CN113139678A - Unmanned aerial vehicle-vehicle combined distribution path optimization method and model construction method thereof - Google Patents
Unmanned aerial vehicle-vehicle combined distribution path optimization method and model construction method thereof Download PDFInfo
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Abstract
The invention discloses a method for constructing an optimization model of an unmanned aerial vehicle-vehicle combined delivery path, which comprises the following steps: marking all special points, planning the path of the unmanned aerial vehicle and the vehicle which are delivered once, and optimizing the whole path by taking the minimum total delivery distance as a target. The problem is solved using genetic algorithms and single delivery end optimization, and the joint delivery herein is compared with traditional vehicle delivery, and independent delivery of drones and vehicles, with the results showing: unmanned aerial vehicle and vehicle can cooperate each other, accomplish the delivery of all customer demand points, and unmanned aerial vehicle-vehicle joint delivery can effectively reduce total delivery distance. Finally, sensitivity analysis is carried out on the maximum load capacity, the maximum flight distance, the relative speed of the unmanned aerial vehicle and the impedance coefficient of the unmanned aerial vehicle, the condition limit of the unmanned aerial vehicle is widened, more customer points can be distributed by the unmanned aerial vehicle at a time, and the distribution task can be efficiently completed by combining the unmanned aerial vehicle with the vehicle.
Description
Technical Field
The invention relates to the technical field of unmanned aerial vehicle application technology, in particular to an unmanned aerial vehicle-vehicle combined delivery path optimization method and a model construction method thereof.
Background
Wisdom traffic is constantly developing, and the high-efficient logistics theory that is faster, more provincial is that enterprise and customer pursue. The last kilometer is taken as the last link of logistics distribution and is also the only link directly in face-to-face contact with customers, so that the problem of distribution of the last kilometer is always a key point and a difficult point of research. With the vigorous development of electronic commerce in recent years, rural areas show strong potential, but compared with urban areas, logistics distribution in rural areas is often blocked by mountains and waters due to the reasons of complex terrain environment, poor traffic conditions and the like, and how to efficiently finish the distribution in the last kilometer in rural areas is a difficult problem to be solved urgently, and the rise of civil unmanned aerial vehicles provides a solution for the problem.
Unmanned Aerial vehicle (uav) is an aircraft that is operated by a radio remote control device and a self-contained program control device, and generally has the functions of autonomous flight and independent completion of a certain task. Initially, unmanned aerial vehicles were primarily used for cooperative combat in the military field[1]. In recent years, civil unmanned aerial vehicles are rapidly developed, and by means of the advantages of convenience in operation, flexibility in use, high operation efficiency, low relative cost and the like, the application range is expanded to multiple fields of logistics distribution, geographic detection, monitoring and cruise, emergency rescue, medicine transportation and the like. However, the cargo distribution is limited due to the fact that the load capacity is small and the cargo distribution cannot support long-distance flight, the traditional distribution vehicle has the advantages of being large in load capacity and capable of being transported in a long distance, and the combined distribution of the load capacity and the long-distance flight is widely concerned by domestic and foreign scholars.
Wohlsen et al first proposed the use of trucks and drones for coordinated delivery of goods, where drones could accomplish delivery to customers independently of each other, but the drones would need to return to the truck to take off a package after each delivery is complete. From this idea, Agatz et al refer to this path Problem as the drone traveler Problem TSP-D (tracking Salesman profile with drone), and with the goal of minimizing delivery costs, the Problem is solved by constructing a mixed integer model of TSP-D, based on local search and dynamic programming, using a two-stage heuristic algorithm of routing first and then clustering. Bouman et al improved the dynamic programming algorithm of the traditional TSP problem and combined with the algorithm to optimize, making it suitable for solving the large scale TSP-D problem. Ha et al propose a greedy random adaptive search algorithm with clustering followed by routing aiming at TSP-D problems of single trucks and single drones and with the goal of minimizing the total delivery cost and the penalty cost of waiting for drones by trucks.
Mario etc. utilizes unmanned aerial vehicle to wrap up the delivery for furthest, proposes the truck and not only can receive and dispatch unmanned aerial vehicle at fixed node, can carry out unmanned aerial vehicle's transmission and recovery along the delivery route moreover. In addition, Murray et al propose two models, fstsp (flying sidekit tracking sampling reporting scheme) and PDSTSP (parallel road scheduling tracking sampling reporting), for cooperative delivery of unmanned aerial vehicles and trucks, aiming at minimizing service time. Yurek et al designs a two-stage iterative algorithm for solving the FSTSP, and compares the two-stage iterative algorithm with the solution time of CPLEX, and the result shows that the algorithm can reduce the solution time of the mesoscale example. The FSTSP is expanded to the problem of joint distribution of multiple trucks and unmanned planes, a heuristic algorithm capable of solving the large-scale problem is designed, and the heuristic algorithm is compared with the distribution result of a single truck. Ham expands PDSTSP to allow for unmanned simultaneous pick-up or delivery at warehouse or customer sites and verifies with the co-delivery problem of multi-truck, multi-drone and multi-warehouse at 100 customer sites.
Wang et al, considering the vehicle Routing Problem VRP-d (vehicle Routing with drone) of an unmanned aerial vehicle under the limit of cruising ability, propose that an unmanned aerial vehicle can transmit and receive from a truck in a warehouse or any customer location and derive the influence of the speed ratio of the truck and the unmanned aerial vehicle for coordinated delivery of multiple trucks and unmanned aerial vehicles. Dorling considers the relationship between the flight distance and the load of the unmanned aerial vehicle, verifies that the energy consumption and the load of the unmanned aerial vehicle are in a linear relationship, and solves the model by applying a simulated annealing algorithm to obtain the condition that the energy consumption and the delivery time cannot be optimal simultaneously. Carlsson et al demonstrated that delivery efficiency increases in proportion to the truck-to-drone speed ratio by using euclidean and road physical distances. Campbell et al use successive approximation for modeling and compare with pure truck delivery to arrive at a benefit that depends on relative operating costs and marginal costs in the case of single truck with multiple drones. Chowdhury and the like determine the optimal position of a distribution center by using a continuous approximation method aiming at emergency material allocation of disaster areas, and carry out sensitivity analysis on parameters of the unmanned aerial vehicle. Othman et al demonstrate that this type of path problem is an NP-hard problem and propose a polynomial time approximation algorithm that yields the bounds of the approximation ratio. Ferrandez and the like compare two modes of serial distribution and independent distribution, aim at minimizing energy consumption and distribution time, firstly determine the launching point of the unmanned aerial vehicle by adopting K-means clustering, and then determine the distribution routes of the truck and the unmanned aerial vehicle by using a genetic algorithm. Chang, etc. combines the path problem with K-means clustering, designs a moving weight model based on a clustering center, and compares the moving weight model with the condition of no moving weight or no clustering, thereby proving the effectiveness of the design model. Sacramento et al propose a self-adaptive large neighborhood search meta-heuristic algorithm and perform sensitivity analysis on relevant parameters of the unmanned aerial vehicle. Scherme et al introduces an effective inequality set VIEQ based on mixed integer linear programming to find the optimal allocation and scheduling of the unmanned aerial vehicle, and the result shows that the proposed model can effectively solve the VRP-D problem.
In general, existing research mostly assumes that vehicles send and receive drones at fixed points, and that drones can only deliver one package at a time. Savuran et al propose a new variant movdrp (mobile Depot vrp) which assumes that the vehicle is moving along a straight line, that there are a large number of customer points distributed on both sides of the route, that the unmanned aerial vehicle delivers as many customer points as possible after departure, and that the designed model is solved based on genetic algorithms. These assumptions are far from practical, especially for roads in rural areas.
Disclosure of Invention
In order to solve the technical problems, the invention provides an unmanned aerial vehicle-vehicle combined distribution path optimization method and a model construction method thereof, based on a single unmanned aerial vehicle and single vehicle scene, the terrain influence of rural areas is considered, as many customer points as possible are distributed to the unmanned aerial vehicle for distribution, the unmanned aerial vehicle can distribute a plurality of packages at one time under the limitation of load and flight distance, the vehicle can carry the unmanned aerial vehicle for distribution and can also simultaneously distribute with the unmanned aerial vehicle, the unmanned aerial vehicle and the vehicle are combined and cooperated to jointly complete distribution tasks, and the feasibility of an algorithm verification model is designed.
The technical purpose of the invention is realized by the following technical scheme:
a construction method of an unmanned aerial vehicle-vehicle combined delivery path optimization model comprises the following steps:
marking special points: marking all customer demand points, and then marking R demand points in which goods in the customer demand points exceed the maximum load limit of the unmanned aerial vehiclemAnd the demand point exceeding the maximum flight distance limit of the unmanned aerial vehicle is marked as RdThen the path optimization model is as follows:
wherein:
|Tkthe specific value is |, which is the number of customer demand points distributed by the vehicle at the kth time, C is the set of all the customer demand points, and C is {1, 2, …, n }; s is the set of all nodes, S ═ {1, 2, …, n, n +1}, where n +1 denotes the distribution center; n is the total number of points of customer demand.
As a preferred scheme, the system further comprises a single path planning model, wherein the single path planning model comprises an unmanned aerial vehicle path model and a vehicle path model;
determining the maximum flight distance D of the unmanned aerial vehicle and the maximum load capacity M of the unmanned aerial vehicle; determining an unmanned aerial vehicle path model:
wherein: n is the set of customer demand points that are not serviced, N ═ 1, 2, …, N }; u shapekA set of customer demand points distributed by the unmanned aerial vehicle for the kth distribution; k is the total number of deliveries, K ═ 1, 2, …, K }; dijThe distance of a straight path from the node i to the node j is obtained;
determining average airspeed v of a drone1(ii) a Average traveling speed v of vehicle2(ii) a Determining a vehicle path model:
wherein: t iskFor the kth dispatch, the vehicle dispatches a set of customer demand points.
As a preferred scheme, the overall path optimization is performed again on the obtained model, and the method specifically comprises the following steps:
repeating the calculation of the single-time path planning model by taking the end point recorded by the single-time distribution path as the starting point of the next distribution path until all the customer demand points are completely distributed; adding the distribution distances of the vehicles and the unmanned aerial vehicles, and optimizing the path selection of each distribution by taking the shortest total distribution distance as an objective function to obtain the following overall path optimization model:
|Tk|＝1，|Ukif | ≠ 0
Wherein: p is the set of all the stop points; ε is the road impedance coefficient.
An unmanned aerial vehicle-vehicle combined delivery path optimization method is based on the construction method of the unmanned aerial vehicle-vehicle combined delivery path optimization model, and comprises the following steps:
s1: chromosome coding;
s2: initializing a population;
s3: calculating a fitness function;
s4: selecting;
s5: crossing;
s6: mutation;
s7: reversal of evolution
S8: optimizing the end of single delivery to obtain a new population;
s9: judging whether the maximum genetic algebra is reached, if so, outputting a result; if not, the process returns to S3.
As a preferred embodiment, the chromosomal coding comprises in particular the following steps:
randomly generating a chromosome consisting of 1-n integers by adopting an integer arrangement coding method, wherein each integer gene corresponds to n customer demand points, and a distribution center is represented by n + 1; each chromosome can be divided into several different parts, and each part is a set of unmanned aerial vehicles and vehicle paths of different delivery passes; determining the distribution sequence of the corresponding nodes according to the arrangement sequence of the genes, adding the nodes to the distribution paths of the unmanned aerial vehicle and the vehicle in sequence from the distribution center, calculating whether the constraint condition is met or not when adding one node, and continuing to add the next node until the constraint condition is exceeded and entering the distribution of the next time when the constraint condition is not exceeded; the distribution is repeated for k times, and the distribution paths of all the times are obtained, and the sequence of the distribution paths of each time is combined to form the total distribution path.
As a preferred scheme, the population initialization comprises the following steps:
after the chromosome coding is finished, generating an initial population containing a plurality of chromosomes;
the calculating the fitness function specifically comprises the following steps:
taking the minimum total path distance as a target, taking the inverse of an objective function as a fitness value, and calculating the fitness value as follows:
as a preferred scheme, the selection specifically comprises the following steps:
and selecting part of individuals from the original population to a new population according to the size of the fitness value with a certain probability, wherein the higher the fitness is, the higher the probability is.
As a preferred scheme, the crossing specifically comprises the following steps:
the crossover operator adopts partial mapping hybridization; randomly generating two integers in the [1, n ] interval, determining the positions of two crossed end points, sequentially exchanging genes between the two end points in the two chromosomes, removing partially repeated genes which are exchanged in the original chromosome, and sequentially mapping and complementing the chromosomes by utilizing the corresponding relation of the exchanged parts of the two parent chromosomes.
As a preferred embodiment, the mutation specifically comprises the following steps: the mutation operator adopts exchange mutation; randomly generating two integers in the interval of [1, n ], and performing swapping on genes at positions corresponding to the two integers in a chromosome;
the purification reversion specifically comprises the steps of:
randomly generating two integers in the interval of [1, n ], and reversing genes at corresponding positions between the two integers in a chromosome; the reversion operator has single direction, only the chromosome with improved fitness value after reversion can be reserved, otherwise, the reversion is invalid.
As a preferable scheme, S8 specifically includes the following steps: when the unmanned aerial vehicle is responsible for distributing one or more nodes and the vehicle only distributes one node, the single path distance of the unmanned aerial vehicle and the single path distance of the vehicle are calculated as follows:
in conclusion, the invention has the following beneficial effects:
aiming at the problem of single unmanned aerial vehicle and single vehicle combined delivery, an unmanned aerial vehicle can deliver a plurality of customer demand points at one time, a three-step path distribution method of marking special points, single path planning and overall path optimization is designed, the minimum total delivery distance is taken as a target function, a genetic algorithm with terminal optimization is used, the problem is solved through case simulation, and the result shows that: the provided combined distribution mode can improve distribution efficiency, reduce the total distribution path length and well solve the logistics distribution problem in rural areas.
The unmanned aerial vehicle technique further improves in the future, and unmanned aerial vehicle's loading capacity and flying distance are strengthened, and its advantage with low costs, regardless of topography will be more prominent, and faster, more energy-conserving efficient logistics distribution will become the trend. On the basis of the application, the problem of joint distribution of multiple unmanned aerial vehicles and multiple vehicles is considered, and the time window limit of a customer point is increased, so that the logistics distribution in town areas is expanded.
Drawings
Fig. 1 is a schematic diagram of single-drone single-vehicle joint delivery of an embodiment of the present invention;
FIG. 2 is a schematic diagram of an embodiment of a super-hotspot service form;
FIG. 3 is a flow chart of a genetic algorithm according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of an end delivery path arrangement according to an embodiment of the present invention;
fig. 5 is a schematic diagram of the result of the unmanned aerial vehicle-vehicle joint delivery according to the embodiment of the present invention;
FIG. 6 is a diagram illustrating operational results of various scenarios according to an embodiment of the present invention;
FIG. 7 is a graph comparing the results of an embodiment of the present invention;
FIG. 8 is a graphical illustration of parametric results for an embodiment of the present invention;
FIG. 9 is a schematic diagram of the delivery results of an unmanned aerial vehicle and a vehicle at different speeds in accordance with an embodiment of the present invention;
FIG. 10 is a graph showing the distribution results of different impedance coefficients according to the embodiment of the present invention.
Detailed Description
This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. "substantially" means within an acceptable error range, and a person skilled in the art can solve the technical problem within a certain error range to substantially achieve the technical effect.
The terms in upper, lower, left, right and the like in the description and the claims are combined with the drawings to facilitate further explanation, so that the application is more convenient to understand and is not limited to the application.
The present invention will be described in further detail with reference to the accompanying drawings.
The present application gives the following definitions:
(1) vehicle: including trucks, vans, tricycles, etc., can be used for cargo delivery and can support vehicles launched and retracted by unmanned aerial vehicles.
(2) Impedance: the method is not limited to road nonlinear coefficients, gradient, flatness and the like, and factors which can influence the vehicle to keep stable and uniform running are all factors.
(3) And (3) combined delivery: unmanned aerial vehicle need get goods from the vehicle, need return the vehicle after the delivery, and vehicle portability unmanned aerial vehicle delivers, also can get the delivery of carrying out other customer points in step after the goods at unmanned aerial vehicle, and both accomplish the delivery of all customer points according to the concrete characteristic of customer point in a coordinated manner.
(4) Independent distribution: the vehicles and the unmanned aerial vehicles do not cooperate, and respective distribution tasks are independently completed.
(5) A docking point: can supply the vehicle to stop and wait unmanned aerial vehicle, unmanned aerial vehicle accomplishes here that battery change, goods take out, or descend to retrieve, and the stop can be arbitrary customer point or delivery center.
A simple model for single drone and single vehicle co-delivery is shown in fig. 1. In the figure, the unmanned aerial vehicle and the vehicle can respectively carry goods to leave the distribution center, and the vehicle can also carry the unmanned aerial vehicle to return to the distribution center; when the vehicles are delivered by the unmanned aerial vehicle, the vehicles can synchronously deliver customer points without stopping on site for waiting; a single delivery of a drone may serve multiple customer points simultaneously. Simultaneously, marked the super far point that surpasses the maximum flight distance of unmanned aerial vehicle with red, super far customer point is because of unmanned aerial vehicle can't long distance come and go, only can accomplish the distribution by the vehicle. The overweight point that surpasss the biggest loading capacity of unmanned aerial vehicle has been marked with yellow, and overweight customer is ordered because of the unable load goods of unmanned aerial vehicle, also can only be accomplished the delivery by the vehicle, but unmanned aerial vehicle can fly to stop to overweight point. Three service forms of the super-emphasis point are shown in fig. 2: in the diagram (a), the super-emphasis point can be used as a stop point of the unmanned aerial vehicle and the vehicle; in diagram (b), the vehicle may carry the unmanned aerial vehicle to deliver the super-emphasis point; in diagram (c), both the drone and the vehicle deliver to the customer site, the overweight site being in charge of the vehicle.
Based on the above problems, the present application makes the following assumptions:
(1) the positions and the demands of the distribution center and the customer points are known, and the demand of the distribution center is 0;
(2) all customer points must be serviced regardless of the time window limitations of the customer points;
(3) the maximum load capacity and the maximum endurance mileage of the unmanned aerial vehicle are known;
(4) under the condition that the limit condition is met, the unmanned aerial vehicle can serve a plurality of customer points at one time;
(5) the load limit and the endurance limit of the vehicle are not considered;
(6) the vehicle must arrive at a stopping point before the unmanned aerial vehicle, and the unmanned aerial vehicle cannot hover at the stopping point for flying;
(7) after the unmanned aerial vehicle finishes each distribution, the unmanned aerial vehicle needs to return to a vehicle for taking goods and replace a battery;
(8) the service time of a customer point and the goods taking and battery replacing time of the unmanned aerial vehicle are not considered;
(9) carry sufficient unmanned aerial vehicle power on the vehicle.
Description of the parameters
The parameters used in the model building process are as follows:
s: a set of all nodes, S ═ {1, 2, …, n, n +1}, where n +1 denotes a distribution center;
c: a set of all customer demand points, C ═ {1, 2, …, n };
n: a set of unserviced customer demand points, N ═ {1, 2, …, N };
Rm: a set of customer point demand points exceeding the maximum load limit of the unmanned aerial vehicle;
Rd: the distance between the customer point demand point set and other customer points exceeds the maximum flight distance limit of the unmanned aerial vehicle;
u: set of customer demand points distributed by unmanned aerial vehicle, U ═ U1，U2，…，Uk}；
Uk: the kth distribution, namely a set of customer demand points distributed by the unmanned aerial vehicle;
t: set of customer demand points for vehicle delivery, T ═ T1，T2，…，Tk}；
Tk: the k delivery, the set of customer demand points delivered by the vehicle;
p: a set of all docking points;
k: total number of deliveries, K ═ 1, 2, …, K };
n: customer demand point total;
|Ukl: the kth distribution, the customer demand points distributed by the unmanned aerial vehicle;
|Tkl: the number of customers who distribute the k time and distribute the vehicle
mi: the cargo demand of node i;
dij: the straight-line path distance from the node i to the node j;
m: the maximum payload capacity of the drone;
d: the maximum flight distance of the unmanned aerial vehicle;
v1: average flight speed of the drone;
v2: the average traveling speed of the vehicle;
epsilon: a road impedance coefficient;
Ek: the k delivery and the sum of the path distances delivered by the unmanned aerial vehicle;
Fk: the k delivery and the sum of the path distances of vehicle delivery;
model building
The method aims at minimizing the total distribution distance, and specifically comprises the following three steps.
(1) First marking of special points
The vehicle may be delivered to all customer demand points. Because the unmanned aerial vehicle has maximum load limit and maximum flight distance limit in single flight, demand points of the demand points of all customers, the goods of which exceed the maximum load limit of the unmanned aerial vehicle, are marked as RmAnd the demand point exceeding the maximum flight distance limit of the unmanned aerial vehicle is marked as RdAll marked points can only be delivered by the vehicle, but are marked as RmThe customer demand point can be used as a terminal point of single arrival of the unmanned aerial vehicle under the condition of meeting the flight distance limit of the unmanned aerial vehicle.
The formula (1) and the formula (2) ensure that the marking points are distributed by the vehicle; the expressions of formula (3) and formula (4) are labeled RdThe customer points are not distributed by the unmanned aerial vehicle; formulas (5) and (6) show that the unmanned aerial vehicle and the vehicle can respectively enter and exit from the distribution center independently, and the vehicle can also carry the unmanned aerial vehicle to enter and exit together; equation (7) represents that the vehicle serves at least one customer site per delivery.
(2) Second step single path planning
Unmanned aerial vehicle route
Because of unmanned aerial vehicle's electric quantity restriction, in the flying distance radius that unmanned aerial vehicle furthest can reach, and satisfy under the condition of the restriction of unmanned aerial vehicle maximum load, as far as possible give unmanned aerial vehicle distribution customer demand point, to within the given flying radius, but the customer point that unmanned aerial vehicle single delivery can be served is at most limited. The single arrival endpoint is recorded after each allocation is completed.
Equation (8) is to maximize the number of customer nodes served by a single drone; formula (9) ensures that the weight of the cargo carried by a single unmanned aerial vehicle does not exceed the maximum load capacity of the unmanned aerial vehicle; the formula (10) ensures that the total distance of single unmanned aerial vehicle distribution does not exceed the maximum flight distance of the unmanned aerial vehicle; equation (11) indicates that among all customer nodes not served, the drone does not enter the node more than once; similarly, equation (12) represents that the drone flies no more than once from the node; equation (13) ensures that after each allocation of a customer node serviced by a drone, it is removed from the previous set of unserviced customer nodes.
② vehicle path
The unmanned aerial vehicle needs to be replenished with electricity after being delivered once, and for safety, hovering waiting at a stop point cannot be performed, so a vehicle must arrive before the unmanned aerial vehicle arrives. The terminal point recorded by the unmanned aerial vehicle single path planning is used as the terminal point of the vehicle distribution, and on the premise of meeting the requirement of reaching in advance, the customer demand points are distributed to the vehicle as much as possible. Due to delivery time limitations, the maximum number of customer points that can be serviced by a single delivery of a vehicle is limited.
Equation (14) is to maximize the number of customer nodes for a single vehicle service; equation (15) ensures that the vehicle must arrive before the drone arrives; equation (16) indicates that, of all customer nodes that are not serviced, a vehicle enters the node no more than once; similarly, equation (17) indicates that the vehicle has not exited from the node more than once; equation (18) ensures that after each allocation of a customer node delivered by a drone, it is removed from the previous set of unserviced customer nodes.
(3) Third step global path optimization
And repeating the second step by taking the end point recorded by the single distribution route as the starting point of the next distribution route until all the customer demand points are completely distributed. And adding the distribution distances of the vehicles and the unmanned aerial vehicles, and optimizing the path selection of each distribution by taking the shortest total distribution distance as an objective function.
|Tk|＝1，|UkIf | ≠ 0
The objective function (19) is to minimize the total delivery distance of the drone and the vehicle; equations (20) and (21) indicate that all non-parked customer nodes are only delivered once by the drone or vehicle; equations (22) and (23) represent that all parked node vehicles only go in and out once; equation (24) may reduce unnecessary loops; the value ranges of the parameters are given by the formula (25) and the formula (26). Equations (5) - (6) and equations (20) - (23) together give the entrance and exit rules when the distribution center is used as a stop point and a non-stop point, and ensure that the unmanned aerial vehicle and the vehicle exit from the distribution center and finally return to the distribution center without visiting the distribution center again in the middle.
Algorithm design
Since the problem grows exponentially with the increase of nodes, the method solves the problem of the designed joint distribution path by adopting a genetic algorithm. The genetic algorithm is a heuristic search algorithm based on biological evolution, can be quickly converged to an optimal solution, and can effectively solve the problems provided by the application by setting different genetic operators. The calculation flow of the genetic algorithm is shown in fig. 3.
Genetic algorithm
(1) Chromosomal coding
By adopting an integer arrangement coding method, chromosomes consisting of 1-n integers are randomly generated, each integer gene corresponds to n customer demand points, and the distribution center is represented by n + 1. Each chromosome may be divided into several different parts, each part being a set of unmanned aerial vehicles and vehicle paths for different delivery passes. And determining the distribution sequence of the corresponding nodes according to the arrangement sequence of the genes, adding the nodes to the distribution paths of the unmanned aerial vehicle and the vehicle in sequence from the distribution center, calculating whether the constraint condition is met or not when adding one node, and continuing to add the next node until the constraint condition is exceeded, and entering the distribution of the next time when the constraint condition is not exceeded. The distribution is repeated for k times, and the distribution paths of all the times are obtained, and the sequence of the distribution paths of each time is combined to form the total distribution path.
(2) Population initialization and fitness function
After the chromosome coding is completed, an initial population containing a number of chromosomes is generated based on the characteristics of the problem under study. The fitness function is an important index for evaluating the quality of a chromosome, and the higher the fitness value is, the more possible the fitness function is to be inherited to offspring. The application aims at minimizing the total path distance, and the fitness value is obtained by taking the reciprocal of an objective function and is calculated as shown in formula (27).
(3) Selecting
The selection is to select part of individuals from the original population to a new population according to the size of the fitness value and with a certain probability, wherein the higher the fitness is, the higher the probability is. The operator is selected by adopting random traversal sampling, so that monopoly descendants caused by individual influence with high fitness are avoided.
(4) Crossing
The crossover operator uses partial mapping hybridization. Randomly generating two integers in the [1, n ] interval, determining the positions of two crossed end points, sequentially exchanging genes between the two end points in the two chromosomes, removing partially repeated genes which are exchanged in the original chromosome, and sequentially mapping and complementing the chromosomes by utilizing the corresponding relation of the exchanged parts of the two parent chromosomes.
(5) Variation of
Mutation operators employ crossover mutations. Randomly generating two integers in the [1, n ] interval, and exchanging genes at the positions corresponding to the two integers in a chromosome.
(6) Reversal of evolution
In order to improve the local search capability of the genetic algorithm, a plurality of continuous evolution reversion operations are introduced. Randomly generating two integers in the [1, n ] interval, and reversing genes at corresponding positions between the two integers in a chromosome. The reversion operator has single direction, only the chromosome with improved fitness value after reversion can be reserved, otherwise, the reversion is invalid.
Single delivery end optimization
Aiming at the problem of single unmanned aerial vehicle and single vehicle, the minimum distance of the total delivery path is taken as a target function, the vehicle does not wait for the return of the unmanned aerial vehicle in situ, and the tail end optimization can be carried out on part of the combined delivery path. In combination with equation (24), when the drone is responsible for delivering one or more nodes and the vehicle delivers only one node (this node is a stop point and may include a delivery center), the two path schemes are shown in fig. 4, in order to minimize the path distance, the drone single path distance calculation is shown in equation (28), and the vehicle single path distance calculation is shown in equation (29). When (E)k+Fk)≤εEkWhen the scheme is adopted, the scheme shown in figure 4(a) is adopted; when (E)k+Fk)≥εEkThen, the scheme shown in FIG. 4(b) is employed.
Example analysis
In order to solve the path optimization problem of the application, MATLAB R2019a is adopted for programming according to a designed genetic algorithm, and the method is operated on a computer with an Intel (R) core (TM) i7-8550U and 8G internal memory as a processor and an Win1064 bit operating system. The population scale of the genetic algorithm is set to be 200, the selection probability is 0.9, the cross probability is 0.9, the mutation probability is 0.05, and the maximum genetic algebra is 300. The model parameter settings are shown in table 1.
TABLE 1 model parameters
Case simulation
In consideration of the location characteristics of rural areas, the cargo demand of part of the customer demand points is modified according to the data of the RC201 in the Solomon example data set, two super-emphasis points and two super-far points are additionally added, a case containing 30 customer demand points is generated, and the specific data of each node is shown in Table 2. And inputting data, running the program for 30 times, and counting simulation results.
Table 2 node data
The case delivery results are shown in fig. 5, and the simulation results are shown in table 3. As can be seen from the figure, the drone can deliver multiple customer demand points at a single time, and while the drone delivers, the vehicle can also deliver without waiting on site. In addition, overweight point can regard as unmanned aerial vehicle's stop, and the delivery is accomplished only by the vehicle to the super remote point, and unmanned aerial vehicle and vehicle leave delivery center respectively, carry unmanned aerial vehicle by the vehicle at last, return delivery center simultaneously. And the single unmanned aerial vehicle and the single vehicle are jointly distributed, and the tasks of all customer demand points are completed cooperatively. By the data that gathers in the table, the customer point that the vehicle is responsible for still is more than unmanned aerial vehicle, this because rural area customer point dispersion and relative distance are far away, and unmanned aerial vehicle receives the maximum flight distance restriction, and single flight can't come and go long distance.
Table 3 case simulation results
Scene design
In order to verify the effectiveness of the model, three scenes of vehicle independent distribution, unmanned aerial vehicle-vehicle independent distribution and unmanned aerial vehicle-vehicle combined distribution are designed.
Scene one: the vehicle is independently distributed, namely the traditional TSP problem, the vehicle has no load and endurance limit, and the vehicle starts from the distribution center, finishes distribution of all customer demand points and returns to the distribution center by considering the influence of impedance.
Scene two: unmanned aerial vehicle-vehicle independent delivery, namely the problem of multi-vehicle type route with capacity limitation, is not jointly delivered, and the vehicle and the unmanned aerial vehicle are responsible for respective customer points without cooperation, and the unmanned aerial vehicle single delivery needs to be returned to a delivery center for goods taking and power supply replacement.
Scene three: unmanned aerial vehicle-vehicle joint delivery, the route optimization problem that this application provided.
The three scenes were solved by genetic algorithm with the goal of minimizing the path distance, using 30 customer point data of the previous subsection, with the remaining parameters unchanged, and each scene was independently run 30 times, and fig. 6 shows the results of each run, the statistical results and the variation ratio with respect to scene one, for example, as shown in table 4, and the result pairs for different scenes are shown in fig. 7.
TABLE 4 statistical results for each scene
As can be seen from fig. 6, the first scene fluctuation is relatively stable, and the second scene fluctuation is maximum, which is that after some special customer demand points are allocated to the unmanned aerial vehicle for distribution, the calculation result falls into local optimum, and the third scene fluctuation is relatively stable. In table 4, both the second scenario and the third scenario optimal results delivered by the unmanned aerial vehicle are smaller than the first scenario delivered by the vehicle only, the unmanned aerial vehicle-vehicle combined delivery with the optimal solution as the third scenario is achieved, the optimal value is 522.89, compared with the traditional vehicle delivery, the path distance is reduced by 1.38%, it is seen that the unmanned aerial vehicle is added for delivery, the overall path distance can be reduced, but the path problem becomes more complex due to the particularity of the unmanned aerial vehicle as a delivery tool, in the heuristic algorithm solution, the solution is prone to fall into local optimal, and partial results are obviously inferior to those delivered by the vehicle only, which can also be seen in fig. 7, and the results are affected by partial maximum values.
When all customer points exceed the unmanned aerial vehicle constraint limit, the joint delivery is degraded into the problem of vehicle individual delivery paths; when the unmanned aerial vehicle is limited to only use the distribution center as a stop point, the problem of unmanned aerial vehicle-vehicle independent distribution path is solved. In general, unmanned aerial vehicle-vehicle combined distribution designed by the application is superior to pure vehicle distribution and unmanned aerial vehicle-vehicle independent distribution in distribution path distance.
Sensitivity analysis
Considering that the selected parameter values can influence the distribution result, and aiming at the problem of single unmanned aerial vehicle and single vehicle combined distribution of the single unmanned aerial vehicle, sensitivity analysis is carried out on 5 parameters in table 4-1. The node data in table 4-1 is still used, the rest parameters except the sensitivity analysis parameter are set as before, the minimum path length is taken as the target, the genetic algorithm is used for solving, and the minimum value is taken after each group of results independently run for 20 times.
(1) Maximum payload and maximum flight distance of unmanned aerial vehicle
Unmanned aerial vehicle still need to carry sufficient power because of the volume is less, and the goods volume of ability load is very limited, and in addition, it is limited to carry battery power, has restricted unmanned aerial vehicle's maximum flight distance. However, in single delivery, the unmanned aerial vehicle may go out of the low full load rate and fly back to the vehicle after short-distance delivery, in order to maximize the utilization efficiency of the unmanned aerial vehicle, the maximum load capacity and the maximum flight distance of the unmanned aerial vehicle are divided into 5 groups, which are analyzed respectively, the grouping is shown in table 5, and the result is shown in fig. 8.
TABLE 5 grouping of parameters
As can be seen from the figure, as the maximum load capacity of the unmanned aerial vehicle increases, the number of customer points that can be distributed by the unmanned aerial vehicle increases, the number of tasks shared in the total distribution tasks increases, and the total path length decreases due to the increase of the distribution points that the unmanned aerial vehicle is responsible for. However, when the maximum payload capacity of the unmanned aerial vehicle is increased to a certain extent, the maximum payload capacity is affected by the density of surrounding customer demand points, points within the maximum flight distance may be completely allocated, and the total path length cannot be reduced any more by increasing the payload capacity. And keep unmanned aerial vehicle maximum payload unchangeable, along with the increase of the biggest flight distance of unmanned aerial vehicle, total delivery distance is higher than steeply increasing after 40 at the biggest flight distance, because of the difference of customer point dispersion degree, when unmanned aerial vehicle flight distance is less, when being not enough to accomplish the delivery of a plurality of customer points, the preferential distribution customer point delivers for unmanned aerial vehicle, the route of unmanned aerial vehicle and vehicle with, can be greater than the vehicle and deliver alone, when the biggest flight distance improves to a plurality of customer points of single delivery can be served, unmanned aerial vehicle-vehicle's joint delivery can effectively reduce total delivery route. But is finally limited by the maximum load capacity of the unmanned aerial vehicle, and the maximum flight distance is continuously increased, so that the unmanned aerial vehicle can remotely distribute customer points, and the round-trip stop points greatly increase the total path length.
(2) Average flight speed of unmanned aerial vehicle and average running speed of vehicle
The vehicle needs to arrive at a stop point before the unmanned aerial vehicle arrives, and under the condition of meeting the maximum flight distance of the unmanned aerial vehicle, the average flight speed of the unmanned aerial vehicle and the average running speed of the vehicle determine the maximum distribution distance which can be respectively run. How to coordinate the relative speeds of the unmanned aerial vehicle and the vehicle is analyzed, so that the unmanned aerial vehicle and the vehicle are better matched, and the distribution task of a customer point is completed. The combination of drone and vehicle at different speed ratios is shown in table 6, and the delivery results are shown in figure 9.
TABLE 6 different speed combinations of UAV and vehicle
From fig. 9, when the drone speed is much less than the vehicle speed, the vehicle cannot arrive before the drone reaches the stop, most customer points are therefore allocated to the vehicle for delivery, and the drone is allocated only a very few customer demand points. The flight speed of the unmanned aerial vehicle is improved, the unmanned aerial vehicle is divided into more customer points, and the joint distribution is not necessarily smaller than the independent distribution of vehicles on the path length due to the fact that the customer points of single service are limited. When unmanned aerial vehicle flying speed surpassed vehicle speed gradually, when unmanned aerial vehicle can accomplish the delivery task of a plurality of customer points, total delivery distance had obvious decline, nevertheless surpassed vehicle speed 2 backs, still received unmanned aerial vehicle's maximum loading capacity and flying distance restriction, path length no longer reduces.
(3) Coefficient of impedance
The vehicle distributes under different environment, receives various topography influences easily, and the more complicated its impedance coefficient of topography is also higher, and the delivery route of vehicle consequently needs to carry out appropriate adjustment, and the route of unmanned aerial vehicle also can receive the influence of vehicle. Distribution results under different impedance coefficients are shown in fig. 10, and the total distribution distance almost linearly increases along with the rise of the impedance coefficient, so that vehicles still occupy the dominant position in unmanned aerial vehicle-vehicle combined distribution due to the condition limitation of unmanned aerial vehicles, and particularly in rural areas, the customer points are more dispersed.
Generally speaking, unmanned aerial vehicle-vehicle joint delivery efficiency is limited by the above parameters, and when the number of customers that unmanned aerial vehicle can deliver is sufficient, the maximum carrying capacity and the maximum flight distance of unmanned aerial vehicle are increased, and the relative speed of unmanned aerial vehicle and vehicle can effectively reduce the total path length. Unmanned aerial vehicle single distributable customer point increases, and total distributed customer point quantity also can increase, and overall delivery efficiency rises. But promote to a certain extent after, the distribution of customer points around can exert an influence to the distribution result, unmanned aerial vehicle and vehicle probably have long distance to come and go, have increased the distribution distance.
The present embodiment is only for explaining the present invention, and it is not limited to the present invention, and those skilled in the art can make modifications of the present embodiment without inventive contribution as needed after reading the present specification, but all of them are protected by patent law within the scope of the claims of the present invention.
Claims (10)
1. A construction method of an unmanned aerial vehicle-vehicle combined delivery path optimization model is characterized by comprising the following steps:
marking special points: marking all customer demand points, and then marking R demand points in which goods in the customer demand points exceed the maximum load limit of the unmanned aerial vehiclemAnd the demand point exceeding the maximum flight distance limit of the unmanned aerial vehicle is marked as RdThen the path optimization model is as follows:
wherein:
|Tkthe specific value is |, which is the number of customer demand points distributed by the vehicle at the kth time, C is the set of all the customer demand points, and C is {1, 2, …, n }; s is the set of all nodes, S ═ {1, 2, …, n, n +1}, where n +1 denotes the distribution center; n is the total number of points of customer demand.
2. The method for constructing the unmanned aerial vehicle-vehicle combined delivery path optimization model according to claim 1, further comprising a single path planning model, wherein the single path planning model comprises an unmanned aerial vehicle path model and a vehicle path model;
determining the maximum flight distance D of the unmanned aerial vehicle and the maximum load capacity M of the unmanned aerial vehicle; determining an unmanned aerial vehicle path model:
wherein: n is the set of customer demand points that are not serviced, N ═ 1, 2, …, N }; u shapekA set of customer demand points distributed by the unmanned aerial vehicle for the kth distribution; k is the total number of deliveries, K ═ 1, 2, …, K }; dijThe distance of a straight path from the node i to the node j is obtained;
determining average airspeed v of a drone1(ii) a Average traveling speed v of vehicle2(ii) a Determining a vehicle path model:
wherein: t iskFor the kth dispatch, the vehicle dispatches a set of customer demand points.
3. The method for constructing the unmanned aerial vehicle-vehicle combined distribution route optimization model according to claim 2, wherein the obtained model is subjected to integral route optimization again, and the method specifically comprises the following steps:
repeating the calculation of the single-time path planning model by taking the end point recorded by the single-time distribution path as the starting point of the next distribution path until all the customer demand points are completely distributed; adding the distribution distances of the vehicles and the unmanned aerial vehicles, and optimizing the path selection of each distribution by taking the shortest total distribution distance as an objective function to obtain the following overall path optimization model:
|Tk|＝1，|Ukif | ≠ 0
Wherein: p is the set of all the stop points; ε is the road impedance coefficient.
4. An unmanned aerial vehicle-vehicle joint delivery route optimization method based on the construction method of the unmanned aerial vehicle-vehicle joint delivery route optimization model of any one of claims 1 to 3, characterized by comprising the following steps:
s1: chromosome coding;
s2: initializing a population;
s3: calculating a fitness function;
s4: selecting;
s5: crossing;
s6: mutation;
s7: reversal of evolution
S8: optimizing the end of single delivery to obtain a new population;
s9: judging whether the maximum genetic algebra is reached, if so, outputting a result; if not, the process returns to S3.
5. The method for optimizing the unmanned aerial vehicle-vehicle joint delivery path according to claim 4, wherein the chromosome coding comprises the following steps:
randomly generating a chromosome consisting of 1-n integers by adopting an integer arrangement coding method, wherein each integer gene corresponds to n customer demand points, and a distribution center is represented by n + 1; each chromosome can be divided into several different parts, and each part is a set of unmanned aerial vehicles and vehicle paths of different delivery passes; determining the distribution sequence of the corresponding nodes according to the arrangement sequence of the genes, adding the nodes to the distribution paths of the unmanned aerial vehicle and the vehicle in sequence from the distribution center, calculating whether the constraint condition is met or not when adding one node, and continuing to add the next node until the constraint condition is exceeded and entering the distribution of the next time when the constraint condition is not exceeded; the distribution is repeated for k times, and the distribution paths of all the times are obtained, and the sequence of the distribution paths of each time is combined to form the total distribution path.
6. The unmanned aerial vehicle-vehicle joint delivery path optimization method of claim 5, wherein the population initialization comprises the steps of:
after the chromosome coding is finished, generating an initial population containing a plurality of chromosomes;
the calculating the fitness function specifically comprises the following steps:
taking the minimum total path distance as a target, taking the inverse of an objective function as a fitness value, and calculating the fitness value as follows:
7. the unmanned aerial vehicle-vehicle joint delivery path optimization method of claim 6, wherein the selecting specifically comprises the steps of:
and selecting part of individuals from the original population to a new population according to the size of the fitness value with a certain probability, wherein the higher the fitness is, the higher the probability is.
8. The unmanned aerial vehicle-vehicle joint delivery path optimization method of claim 7, wherein the intersection specifically comprises the steps of:
the crossover operator adopts partial mapping hybridization; randomly generating two integers in the [1, n ] interval, determining the positions of two crossed end points, sequentially exchanging genes between the two end points in the two chromosomes, removing partially repeated genes which are exchanged in the original chromosome, and sequentially mapping and complementing the chromosomes by utilizing the corresponding relation of the exchanged parts of the two parent chromosomes.
9. The method for optimizing the unmanned aerial vehicle-vehicle joint distribution route according to claim 8, wherein the mutation specifically comprises the steps of: the mutation operator adopts exchange mutation; randomly generating two integers in the interval of [1, n ], and performing swapping on genes at positions corresponding to the two integers in a chromosome;
the purification reversion specifically comprises the steps of:
randomly generating two integers in the interval of [1, n ], and reversing genes at corresponding positions between the two integers in a chromosome; the reversion operator has single direction, only the chromosome with improved fitness value after reversion can be reserved, otherwise, the reversion is invalid.
10. The unmanned aerial vehicle-vehicle joint distribution route optimization method according to claim 9, wherein the S8 specifically comprises the steps of: when the unmanned aerial vehicle is responsible for distributing one or more nodes and the vehicle only distributes one node, the single path distance of the unmanned aerial vehicle and the single path distance of the vehicle are calculated as follows:
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