An unmanned delivery method based on heterogeneous facility joint delivery

Abstract

The present application relates to the technical field of unmanned distribution, and particularly relates to an unmanned distribution method based on heterogeneous facility joint distribution. The method comprises the following steps: constructing an unmanned distribution mathematical programming model based on the joint of unmanned self-service cabinets and multifunctional unmanned distribution stations, carrying out heterogeneous unmanned facility configuration, customer allocation and robot vehicle path integrated optimization for personalized demand; based on the integrated optimization decision, designing a solution representation method which is coupled with two-way vector mapping of allocation relationship and path planning; designing a variable neighborhood search algorithm which is fused with multiple advanced search strategies. The unmanned distribution method based on heterogeneous facility joint distribution can provide efficient last kilometer personalized distribution service and solve the heterogeneous facility site selection-coverage-path for personalized demand by improving the distribution method and planning the route in the distribution, and further solve the distribution demand of large-scale distribution customers in the actual operation process.

Description

Technical Field

[0001] This invention relates to the field of unmanned delivery technology, and in particular to an unmanned delivery method based on the joint delivery of heterogeneous facilities. Background Technology

[0002] In recent years, intensified competition and rising human resource costs in the logistics industry have prompted logistics companies to continuously seek new technologies and models to gain a competitive edge. Unmanned delivery technology, with its ability to provide more efficient delivery services, is bringing about a revolutionary development in last-mile delivery.

[0003] Unattended parcel lockers (UPLs) are an important application of unmanned delivery technology. These facilities are typically located in residential or commercial areas to provide customers with 24 / 7 "click-and-pick" service (Faugere and Montreuil, 2020). Figure 1 As shown in (a). Another application is the multi-functional delivery station (MDS), a type of facility originally designed by JD.com in 2018, such as... Figure 1 As shown in (b), the facility serves both as an unmanned parcel locker for customer pickup and as a small warehouse equipped with unmanned delivery robots for door-to-door delivery. Given the limited capacity of the robots, they must return to the station after completing their current delivery task, reload, and perform multiple deliveries.

[0004] Because MDS facilities integrate delivery robots and necessary automated equipment for loading packages, their construction costs are typically higher than those of UPL facilities.

[0005] To address this issue, an unmanned delivery method based on heterogeneous facility joint delivery is designed to provide an alternative technical solution. Summary of the Invention

[0006] Therefore, it is necessary to provide an unmanned delivery method based on heterogeneous facility joint delivery to address the aforementioned technical problems.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] An unmanned delivery method based on heterogeneous facility joint delivery, the method comprising:

[0009] Construct a mathematical programming model for unmanned delivery based on the combination of unmanned self-service lockers and multi-functional unmanned delivery stations, and carry out integrated optimization of heterogeneous unmanned facility configuration, customer allocation and robot vehicle path integration for personalized needs;

[0010] Based on integrated optimization decision-making, a solution representation method is designed that integrates allocation relationships and path planning with a two-vector mapping coupling.

[0011] A variable neighborhood search algorithm integrating multiple advanced search strategies was designed to obtain an operation scheme for an unmanned delivery system under the joint operation of heterogeneous unmanned facilities.

[0012] As a preferred embodiment of the unmanned delivery method based on heterogeneous facility joint delivery provided by the present invention, the unmanned delivery mathematical programming model is constructed, and the steps are as follows:

[0013] Customer needs are categorized into three types: self-pickup, door-to-door delivery with a time window, and flexible services. Expression models for each type of need are established, and a delivery model with the goal of minimizing total cost is established based on the service relationship between heterogeneous unmanned facilities and the three types of needs.

[0014] As a preferred embodiment of the unmanned delivery method based on heterogeneous facility joint delivery provided by the present invention, the objective function expression is:

[0015]

[0016] In the formula, F p For the fixed cost of the unmanned self-pickup facility p, F v For the fixed cost of the multi-functional unmanned delivery station p, r ij Let c be the path cost from node i to node j. ip Let A be the connection cost from client node i to facility p, and R be the arc set. p For the set of delivery robot trips of self-pickup facility p, N p For the set of candidate facilities, N FS For flexible customer groups, N CP For customers who wish to pick up their orders in person; Let be a variable representing the decision to open unmanned self-pickup facilities; Let be a variable representing the decision to open a multi-functional unmanned delivery station; Let be a variable, representing the path arc (i,j) traversed by the delivery robot of facility p in the r-th formation; y ip Let be a variable, representing that customer i is served by facility p.

[0017] As a preferred embodiment of the unmanned delivery method based on heterogeneous facility joint delivery provided by the present invention, a solution representation is constructed by an allocation relationship component F and a path planning component R, and the two components are mapped to each other. The steps are as follows:

[0018] A. Component F consists of a fixed length of |N CThe string consists of three layers of integers, representing the customer index, three types of customer service models, and the corresponding customer's service facilities, where |N C | For the total number of customers;

[0019] B. Component R represents the delivery route of the delivery robot, which consists of self-pickup facilities, HD customers, and FS customers; the self-pickup facility index is used to distinguish the delivery routes of different robots and to divide the trip within a single delivery route, and the composition of the nodes in the route is based on component F.

[0020] As a preferred embodiment of the unmanned delivery method based on heterogeneous facility joint delivery provided by the present invention, an initial solution is quickly constructed for the variable neighborhood search algorithm through a two-stage construction heuristic, and the steps are as follows:

[0021] 1) Conduct site selection and customer allocation for heterogeneous unmanned facilities using a greedy rule;

[0022] 2) Based on the facility location and customer allocation results in step 1), the generalized insertion heuristic for solving TSPW is used to construct an open multi-functional delivery station robot delivery path plan.

[0023] As a preferred embodiment of the unmanned delivery method based on heterogeneous facility joint delivery provided by the present invention, a variable neighborhood search algorithm integrating three improved search strategies is designed to optimize the initial path in delivery route planning.

[0024] As a preferred embodiment of the unmanned delivery method based on heterogeneous facility joint delivery provided by the present invention, an adaptive jitter strategy is used to select from the operator set N Shaking The steps for dynamically selecting operators in the middle are as follows:

[0025] All neighborhood structures are assigned an equal initial weight of zero. During the algorithm search process, the weights are updated after each iteration of the main loop of the variable neighborhood search algorithm.

[0026] By evaluating the neighborhood structure at a certain number of main iterations I shaking The historical solutions obtained internally are used to adaptively identify promising solutions;

[0027] For each neighborhood structure s∈N Shaking Define the weight ω s The formula for calculating its selection probability is as follows:

[0028]

[0029] Where, n s In the past, I iter The number of times the neighborhood structure s is used in each iteration. F represents the improvement in the target value achieved by using the neighborhood structure s; u and F l Corresponding to the past I shaking The target values ​​of the worst and best solutions encountered in each iteration.

[0030] As a preferred embodiment of the unmanned delivery method based on heterogeneous facility joint delivery provided by the present invention, a local search is performed on the variable neighborhood search algorithm using a variable neighborhood depth probing algorithm, and the steps are as follows:

[0031] Four sets of local search structures based on problem features are defined as follows:

[0032] N VND =N rt ∪N fs ∪N ca ∪N rs

[0033] Where, N rt N fs N ca and N rs These correspond to path, FS customer service, customer allocation, and path neighborhood, respectively.

[0034] The variable neighborhood depth probing algorithm employs an initial improvement strategy to systematically explore all possible movement operations in the neighborhood structure in order to seek improved solutions. When the first improved solution is found, it jumps out of the current operator and moves to the next operator to continue the search.

[0035] As a preferred embodiment of the unmanned delivery method based on heterogeneous facility joint delivery provided by the present invention, the variable neighborhood search algorithm is allowed to escape the current optimal solution through a skewed acceptance strategy to promote global optimization. The steps are as follows:

[0036] For a pair of solutions Introduction of functions To represent the similarity between the two;

[0037] function If the self-pickup facility i is in the solution S and If both sides are open, the function's value is 1; otherwise, it is 0.

[0038] function If facility i is in solution S and If Zhongdu is opened as a multi-functional unmanned delivery station, then the value of this function is 1; otherwise, it is 0.

[0039] For a pair of solutions Similarity function between the two The definition is as follows:

[0040]

[0041] As a preferred embodiment of the unmanned delivery method based on heterogeneous facility joint delivery provided by the present invention, the VNS balances diversification and centralization in its exploration through a regret and backtracking strategy, and the steps are as follows:

[0042] The search process summarizes and records the best solution S found in every k iterations. cbest ;

[0043] If the current skew solution S cur If there is no improvement in k main iterations of MVNS, then use S. cbest Restart the search process.

[0044] It is clear without a doubt that the technical solution described above in this application can solve the technical problem that this application aims to address.

[0045] Meanwhile, through the above technical solutions, the present invention has at least the following beneficial effects:

[0046] This invention provides an unmanned delivery method based on heterogeneous facility joint delivery. By constructing an unmanned delivery system and utilizing a designed efficient intelligent algorithm for facility configuration and delivery robot path planning, and by carrying out integrated decision-making on heterogeneous facility site selection, coverage, and path optimization to meet personalized needs, it can provide efficient last-mile personalized delivery services. This addresses the delivery needs of large-scale customers in actual operation, achieving multiple goals of customer satisfaction, green and low-carbon development, and economic efficiency. Attached Figure Description

[0047] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 These are schematic diagrams of two types of unmanned delivery facilities in existing technologies;

[0049] Figure 2 This is a schematic diagram of the HF-LCRP-PR of the present invention;

[0050] Figure 3 This is a schematic diagram representing the solution scheme of the present invention;

[0051] Figure 4 This is a schematic diagram of the R&TB operation of the present invention;

[0052] Figure 5This is a schematic diagram of example 100-8-8a of the present invention;

[0053] Figure 6 This is a schematic diagram of the results of the I300-15-15a example set of the present invention;

[0054] Figure 7 This is a schematic diagram of the results of the I300-15-15c example set of the present invention;

[0055] Figure 8 This is a schematic diagram illustrating the analysis results of different robot travel distances according to the present invention.

[0056] Figure 9 This is a schematic diagram illustrating the analysis results of different robot loading capacities according to the present invention;

[0057] Figure 10 This is a schematic diagram illustrating the cost analysis under different |NFS| conditions of the present invention;

[0058] Figure 11 This is a schematic diagram illustrating the number of FS customers in the path of this invention;

[0059] Figure 12 This is a schematic diagram showing the number of open facilities in this invention. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0061] To enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0062] It should be noted that, unless otherwise specified, the embodiments and features and technical solutions in the present invention can be combined with each other.

[0063] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0064] Reference Figures 1-12 An unmanned delivery method based on joint delivery of heterogeneous facilities.

[0065] 1. Problem Explanation

[0066] Last-mile delivery systems in urban environments typically employ a two-tiered delivery network. The second tier handles the final delivery stage, strategically utilizing unattended parcel lockers (UPLs) and multi-functional delivery stations (MDSs) to meet customer delivery needs. Large trucks transport parcels from distribution centers to UPL and MDS facilities, as illustrated in the diagram. Figure 2 As shown. In actual operation, to ensure the stability of the delivery service, the delivery area is usually divided into several sub-areas, each served by a fixed truck that transports packages from the distribution center to the self-pickup facility.

[0067] Due to the high concentration of customers in urban environments and restrictions on large vehicles, each sub-region is relatively small, resulting in a more concentrated spatial distribution of the limited number of self-pickup facilities. In this context, optimizing the first-tier logistics network does not yield significant cost benefits.

[0068] Determine the number and location of open UPL and MDS facilities, assign customers with self-pickup (CP) and FS needs to the corresponding UPL or MDS facilities, and develop delivery routes for each MDS robot to serve customers with time-window delivery (HD) and flexible service (FS) needs to minimize operating costs.

[0069] In a given mixed directed graph G = (N, A, C), N is the set of vertices, and A and C are the sets of directed arcs, respectively. The vertex set N = N C ∪D P D P This represents a collection of self-pickup facilities, which is further divided into D. U ∪D A D U and D A This refers to a collection of unmanned parcel lockers (UPL) and multi-functional distribution stations (MDS). Collection N C This represents a group of customers, which is further divided into N. C =N HD ∪N CP ∪N FS Different sets are defined as follows:

[0070] Each customer i∈N C Define the number of packages to be delivered, q. i and corresponding service time s i This is the time required to provide service based on customer type. Furthermore, for customer i∈N HD ∪N FS There is a service time window [e]i ,l i ], where e i and l i These are the earliest and latest times when delivery will begin.

[0071] Arc set A consists of a set of path arcs, defined as A = {(i,j): i ≠ j, i,j ∈ N} R}, where N R =N HD ∪N FS ∪D P Each arc (i,j)∈A corresponds to a path cost r. ij and travel time t ij .

[0072] The set C consists of a set of assignment arcs, defined as C = {(i, p): i ∈ N} CP ∪N FS ,p∈D P The connection cost for each arc (i,p)∈C is c. ip Specifically, for customer i∈N CP ∪N FS There exists an expected self-pickup distance D. If the self-pickup distance exceeds the expected distance, distance-related compensation will occur due to decreased service satisfaction. Assume that the compensation is linearly positively correlated with the distance exceeding the expected self-pickup distance. Therefore, for any arc (i,p)∈C, we have c ip =max{0,c u (d ip -D)}, where c u It is the compensation coefficient. According to this definition, if d ip If ≤D, then customer i∈N CP ∪N FS Covered by self-pickup facility p, otherwise by c ip >0 will be compensated and covered.

[0073] Each customer i∈N C A set of candidate allocation arcs corresponds to the customer type. Specifically, N CP Customers in the D can be assigned to D U The facilities in N HD Customers in the D can be assigned to D A The facilities in, and N FS Customers in the D can be assigned to D P Facilities within. C i The set is based on customers and D P Definition of the correspondence between facilities.

[0074] Each self-pickup facility p∈N p The fixed cost is Fp The capacity is Q P Furthermore, for each facility k∈D A Each facility is equipped with one delivery robot for door-to-door delivery service. If a self-pickup facility is open as an MDS facility, then that facility will be equipped with one delivery robot. Each robot has a fixed cost F. v , capacity Q v and maximum driving distance L v Delivery robot k∈D A The itinerary was recorded as R k For each journey r∈R k There is a setup time for loading robots. It is related to the total number of packages delivered in the trip r and the loading time β per package.

[0075] N CP ∪N FS Customers can pick up their packages from open UPL or MDS facilities. Delivery robots depart from MDS and deliver to N. HD ∪N FS Customers in the area receive door-to-door delivery services, and after completing their current journey, they return to the same MDS to reload packages, and in L v Perform another trip within the country.

[0076] The problem aims to configure two types of facilities, assign customers to facilities, and design vehicle routes for delivery robots in each MDS based on customers' personalized service needs, thereby minimizing the sum of the opening costs, routing costs, and connectivity costs (compensation costs incurred for customers with CP and FS needs due to violations of expected self-pickup distances) for both types of facilities.

[0077] The symbols used in this embodiment have the meanings shown in Table 1.

[0078] Table 1: Symbols and their corresponding meanings

[0079]

[0080]

[0081] 2. Model Building

[0082] The mathematical model of HF-LCRP-PR can be represented as follows:

[0083] The objective function formula (1) minimizes the sum of facility opening costs, fixed robot costs, robot route costs, and compensation for violating expected self-pickup distances, as expressed below:

[0084]

[0085] Constraint formula (2) requires that every customer with CP needs must be covered by UPL facilities, as expressed below:

[0086]

[0087] Constraint formula (3) ensures that each customer with HD needs must be accessed by the robot exactly once, as shown in the following expression:

[0088]

[0089] Constraint formula (4) ensures that each customer with FS needs is either covered by UPL facilities or accessed by a robot, as expressed below:

[0090]

[0091] The constraint formulas (5)-(7) represent the flow conservation for a single stroke, and their expressions are as follows:

[0092]

[0093] Constraint formula (8) ensures that the demand delivered by the robot in each stroke does not exceed the robot's capacity, and its expression is as follows:

[0094]

[0095] The constraint formulas (9) to (11) ensure the feasibility of the time window, and their expressions are as follows:

[0096]

[0097] Constraint formula (12) defines the robot loading time for the stroke, and its expression is as follows:

[0098]

[0099] Constraint formulas (13)-(14) ensure the correct stroke sequence for a single robot, and their expressions are as follows:

[0100]

[0101] The constraint formula (15) indicates that the robot's travel distance cannot be exceeded, and the expression is as follows:

[0102]

[0103] The constraint formula (16) states that the total demand served by the self-pickup facility cannot exceed the capacity, as expressed below:

[0104]

[0105] Constraint formula (17) implies that the number of available robots should not be violated, as expressed below:

[0106]

[0107] Constraint formulas (18)-(20) indicate the relationship between decision variables, as shown in the following expressions:

[0108]

[0109] Constraint formulas (21)-(25) define the domain of the variables, and their expressions are as follows:

[0110]

[0111] 3. Solution

[0112] The improved variable neighborhood search (MVNS) algorithm is used to solve the model and address the delivery needs of large-scale delivery customers in actual operation.

[0113] The VNS algorithm was originally developed by A metaheuristic method proposed by Hansen (1997);

[0114] The VNS algorithm typically begins with an initial solution and a set of k... max The set of neighborhood structures N of each neighborhood structure K The main program of the algorithm executes the dithering and local search components sequentially until the algorithm's termination condition is met. For a given current solution S, each main loop performs a dithering operation once, randomly generating a new solution S' using the k-th neighborhood to determine the local optimum S”∈N. K (S'). If the newly generated solution is better than the current solution, then replace S with S'". Then, the main program of the algorithm continues the search with S' as the starting point and k set to 1. If S' does not improve upon S, then S is still used to utilize the subsequent neighborhood structure N. k+1 The starting point for randomly generating the next solution is shown in the pseudocode below:

[0115]

[0116]

[0117] 3.1 Solution Representation

[0118] A solution representation scheme consisting of components F and R is designed based on the characteristics of the problem.

[0119] Component F consists of a fixed length of |N CThe string consists of three layers of integers, representing the customer index, three types of customer service models, and the corresponding customer's service facilities, where |N C The first layer represents the total number of customers. The third layer stores the index of all customers; the second layer represents the delivery service mode corresponding to the customers in the third layer, where "1" refers to HD and "2" refers to CP. The first layer is the index of the open self-pickup facilities. The first and third layers together represent the allocation relationship between customers and self-pickup lockers.

[0120] Component R represents the delivery route of the delivery robot, consisting of self-pickup facilities, HD customers, and FS customers. The self-pickup facility index is used to distinguish the delivery routes of different robots and to divide the trip within a single delivery route. The composition of nodes in the route is based on component F. Figure 2 The solution representation for the example shown is as follows: Figure 3 As shown.

[0121] 3.2 Initial Solution Construction Algorithm

[0122] The initial solution is one of the two key components for starting the VNS algorithm. Based on the problem characteristics, a two-phase construction heuristic (TPCH) is designed to quickly construct the initial solution for MVNS. TPCH focuses on four types of decisions involved in the problem: (1) determining the location of two types of facilities; (2) assigning customers to open facilities; (3) determining the FS customer service mode—whether by vehicle or customer self-pickup; and (4) planning delivery routes for delivery robots at open MDS facilities. Specifically, it includes the following two phases:

[0123] Phase 1: Facility Site Selection and Customer Allocation

[0124] Using greedy rules to select locations for heterogeneous unmanned facilities and allocate customers;

[0125] First, all candidate pickup facilities are opened. Then, based on the capacity limitations of the pickup facilities, each customer is assigned to the nearest facility or the facility with the least compensation. For a pickup facility p∈D p If the self-pickup facility is assigned only to CP customers, it is designated as a UPL facility; otherwise, if there are at least one FS or HD customer, the self-pickup facility is opened as an MDS facility.

[0126] Phase 2: MDS Path Planning

[0127] According to phase 1, set N C The customers in the n have been assigned to n u One UPL facility and n m There are n MDS facilities. Therefore, the robot pathing problem is further decomposed into n mEach sub-problem corresponds to a vehicle path that includes all HD and FS customers currently served by the MDS.

[0128] To solve the subproblems, the generalized insertion heuristic for solving the TSPW proposed by Gendreau et al. (1998) is first used to relax the vehicle capacity constraint and construct a large TSP path. Then, this TSP path is divided into sub-routes according to vehicle capacity. Finally, for each FS customer i∈N FS If c ip If the value is greater than 0, a greedy strategy is used to determine its service model; if... Customers will have their goods delivered to their door by robots. This represents the minimum increase in route cost when inserting customer i into the robot delivery route of MDS facility p. Finally, post-path optimization is performed, which uses a local search algorithm consisting of three classic route operators (exchange, insertion, and 2-Opt) to improve the quality of the current path.

[0129] 3.3 Adaptive Jitter Strategy

[0130] (1) Jitter Domain Structure

[0131] Based on the initial solution, MVNS systematically explores increasingly larger neighborhoods in order to find the global optimum. (Stenger等,2013) Based on this search mechanism, the selection of neighborhood structures is crucial to the algorithm's search efficiency and solution quality. Each neighborhood structure must strike a balance between modifying the current solution and preserving its valid components. (Hemmelmayr等,2009) .

[0132] Based on the spatial structure of the HF-LCRP-PR solution, five neighborhood structures are defined as follows:

[0133] • Facility Change (N1). This neighborhood structure involves the opening or closing of individual facilities. Randomly select a facility and change its status. Ensure the total open facility capacity meets... Under the premise of the lower limit, the facility will be changed from open to closed or from closed to open.

[0134] • Facility Exchange (N2). Select a closed facility and open it, while simultaneously closing another open facility. This operation must ensure that the total capacity of the open facilities meets the delivery needs of all customers.

[0135] • MDS is converted to UPL(N3). When the existing solution has no time window or the robot travel time is violated, MDS is replaced with UPL.

[0136] • Convert UPL to MDS(N4). Replace UPL with MDS when the existing solution has a time window or the robot travel time is violated.

[0137] • Customer reassignment (N5). Randomly select n rl Individual customers are reassigned to other facilities by applying customer mobility actions (such as decharacterization steps).

[0138] (2) Adaptive mechanism

[0139] Considering that completely random selection of the neighborhood structure during the jitter phase can lead to highly unstable behavior of VNS in certain complex optimization problems. (Stenger等,2013) Adaptive mechanisms help to better manage the jitter process. (Pisinger和Ropke,2007；Sadati等,2021；Stenger等,2013；Wei等,2014) Given that the five designed neighborhood structures have different exploration granularities in the solution space, an adaptive neighborhood structure selection mechanism is designed to manage the jitter process. Unlike the classical method that updates probabilities based on the number of improvements made by each operator, this invention designs an adaptive jitter mechanism based on solution quality from the jitter set N. Shaking Dynamically select operators in {N1, N2, N3, N4, N5}.

[0140] Specifically, by evaluating the structure of each neighborhood at a certain number of main iterations I Shaking The historical solutions obtained within the neighborhood are adaptively used to identify promising solutions. For each neighborhood structure s∈N Shaking Define the weight ω s The formula for calculating its selection probability is as follows:

[0141]

[0142] Where, n s In the past, I iter The number of times the neighborhood structure s is used in each iteration. This represents the improvement in the target value achieved by using the neighborhood structure s. Furthermore, F u and F l Corresponding to the past I Shaking The target values ​​of the worst and best solutions encountered in each iteration.

[0143] All neighborhood structures are assigned an equal initial weight of zero. During the algorithm's search process, the weights are updated after each iteration of the MVNS main loop. Because... When using the roulette wheel selection method to select operators, operators that provide greater improvement to the solution have a higher probability of being selected.

[0144] 3.4 Variable Neighborhood Depth Detection Algorithm

[0145] During the jitter phase, a local search is employed to obtain locally optimal solutions. Within the MVNS framework, a Variable Neighborhood Descent (VND) algorithm is used for local search, which focuses on improving solution quality by exploring vehicle routes, customer allocation, and service patterns of FS customers.

[0146] (1) Local search operation

[0147] Considering the composition of the solution space, four sets of local search structures based on problem characteristics are defined, containing a total of eight move operations, denoted as N. VND =N rt ∪N fs ∪N ca ∪N rs Among them, N rt N fs N ca and N rs These correspond to path, FS customer service, customer allocation, and path neighborhood, respectively.

[0148] ① Path Neighborhood

[0149] To quickly explore the vehicle path space, three commonly used operators for solving the Traveling Salesman Problem and the Vehicle Routing Problem are employed to improve path quality: insertion (N6), exchange (N7), and 2-opt (N8). Since the vehicle path table is represented as a path vector in the solution representation, these three operations can also help adjust the robot's delivery route when changing the path order.

[0150] ②FS service conversion neighborhood

[0151] Service Transformation (N9) aims to explore optimal solutions by changing the service model of FS customers. Specifically, suppose an FS customer is receiving home delivery via a delivery robot. In this case, the neighborhood structure will remove the customer from the robot's delivery path and reassign the customer to the nearest open facility (sr→sp). Conversely, if the customer chooses the CP service, the customer will be inserted into the robot's delivery path according to the minimum path cost insertion principle (sp→sr). Since when d ip When ≤D, FS client i∈N FS Completely covered by facility p, therefore only in d ip >D only has value when sr→sp.

[0152] ③ Customer Neighborhood

[0153] Two customer relationship operation operators are introduced to carry out customer allocation management.

[0154] Customer Exchange (N10). For two randomly selected customers i and j assigned to different facilities p1 and p2, swap the facilities to which these two customers belong, that is, assign customer j to facility p1 and assign customer i to facility p2. This operation operator is only valid if i∈N. CP ∪N FS and It is only valuable in scenarios where the capacity limits of p1 and p2 are not violated.

[0155] Customer movement (N11). For a random customer j assigned to facility p1, move them to another open facility. For this operator, the following three scenarios help improve search efficiency:

[0156] (i)i∈N HD Remove customer i from the current facility and insert it into an open facility according to the principle of minimum insertion cost;

[0157] (ii) i∈N CP and Insert customer i into In facility p2;

[0158] (iii) i∈N FS and Insert customer i into In facility p2, or inserted into the detour distance Δd(j,p2)<c u (d ip -D) facilities.

[0159] ④ Travel Neighborhood

[0160] Two types of neighborhood structures, namely trip release and trip addition, are introduced to conduct targeted multi-trip search for robots.

[0161] Run Release (N12). Randomly release one feasible run in a given path to reduce the total cost. This neighborhood structure is not applicable when all runs in the path are infeasible. Therefore, this neighborhood structure is activated only when there are at least two feasible runs in the path.

[0162] Add a new trip (N13). Add a new trip to the current path. This splits the original trip into two separate trips to resolve infeasible trips, thereby eliminating time window and robot capacity violation issues.

[0163] (2) VND process

[0164] VND employs a first-improvement strategy to systematically explore {N6, N2, ... N} 13VND explores all possible moves in the current operator to find an improved solution. When the first improved solution is found, VND jumps out of the current operator and moves to the next operator to continue the search until the stopping condition is met.

[0165] Given that N12 and N13 offer a coarser-grained solution space exploration approach than other operators, randomly releasing or adding trips may not directly lead to better delivery routes. Preliminary experiments revealed that post-path optimization can improve the search performance of these two operators. Therefore, after adopting N12 or N13, a path local search procedure (LS) is initiated. route ), using N6, N7, and N8 to perform a fine-grained path search on the current solution. In LS route In the process, the three neighborhood structures mentioned above are randomly selected to find a better solution until the algorithm terminates after I iterations. LSr .

[0166]

[0167]

[0168] 3.5 Accepting Decisions

[0169] In traditional VNS, local search is merely a simple depth probing process; that is, it only occurs when a new solution is found. A solution is only accepted as a new solution for subsequent search processes if it is an improvement over the current solution S. However, occasionally accepting non-improving solutions can promote solution diversification and facilitate the exploration of solution spaces far removed from the current solution.

[0170] By employing a similarity-biased acceptance strategy, the algorithm can be encouraged to move beyond the current optimal solution and promote global optimization.

[0171] For a pair of solutions Introduction of functions The similarity between the two is represented by two coarse-grained structures: open self-pickup facilities and open MDS facilities. Considering the composition of the solution space, we mainly use two coarse-grained structures as two similarity calculation indices. For the two types of structures, we have the following structural similarity measure functions.

[0172] function If the self-pickup facility is in the solution and If both sides are open, the value of the function is 1; otherwise, it is 0.

[0173] function If facility i is in solution S and If all values ​​are open as MDS, the value of this function is 1; otherwise, it is 0.

[0174] For a pair of solutions Similarity function between the two The definition is as follows:

[0175]

[0176] Obviously, there are Based on the above definition, a dynamic acceptance criterion based on similarity is proposed to accept solutions. When or At that time, accept the solution Unlike using a fixed value, ρ starts from τ0 and gradually decreases in the main program with steps of μ, eventually reaching the final value τ. f The gradually decreasing ρ enables VNS to initially search a larger solution space, and this capability gradually increases as the search progresses.

[0177] 3.6 Regret and Retrospection

[0178] To prevent the search process from becoming overly focused on exploring the solution space far from the current solution and thus neglecting to find a better solution, a regret and backtracking (R&TB) strategy is proposed. This strategy aims to help VNS balance diversity and focus during its exploration.

[0179] The search process summarizes and records the best solution S found in every k iterations. cbest If the current skew solution S cur If there is no improvement in k main iterations of MVNS, then use S. cbest Restart the search process. The operation of the R&TB strategy is illustrated below. Figure 4 The detailed R&T search process is as follows:

[0180]

[0181] 3.7 Improved VNS Algorithm Framework

[0182] Based on the above definitions and algorithm component descriptions, the MVNS framework algorithm provides complete pseudocode for the MVNS algorithm. Based on the given neighborhood structure N... VND ∪N shaking The algorithm, along with its parameters, starts with an initial solution generated by the construction heuristic (line 2). The main program repeatedly executes the adaptive jitter phase (line 5) and the VND local search component (line 6) until the predetermined algorithm termination condition is met, as follows:

[0183]

[0184]

[0185] 4. Simulation Testing

[0186] The effectiveness of the MVNS algorithm was demonstrated through extensive experimental simulations, and management insights were discovered by analyzing the proposed model and its sensitivity to key parameters.

[0187] 4.1 Parameter Calibration

[0188] A hybrid set of examples, consisting of standard LRP examples and generated examples, was used to construct the algorithm parameter calibration example set. Parameter calibration was divided into two stages: first, the range of main parameters was defined based on preliminary experimental results; then, specific parameter values ​​were clarified through further experiments. The final established parameter values ​​are as follows: I nimp =30, I VND =50, I LSr =20, I shaking =20, k=30, ρ=0.75 and τ f =0.95. It is worth noting that μ and |D p | Closely related, with a value of μ = 0.01 / |D p |

[0189] 4.2 Algorithm Performance Analysis Based on Standard Examples

[0190] Since the problem studied is a variant of LRP, the performance of MVNS is compared with current state-of-the-art methods for solving LRP problems based on the LRP benchmark set generated by Prins et al. (2006) to verify the effectiveness of the algorithm.

[0191] Recent methods for solving LRP include The following algorithms were proposed: Bartolini's (2023) Greedy Random Adaptive Search Program + Variable Neighborhood Search (GRASP+VNS), Arnold and Soerensen's (2021) Stepwise Selection (PF), Schneider and Loeffler's (2019) Tree-Based Search Algorithm (TBSA), Lopes et al.'s (2016) Hybrid Genetic Algorithm (GA), Escobar et al.'s (2014) Variable Granularity Taboo Neighborhood Search (GVTNS), Ting and Chen's (2013) Multi-Ant Colony Optimization Algorithm (MACO), Hemmelmayr et al.'s (2012) Adaptive Large Neighborhood Search (ALNS), Duhamel et al.'s (2010) Greedy Random Adaptive Search + Evolutionary Local Search (GRASP+ELS), and Prins and Prodhon's (2007) Lagrange Relaxation + Granular Taboo Search (LRGTS).

[0192] Table 2 compares MNVS with the above heuristic algorithms in the Prins et al. (2006) LRP standard example. For each method, the average deviation (Gap) from the known best solution (BKS) and the number of BKS found (n) are shown.BKS The results for each calculation on each example are shown in Tables 3 and 4, along with the average runtime (t) for all examples.

[0193] Table 2 Summary of LRP case results and comparison with existing advanced methods

[0194]

[0195] A comparison of the performance of various algorithms reveals that TBSA has the highest average efficiency, followed by PF, GRASP+VNS, hybrid GA, GVTNS, MACO, ALNS, LRGTS, and GRASP+ELS. The MVNS proposed in this invention performs similarly to GRASP+VNS in terms of average bias and outperforms hybrid GA, GVTNS, ALNS, GRASP+ELS, and LRGTS in terms of average solution. However, compared to GRASP+VNS, hybrid GA, GVTNS, and LRGTS, MVNS has a relatively longer computation time.

[0196] Overall, considering the different computational environments in which the above algorithms operate, and that the MVNS algorithm is not specifically tailored for the classic LPR problem, the proposed MVNS is still a highly competitive algorithm compared to the current state-of-the-art methods.

[0197] Table 3: Comparison of LRP Case Results: Part 1

[0198]

[0199] Table 4: Comparison of LRP Case Results: Part 2

[0200]

[0201] 4.3 Results Analysis Based on Real-World Cases

[0202] MVNS was applied to evaluate the effectiveness of key components of the algorithm based on real-world scenarios, and sensitivity analysis of key parameters was conducted to provide valuable management insights.

[0203] (1) Test Case

[0204] Since HF-LCRP-PR is a new variant derived from LRP, there are no readily available standard examples for analysis. Therefore, test examples are generated based on the real-world last-mile delivery environment. To ensure the effectiveness of these generated examples, the coordinate granularity concept proposed by Zhou et al. (2018) is adopted, which considers the minimum coordinate difference between any two generated nodes. This method helps to ensure that the node positions are consistent with the actual situation in the real world.

[0205] All calculations were generated within a 5.0km × 5.0km service area. First, based on the coordinate granularity τ... f The location of candidate self-pickup facilities was determined using a coordinate granularity τ = 0.5 km. Subsequently, based on the location of the self-pickup facilities, coordinate granularity τ was used to determine the location of each facility. f Customer locations are generated with a radius of 0.01km. 80% of customers are randomly distributed within a 1.0km radius centered on the facility location, while the remaining 20% ​​are randomly distributed within the service area. Indices 1, 2, and 3 represent customers with HD, CP, and FS needs, respectively. The number of customers with HD needs is allocated according to their proportion among all customers, while customers with FS and CP needs are randomly assigned. For customers with HD needs, the time window length is a random value from the set {30, 45, 60, 75, 90}. Other parameters are determined based on the real-world environment. A total of 27 representative cases were generated, with the number of self-pickup facilities ranging from 3 to 15 and the number of customers ranging from 30 to 300.

[0206] The examples adopted the following naming scheme: I <customers> - <facilities> - <mdss> - <identifier>Customers represents the number of customers, facilities represents the number of self-pickup facilities, MDSs represents the maximum number of open MDSs, identifier represents the proportion of customers with HD demand in the calculation, and a, b, and c represent the proportions of 10%, 30%, and 50%, respectively.

[0207] The node distribution of example 100-8-8a constructed according to the above method is as follows: Figure 5 As shown.

[0208] (2) Algorithm Component Analysis

[0209] (2) Algorithm Component Analysis

[0210] The MVNS algorithm proposes three main search strategies: Adaptive Jitter (AS) strategy, Dynamic Acceptance of Non-Optimal Solutions (DISA) strategy, and Regret and Backtracking (R&TB) strategy. Experiments are conducted to evaluate the contribution of each strategy to the algorithm's solution quality and runtime efficiency.

[0211] For the three strategies, ablation experiments were conducted to remove the corresponding strategies, resulting in three variant versions of the MVNS algorithm. The "MVNS-AS" version uses a random selection process instead of the AS strategy in the selection of the jitter operator; the "MVNS-DISA" version uses a solution quality-based reception mechanism instead of DISA; and the "MVNS-R&TB" version removes the R&TB strategy.

[0212] Each algorithm was run 10 times for each example, and the best and average solutions (Avg.) and the running time in seconds were calculated for each of the 10 runs. Table 5 shows the solution results for different MVNS algorithm variants in constructing examples.

[0213] The results show that each strategy significantly improves the performance of MVNS. In particular, the impact of these three strategies on algorithm performance becomes increasingly pronounced as the sample size increases. Regarding solution quality, R&TB has the greatest impact on algorithm performance, followed by DISA and AS. In terms of solution speed, AS has a more significant negative impact on the algorithm's solution time.

[0214] Table 5: Comparison Results of MVNS Algorithm Components

[0215]

[0216] (3) Sensitivity analysis

[0217] Sensitivity analysis was conducted on key parameters related to the problem to uncover valuable management insights to support operational decisions. First, the impact of the customer's expected self-pickup distance (D) was analyzed; second, the delivery robot's mileage (L) was analyzed. v and capacity Q v The impact of three types of customer needs on the results is then analyzed; finally, the impact of facility type and multiple trips is analyzed. For each case study, the MVNS algorithm is run 10 times, and the best solution found in the 10 runs is selected for result analysis.

[0218] ① Expected self-pickup distance

[0219] To analyze the impact of the expected self-pickup distance D on the delivery system, two sets of calculation examples were generated based on I300-15-15a and I300-15-15c. Each set contains four calculation examples with D values ​​of 0.2, 0.6, 1.0, and 1.4, respectively. Figure 6 and Figure 7 The detailed solution cost composition for these two sets of examples is shown, along with information on the total number of open facilities (nTF), the number of open UPL facilities (nUPL), and the number of open MDS facilities (nMDS).

[0220] It can be seen that the expected self-pickup distance has a certain impact on the delivery system. According to... Figure 6 The increase in D leads to a reduction in connection costs, resulting in a better solution while keeping nTF, nUPL, and nMDS constant. Furthermore, with... Figure 7 Compared to the results of example I300-15-15c, the more HD customers there are, the more significant the coverage effect. Clearly, in addition to reducing link costs, increasing D helps reduce the number of open facilities and MDS facilities. Comparing the results at D=1.4 and D=0.2 shows that the total cost is reduced by 18.1%.

[0221] ② The driving range and capacity of the delivery robots

[0222] Since the size and battery capacity of a delivery robot affect its load capacity and range, analyzing these parameters is crucial for the delivery system.

[0223] First, we will conduct a survey on the delivery robot's driving mileage L. v The impact. Based on example I300-15-15c, L is generated. v The six examples have values ​​of 10, 15, 20, 25, 30, and 35. Figure 8 Results for different calculation examples are given.

[0224] It can be seen that the increase in robot mileage leads to a continuous reduction in delivery costs, mainly because the reduced number of open MDS facilities significantly promotes cost reduction. The results indicate that using delivery robots with longer battery life is beneficial to the delivery system. Since the battery capacity of delivery robots is typically limited, it is essential to charge or replace the batteries during delivery.

[0225] In order to develop the delivery robot capacity Q v Sensitivity analysis was performed using two sets of cases, I300-15-15b and I300-15-15c. Each set of cases contains Q... v Five examples with values ​​of 8, 10, 15, 18, and 20. Figure 9 The total cost, nUPL, and nMDS for the above 10 examples are given.

[0226] according to Figure 9 (a), in Q v =15 before Q v The increase will reduce the total cost. Combined with... Figure 9 As can be seen from nMDS in (b), larger-capacity delivery robots help reduce the number of continued deployments. Meanwhile, with Q... v With the continued increase in nTF and nMDS, the optimal robot load capacity exists for any delivery system.

[0227] ③ Customer demand ratio

[0228] As shown in Table 5, since the total cost of the three cases within each case group (with series identifiers a, b, c) is different, the proportion of HD customers has a significant impact on the delivery system, and the higher the proportion of HD customers, the higher the cost of the delivery system.

[0229] This study focuses on the impact of the number of FS customers on the delivery system. A large-scale example, I300-15-15b, is selected as the base example. In this example, the proportion of HD customers is moderate, and |N... HD |=30%|N C Based on this example, five test cases are generated, where |N FS |each accounts for|N C | 10%, 20%, 30%, 40%, and 50%. Figure 10 Provide information on total cost, connection cost, and path cost for five examples.

[0230] Depend on Figure 10 (a) It can be seen that as |N FS The increase in | indicates a continuous decrease in total cost. To analyze how FS customers influence the delivery system, Figure 11 The number of FS customers served by the delivery robot in each example is given, and in Figure 12 The values ​​of nTF, nUPL, and nMDS for each example are given.

[0231] Analysis revealed that FS customers primarily exert a positive influence on the delivery system through the following two methods:

[0232] First, delivery robots provide door-to-door delivery services for FS customers, helping to reduce self-pickup connection costs through a smaller route cost increase. This phenomenon can be summarized as follows: Figure 10 (b) Figure 11 and Figure 12 Comparison example | N FS |=10%|N C | and | N FS |=20%|N C | and example |N FS |=40%|N C | and | N FS |=50%|N C It can be seen that both pairs of examples have the same nTF, nMDS, and nUPL. The more FS customers in the examples, the more FS customers are served by the delivery robot, resulting in a greater reduction in connection costs. FS |=40%|N C | and |N FS |=50%|N C This is particularly evident in the numerical examples.

[0233] Secondly, FS customers can help achieve better configurations for both MDS and UPL facilities. (Based on the example | N) FS |=20%|N C |、|N FS |=30%|N C | and |N FS |=40%|N C It can be seen that as the number of FS customers increases, nTF, nMDS, and nUPL are dynamically adjusting towards reducing facility opening costs.

[0234] ④ Facility types and multiple itineraries

[0235] Table 6 presents the number of open facilities (nTF, nMDS, nUPL) and the average number of trips for the delivery robots in 27 cases. It can be seen that 20 of the 27 cases (such as I40-4-4a and I100-8-8a) use a combination of UPL and MDS facilities. The proportion of HD customers in these cases does not exceed 30% (cases with series identifiers a and b). However, for the case with an HD customer proportion of 50% (series identifier c), all open facilities are MDS.

[0236] This demonstrates the significant value of combining UPL and MDS facilities in situations with fewer HD customers. Furthermore, it can be observed that the average journey of the delivery robot in almost all the examples exceeded one, indicating that multiple journey planning for the delivery robot is beneficial to the delivery system.

[0237] Table 6: Facilities and Itinerary Information

[0238]

[0239]

[0240] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.< / identifier> < / mdss> < / facilities> < / customers>

Claims

1. An unmanned delivery method based on joint delivery of heterogeneous facilities, characterized by, The method comprises: Constructing an unmanned distribution mathematical programming model based on the combination of unmanned self-service cabinets and multifunctional unmanned distribution stations, and carrying out heterogeneous unmanned facility configuration, customer allocation and robot vehicle path integrated optimization for personalized demand; Based on the integrated optimization decision, a solution representation method is designed, which integrates the allocation relationship and the path planning two-way vector mapping coupling; A variable neighborhood search algorithm integrating multiple advanced search strategies is designed to obtain the unmanned distribution system operation scheme under the combination of heterogeneous unmanned facilities; From the operator set using an adaptive jitter strategy The steps for dynamically selecting operators are as follows: All neighborhood structures are assigned an initial weight of zero, and the weight is updated after each main loop iteration of the variable neighborhood search algorithm during the algorithm search process; By evaluating the history of solutions obtained for each neighborhood structure at a certain number of main iterations to adaptively identify promising solutions; For each neighborhood structure , a weight is defined, the selection probability of which is calculated as follows: ； wherein, denotes the target value improvement achieved by using the neighborhood structure s; denotes the number of times the neighborhood structure s is used in the past iterations, denotes the target value improvement achieved by using the neighborhood structure s; denotes the target value of the worst and best solution encountered in the past iterations, respectively. The variable neighborhood search algorithm is locally searched by the variable neighborhood depth detection algorithm, and the steps are as follows: Define four groups of local search structures based on problem characteristics, and the expressions are as follows: ； wherein, , , , corresponding to path, FS customer service, customer allocation and path neighborhood, respectively; The variable neighborhood depth detection algorithm uses the first improvement strategy to systematically explore all possible movement operations in the neighborhood structure to seek improved solutions, and jumps out of the current operator and moves to the next operator for continuous search when the first improved solution is found; The variable neighborhood search algorithm is promoted to jump out of the current optimal solution through the skew acceptance strategy to promote global optimization, and the steps are as follows: For a pair of solutions , introduce a function to represent the similarity between them; function , if the pickup facility is open at the solution and , the value of the function is 1; otherwise, 0; function , if the facility is open as a multi-purpose unmanned delivery station in the solution and , then the value of the function is 1; otherwise 0; For a pair of solutions Similarity function between the two The definition is as follows: ； Through the regret and backtracking strategy, VNS balances diversification and centralization in its exploration, and the steps are as follows: In the search process summary records and keep the best solution found every k iterations ; If the current biased solution No improvement in k MVNS main iterations, then use Restart the search process. 2.The unmanned delivery method based on heterogeneous facility joint delivery according to claim 1, wherein, Construct the unmanned distribution mathematical programming model, and the steps are as follows: The customer's demand is divided into self-service, on-site delivery with time window and flexible service, and the expression models of the three types of demand are established, and according to the service relationship between the heterogeneous unmanned facilities and the three types of demand, a distribution model with the minimum total cost as the target is established. 3.The unmanned delivery method based on heterogeneous facility joint delivery according to claim 2, characterized in that, The target function expression is: ； wherein is the fixed cost of an unattended pick-up facility , is the fixed cost of a multi-functional unattended delivery station , is the path cost of a node to a node , is the connection cost of a customer node to a facility , A is the arc set, is the delivery robot trip set of a pick-up facility , is the candidate facility set, is the flexible customer set, is the pick-up customer set; is a variable representing the unattended pick-up facility opening decision; is a variable representing the multi-functional unattended delivery station opening decision; is a variable representing the delivery robot of a facility passes through path arc in the th formation; is a variable representing the customer is served by a facility . 4.The unmanned delivery method based on heterogeneous facility joint delivery of claim 1, wherein, The solution representation is composed of the allocation relationship component F and the path planning component R, and the two components are mapped to each other, and the steps are as follows: A. Component F consists of three layers of integer strings of fixed length corresponding to customer index, three types of customer service mode and service facilities corresponding to customers, respectively, where is the number of all customers; B. Component R represents the distribution path of the distribution robot, which is composed of self-service facilities, HD customers and FS customers; the self-service facility index is used to distinguish different distribution paths of robots and is used to divide the journey within a single distribution path, and the composition of nodes in the path is based on component F. 5.The unmanned delivery method based on heterogeneous facility joint delivery of claim 1, wherein, The two-stage heuristic is used to quickly construct the initial solution for the variable neighborhood search algorithm, and the steps are as follows: 1) Carry out heterogeneous unmanned facility location and customer allocation through greedy rules; 2) According to the facility location and customer allocation results in step 1), use the generalized insertion heuristic for solving TSPTW to construct the open multifunctional distribution station robot distribution path planning. 6.The unmanned delivery method based on heterogeneous facility joint delivery according to claim 5, wherein, The variable neighborhood search algorithm integrating three improved search strategies is used to optimize the initial path in the distribution path planning.

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