CN117726059B - Truck unmanned aerial vehicle task allocation method under time window constraint - Google Patents
Truck unmanned aerial vehicle task allocation method under time window constraint Download PDFInfo
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Abstract
The invention discloses a truck unmanned aerial vehicle task allocation method under the constraint of a time window, which belongs to the technical field of task allocation, and aims to minimize the total travel cost generated by a truck and an unmanned aerial vehicle while meeting the constraint of the limited load and the working time of the truck and the unmanned aerial vehicle by determining the allocation route of a customer cooperatively visited by the truck and the unmanned aerial vehicle; compared with the traditional nearest neighbor algorithm for constructing the initial route of the truck, the method well considers the time window constraint of the customer, and reduces the cost caused by violating the time window of the customer. In the iterative optimization stage, the double variable neighborhood search algorithm designs a plurality of neighborhood structures to search the solution space, so that the search capability of local solutions can be enhanced, and the routes of single trucks and unmanned aerial vehicles carried by the single trucks can be optimized independently; meanwhile, the double variable neighborhood search algorithm designs a neighborhood structure operator considering the constraint of a customer time window, so that a solution conforming to the constraint of the time window can be generated with high probability when an iterative optimization stage is executed.
Description
Technical Field
The invention belongs to the technical field of task allocation, and particularly relates to a task allocation method of a truck unmanned aerial vehicle under the constraint of a time window.
Background
The task allocation problem of the collaborative parcel delivery of the unmanned aerial vehicle of the truck under the constraint of the time window is one of the key problems in the logistics field. With the development of electronic commerce, the demand of customers for quick distribution is continuously increased, and innovation of the logistics industry is driven to a great extent. However, conventional pure truck delivery modes may be limited by increasingly complex urban traffic and road congestion, resulting in slower delivery speeds and reduced customer satisfaction. With the maturation of unmanned aerial vehicle technique, unmanned aerial vehicle can be under the complex circumstances of urban traffic quick delivery parcel, consequently shortens delivery time by a wide margin, satisfies the demand of customer to instant response. However, the unmanned aerial vehicle is also constrained by load, endurance, and the like. The truck unmanned aerial vehicle system well combines the advantages of the truck and the unmanned aerial vehicle, provides more flexible delivery selection, creates more competitive services for electronic commerce, and is an innovative delivery mode for exploring efficient delivery solutions. The key research content of the problem is to optimize the delivery route of the package delivery by a plurality of trucks and a plurality of unmanned aerial vehicles under the premise of considering the time window of customers. Each truck only carries one unmanned aerial vehicle, and the unmanned aerial vehicle can provide services for other customers while the trucks deliver goods. The customer has soft time window constraint, and if the truck unmanned aerial vehicle violates the time window constraint of the customer in the delivery process, corresponding punishment cost is generated. The objective function is to minimize the total travel costs incurred by trucks and drones.
In the prior art, task allocation methods are generally divided into precise algorithms and heuristic algorithms. Aiming at the task allocation problem of time window constraint, limited load and working time constraint, the basic idea of the classical precise algorithm is to search all feasible solution spaces of the optimization problem under the constraint condition, and when the feasible solution spaces are overlarge and the constraint is more, the search efficiency is lower, and the NP-hard problem cannot be solved optimally in polynomial time; classical heuristic algorithms have a variable neighborhood search algorithm (VNS): the variable neighborhood search algorithm is simple in principle and strong in local search capability, can adopt a plurality of different neighborhoods to perform systematic search, and obtains a suboptimal solution of a large-scale optimization problem within a certain time, but lacks some heuristic guiding information in the search process, and the search is too random.
Disclosure of Invention
Aiming at the defects in the prior art, the task allocation method for the truck unmanned aerial vehicle under the constraint of the time window solves the problems that the existing allocation method for the delivery task is low in searching efficiency and cannot obtain the optimal task allocation result in the implementation process.
In order to achieve the aim of the invention, the invention adopts the following technical scheme: a truck unmanned aerial vehicle task allocation method under time window constraint comprises the following steps:
s1, determining basic information of a distribution task;
s2, constructing an initial delivery route of the truck based on the basic information;
S3, generating an unmanned aerial vehicle route based on an initial delivery route of the truck, and obtaining a solution of the delivery route of the unmanned aerial vehicle of the truck;
S4, constructing a neighborhood structure;
And S5, based on the neighborhood structure, performing iterative optimization on a solution of the truck unmanned aerial vehicle delivery route by adopting a double variable neighborhood search algorithm to obtain an optimal truck unmanned aerial vehicle delivery route.
Further, the basic information in the step S1 includes a distance matrix corresponding to the initial position of the customer, a time constraint matrix corresponding to the time window of the customer, and the number of trucks required for the delivery task;
Wherein, based on n customer points Determining a cost matrix of Euclidean distance between every two customers, namely a distance matrix D;
The time window of the ith customer is Obtaining a corresponding time sequence constraint matrix as/>, according to time windows of all customers；/>Representing a timing constraint matrix/>(1 /)Line/>Column elements, if/>Then/>Otherwise/>; Wherein/>Representing the time that customer i was allowed to be accessed earliest,/>Indicating the time at which customer i was allowed to be accessed the latest.
Further, in the step S1, the method for determining the number of trucks required for the delivery task is as follows:
S11, calculating average time of running of a truck between any two customer points ；
S12, calculating the average time of the customer to be served；
S13, according to the average timeAnd/>Calculating the maximum working time/>, of a truckAverage number of customers accessible per unit area/>；
S14, according to the average number of customersAnd number of customers n, calculating the number of trucks needed in the delivery mission/>。
Further, the step S2 specifically includes:
S21, initializing a truck route Adding warehouse Point 0 to the set of currently accessed points/>In (a) and (b);
meanwhile, the truck with the shortest current driving distance is recorded as And when there are a plurality of trucks with the same driving distance, randomly extracting one truck from the plurality of trucks is recorded as/>；
S22, according to the time sequence constraint matrixObtain the result of/>Set B composed of indexes of all zero columns, and determining customer points/>, to be inserted, based on set BAnd insert it into truck/>Is the current route of (1);
S23, based on truck Update set/>Time series matrix/>And truck/>Route/>And updates/> based on all truck routes；
S24, judging the current setWhether all customer point indices are included;
If yes, go to step S25;
if not, returning to the step S22;
S25, taking all the current truck routes as initial delivery routes.
Further, in the step S22, a customer point to be insertedThe method comprises the following steps:
in the method, in the process of the invention, Representing truck/>Index of last customer on current route,/>Representing truck/>From the customer site/>To customer site/>Is a travel time of (2);
In the step S23, the set Time series matrix/>And truck/>Route/>The updated formula of (2) is:
in the method, in the process of the invention, Representing that the elements in the collection are only customer points/>Set of (I)/>Representing a timing matrix/>Middle/>All elements of a line,/>Representing a union.
Further, the step S3 specifically includes:
preliminary optimization is carried out on an initial delivery route of the truck by using a Fast-2Opt strategy, then an unmanned aerial vehicle route is generated by using a FindSortie strategy, and then initial solution of the delivery route of the unmanned aerial vehicle of the truck is obtained And initializing the current solution/>Globally optimal solution/>And remember/>Travel cost of/>，/>Travel cost of/>。
Further, in the step S4, the neighborhood operation of the constructed neighborhood structure includes:
(1) Random switching point: randomly taking two points in the upper vector of the solution vector, and exchanging the positions of the two points;
(2) Random switching overall: randomly rounding two columns in the whole vector, and exchanging the positions of the two columns;
(3) Random insertion points: randomly picking a point in an upper vector of the solution vector, and randomly inserting the point into other positions of the upper vector;
(4) Randomly inserting the whole: randomly taking a column in the whole solution vector, and randomly inserting the column into other positions of the whole solution vector;
(5) Removing the unmanned aerial vehicle route: randomly taking the point with the element value of 1 in the lower vector of the solution vector, and changing the value of the point into 0;
(6) Adding unmanned aerial vehicle routes: randomly taking the point with the element value of 0 in the lower vector of the solution vector, and changing the value of the point into 1;
(7) Random turning points: randomly taking two points in a lower vector of the solution vector, and then turning over a sequence between the two points in the lower vector;
(8) Randomly changing the value: randomly taking a segment of sequence in the lower vector of the solution vector, and then converting the value of the segment of sequence;
(9) Different values are randomly exchanged: randomly taking points with different values of two elements in a lower vector of the solution vector, and carrying out position exchange;
(10) Random insertion of the lower vector: randomly picking a point in a lower vector of the solution vector, and randomly inserting the point into other positions of the lower vector;
(11) Random proportional switching point: according to the number of trucks Dividing the solution vector into corresponding/>And randomly taking two sequences in the upper vectors of the two partial solution vectors, wherein the sequences satisfy the following conditions:
(12) Random scale exchange overall: according to the number of trucks Dividing the solution vector into corresponding/>And randomly taking two sequences in two whole partial solution vectors, wherein the two sequences satisfy the following conditions:
in the method, in the process of the invention, 、/>The length of the upper vector of the two partial solution vectors,/>, respectively、/>The length of the segment sequence in the upper vector corresponding to its local solution vector, respectively.
Further, the step S5 specifically includes:
S51, initializing the iteration number k=1;
s52, randomly adopting a neighborhood structure pair solution Performing primary neighborhood disturbance to obtain a solution of/>And clarify/>Travel cost of/>；
S53, adopt operationTo solution/>Iterative optimization is carried out to obtain a new solution/>And corresponding travel cost/>And judge/>Whether or not to establish;
if yes, then will be solved Give solution/>Travel cost/>Give/>Solution/>Giving globally optimal solutions/>Travel cost/>Give/>Returning to step S52 by setting the value of k to 1;
if not, increasing the value of k by 1, and proceeding to step S54;
S54, judging Whether or not it is:
If yes, return to step S52;
if not, go to step S55;
s55, initializing the iteration number k=1 again;
S56, will solve Decomposition into/>Each local solution vector corresponds to the route of each truck and the unmanned aerial vehicle carried by the truck; simultaneously record local solution/>To get the current solution/>(1 /)A local solution vector representing the/>Solution of route of vehicle truck and unmanned aerial vehicle carried by same, and/>For/>Corresponding travel costs;
s57, adopt operation For local solution/>Performing iterative optimization to obtain a new local solution/>And will solve locally/>Substitution solution/>In/>Part, get new overall solution/>At the same time update its travel cost/>；
S58, judgingWhether or not to establish;
if yes, the value of k is increased by 1, and the step S57 is returned;
If not, then the whole solution Give/>Overall solution/>Travel cost giving/>And proceeds to step S59;
s59, judging whether the algorithm running time reaches a preset time;
If yes, outputting the current global optimal solution And corresponding travel cost/>Stopping iteration to obtain an optimal truck unmanned aerial vehicle delivery route;
if not, the value of k is set to 1, and the process returns to step S52.
Further, in the step S53, operations are performedThe implementation method of the method comprises the following steps:
S531, take Record/>Representation of the/>, using 12 neighborhood structuresIndividual neighborhood structure pair solution/>Performing neighborhood disturbance;
S532, execution of Neighborhood manipulation yields a new solution/>And clarify/>Travel cost of/>；
Judging</>Whether or not to establish;
if yes, then will be solved Give solution/>Travel cost/>, of the current local optimal solution is updated simultaneouslyLet q=1, and randomly shuffle the order of the current 12 neighborhood structures, and enter step S533;
if not, the value of q is increased by 1, and the process proceeds to step S533;
S533, judging Whether or not to establish;
If yes, return to step S532;
if not, then will solve Give/>Travel cost/>Value assignment/>Complete the solution/>Is described.
Further, in the step S57, the operationThe implementation method of the method comprises the following steps:
s571 taking Record/>Representing the local solution/>, using the qth neighborhood pair of the first 10 neighborsPerforming neighborhood disturbance;
S572, execution of Neighborhood operation gets new local solution/>And record the local solution/>Travel cost of/>；
JudgingWhether or not to establish;
If yes, then will be locally solved Imparting local solution/>Travel costs for simultaneous updating of current local optimal solutionsLet q=1 and randomly shuffle the order of the current first 10 neighborhood structures;
if not, the value of q is increased by 1, and the process proceeds to step S573;
S573, judge Whether or not to establish;
If yes, return to step S572;
If not, then the local solution is performed Give/>And (5) completing iterative optimization of the local solution.
The beneficial effects of the invention are as follows:
1) Aiming at the time window constraint of customers in logistics, the invention provides a new construction algorithm of the initial truck route, which converts the time window of the customers into time sequence constraint among the customers, and then determines which customer is inserted into the current truck route according to the time margin, so as to ensure that the initial truck delivery route is generated at a lower cost violating the time window.
2) In the method, a local optimization strategy for the routes of the single truck and the unmanned aerial vehicle carried by the single truck is added into a heuristic algorithm VNS, and 6 new neighborhood structures are provided to ensure further exploration of solutions.
3) The initial solution of the truck route can be well obtained by the truck initial delivery route construction algorithm provided by the invention, and the initial solution of the truck route can be better searched by combining with the iterative optimization heuristic algorithm, so that the solution with better quality can be obtained in the same time compared with the existing method.
Drawings
Fig. 1 is a flowchart of a task allocation method for a truck unmanned aerial vehicle under a time window constraint provided by an embodiment of the present invention.
Fig. 2 is a schematic diagram of a collaborative distribution route of a truck unmanned aerial vehicle according to an embodiment of the present invention.
Fig. 3 is a solution representation of a collaborative delivery route of a truck unmanned aerial vehicle according to an embodiment of the present invention.
FIG. 4 is a comparison of the four algorithms NV, PV, ND and PD at travel cost for a small-scale customer scenario provided by an embodiment of the present invention.
FIG. 5 is a graph showing average time versus convergence of four algorithms NV, PV, ND and PD for small-scale customers according to an embodiment of the present invention.
Fig. 6 is a schematic diagram showing a possible solution for convergence of four algorithms NV, PV, ND and PD under a large-scale customer according to an embodiment of the present invention.
FIG. 7 is a comparison of the four algorithms NV, PV, ND and PD at travel cost for a large-scale customer scenario provided by an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and all the inventions which make use of the inventive concept are protected by the spirit and scope of the present invention as defined and defined in the appended claims to those skilled in the art.
The embodiment of the invention provides a truck unmanned aerial vehicle task allocation method under time window constraint, which is shown in fig. 1 and comprises the following steps:
s1, determining basic information of a distribution task;
s2, constructing an initial delivery route of the truck based on the basic information;
S3, generating an unmanned aerial vehicle route based on an initial delivery route of the truck, and obtaining a solution of the delivery route of the unmanned aerial vehicle of the truck;
S4, constructing a neighborhood structure;
And S5, based on the neighborhood structure, performing iterative optimization on a solution of the truck unmanned aerial vehicle delivery route by adopting a double variable neighborhood search algorithm to obtain an optimal truck unmanned aerial vehicle delivery route.
In step S1 of the embodiment of the present invention, the basic information includes a distance matrix corresponding to an initial position of a customer, a time constraint matrix corresponding to a time window of the customer, and the number of trucks required for a delivery task;
Wherein, based on n customer points Determining a cost matrix of Euclidean distance between every two customers, namely a distance matrix D;
The time window of the ith customer is Obtaining a corresponding time sequence constraint matrix as/>, according to time windows of all customers；/>Representing a timing constraint matrix/>(1 /)Line/>Column elements, if/>Then/>Otherwise/>; Wherein/>Representing the time that customer i was allowed to be accessed earliest,/>Indicating the time at which customer i was allowed to be accessed the latest.
In step S1 of the embodiment of the present invention, the method for determining the number of trucks required for the delivery task is:
S11, calculating average time of running of a truck between any two customer points ；
In the method, in the process of the invention,Is the/>, of the cost matrixLine/>Column element,/>Is the speed of travel of the truck,/>；
S12, calculating the average time of the customer to be served；
In the method, in the process of the invention,Representing service customer/>The required service time can be defined artificially/>Is a value of (2);
s13, according to the average time And/>Calculating the maximum working time/>, of a truckAverage number of customers accessible per unit area/>；
S14, according to the average number of customersAnd number of customers n, calculating the number of trucks needed in the delivery mission/>；
And then get the truck set。
The step S2 of the embodiment of the invention specifically comprises the following steps:
S21, initializing a truck route Adding warehouse Point 0 to the set of currently accessed points/>In (a) and (b);
meanwhile, the truck with the shortest current driving distance is recorded as And when there are a plurality of trucks with the same driving distance, randomly extracting one truck from the plurality of trucks is recorded as/>; Wherein/>；
S22, according to the time sequence constraint matrixObtain the result of/>Set B composed of indexes of all zero columns, and determining customer points/>, to be inserted, based on set BAnd insert it into truck/>Is the current route of (1);
S23, based on truck Update set/>Time series matrix/>And truck/>Route/>And updates/> based on all truck routes；
S24, judging the current setWhether all customer point indices are included, i.e., determining whether all customer points currently have been inserted into the truck route;
If yes, go to step S25;
if not, returning to the step S22;
S25, taking all the current truck routes as initial delivery routes.
In step S22 of the present embodiment, the customer point to be insertedThe method comprises the following steps:
in the method, in the process of the invention, Representing truck/>Index of last customer on current route,/>Representing truck/>From the customer site/>To customer site/>Is a travel time of (2);
In step S23 of the present embodiment, the set Time series matrix/>And truck/>Route/>The updated formula of (2) is:
in the method, in the process of the invention, Representing that the elements in the collection are only customer points/>Set of (I)/>Representing a timing matrix/>Middle/>All elements of a line,/>Representing a union.
The step S3 of the embodiment of the invention specifically comprises the following steps:
preliminary optimization is carried out on an initial delivery route of the truck by using a Fast-2Opt strategy, then an unmanned aerial vehicle route is generated by using a FindSortie strategy, and then initial solution of the delivery route of the unmanned aerial vehicle of the truck is obtained And initializing the current solution/>Globally optimal solution/>And remember/>Travel cost of/>，/>Travel cost of/>。
In step S4 of the embodiment of the present invention, the neighborhood operation of the constructed neighborhood structure includes:
(1) Random switching point: randomly taking two points in the upper vector of the solution vector, and exchanging the positions of the two points;
(2) Random switching overall: randomly rounding two columns in the whole vector, and exchanging the positions of the two columns;
(3) Random insertion points: randomly picking a point in an upper vector of the solution vector, and randomly inserting the point into other positions of the upper vector;
(4) Randomly inserting the whole: randomly taking a column in the whole solution vector, and randomly inserting the column into other positions of the whole solution vector;
(5) Removing the unmanned aerial vehicle route: randomly taking the point with the element value of 1 in the lower vector of the solution vector, and changing the value of the point into 0;
(6) Adding unmanned aerial vehicle routes: randomly taking the point with the element value of 0 in the lower vector of the solution vector, and changing the value of the point into 1;
(7) Random turning points: randomly taking two points in a lower vector of the solution vector, and then turning over (including) a sequence between the two points in the lower vector;
(8) Randomly changing the value: randomly taking a sequence in the lower vector of the solution vector, and then converting the value of the sequence (namely, 1 is changed into 0 and 0 is changed into 1);
(9) Different values are randomly exchanged: randomly taking points with different values of two elements in a lower vector of the solution vector, and carrying out position exchange;
(10) Random insertion of the lower vector: randomly picking a point in a lower vector of the solution vector, and randomly inserting the point into other positions of the lower vector;
(11) Random proportional switching point: according to the number of trucks Dividing the solution vector into corresponding/>And randomly taking two sequences in the upper vectors of the two partial solution vectors, wherein the sequences satisfy the following conditions:
(12) Random scale exchange overall: according to the number of trucks Dividing the solution vector into corresponding/>And randomly taking two sequences in two whole partial solution vectors, wherein the two sequences satisfy the following conditions:
in the method, in the process of the invention, 、/>The length of the upper vector of the two partial solution vectors,/>, respectively、/>The length of the segment sequence in the upper vector corresponding to its local solution vector, respectively.
The step S5 of the embodiment of the invention specifically comprises the following steps:
S51, initializing the iteration number k=1;
S52, executing a neighborhood disturbance strategy: randomly adopting a neighborhood structure pair solution Performing primary neighborhood disturbance to obtain a solution of/>And clarify/>Travel cost of/>；
S53, performing iterative optimization on the whole route: by operation ofTo solution/>Iterative optimization is carried out to obtain a new solution/>And corresponding travel cost/>And judge/>Whether or not to establish;
if yes, then will be solved Give solution/>Travel cost/>Give/>Solution/>Giving globally optimal solutions/>Travel cost/>Give/>Returning to step S52 by setting the value of k to 1;
if not, increasing the value of k by 1, and proceeding to step S54;
S54, judging Whether or not it is:
If yes, return to step S52;
if not, go to step S55;
s55, initializing the iteration number k=1 again;
S56, performing iterative optimization on the single route: will be solved Decomposition into/>Each local solution vector corresponds to the route of each truck and the unmanned aerial vehicle carried by the truck; simultaneously record local solution/>To get the current solution/>(1 /)A local solution vector representing the/>Solution of route of vehicle truck and unmanned aerial vehicle carried by same, and/>For/>Corresponding travel costs;
s57, adopt operation For local solution/>Performing iterative optimization to obtain a new local solution/>And will solve locally/>Substitution solution/>In/>Part, get new overall solution/>At the same time update its travel cost/>；
S58, judgingWhether or not to establish;
if yes, the value of k is increased by 1, and the step S57 is returned;
If not, then the whole solution Give/>Overall solution/>Travel cost giving/>And proceeds to step S59;
s59, judging whether the algorithm running time reaches a preset time;
If yes, outputting the current global optimal solution And corresponding travel cost/>Stopping iteration to obtain an optimal truck unmanned aerial vehicle delivery route;
if not, the value of k is set to 1, and the process returns to step S52.
In step S53 of the present embodiment, the operationThe implementation method of the method comprises the following steps:
S531, take Record/>Representation of the/>, using 12 neighborhood structuresIndividual neighborhood structure pair solution/>Performing neighborhood disturbance;
S532, execution of Neighborhood manipulation yields a new solution/>And clarify/>Travel cost of/>；
Judging</>Whether or not to establish;
if yes, then will be solved Give solution/>Travel cost/>, of the current local optimal solution is updated simultaneouslyLet q=1, and randomly shuffle the order of the current 12 neighborhood structures, and enter step S533;
if not, the value of q is increased by 1, and the process proceeds to step S533;
S533, judging Whether or not to establish;
If yes, return to step S532;
if not, then will solve Give/>Travel cost/>Value assignment/>Complete the solution/>Is described.
In step S57 of the present embodiment, the operationThe implementation method of the method comprises the following steps:
s571 taking Record/>Representing the local solution/>, using the qth neighborhood pair of the first 10 neighborsPerforming neighborhood disturbance;
S572, execution of Neighborhood operation gets new local solution/>And record the local solution/>Travel cost of/>；
JudgingWhether or not to establish;
If yes, then will be locally solved Imparting local solution/>Travel costs for simultaneous updating of current local optimal solutionsLet q=1 and randomly shuffle the order of the current first 10 neighborhood structures;
if not, the value of q is increased by 1, and the process proceeds to step S573;
S573, judge Whether or not to establish;
If yes, return to step S572;
If not, then the local solution is performed Give/>And (5) completing iterative optimization of the local solution.
Based on the above process, the embodiment of the invention provides a multi-truck multi-unmanned aerial vehicle package delivery task allocation method based on the constraint of a customer time window and under the constraint of limited loads and working time of trucks and unmanned aerial vehicles; namely: the delivery route for the truck and drone to cooperatively visit the customer is determined such that the total travel costs incurred by the truck and drone are minimized while meeting the truck and drone limited load and length of service constraints.
Specifically, in constructing the initial delivery route of the truck, a time-time margin-based algorithm is used: a corresponding timing matrix is first generated from the customer's time window and an initial route for the truck to visit all customers is generated based on the time margin. Compared with the traditional nearest neighbor algorithm for constructing the initial route of the truck, the method well considers the time window constraint of the customer, and reduces the cost caused by violating the time window of the customer. In the iterative optimization stage, the double variable neighborhood search algorithm designs a plurality of neighborhood structures to search the solution space. Unlike the traditional variable neighborhood search operator which only optimizes the global solution, the neighborhood operator designed by the double variable neighborhood search algorithm can strengthen the search capability of the local solution and can independently optimize the routes of a single truck and unmanned aerial vehicles carried by the single truck. Furthermore, the dual variant neighborhood search algorithm also designs neighborhood structure operators that take into account customer time window constraints, which allows for a greater probability of generating solutions that fit the time window constraints when performing the iterative optimization phase.
In this embodiment, an example of a coordinated delivery route of a truck and a drone is shown in fig. 2, and fig. 3 is a representation of a solution of the delivery route in fig. 2, the representation being composed of an upper vector and a lower vector. The total length of the upper vector is（/>: Number of customers,/>: Number of trucks), the lower vector length is the same as the upper vector. The upper vector reflects the route of the truck and drone, where a "0" represents the start of the new route and/or the end of the current route (i.e., warehouse), and a non-zero value represents the customer point. The lower vector consists of binary digits, the numerical value determining whether the corresponding customer point is accessed by a truck or a drone. Given value/>The lower vector will operate according to the following rules: 1) If the value of the upper vector index is "0", the value of the lower vector corresponding index is also "0"; 2) If lower vector index/>The value of "0", then upper vector index/>The corresponding customer point will be accessed by the truck; 3) If lower vector index/>The value of "1", and indexThe value of "0", then upper vector index/>The corresponding customer point will be accessed by the drone; 4) If lower vector index/>The value of "1", and index/>The upper vector index/>, is also "1"The corresponding customer point will be accessed by the truck; 5) Given a numerical sequence with a lower vector value of "1", the launch point and recovery point of the drone are represented by the customer points corresponding to the previous and subsequent indices of the sequence, respectively.
In one embodiment of the present invention, as shown in fig. 4-7 (in which the abscissa n represents the number of customers and w represents the width of the time window of the customers), simulation experiment results of the problem of allocation of the collaborative package delivery tasks of the unmanned truck aircraft under the constraint of the time window are shown, and all points in fig. 4-7, including warehouse points and customer points, are distributedWhere n represents the number of customer points and w represents the time window width of the customer points. The running speed of the truck is 35 kph, and the maximum load capacity is 1400 kg; the flight rate of the unmanned aerial vehicle is 50 kph, and the maximum load capacity is 5 kg; the maximum working time of a truck driver is 480 min, and the time required by the truck to launch and recycle the unmanned aerial vehicle is 1 min; the duration of the unmanned aerial vehicle is 30 min. PD in the figure is an algorithm of the invention (P represents a truck initial solution construction algorithm in the invention, D represents a local optimization algorithm in the invention), NV is an existing task allocation method (N represents the truck initial solution construction algorithm, namely a nearest neighbor algorithm (Nearest Neighbor approach), V represents the local optimization algorithm, namely a variable neighborhood search algorithm (Variable Neighborhood search)), and PV and ND are respectively obtained by splitting and combining the two algorithms.
Fig. 4 and 5 are comparisons of the four algorithms in the case of small-scale customers, it can be seen that the algorithm PD of the present invention achieves a better solution in each case than the NV algorithm, i.e. the overall travel cost of the truck and drone is lower. While fig. 5 also shows that the convergence rate of the PD algorithm is faster than that of the algorithm NV on the premise of obtaining a better solution, which further illustrates the effectiveness and efficiency of the algorithm PD. Fig. 6 and 7 are comparisons of four algorithms in the case of a large-scale customer, and it can be seen from fig. 6 that the algorithm NV does not necessarily get a valid solution each time in the case of a large-scale customer, i.e. that there is a violation of the time window in the solution. While the other three algorithms can all obtain 100% of effective solutions. By comparing the effects of the algorithms NV and PV, it can be seen that the truck initial solution construction algorithm of the present invention can well plan the initial route to reduce the cost of violating the time window. By comparing the algorithms NV and ND, the double variable neighborhood search algorithm can be found to strengthen the search capability of local solutions, and further obtain effective solutions. The algorithm PD combines the advantages of the truck initial solution construction algorithm and the dual variable neighborhood search algorithm, and can well obtain an effective solution. As can be seen from fig. 7, in the resulting effective solution, the performance of the four algorithms is represented as: PD > PV > ND > NV, which further illustrates the superiority of the PD algorithm in the present invention.
The principles and embodiments of the present invention have been described in detail with reference to specific examples, which are provided to facilitate understanding of the method and core ideas of the present invention; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.
Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.
Claims (2)
1. The method for distributing the tasks of the unmanned aerial vehicle of the truck under the constraint of the time window is characterized by comprising the following steps of:
s1, determining basic information of a distribution task;
s2, constructing an initial delivery route of the truck based on the basic information;
S3, generating an unmanned aerial vehicle route based on an initial delivery route of the truck, and obtaining a solution of the delivery route of the unmanned aerial vehicle of the truck;
S4, constructing a neighborhood structure;
S5, based on the neighborhood structure, carrying out iterative optimization on a solution of the truck unmanned aerial vehicle delivery route by adopting a double variable neighborhood search algorithm to obtain an optimal truck unmanned aerial vehicle delivery route;
The basic information in the step S1 includes a distance matrix corresponding to an initial position of the customer, a time sequence constraint matrix corresponding to a time window of the customer, and the number of trucks required by the delivery task;
Wherein, based on n customer points Determining a cost matrix of Euclidean distance between every two customers, namely a distance matrix D;
The time window of the ith customer is Obtaining a corresponding time sequence constraint matrix as/>, according to time windows of all customers；Representing a timing constraint matrix/>(1 /)Line/>Column elements, if/>Then/>Otherwise/>; Wherein/>Representing the time that customer i was allowed to be accessed earliest,/>Representing the time that customer i was allowed to be accessed the latest;
the step S2 specifically comprises the following steps:
S21, initializing a truck route Adding warehouse Point 0 to the set of currently accessed points/>In (a) and (b);
meanwhile, the truck with the shortest current driving distance is recorded as And when there are a plurality of trucks with the same driving distance, randomly extracting one truck from the plurality of trucks is recorded as/>；
S22, according to the time sequence constraint matrixObtain the result of/>Set B composed of indexes of all zero columns, and determining customer points/>, to be inserted, based on set BAnd insert it into truck/>Is the current route of (1);
S23, based on truck Update set/>Time series matrix/>And truck/>Route/>And updates/> based on all truck routes；
S24, judging the current setWhether all customer point indices are included;
If yes, go to step S25;
if not, returning to the step S22;
S25, taking all current truck routes as initial delivery routes;
in step S22, the customer point to be inserted The method comprises the following steps:
in the method, in the process of the invention, Representing truck/>Index of last customer on current route,/>Representing truck/>From the customer site/>To customer site/>Is a travel time of (2);
In the step S23, the set Time series matrix/>And truck/>Route/>The updated formula of (2) is:
in the method, in the process of the invention, Representing that the elements in the collection are only customer points/>Set of (I)/>Representing a timing matrix/>Middle/>All elements of a line,/>Representing a union;
the step S3 specifically comprises the following steps:
preliminary optimization is carried out on an initial delivery route of the truck by using a Fast-2Opt strategy, then an unmanned aerial vehicle route is generated by using a FindSortie strategy, and then initial solution of the delivery route of the unmanned aerial vehicle of the truck is obtained And initializing the current solution/>Globally optimal solution/>And remember/>Travel cost of/>，/>Travel cost of/>；
In the step S4, the neighborhood operation of the constructed neighborhood structure includes:
(1) Random switching point: randomly taking two points in the upper vector of the solution vector, and exchanging the positions of the two points;
(2) Random switching overall: randomly rounding two columns in the whole vector, and exchanging the positions of the two columns;
(3) Random insertion points: randomly picking a point in an upper vector of the solution vector, and randomly inserting the point into other positions of the upper vector;
(4) Randomly inserting the whole: randomly taking a column in the whole solution vector, and randomly inserting the column into other positions of the whole solution vector;
(5) Removing the unmanned aerial vehicle route: randomly taking the point with the element value of 1 in the lower vector of the solution vector, and changing the value of the point into 0;
(6) Adding unmanned aerial vehicle routes: randomly taking the point with the element value of 0 in the lower vector of the solution vector, and changing the value of the point into 1;
(7) Random turning points: randomly taking two points in a lower vector of the solution vector, and then turning over a sequence between the two points in the lower vector;
(8) Randomly changing the value: randomly taking a segment of sequence in the lower vector of the solution vector, and then converting the value of the segment of sequence;
(9) Different values are randomly exchanged: randomly taking points with different values of two elements in a lower vector of the solution vector, and carrying out position exchange;
(10) Random insertion of the lower vector: randomly picking a point in a lower vector of the solution vector, and randomly inserting the point into other positions of the lower vector;
(11) Random proportional switching point: according to the number of trucks Dividing the solution vector into corresponding/>And randomly taking two sequences in the upper vectors of the two partial solution vectors, wherein the sequences satisfy the following conditions:
(12) Random scale exchange overall: according to the number of trucks Dividing the solution vector into corresponding/>And randomly taking two sequences in two whole partial solution vectors, wherein the two sequences satisfy the following conditions:
in the method, in the process of the invention, 、/>The length of the upper vector of the two partial solution vectors,/>, respectively、/>The length of the segment of sequence in the upper vector corresponding to the partial solution vector;
the step S5 specifically comprises the following steps:
S51, initializing the iteration number k=1;
s52, randomly adopting a neighborhood structure pair solution Performing primary neighborhood disturbance to obtain a solution of/>And memorizeTravel cost of/>；
S53, adopt operationTo solution/>Iterative optimization is carried out to obtain a new solution/>And corresponding travel cost/>And judge/>Whether or not to establish;
if yes, then will be solved Give solution/>Travel cost/>Give/>Solution/>Giving globally optimal solutions/>Travel cost/>Give/>Returning to step S52 by setting the value of k to 1;
if not, increasing the value of k by 1, and proceeding to step S54;
S54, judging Whether or not it is:
If yes, return to step S52;
if not, go to step S55;
s55, initializing the iteration number k=1 again;
S56, will solve Decomposition into/>Each local solution vector corresponds to the route of each truck and the unmanned aerial vehicle carried by the truck; simultaneously record local solution/>To get the current solution/>(1 /)A local solution vector representing the/>Solution of route of vehicle truck and unmanned aerial vehicle carried by same, and/>For/>Corresponding travel costs;
s57, adopt operation For local solution/>Performing iterative optimization to obtain a new local solution/>And will solve locally/>Substitution solution/>In/>Part, get new overall solution/>At the same time update its travel cost/>；
S58, judgingWhether or not to establish;
if yes, the value of k is increased by 1, and the step S57 is returned;
If not, then the whole solution Give/>Overall solution/>Travel cost giving/>And proceeds to step S59;
s59, judging whether the algorithm running time reaches a preset time;
If yes, outputting the current global optimal solution And corresponding travel cost/>Stopping iteration to obtain an optimal truck unmanned aerial vehicle delivery route;
if not, the value of k is set to 1, and the step S52 is returned; in the step S53, an operation The implementation method of the method comprises the following steps:
S531, take Record/>Representation of the/>, using 12 neighborhood structuresIndividual neighborhood structure pair solution/>Performing neighborhood disturbance;
S532, execution of Neighborhood manipulation yields a new solution/>And clarify/>Travel cost of/>；
Judging</>Whether or not to establish;
if yes, then will be solved Give solution/>Travel cost/>, of the current local optimal solution is updated simultaneouslyLet q=1, and randomly shuffle the order of the current 12 neighborhood structures, and enter step S533;
if not, the value of q is increased by 1, and the process proceeds to step S533;
S533, judging Whether or not to establish;
If yes, return to step S532;
if not, then will solve Give/>Travel cost/>Value assignment/>Complete the solution/>Is optimized for iteration;
in the step S57, an operation The implementation method of the method comprises the following steps:
s571 taking Record/>Representing the local solution/>, using the qth neighborhood pair of the first 10 neighborsPerforming neighborhood disturbance;
S572, execution of Neighborhood operation gets new local solution/>And record the local solution/>The travel cost of (2) is；
JudgingWhether or not to establish;
If yes, then will be locally solved Imparting local solution/>Travel costs for simultaneous updating of current local optimal solutionsLet q=1 and randomly shuffle the order of the current first 10 neighborhood structures;
if not, the value of q is increased by 1, and the process proceeds to step S573;
S573, judge Whether or not to establish;
If yes, return to step S572;
If not, then the local solution is performed Give/>And (5) completing iterative optimization of the local solution.
2. The method for allocating tasks to the unmanned aerial vehicle on the truck under the constraint of the time window according to claim 1, wherein in the step S1, the method for determining the number of trucks required for the task is as follows:
S11, calculating average time of running of a truck between any two customer points ；
S12, calculating the average time of the customer to be served；
S13, according to the average timeAnd/>Calculating the maximum working time/>, of a truckAverage number of customers accessible；
S14, according to the average number of customersAnd number of customers n, calculating the number of trucks needed in the delivery mission/>。
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