Unmanned delivery method based on heterogeneous facility joint delivery

Abstract

The invention relates to the technical field of unmanned delivery, in particular to an unmanned delivery method based on joint delivery of heterogeneous facilities. The method comprises the following steps: constructing an unmanned distribution mathematical planning model based on the combination of an unmanned self-service cabinet and a multifunctional unmanned distribution station, and carrying out heterogeneous unmanned facility configuration, customer distribution and robot vehicle path integrated optimization according to individual requirements; based on an integrated optimization decision, designing a solution scheme characterization method fusing a distribution relation and path planning two-way quantity mapping coupling; and designing a variable neighborhood search algorithm fusing multiple advanced search strategies. According to the unmanned delivery method based on heterogeneous facility joint delivery provided by the invention, through improvement of the delivery method and route planning in delivery, efficient personalized delivery service of the last kilometer can be provided, and heterogeneous facility site selection-coverage-path oriented to personalized requirements can be solved; and therefore, the distribution requirements of large-scale distribution customers in the actual operation process can be met.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned distribution, and particularly to an unmanned distribution method based on combined distribution of heterogeneous facilities. Background Art

[0002] In recent years, the intensifying competition in the logistics industry and the rising cost of human resources have prompted logistics enterprises to continuously seek new technologies and new models to gain a competitive advantage. The unmanned distribution technology is bringing a revolutionary development in the last-mile distribution due to its ability to provide more efficient distribution services.

[0003] The Unattended parcel locker (UPL) is an important application of the unmanned distribution technology. Such facilities are usually set up in residential areas or business districts to provide customers with round-the-clock "click and collect" services (Faugere and Montreuil, 2020), as shown in Figure 1 (a). Another application is the Multi-functional delivery station (MDS). Such facilities were initially designed by JD.com in 2018, as shown in Figure 1 (b). This facility can not only serve as an unmanned parcel locker for customers to pick up packages, but also act as a small warehouse equipped with unmanned delivery robots to provide door-to-door delivery services. Considering the limited capacity of the robots, the robots must return to the station after completing the delivery tasks of the current trip, reload and conduct multiple trips of delivery.

[0004] Since the MDS facility integrates delivery robots and necessary automated equipment for loading packages, the construction cost of the MDS facility is usually higher than that of the UPL facility.

[0005] Therefore, it is necessary to design an unmanned distribution method based on combined distribution of heterogeneous facilities to provide another technical solution to the above technical problems. Summary of the Invention

[0006] Based on this, it is necessary to provide an unmanned distribution method based on combined distribution of heterogeneous facilities to solve the technical problems raised in the above background art.

[0007] To solve the above technical problems, the present invention adopts the following technical solutions:

[0008] An unmanned distribution method based on combined distribution of heterogeneous facilities, the method comprising:

[0009] Construct an unmanned distribution mathematical programming model based on the combination of unmanned self-service lockers and multi-functional unmanned distribution stations, and conduct integrated optimization of heterogeneous unmanned facility configuration, customer allocation, and robot vehicle routing for personalized needs;

[0010] Based on integrated optimization decision-making, design a solution representation method that integrates the two-way vector mapping coupling of distribution relationships and path planning;

[0011] Design a variable neighborhood search algorithm that integrates a variety of advanced search strategies to obtain the operation plan of the unmanned distribution system under the joint operation of heterogeneous unmanned facilities.

[0012] As a preferred implementation of the unmanned distribution method based on the joint distribution of heterogeneous facilities provided by the present invention, construct an unmanned distribution mathematical programming model, and the steps are as follows:

[0013] Divide the customer's demands into three categories: self-pickup, door-to-door delivery with time windows, and flexible services. Establish expression models for the three categories of demands respectively, and establish a distribution model with the minimum total cost as the goal according to the service relationship between heterogeneous unmanned facilities and the three categories of demands.

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

[0015]

[0016] In the formula, F p is the fixed cost of the unmanned self-pickup facility p, F v is the fixed cost of the multi-functional unmanned distribution station p, r ij is the path cost from node i to node j, c ip is the connection cost from customer node i to facility p, A is the arc set, R p is the set of delivery robot trips of the self-pickup facility p, N p is the set of candidate facilities, N FS is the set of flexible customers, N CP is the set of self-pickup customers; is a variable representing the opening decision of the unmanned self-pickup facility; is a variable representing the opening decision of the multi-functional unmanned distribution station; is a variable representing that the delivery robot of facility p passes through the path arc (i, j) in the r-th formation; y ip is a variable representing that customer i is served by facility p.

[0017] As a preferred implementation of the unmanned distribution method based on the joint distribution of heterogeneous facilities provided by the present invention, the solution representation is composed of a distribution relationship component F and a path planning component R, and the two components are mutually mapped. The steps are as follows:

[0018] A. The component F consists of a fixed length of |N CIt consists of a three - layer integer string, corresponding to the customer index, three types of customer service models, and the service facilities for the corresponding customers respectively, where |N C | is the total number of all customers;

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

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

[0021] 1). Conduct heterogeneous unmanned facility location and customer allocation through greedy rules;

[0022] 2). According to the facility location and customer allocation results in step 1), use the generalized insertion heuristic for solving TSPTW to construct the delivery path planning of the open multi - functional delivery station robot.

[0023] As a preferred implementation 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 the delivery path planning.

[0024] As a preferred implementation of the unmanned delivery method based on heterogeneous facility joint delivery provided by the present invention, operators are dynamically selected from the operator set N Shaking through an adaptive jitter strategy, and the steps are as follows:

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

[0026] By evaluating the historical solutions obtained by each neighborhood structure within a certain number of main iterations I shaking to adaptively identify promising solutions;

[0027] For each neighborhood structure s ∈ N Shaking , a weight ω s is defined, and its selection probability calculation formula is as follows:

[0028]

[0029] where, n s represents the number of times the neighborhood structure s has been used in the past I iter iterations, Denote the improvement of the objective value achieved by using the neighborhood structure s; F u and F l correspond to the objective values of the worst and best solutions encountered in the past I shaking iterations, respectively.

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

[0031] Define four groups of local search structures based on problem characteristics, and the expressions are as follows:

[0032] N VND = N rt ∪ N fs ∪ N ca ∪ N rs

[0033] where N rt , N fs , N ca and N rs correspond to path, FS customer service, customer allocation, and path neighborhood, respectively;

[0034] The variable neighborhood depth detection algorithm adopts the first improvement strategy to systematically explore all possible move operations in the neighborhood structure to seek an improved solution, and jumps out of the current operator and moves to the next operator to continue the search when the first improved solution is found.

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

[0036] For a pair of solutions introduce the function to represent their similarity;

[0037] The function If the pickup facility i is open in both solutions S and , the value of this function is 1; otherwise it is 0;

[0038] The function If the facility i is open as a multi-functional unmanned distribution station in both solution S and , the value of this function is 1; otherwise it is 0;

[0039] For a pair of solutions the similarity function is defined as follows:

[0040]

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

[0042] Record and retain the best solution S found in every k iterations during the search process cbest ;

[0043] If the current skewed solution S cur has not been improved in k main iterations of MVNS, then use S cbest to restart the search process.

[0044] It can be undoubtedly seen that through the above technical solution of the present application, the technical problems to be solved by the present application can surely be solved.

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

[0046] An unmanned distribution method based on heterogeneous facility joint distribution provided by the present invention, by constructing an unmanned distribution system and using the designed efficient intelligent algorithm to carry out facility configuration and path planning of distribution robots, through carrying out integrated decision-making of heterogeneous facility location - coverage - path optimization for personalized needs, can provide efficient last-mile personalized distribution services, and further solve the distribution needs for large-scale distribution customers in the actual operation process, achieving multiple goals of customer satisfaction, green low-carbon and economic efficiency. Brief Description of the Drawings

[0047] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for description in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0048] Figure 1 Schematic diagrams of two types of unmanned distribution facilities in the prior art;

[0049] Figure 2 Schematic diagram of HF-LCRP-PR of the present invention;

[0050] Figure 3 Schematic diagram of the solution representation of the present invention;

[0051] Figure 4 Schematic diagram of the R&TB operation of the present invention;

[0052] Figure 5Schematic diagram of Example 100-8-8a of the present invention;

[0053] Figure 6 Schematic diagram of the results of Example Group I300-15-15a of the present invention;

[0054] Figure 7 Schematic diagram of the results of Example Group I300-15-15c of the present invention;

[0055] Figure 8 Schematic diagram of the analysis results at different driving mileages of the robots of the present invention;

[0056] Figure 9 Schematic diagram of the analysis results at different loading capacities of the robots of the present invention;

[0057] Figure 10 Schematic diagram of the cost analysis at different |NFS| of the present invention;

[0058] Figure 11 Schematic diagram of the number of FS customers in the path of the present invention;

[0059] Figure 12 Schematic diagram of the number of open facilities of the present invention. Detailed implementation manners

[0060] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present 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 only used to explain the present invention and are not used to limit the present invention.

[0061] In order to enable those skilled in the art to better understand the solution of 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, without conflict, the embodiments in the present invention and the features and technical solutions in the embodiments can be combined with each other.

[0063] It should be noted that similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

[0064] Refer to Figures 1 - 12 , an unmanned distribution method based on joint distribution of heterogeneous facilities.

[0065] 1. Problem explanation

[0066] The last-mile delivery system in an urban environment is usually a two-tier delivery network. The second tier is responsible for the final delivery stage, meeting the delivery needs of customers by strategically selecting Unattended parcel locker (UPL) and Multi-functional delivery station (MDS) facilities. Large trucks transport parcels from the distribution center to UPL and MDS facilities, and the operation is shown as Figure 2 shown. In the actual operation process, 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 parcels from the distribution center to the pick-up facilities.

[0067] Due to the high concentration of customers in the urban environment and the restrictions on large vehicles, the scale of each sub-area is relatively small, resulting in a more concentrated spatial distribution of a limited number of pick-up facilities. In this case, optimizing the first-tier logistics network will not generate significant cost benefits.

[0068] Determine the opening quantity and location of UPL and MDS facilities, allocate customers with click-and-collect (CP) and FS demands to the corresponding UPL or MDS facilities, and formulate delivery routes for the robots at each MDS to serve customers with home delivery (HD) and flexible service (FS) demands with time windows to minimize the operating cost.

[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 , where D P represents the set of pick-up facilities and is further divided into D U ∪ D A , where D U and D A are the sets of unattended parcel lockers (UPL) and multi-functional delivery stations (MDS) facilities respectively. The set N C represents a group of customers and is further divided into N C = N HD ∪ N CP ∪ N FS , and the different sets are defined as follows:

[0070] Each customer i ∈ N C defines the parcel delivery quantity q i and the corresponding service time s i , which is the time required to provide services based on customer types. In addition, for customer i ∈ N HD ∪ N FS , there is a service time window [ei , l i , where e i and l i are the earliest and latest times to start door-to-door delivery, respectively.

[0071] The arc set A consists of a set of path arcs and is 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 a travel time t ij .

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

[0073] Each customer i ∈ N C corresponds to a set of candidate assignment arc sets according to the customer type Specifically, the customers in N CP can be assigned to the facilities in D U , the customers in N HD can be assigned to the facilities in D A , and the customers in N FS can be assigned to the facilities in D P . The C i set is defined based on the correspondence between customers and the facilities in D P .

[0074] The fixed cost of each self-pickup facility p ∈ N p is Fp , with a capacity of Q P . In addition, for each facility k ∈ D A , a delivery robot for door-to-door service is configured. If a pick-up facility is opened as an MDS facility, this facility will be equipped with a delivery robot. Each robot has a fixed cost F v , capacity Q v , and a maximum travel distance L v . The itinerary of delivery robot k ∈ D A is denoted as R k , and for each itinerary r ∈ R k , there is a setup time for loading the robot associated with the total number of packages delivered in itinerary r and the unit package loading time β

[0075] N CP ∪N FS The customers in can pick up packages from the open UPL or MDS facilities. The delivery robot departs from the MDS and provides door-to-door service for the customers in N HD ∪N FS , and returns to the same MDS to reload packages after completing the tasks of the current itinerary, and performs another itinerary within L v .

[0076] The problem aims to configure two types of facilities, assign customers to the facilities, and design the vehicle routes of the delivery robots in each MDS according to the personalized service requirements of the customers, so as to minimize the sum of the opening costs of the two types of facilities, the route costs, and the connection costs (compensation costs for customers with CP and FS requirements due to violation of the expected pick-up distance).

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

[0078] Table 1: Symbols and Their Corresponding Meanings

[0079]

[0080]

[0081] 2. Model Construction

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

[0083] The objective function formula (1) minimizes the sum of the facility opening cost, the fixed robot cost, the robot route cost, and the compensation for violating the expected pick-up distance, and the expression is as follows

[0084]

[0085] Constraint formula (2) requires that each customer with CP demand must be covered by the UPL facility, and the expression is as follows:

[0086]

[0087] Constraint formula (3) ensures that each customer with HD demand must be accessed by the robot and only accessed once, and the expression is as follows:

[0088]

[0089] Constraint formula (4) ensures that each customer with FS demand is either covered by the UPL facility or accessed by the robot, and the expression is as follows:

[0090]

[0091] Constraint formulas (5)-(7) are single-trip flow conservation, and the expression is as follows:

[0092]

[0093] Constraint formula (8) ensures that the demand delivered by the robot in each trip cannot exceed the capacity of the robot, and the expression is as follows:

[0094]

[0095] Constraint formulas (9)-(11) ensure the feasibility of the time window, and the expression is as follows:

[0096]

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

[0098]

[0099] Constraint formulas (13)-(14) ensure the correct trip sequence of a single robot, and the expression is as follows:

[0100]

[0101] Constraint formula (15) indicates that the driving mileage of the robot cannot be exceeded, and the expression is as follows:

[0102]

[0103] Constraint formula (16) shows that the total demand served by the self-pickup facility cannot exceed the capacity, and the expression is as follows:

[0104]

[0105] Constraint formula (17) means that the number of available robots should not be violated, and the expression is as follows:

[0106]

[0107] Constraint formulas (18) - (20) indicate the relationships between decision variables, and the expression is as follows:

[0108]

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

[0110]

[0111] 3. Solutions

[0112] Solve the model through the improved variable neighborhood search algorithm (Modified variable neighborhood search, MVNS) to meet the distribution requirements for a large number of distribution customers during the actual operation process;

[0113] The VNS algorithm was initially proposed by and Hansen (1997) as a meta - heuristic method;

[0114] The VNS algorithm usually starts with an initial solution and a set of neighborhood structure sets N with k max neighborhood structures. K , and the main program of the algorithm sequentially executes the shaking and local search components until the algorithm termination condition is met. For a given current solution S, each main loop performs a shaking operation, randomly generates a new solution S' using the k - th neighborhood to determine the local optimal solution 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 starts with S” and sets k to 1 to continue the search. If S” has no improvement compared to S, then S is still used as the starting point for randomly generating the next solution using the subsequent neighborhood structure N k+1 , and the pseudocode is as follows:

[0115]

[0116]

[0117] 3.1 Solution representation

[0118] Design a solution representation scheme composed of components F and R based on the problem characteristics.

[0119] Component F has a fixed length of |Ν CIt consists of three layers of integer strings, corresponding to customer indices, three types of customer service models, and service facilities for corresponding customers respectively, where |N C | is the total number of all customers. The third layer stores all customer indices; the second layer represents the distribution service models 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 opened self-pickup facilities. The combination of the first layer and the third layer characterizes the allocation relationship between customers and self-pickup cabinets.

[0120] Component R represents the distribution path of the distribution robot, which consists of self-pickup facilities, HD customers, and FS customers. The self-pickup facility index is used to distinguish the distribution paths of different robots and is used to divide the trips within a single distribution path. The composition of the nodes in the path is based on component F; Figure 2 The solution corresponding to the example shown in Figure 3 is shown as

[0121] 3.2 Initial solution construction algorithm

[0122] The initial solution is one of the two key components for starting the VNS algorithm. According to the problem characteristics, a two-phase construction heuristic (TPCH) is designed to quickly construct an initial solution for MVNS. TPCH focuses on four types of decisions involved in the problem: (1) determining the locations of two types of facilities; (2) allocating customers to the opened facilities; (3) determining the service models for FS customers - whether serviced by vehicles or self-picked up by customers; (4) planning the distribution routes for the distribution robots of the opened MDS facilities. It specifically includes the following two phases:

[0123] Phase 1: Facility location and customer allocation

[0124] Carry out heterogeneous unmanned facility location and customer allocation through greedy rules;

[0125] First, open all candidate self-pickup facilities. Subsequently, according to the capacity limit of the self-pickup facilities, each customer is allocated to the nearest facility or the self-pickup facility with the least compensation. For a self-pickup facility p ∈ D p , if it is only allocated to CP customers, then this self-pickup facility is designated as a UPL facility; otherwise, if there is at least one FS or HD customer, then this self-pickup facility is opened as an MDS facility.

[0126] Phase 2: MDS path planning

[0127] According to Phase 1, the customers in the set N C have been allocated to n u UPL facilities and n m MDS facilities. Therefore, the robot path problem is further decomposed into n mSub-problems, and each sub-problem corresponds to constructing a vehicle route that includes all HD customers and FS customers currently served by the MDS.

[0128] To solve each sub-problem, first, the generalized insertion heuristic for solving TSPTW proposed by Gendreau et al. (1998) is adopted to relax the vehicle capacity constraint and construct a large TSP route. Subsequently, this TSP route is divided into sub-routes according to the vehicle capacity. Finally, for each FS customer i ∈ N FS , if c ip > 0, then a greedy strategy is adopted to determine its service mode; if the customer will be delivered to the door by a robot. Among them, represents the minimum increase in the route cost when inserting customer i into the robot delivery route of MDS facility p. Finally, post-optimization of the route is carried out. In this stage, a local search algorithm composed of three classic route operators (swap, insertion, and 2-Opt) is used to improve the quality of the current route.

[0129] 3.3 Adaptive Jitter Strategy

[0130] (1) Jitter Neighborhood Structure

[0131] Based on the initial solution, the MVNS systematically explores larger and larger neighborhoods to find the global optimal solution (Stenger等,2013) . Based on this search mechanism, the choice of neighborhood structure is crucial for the search efficiency and solution quality of the algorithm. Each neighborhood structure must balance modifying the current solution and retaining its effective 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 a single facility. A facility is randomly selected and its state is changed. On the premise of ensuring that the total open facility capacity meets the lower limit, the facility is changed from open to closed or from closed to open.

[0134] · Facility Exchange (N2). Select a closed facility to open it, and at the same time close another open facility. This operation should ensure that the total open facility capacity meets the delivery requirements of all customers.

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

[0136] · UPL Conversion to MDS (N4). When the existing solution has a time window or the robot travel time is violated, replace UPL with MDS.

[0137] · Customer reallocation (N5). Randomly select n rl customers and reallocate them to other facilities by applying customer movement operations (such as the de-representation step).

[0138] (2) Adaptive mechanism

[0139] Considering that randomly selecting the neighborhood structure completely during the shaking stage will cause VNS to exhibit highly unstable behavior in some complex optimization problems (Stenger等,2013) , adopting an adaptive mechanism helps to better manage the shaking 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 for the solution space, an adaptive neighborhood structure selection mechanism is designed to manage the shaking process. Different from the classical method of updating probabilities based on the number of improvements made by each operator, the present invention designs an adaptive shaking mechanism based on solution quality to dynamically select operators from the shaking set N Shaking = {N 1 , N 2 , N 3 , N 4 , N 5}.

[0140] Specifically, by evaluating the historical solutions obtained by each neighborhood structure within a certain number of main iterations I Shaking , promising solutions are adaptively identified. For each neighborhood structure s ∈ N Shaking , a weight ω s is defined, and its selection probability is calculated as follows:

[0141]

[0142] where n s represents the number of times the neighborhood structure s has been used in the past I iter iterations, represents the improvement in the objective value achieved by using the neighborhood structure s. In addition, F u and F l correspond to the objective values of the worst and best solutions encountered in the past I Shaking iterations, respectively.

[0143] All neighborhood structures are assigned an equal initial weight of zero, and during the algorithm search process, the weights are updated after each MVNS main loop iteration. Since when using the roulette wheel selection method to select operators, those operators that improve the solution more have a higher probability of being selected.

[0144] 3.4 Variable neighborhood depth search algorithm

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

[0146] (1) Local search operation

[0147] Considering the solution space composition, four groups of local search structures based on problem characteristics are defined, which altogether contain 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 correspond to route, FS customer service, customer assignment, and route neighborhood respectively.

[0148] ① Route neighborhood

[0149] To quickly explore the vehicle route space, three operation operators commonly used to solve the Traveling Salesman Problem and Vehicle Routing Problem are adopted to improve the route quality, namely insertion (N6), swap (N7), and 2-opt (N8). Since the vehicle route table is represented as a route vector in the solution representation, the above three operations also help to adjust the delivery itinerary of the robot when changing the route order.

[0150] ② FS service transformation neighborhood

[0151] Service transformation (N9) aims to explore a better solution by changing the service pattern of FS customers. Specifically, assume that an FS customer is receiving door-to-door delivery service by a delivery robot. In this case, this neighborhood structure will remove the customer from the robot delivery route and reassign the customer to the nearest open facility (abbreviated as sr→sp). Conversely, if the customer selects CP service, the customer will be inserted into the robot delivery route according to the minimum path cost insertion principle (abbreviated as sp→sr). Since when d ip ≤ D, FS customer i ∈ N FS is completely covered by facility p, so sr→sp is only valuable when d ip > D.

[0152] ③ Customer neighborhood

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

[0154] Customer exchange (N10). For two randomly selected customers i and j assigned to different facilities p 1 and p 2 , swap the facilities to which these two customers belong, that is, assign customer j to facility p 1 , and assign customer i to facility p 2 . This operator is only valuable when i ∈ N CP ∪N FS and and there is no scenario that violates the capacity limits of p 1 and p 2 .

[0155] Customer movement (N11). For a randomly selected customer j assigned to facility p 1 , move it to another open facility. For this operator, the following three cases of operation methods are helpful to improve the search efficiency:

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

[0157] (ii) i ∈ N CP and insert customer i into the facility p 2 ;

[0158] (iii) i ∈ N FS and insert customer i into the facility p 2 , or insert it into a facility where the detour distance Δd(j, p 2 ) < c u (d ip -D).

[0159] ④ Itinerary neighborhood

[0160] Introduce two types of neighborhood structures, itinerary release and itinerary addition, to specifically conduct multi - itinerary search for robots.

[0161] Itinerary release (N12). Randomly release a feasible itinerary in a given path to reduce the total cost. This neighborhood structure will not apply when all itineraries in the path are infeasible. Therefore, this neighborhood structure will only be activated when there are at least two feasible itineraries in the path.

[0162] Itinerary addition (N13). Add a new itinerary to the current path and split the original itinerary into two independent itineraries to solve the infeasible itinerary, thus eliminating the problems of time window and robot capacity violation.

[0163] (2) VND process

[0164] The VND adopts the first improvement strategy to systematically explore all possible move operations in {N 6 , N 2 ,... N 13} to seek improved solutions. The VND explores all possible moves of the current operator and jumps out of the current operator and moves to the next operator to continue the search when the first improved solution is found until the stopping condition is met.

[0165] Given that N12 and N13 provide a coarser-grained solution space exploration method than other operators, randomly releasing or adding trips may not directly lead to better delivery routes. Through preliminary experiments, it is found that post-route optimization can improve the search effectiveness of these two operators. Therefore, after adopting N12 or N13, a local search program for routes (LS route ) will be launched, and N6, N7, and N8 will be used to conduct a refined search for the routes of the current solution. In LS route , the above three neighborhood structures are randomly called to find better solutions until the algorithm terminates the iteration count I LSr .

[0166]

[0167]

[0168] 3.5 Acceptance Decision

[0169] In traditional VNS, local search is only used as a simple depth exploration process, that is, only when the new solution is better than the current solution S will it be accepted as a new solution to enter the subsequent search process. However, occasionally accepting non-improved solutions is beneficial to promoting the diversification of solutions and easily exploring the solution space far from the current solution.

[0170] By means of a skewed acceptance strategy based on similarity, it helps the algorithm jump out of the current optimal solution and promote global optimization.

[0171] For a pair of solutions introduce the function to represent their similarity. Considering the composition of the solution space, the two coarse-grained structures of the opening of pick-up facilities and the opening of MDS facilities are mainly adopted as two calculation indicators for the similarity of solutions. For these two types of structures, there are the following structure similarity measure functions.

[0172] The function If pick-up facility i is open in both solution S and , the value of this function is 1; otherwise it is 0.

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

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

[0175]

[0176] Obviously, there is According to the above definition, a similarity-based dynamic acceptance criterion is proposed to accept solutions. When or then accept the solution Different from using a fixed value, ρ starts from τ 0 and gradually decreases in the main program with a step size of μ, and finally reaches the final value τ f . The gradually decreasing ρ enables VNS to initially search a larger solution space and gradually intensify as the search process progresses.

[0177] 3.6 Regret and Backtracking

[0178] To prevent the search process from being overly focused on exploring the solution space far from the current solution and unable to focus on finding better solutions, a regret and backtracking (R&TB) strategy is proposed. This strategy aims to help VNS balance diversification and intensification in its exploration.

[0179] Record and retain the best solution S found in every k iterations during the search process cbest . If the current skewed solution S cur has not been improved in k main MVNS iterations, then use S cbest to restart the search process. The operation of the R&TB strategy is illustrated in Figure 4 , and the detailed R&TB search process is as follows:

[0180]

[0181] 3.7 Improved VNS Algorithm Framework

[0182] According to the above definition and algorithm component description, the MVNS framework algorithm gives the complete MVNS algorithm pseudocode. Based on the given neighborhood structure N VND ∪N shaking and related algorithm parameters, the algorithm starts from the initial solution generated by the construction heuristic (line 2), and the main program repeatedly executes the adaptive shaking phase (line 5) and the VND local search component (line 6) until the established algorithm termination conditions are met, as follows:

[0183]

[0184]

[0185] 4. Simulation tests

[0186] The effectiveness of the MVNS algorithm is carried out through a large number of experimental simulations, and management implications are discovered by analyzing the proposed model and the sensitivity of key parameters.

[0187] 4.1 Parameter calibration

[0188] A set of examples for algorithm parameter calibration is composed of a mixed set of examples consisting of LRP standard examples and generated examples. Parameter correction is divided into two stages. First, the main parameter ranges are defined according to the preliminary experimental results; then the specific parameter values are clarified through further experiments. The finally 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 should be noted that μ is closely related to |D p |, and the value of μ = 0.01 / |D p |.

[0189] 4.2 Algorithm performance analysis based on standard examples

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

[0191] Recent solution methods for LRP include and the Greedy Randomized Adaptive Search Procedure + Variable Neighborhood Search (GRASP+VNS) by Bartolini (2023), the Progressive Filtering (PF) by Arnold and Soerensen (2021), the Tree-Based Search Algorithm (TBSA) by Schneider and Loeffler (2019), the Hybrid Genetic Algorithm (GA) by Lopes et al. (2016), the Granular Variable Tabu Neighborhood Search (GVTNS) by Escobar et al. (2014), the Multiple Ant Colony Optimization Algorithm (MACO) by Ting and Chen (2013), the Adaptive Large Neighborhood Search (ALNS) by Hemmelmayr et al. (2012), the Greedy Randomized Adaptive Search + Evolutionary Local Search (GRASP+ELS) by Duhamel et al. (2010), and the Lagrangian Relaxation + Granular Tabu Search (LRGTS) by Prins and Prodhon (2007).

[0192] Table 2 compares MNVS with the above heuristic algorithms in the Prins et al. (2006) LRP standard test cases. For each method, the average deviation (Gap) from the known best solution (BKS), the number of BKS found (n BKS ) and the average running time (t) of all test cases are shown. The detailed results of each algorithm on each test case are shown in Tables 3 and 4.

[0193] Table 2 Summary of LRP Test Case Results and Comparison with Existing Advanced Methods

[0194]

[0195] By comparing the performance of each algorithm, it can be seen that TBSA has the highest average efficiency, followed by PF, GRASP+VNS, hybrid GA, GVTNS, MACO, ALNS, LRGTS, and GRASP+ELS. The proposed MVNS in the present invention performs similarly to GRASP+VNS in terms of average deviation and is superior to hybrid GA, GVTNS, ALNS, GRASP+ELS, and LRGTS in terms of average solution. However, compared with GRASP+VNS, hybrid GA, GVTNS, and LRGTS, MVNS has a relatively longer computational time.

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

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

[0198]

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

[0200]

[0201] 4.3 Results Analysis Based on Practical Cases

[0202] The MVNS is applied to the test cases generated according to the real scenarios to evaluate the effectiveness of the key components of the algorithm and conduct a sensitivity analysis of the main parameters to provide valuable management findings.

[0203] (1) Test Cases

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

[0205] All examples are generated within a service area of 5.0 km × 5.0 km. First, the positions of candidate pick-up facilities are determined according to the coordinate granularity τ f = 0.5 km. Subsequently, based on the pick-up facility positions, customer positions are generated using the coordinate granularity τ f = 0.01 km. 80% of the customers are randomly distributed in the area centered at the facility position with a radius of 1.0 km, and the remaining 20% of the customers are randomly distributed within the service area. Indices 1, 2, and 3 represent customers with HD, CP, and FS demands respectively. The number of customers with HD demand is allocated according to their proportion among all customers, while the customers with FS and CP demands are randomly allocated. For customers with HD demand, the length of their time window is a random value from the set {30, 45, 60, 75, 90}. Other parameters are determined according to the real environment. A total of 27 representative examples are generated, with the number of pick-up facilities ranging from 3 to 15 and the number of customers ranging from 30 to 300.

[0206] The examples adopt the following naming scheme: I <customers> - <facilities> - <mdss> - <identifier>customers represents the number of customers, facilities represents the number of pick-up facilities, MDSs represents the number of the largest open MDSs, identifier represents the proportion of customers with HD demand in the instance, and a, b, and c represent 10%, 30%, and 50% respectively.

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

[0208] (2) Algorithm component analysis

[0209] (2) Algorithm component analysis

[0210] The MVNS algorithm proposes three main search strategies: the adaptive shaking (AS) strategy, the dynamic inferior solution acceptance (DISA) strategy, and the regret and backtracking (R&TB) strategy. Each strategy's contribution to the algorithm's solution quality and running efficiency is evaluated through experimental analysis.

[0211] For the three strategies, ablation experiments are conducted to remove the corresponding strategies respectively to obtain three variant versions of the MVNS algorithm. "MVNS - AS" version: Use a random selection process to replace the AS strategy in the selection of the shaking operator; "MVNS - DISA" version: Adopt a solution quality - based acceptance mechanism to replace DISA; "MVNS - R&TB" version: Remove the R&TB strategy.

[0212] Each algorithm runs each instance 10 times, and the best solution (Best), average solution (Avg.), and running time in seconds (Time) in the 10 runs are statistically counted. The solution results of different MVNS algorithm variants on the constructed instances are shown in Table 5.

[0213] The results show that each strategy significantly improves the performance of MVNS. In particular, as the instance scale increases, the influence of these three strategies on the algorithm performance becomes more and more obvious. In terms of solution quality, the influence of R&TB on the algorithm performance is the largest, followed by DISA and AS. In terms of solution speed, the negative impact of AS on the algorithm's solution time is relatively significant.

[0214] Table 5: Comparison results of MVNS algorithm components

[0215]

[0216] (3) Sensitivity analysis

[0217] Conduct sensitivity analysis on the important parameters related to the problem to discover valuable management implications to support operational decisions. First, analyze the influence of the customer's expected pick-up distance D; second, analyze the driving mileage L v and capacity Q v The impact. Then, analyze the impact of three types of customer demands on the results; finally, analyze the impact of facility types and multiple trips. For each instance, the algorithm MVNS is run 10 times, and the best solution found in the 10 runs is selected for result analysis.

[0218] ① Expected pick-up distance

[0219] To analyze the impact of the expected pick-up distance D on the distribution system, two sets of instances are generated based on I300-15-15a and I300-15-15c respectively. Each set contains four instances, and D is 0.2, 0.6, 1.0, and 1.4 respectively. Figure 6 and Figure 7 respectively show the detailed solution cost composition of these two sets of instances, as well as 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 pick-up distance has a certain impact on the distribution system. According to Figure 6 , the increase in D leads to a decrease in the connection cost, thus obtaining a better solution while keeping nTF, nUPL, and nMDS unchanged. In addition, compared with the results of instance I300-15-15c in Figure 7 , the more HD customers there are, the more significant the coverage effect is. Obviously, in addition to reducing the link cost, the increase in D helps to reduce the number of open facilities and the number of MDS facilities. Comparing the results under D = 1.4 and D = 0.2, it can be seen that the total cost is reduced by 18.1%.

[0221] ② Travel distance and capacity of the delivery robot

[0222] Since the volume and battery power of the delivery robot will affect the loading capacity and travel distance, it is very important to analyze the loading capacity and travel distance of the robot for this distribution system.

[0223] First, conduct an analysis on the travel distance L of the delivery robot v 's impact. Six instances with L v values of 10, 15, 20, 25, 30, and 35 are generated based on instance I300-15-15c. Figure 8 The results of different instances are given.

[0224] It can be seen that the increase in the travel distance of the robot will bring about a continuous reduction in the distribution cost. The main reason is that it reduces the number of open MDS facilities, thus significantly promoting cost reduction. The results show that using a delivery robot with a stronger endurance is beneficial to the distribution system. Since the battery capacity of the delivery robot is usually limited, it is very necessary to charge or replace the battery of the delivery robot during the distribution process.

[0225] To conduct the sensitivity analysis of the capacity Q of the delivery robot v two sets of examples are generated based on Examples I300 - 15 - 15b and I300 - 15 - 15c. Each set of examples contains 5 examples with Q v = 8, 10, 15, 18, 20. Figure 9 The total cost, nUPL, and nMDS of these 10 examples are given.

[0226] According to Figure 9 (a), before Q v = 15, the increase in Q v will reduce the total cost. Combining with the nMDS in Figure 9 (b), it can be seen that a delivery robot with a larger capacity helps to reduce the number of continued openings. At the same time, as Q v continues to increase, nTF and nMDS remain unchanged, indicating that there is an optimal robot loading capacity for any delivery system.

[0227] ③ Customer demand ratio

[0228] According to Table 5, since the total costs among the three examples within each example group (with series identifiers a, b, c) are 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] Focus on the impact of the number of FS customers on the delivery system. Select the large - scale example I300 - 15 - 15b as the base example, in which the proportion of HD customers is moderate, with |N HD | = 30%|N C |. Five test examples are generated based on this example, in which |N FS | accounts for 10%, 20%, 30%, 40%, and 50% of |N C | respectively. Figure 10 The total cost, connection cost, and path cost information for the 5 examples are given.

[0230] From Figure 10 (a), it can be seen that the total cost continuously decreases as |N FS | increases. To analyze how FS customers act on the delivery system, Figure 11 the number of FS customers served by the delivery robot in each example is given in Figure 12 and the values of nTF, nUPL, and nMDS for each example are given in

[0231] Through analysis, FS customers mainly have a positive impact on the delivery system in the following two ways:

[0232] First, the delivery robot providing door-to-door delivery service for FS customers helps reduce the pick-up connection cost by a relatively small path cost increase. This phenomenon can be based on Figure 10 (b), Figure 11 and Figure 12 , comparing the cases |N FS | = 10% |N C | with |N FS | = 20% |N C |, and the cases |N FS | = 40% |N C | with |N FS | = 50% |N C |. It can be seen that the results of these two pairs of cases have the same nTF, nMDS, and nUPL. The more FS customers in the cases, the more FS customers served by the delivery robot, thus bringing a greater degree of connection cost reduction, which is particularly evident in the cases of |N FS | = 40% |N C | and |N FS | = 50% |N C |.

[0233] Secondly, FS customers help bring about a more optimal configuration of two types of facilities, MDS and UPL. According to the cases |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 adjusted towards a smaller open facility cost.

[0234] ④ Facility types and multi-trips

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

[0236] This indicates that the combined use of UPL and MDS facilities has significant value when there are fewer HD customers. In addition, it can be seen that the average number of trips of the delivery robot in almost all cases exceeds 1, indicating that the multi-trip planning of the delivery robot is beneficial to the delivery system.

[0237] Table 6: Facility and Itinerary Information

[0238]

[0239]

[0240] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the present invention to the specific embodiments described. Obviously, many modifications and variations can be made according to the content of this specification. These embodiments are selected and specifically described in this specification in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can well understand and utilize the present invention. The present invention is only limited 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 in that: The method comprises: Construct an unmanned delivery mathematical planning model based on the combination of unmanned self-service cabinets and multi-functional unmanned delivery stations, and carry out integrated optimization of heterogeneous unmanned facility configuration, customer allocation and robot vehicle paths according to personalized needs; Based on integrated optimization decision, a solution representation method is designed that integrates the allocation relationship and the path planning dual vector mapping coupling; A variable neighborhood search algorithm that integrates multiple advanced search strategies is designed to obtain an operation plan for the unmanned delivery system under the combination of heterogeneous unmanned facilities.

2. The unmanned delivery method based on heterogeneous facility joint delivery according to claim 1 is characterized in that: To build a mathematical programming model for unmanned delivery, the steps are as follows: Customer demands are divided into three categories: self-pickup, home delivery with time windows, and flexible services. Expression models for the three types of demands are established respectively. Based on the service relationship between heterogeneous unmanned facilities and the three types of demands, a distribution model with the goal of minimizing total cost is established.

3. The unmanned delivery method based on heterogeneous facility joint delivery according to claim 2 is characterized in that: The objective function expression is: In the formula, F p is the fixed cost of the unmanned pickup facility p, F v is the fixed cost of the multifunctional unmanned delivery station p, r ij is the path cost from node i to node j, c ip is the connection cost from customer node i to facility p, A is the arc set, R p is the set of delivery robot trips of the self-pickup facility p, N p is the candidate facility set, N FS is the flexible customer set, N CP Collection for self-collection customers; is a variable, indicating the decision to open the unmanned pick-up facility; is a variable, which indicates the opening decision of the multifunctional unmanned delivery station; is a variable, indicating that the delivery robot of facility p passes through the path arc (i, j) in the rth formation; y ip is a variable indicating that customer i is served by facility p.

4. The unmanned delivery method based on heterogeneous facility joint delivery according to claim 1 is characterized in that: The solution representation is formed by the allocation relationship component F and the path planning component R. The two components are mapped to each other. The steps are as follows: A. Component F consists of a fixed length of |N C |, which respectively correspond to the customer index, three types of customer service modes, and the service facilities corresponding to the customers, where |N C | is the number of all customers; B. Component R represents the delivery path of the delivery robot, which consists of pick-up facilities, HD customers and FS customers. The pick-up facility index is used to distinguish the delivery paths of different robots and to divide the trips within a single delivery path. The composition of the nodes in the path is based on component F.

5. The unmanned delivery method based on heterogeneous facility joint delivery according to claim 1 is characterized in that: The two-stage construction heuristic is used to quickly construct an initial solution for the variable neighborhood search algorithm. The steps are as follows: 1) Conduct heterogeneous unmanned facility site selection and customer allocation through greedy rules; 2). Based on the facility location and customer allocation results in step 1), the generalized insertion heuristic for solving TSPTW is used to construct an open multifunctional distribution station robot delivery path planning.

6. The unmanned delivery method based on heterogeneous facility joint delivery according to claim 5 is characterized in that: A variable neighborhood search algorithm that integrates three improved search strategies is designed to optimize the initial path in distribution route planning.

7. The unmanned delivery method based on heterogeneous facility joint delivery according to claim 6 is characterized in that: Through the adaptive jitter strategy, the operator set N Shaking To dynamically select an operator, follow these steps: All neighborhood structures are assigned equal initial weights of zero. During the algorithm search process, the weights are updated after each iteration of the main loop of the variable neighborhood search algorithm; By evaluating each neighborhood structure at a certain number of main iterations I shaking The historical solutions obtained within the system are used to adaptively identify promising solutions; For each neighborhood structure s∈N Shaking , define the weight ω s , the selection probability calculation formula is as follows: Among them, n s In the past I iter The number of times the neighborhood structure s is used in iterations, represents the improvement of the objective value achieved by using the neighborhood structure s; F u and F l Corresponding to the past I shaking The objective values ​​for the worst and best solutions encountered in iterations.

8. The unmanned delivery method based on heterogeneous facility joint delivery according to claim 6 is characterized in that: The variable neighborhood search algorithm is locally searched by the variable neighborhood depth detection algorithm. The steps are as follows: Define four sets of local search structures based on problem characteristics, the expressions are as follows: N VND =N rt ∪N fs ∪N ca ∪N rs Among them, N rt , N fs , N ca and N rs They correspond to the path, FS customer service, customer allocation and path neighborhood respectively; The variable neighborhood depth detection algorithm adopts the first improvement strategy to systematically explore all possible movement operations in the neighborhood structure to seek improved solutions, and when the first improved solution is found, it jumps out of the current operator and moves to the next operator to continue searching.

9. The unmanned delivery method based on heterogeneous facility joint delivery according to claim 6, characterized in that: The skew acceptance strategy allows the variable neighborhood search algorithm to jump out of the current optimal solution to promote global optimization. The steps are as follows: For a pair of solutions Importing functions To show the similarity between the two; function If the self-pickup facility i is in solution S and If both are open, the value of this function is 1; otherwise, it is 0; function If facility i is in solution S and If Zhongdu is opened as a multi-functional unmanned delivery station, the value of this function is 1; otherwise, it is 0; For a pair of solutions Similarity function between the two The definition is as follows:

10. The unmanned delivery method based on heterogeneous facility joint delivery according to claim 6, characterized in that: The regret and backtracking strategy allows VNS to balance diversification and centralization in its exploration. The steps are as follows: In the search process, the best solution S found in each k iteration is recorded and retained. cbest ; If the current skew solution S cur If there is no improvement in k MVNS main iterations, use S cbest Restart the search process.

Images