an itinerary which minimizes the total distance traveled by the salesman. Note that if t is fixed, then for the problem to have a solution we must have tp ≧ n . For t = 1, p ≧ n , we have the standard traveling salesman problem. Let d ij ( i ≠ j = 0, 1, … , n ) be the distance covered in traveling from city i to city j . The following integer programming problem will be shown to be equivalent to (1): (2) Minimize the linear form ∑ 0≦ i ≠ j ≦ n ∑ d ij x ij over the set determined by the relations ∑ n i =0 i ≠ j x ij = 1 ( j = 1, … , n ) ∑ n j =0 j ≠ i x ij = 1 ( i = 1, … , n ) u i - u j + px ij ≦ p - 1 (1 ≦ i ≠ j ≦ n ) where the x ij are non-negative integers and the u i ( i = 1, …, n ) are arbitrary real numbers. (We shall see that it is permissible to restrict the u i to be non-negative integers as well.) If t is fixed it is necessary to add the additional relation: ∑ n u =1 x i 0 = t Note that the constraints require that x ij = 0 or 1, so that a natural correspondence between these two problems exists if the x ij are interpreted as follows: The salesman proceeds from city i to city j if and only if x ij = 1. Under this correspondence the form to be minimized in (2) is the total distance to be traveled by the salesman in (1), so the burden of proof is to show that the two feasible sets correspond; i.e., a feasible solution to (2) has x ij which do define a legitimate itinerary in (1), and, conversely a legitimate itinerary in (1) defines x ij , which, together with appropriate u i , satisfy the constraints of (2). Consider a feasible solution to (2). The number of returns to city 0 is given by ∑ n i =1 x i 0 . The constraints of the form ∑ x ij = 1, all x ij non-negative integers, represent the conditions that each city (other than zero) is visited exactly once. The u i play a role similar to node potentials in a network and the inequalities involving them serve to eliminate tours that do not begin and end at city 0 and tours that visit more than p cities. Consider any x r 0 r 1 = 1 ( r 1 ≠ 0). There exists a unique r 2 such that x r 1 r 2 = 1. Unless r 2 = 0, there is a unique r 3 with x r 2 r 3 = 1. We proceed in this fashion until some r j = 0. This must happen since the alternative is that at some point we reach an r k = r j , j + 1 < k . Since none of the r 's are zero we have u r i - u r i + 1 + px r i r i + 1 ≦ p - 1 or u r i - u r i + 1 ≦ - 1. Summing from i = j to k - 1, we have u r j - u r k = 0 ≦ j + 1 - k , which is a contradiction. Thus all tours include city 0. It remains to observe that no tours is of length greater than p . Suppose such a tour exists, x 0 r 1 , x r 1 r 2 , … , x r p r p +1 = 1 with all r i ≠ 0. Then, as before, u r 1 - u r p +1 ≦ - p or u r p +1 - u r 1 ≧ p . But we have u r p +1 - u r 1 + px r p +1 r 1 ≦ p - 1 or u r p +1 - u r 1 ≦ p (1 - x r p +1 r 1 ) - 1 ≦ p - 1, which is a contradiction. Conversely, if the x ij correspond to a legitimate itinerary, it is clear that the u i can be adjusted so that u i = j if city i is the j th city visited in the tour which includes city i , for we then have u i - u j = - 1 if x ij = 1, and always u i - u j ≦ p - 1. The above integer program involves n ² + n constraints (if t is not fixed) in n ² + 2 n variables. Since the inequality form of constraint is fundamental for integer programming calculations, one may eliminate 2 n variables, say the x i 0 and x 0 j , by means of the equation constraints and produce an equivalent problem with n ² + n inequalities and n ² variables. The currently known integer programming procedures are sufficiently regular in their behavior to cast doubt on the heuristic value of machine experiments with our model. However, it seems appropriate to report the results of the five machine experiments we have conducted so far. The solution procedure used was the all-integer algorithm of R. E. Gomory [3] without the ranking procedure he describes. The first three experiments were simple model verification tests on a four-city standard traveling salesman problem with distance matrix [ 20 23 4 30 7 27 25 5 25 3 21 26 ] The first experiment was with a model, now obsolete, using roughly twice as many constraints and variables as the current model (for this problem, 28 constraints in 21 variables). The machine was halted after 4000 pivot steps had failed to produce a solution. The second experiment used the earlier model with the x i 0 and x 0 j eliminated, resulting in a 28-constraint, 15-variable problem. Here the machine produced the optimal solution in 41 pivot steps. The third experiment used the current formulation with the x i 0 and x 0 j eliminated, yielding 13 constraints and 9 variables. The optimal solution was reached in 7 pivot steps. The fourth and fifth experiments were used on a standard ten-city problem, due to Barachet, solved by Dantzig, Johnson and Fulkerson [1]. The current formulation was used, yielding 91 constraints in 81 variables. The fifth problem differed from the fourth only in that the ordering of the rows was altered to attempt to introduce more favorable pivot choices. In each case the machine was stopped after over 250 pivot steps had failed to produce the solution. In each case the last 100 pivot steps had failed to change the value of the objective function. It seems hopeful that more efficient integer programming procedures now under development will yield a satisfactory algorithmic solution to the traveling salesman problem, when applied to this model. In any case, the model serves to illustrate how problems of this sort may be succinctly formulated in integer programming terms.