A ship and unmanned aerial vehicle cooperative delivery method and system for a marine environment

Abstract

The application relates to a ship and unmanned aerial vehicle cooperative distribution method and system for a marine environment. The method comprises the following steps: classifying and dividing each distribution island in the sea by a factor analysis method, and determining the logistics demand level of each distribution island; according to the logistics demand level of each distribution island, regarding a ship-unmanned aerial vehicle combined transport model problem as a routing problem of a ship and an unmanned aerial vehicle in series, and constructing a ship-unmanned aerial vehicle cooperative distribution model; solving the ship-unmanned aerial vehicle cooperative distribution model by using a second-order cone program, and obtaining a ship-unmanned aerial vehicle cooperative distribution optimization result; and according to the ship-unmanned aerial vehicle cooperative distribution optimization result, performing logistics distribution on each distribution island in the sea by a ship and unmanned aerial vehicle cooperative distribution mode. Therefore, the requirements of modern logistics for efficiency and flexibility are met, and the efficiency of logistics distribution in the marine environment is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of logistics distribution, in particular to a ship and unmanned aerial vehicle cooperative distribution method and system for marine environment. BACKGROUND

[0002] In the marine environment, the uncertainty of the distribution point and the environmental risk put higher requirements on the efficiency and safety of the logistics distribution system. The traditional logistics distribution mode, such as completely relying on ships for parcel transportation, has been difficult to meet the requirements of modern logistics for efficiency and flexibility.

[0003] Therefore, the efficiency of logistics distribution in the marine environment is currently low. SUMMARY

[0004] Therefore, it is necessary to provide a ship and unmanned aerial vehicle cooperative distribution method and system for marine environment, which can improve the efficiency of logistics distribution in the marine environment.

[0005] A ship and unmanned aerial vehicle cooperative distribution method for marine environment, the method comprises:

[0006] The factor analysis method is used to classify and divide each distribution island in the sea, and the logistics demand level of each distribution island is determined;

[0007] According to the logistics demand level of each distribution island, the ship-unmanned aerial vehicle combined transport model problem is regarded as a routing problem of the series connection of the ship and the unmanned aerial vehicle, and a ship-unmanned aerial vehicle cooperative distribution model is constructed;

[0008] The ship-unmanned aerial vehicle cooperative distribution model is solved by using a second-order cone program, and a ship-unmanned aerial vehicle cooperative distribution optimization result is obtained;

[0009] According to the ship-unmanned aerial vehicle cooperative distribution optimization result, the logistics distribution of each distribution island in the sea is carried out by the ship and unmanned aerial vehicle cooperative distribution mode.

[0010] In one of the embodiments, the factor analysis method is used to classify and divide each distribution island in the sea, and the logistics demand level of each distribution island is determined, which comprises:

[0011] Let the set of ship and unmanned aerial vehicle joint distribution areas be E, and the set of selected social and economic indicators be G, so the matrix can be obtained from the logistics related social and economic data of the distribution area Wherein represents the jth logistics demand index data of the ith island;

[0012] In order to eliminate the differences in dimension and order of magnitude between each logistics demand level indicator, the logistics demand indicator data is standardized to obtain a standardized matrix;

[0013] Based on the logistics demand standardization data, a covariance matrix U is constructed, and by calculating the eigenvalues and eigenvectors of the covariance matrix, the variance contribution rate and the cumulative variance contribution rate are obtained, and by numerical analysis of the cumulative variance contribution rate, the number of factors a required is determined;

[0014] On the basis of the determined number of factors, the factors are rotated, and the contribution rate of each factor is redistributed, and the expression of each factor is obtained as:

[0015] F a =γ1logi1+γ2logi2+...+γ b logi b

[0016] Wherein, F a represents the expression of the a-th factor, logi b is the standardized b-th logistics demand index data, and γ b is the coefficient of the b-th logistics demand index;

[0017] The scores of each factor of each distribution island are added to obtain the comprehensive score, and the expression is:

[0018] SC=β1F1+β2F2+...+β a F a

[0019] Wherein, SC represents the comprehensive score of each island, and β a represents the coefficient of the a-th factor;

[0020] Finally, the order is sorted from high to low according to the comprehensive score.

[0021] In one of the embodiments, the ship-unmanned aerial vehicle combined transport model problem is regarded as a routing problem of the ship and unmanned aerial vehicle in series, which is:

[0022] The ship-unmanned aerial vehicle combined transport model problem is that the ship carries the unmanned aerial vehicle and the package, and the unmanned aerial vehicle is responsible for the package distribution, which is assumed to be: there is a set of distribution sequences S, for each position point s i in S, the unmanned aerial vehicle is launched from the ship, visits S, and then returns to the ship to charge, and the continuous separation time of the unmanned aerial vehicle is limited by the battery capacity, and the unmanned aerial vehicle and the ship are allowed to move independently.

[0023] In one of the embodiments, the expression of the ship-unmanned aerial vehicle cooperative distribution model is:

[0024] The objective function is:

[0025] Constraint condition 1:

[0026] Constraint 2:

[0027] Constraint 3:

[0028] Constraint 4:

[0029] Constraint 5:

[0030] Constraint 6:

[0031] Constraint 7: LP0 = orig

[0032] Constraint 8: AP0 = orig

[0033] Constraint 9: LP n+1 = dest

[0034] Constraint 10: AP n+1 = dest

[0035] wherein, denotes the duration of time the drone is on the vessel after it returns from location point s i and before it is launched again; denotes the time elapsed from when the drone is launched from location point s i until the drone is retrieved by the vessel after it returns from location point s i ; W sc (i) denotes the weight of the location point s i of delivery, n is the number of islands that the delivery needs to reach, constraint 1 is to ensure that the time for the vessel to travel from location AP i to location LP i+1 does not exceed constraint 2 is to ensure that the travel time for the vessel from location LP i to location AP i does not exceed constraint 3 is to limit the distance for the drone to travel from location LP i to location point s i ; constraint 4 is to limit the distance for the drone to travel from location point s i to location AP i ; constraint 5 is to ensure that the sum of the flight times for the drone to travel from location LP i to location point s i and from location point s i to location AP i does not exceed Constraint 6 is to ensure that the UAV is retrieved within its maximum flight time limit, and constraint 7 is to indicate that the LP is accessed by the UAV when i = 0 i is the starting point; constraint 8 is to indicate that the AP is set when i = 0 i is the point at which the UAV is retrieved after completing the delivery task i is the starting point, and constraint 9 is to indicate that the LP is set when i = n + 1 n+1 is the path end point; constraint 10 is to indicate that the AP is set when i = n + 1 n+1 is the path end point.

[0036] In one embodiment, the way in which the ship-UAV collaborative delivery model is solved by using a second-order cone program is as follows:

[0037] The model is solved by using a second-order cone program with a fixed delivery sequence S, and the sub-problem to be solved for the fixed delivery sequence S is denoted as socp(S), which includes:

[0038] (1) If i < j, then the position point s i is accessed by the UAV before s j ;

[0039] (2) The speed of the UAV does not exceed the maximum speed;

[0040] (3) The separation time of the UAV and the ship does not exceed R.

[0041] In one embodiment, the process of solving the model by using a second-order cone program with a fixed delivery sequence S includes:

[0042] First, the value of the current fixed delivery sequence S is initialized as a TSP solution on the set of positions S U {orig}, and the objective value of the ship-UAV collaborative delivery model is constantly optimized by searching for a better solution in the neighborhood of the current fixed delivery sequence S;

[0043] A neighborhood similar to the current fixed delivery sequence S is constructed by modifying the current fixed delivery sequence S, and the neighborhood of any sequence S is defined as Neigh(S), which includes sequences formed by exchanging s i and s j , and any sequence formed by selecting s i and moving it to other positions in the sequence;

[0044] Any sequence formed by deleting consecutive subsequences s i , s i+1 ,..., s j and re-inserting them in reverse order, where i < j;

[0045] After initializing the current fixed distribution sequence S, an iterative process is performed as follows:

[0046] First, a target value is calculated, for each value in the neighborhood Neigh(S), a second-order cone program socp is applied to calculate the corresponding model target value socp(S), if any neighborhood sequence produces a better target value socp(S') than socp(S), replace S with the neighborhood sequence S' and perform a new iteration, if no neighborhood sequence produces a better solution than S, the algorithm terminates and outputs the ship-UAV collaborative distribution optimization result.

[0047] A ship-UAV collaborative distribution system for a marine environment, the system comprising:

[0048] A grade division module for dividing the distribution islands on the sea into grades by factor analysis to determine the logistics demand grades of the distribution islands;

[0049] A model construction module for regarding the ship-UAV intermodal model problem as a routing problem of a ship connected in series with a UAV according to the logistics demand grades of the distribution islands to construct a ship-UAV collaborative distribution model;

[0050] A solution module for solving the ship-UAV collaborative distribution model by a second-order cone program to obtain a ship-UAV collaborative distribution optimization result;

[0051] A distribution module for performing logistics distribution to the distribution islands on the sea by ship-UAV collaborative distribution according to the ship-UAV collaborative distribution optimization result.

[0052] The above ship-UAV collaborative distribution method and system for a marine environment, by factor analysis, the distribution islands on the sea are divided into grades to determine the logistics demand grades of the distribution islands; regarding the ship-UAV intermodal model problem as a routing problem of a ship connected in series with a UAV according to the logistics demand grades of the distribution islands to construct a ship-UAV collaborative distribution model; solving the ship-UAV collaborative distribution model by a second-order cone program to obtain a ship-UAV collaborative distribution optimization result; performing logistics distribution to the distribution islands on the sea by ship-UAV collaborative distribution according to the ship-UAV collaborative distribution optimization result. Thus, in view of the complexity and uncertainty of marine logistics distribution, the ship-UAV joint distribution problem is regarded as a series routing problem, the demand grades of the distribution points are divided, the characteristics of the non-fixed launch point and recovery point of the marine distribution UAV are considered, the optimal distribution problem of the UAV and the ship is considered by a second-order cone program, the ship-UAV collaborative distribution optimization result is obtained to perform logistics distribution, which meets the requirements of efficiency and flexibility of modern logistics and improves the efficiency of logistics distribution in a marine environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 1 is a flow chart of a method for collaborative delivery between a ship and a drone in a marine environment according to one embodiment;

[0054] Figure 2 1 is a flow chart of a method for collaborative delivery between a ship and a drone in a marine environment according to another embodiment;

[0055] Figure 3 1 is a flow chart of a method for collaborative delivery between a ship and a drone in a marine environment according to another embodiment;

[0056] Figure 4 A schematic diagram of a maritime vessel-UAV path planning in one embodiment;

[0057] Figure 5 A scree plot generated according to the degree to which each principal component explains data variation in one embodiment. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0059] In one embodiment, Figure 1 As shown, a method for collaborative delivery between a ship and a drone in a maritime environment is provided, comprising the following steps:

[0060] Step S220: Using factor analysis, the distribution islands on the sea are classified into different levels to determine the logistics demand level of each distribution island.

[0061] In step S240, based on the logistics demand level of each distribution island, the ship-UAV intermodal transport model problem is regarded as a routing problem of ships and UAVs in series, and a ship-UAV collaborative distribution model is constructed.

[0062] In step S260, a second-order cone procedure is used to solve the ship-UAV collaborative delivery model to obtain the ship-UAV collaborative delivery optimization result.

[0063] Step S280: Based on the optimization result of the ship-UAV collaborative distribution, logistics distribution is carried out to each distribution island at sea through the collaborative distribution of ships and drones.

[0064] In one embodiment, the distribution islands at sea are classified into different levels through factor analysis to determine the logistics demand level of each distribution island, including:

[0065] Let the set of the distribution area of the ship and the unmanned aerial vehicle be E, and the set of the selected social and economic indicators be G, so the matrix can be obtained from the logistics-related social and economic data of the distribution area Wherein represents the jth logistics demand index data of the ith island;

[0066] In order to eliminate the differences in dimension and order of magnitude between various logistics demand level indicators, the logistics demand index data is standardized to obtain a standardized matrix;

[0067] Based on the standardized logistics demand data, a covariance matrix U is constructed, and by calculating the eigenvalues and eigenvectors of the covariance matrix, the variance contribution rate and the cumulative variance contribution rate are obtained. Through numerical analysis of the cumulative variance contribution rate, the number of factors a required is determined;

[0068] On the basis of the determined number of factors, the factors are rotated, and the contribution rate of each factor is redistributed, so that the expression of each factor is:

[0069] F a =γ1logi1+γ2logi2+...+γ b logi b

[0070] Wherein, F a represents the expression of the a th factor, logi b is the b th standardized logistics demand index data, and γ b is the coefficient of the b th logistics demand index;

[0071] The scores of each factor of each distribution island are added to obtain a comprehensive score, and the expression of the comprehensive score is:

[0072] SC=β1F1+β2F2+...+β a F a

[0073] Wherein, SC represents the comprehensive score of each island, β a represents the coefficient of the a th factor; and

[0074] Finally, the comprehensive scores are sorted in descending order.

[0075] In one embodiment, the ship-unmanned aerial vehicle combined transport model problem is regarded as a routing problem of the ship and the unmanned aerial vehicle in series, which is:

[0076] Taking the ship as the carrier, the unmanned aerial vehicle and the package are carried, and the ship-unmanned aerial vehicle combined transport model problem is as follows: there is a set of distribution sequences S, for each position point s iThe UAV is launched from the ship, visits S, then returns to the ship to charge, and allows the UAV and the ship to move independently, but the continuous separation time of the UAV is limited by the battery capacity.

[0077] In one embodiment, the expression of the ship-UAV collaborative delivery model is:

[0078] The objective function is:

[0079] Constraint 1:

[0080] Constraint 2:

[0081] Constraint 3:

[0082] Constraint 4:

[0083] Constraint 5:

[0084] Constraint 6:

[0085] Constraint 7: LP0 = orig

[0086] Constraint 8: AP0 = orig

[0087] Constraint 9: LP n+1 = dest

[0088] Constraint 10: AP n+1 = dest

[0089] wherein, represents the duration of the UAV on the ship after returning from the location point s i before being launched again; represents the time elapsed from the launch of the UAV to the location point s i until the UAV is retrieved by the ship after returning from the location point s i ; W sc (i) represents the weight of the delivery location point s i , n is the number of islands that the delivery needs to reach, constraint 1 ensures that the time for the ship to move from location AP i to location LP i+1 does not exceed constraint 2 ensures that the running time of the ship from location LP i to location AP i does not exceed constraint 3 limits the UAV from location LP i to the location point si Constraint 4 is to limit the distance of the UAV from position point s i to position AP i Constraint 5 is to ensure that the sum of the flight times of the UAV from position point LP i to position point s i and from position point s i to position AP i does not exceed Constraint 6 is to ensure that the UAV is picked up within its maximum flight time limit, and constraint 7 is to indicate that LP i is the starting point when i = 0; constraint 8 is to indicate that s i is the point where the UAV is picked up after completing the delivery task when i = 0, and constraint 9 is to indicate that AP i is the ending point of the path when i = n + 1; constraint 10 is to indicate that LP n+1 is the ending point of the path when i = n + 1, and constraint 11 is to indicate that AP n+1 is the ending point of the path when i = n + 1.

[0090] In one embodiment, the way to solve the ship-UAV collaborative delivery model by using a second-order cone program is as follows:

[0091] The model is solved by using a second-order cone program for a fixed delivery sequence S, and the sub-problem to be solved for a fixed delivery sequence S is denoted as socp(S), which includes:

[0092] (1) If i < j, then position point s i is visited by the UAV before position point s j ;

[0093] (2) The speed of the UAV does not exceed the maximum speed;

[0094] (3) The separation time of the UAV and the ship does not exceed R.

[0095] In one embodiment, the process of solving the model by using a second-order cone program for a fixed delivery sequence S includes:

[0096] First, the value of the current fixed delivery sequence S is initialized as a TSP solution on the set of positions S U {orig}, and the objective value of the ship-UAV collaborative delivery model is constantly optimized by finding a better solution in the neighborhood of the current fixed delivery sequence S;

[0097] A neighborhood similar to the current fixed delivery sequence S is constructed by modifying the current fixed delivery sequence S, and the neighborhood of any sequence S is defined as Neigh(S), which includes sequences obtained by swapping s i and s jany sequence formed by deleting consecutive substrings s i any sequence formed by moving them to other positions in the sequence;

[0098] any sequence formed by deleting consecutive substrings s i ,s i+1 ..., s j and reinserting them in reverse order, where i < j;

[0099] After initializing the current fixed distribution sequence S, the iterative process is as follows:

[0100] First, the objective value is calculated, for each value in the neighborhood Neigh(S), the second-order cone program socp is applied to calculate the corresponding model objective value socp(S), if any neighborhood sequence produces a better objective value socp(S') than socp(S), replace S with the neighborhood sequence S' and perform a new iteration, if no neighborhood sequence produces a better solution than S, the algorithm terminates and outputs the ship-unmanned aerial vehicle collaborative distribution optimization result.

[0101] The ship and unmanned aerial vehicle collaborative distribution method for the sea environment, through factor analysis, the distribution islands on the sea are classified by grade, and the logistics demand grade of each distribution island is determined; according to the logistics demand grade of each distribution island, the ship-unmanned aerial vehicle intermodal model problem is regarded as a routing problem of series connection of ship and unmanned aerial vehicle, and a ship-unmanned aerial vehicle collaborative distribution model is constructed; the second-order cone program is used to solve the ship-unmanned aerial vehicle collaborative distribution model, and the ship-unmanned aerial vehicle collaborative distribution optimization result is obtained; according to the ship-unmanned aerial vehicle collaborative distribution optimization result, the logistics distribution of each distribution island on the sea is carried out through the ship and unmanned aerial vehicle collaborative distribution. Therefore, in view of the complexity and uncertainty of sea logistics distribution, the ship and unmanned aerial vehicle joint distribution problem is regarded as a series connection routing problem, the demand grade of the distribution point is divided, and the characteristics of the sea distribution unmanned aerial vehicle launch point and recovery point are considered. The optimal distribution problem of unmanned aerial vehicle and ship is considered through the second-order cone program, the ship-unmanned aerial vehicle collaborative distribution optimization result is obtained to carry out logistics distribution, which meets the requirements of efficiency and flexibility of modern logistics, and improves the efficiency of logistics distribution in the sea environment.

[0102] In one embodiment, a ship and drone cooperative distribution method for offshore distribution is provided, which is used in a ship and drone cooperative logistics distribution scenario in an offshore distribution scenario. In this scenario, the process of distribution is roughly as follows: the logistics demand level is divided by factor analysis method, the traditional TSP problem is improved, and the ship-drones cooperative distribution model is established, aiming to minimize the total running time and maximize the distribution value of each distribution island. The local search algorithm is further used to optimize the greedy sequence to search for the optimal drone access sequence and the best launch point and landing point to approach the optimal solution. Specifically, the method comprises the steps of Figure 2 、 3 as shown in the method

[0103] S1, classifying the distribution points to optimize the distribution value;

[0104] S2, considering the ship-drones combined transport model problem as a routing problem of ship and drone in series;

[0105] S3, solving the ship-drones cooperative distribution model by using the second-order cone program.

[0106] In this embodiment, due to the unstable weather in island areas, some distribution points cannot be directly reached by traditional transportation tools, resulting in the inability to timely meet the distribution needs of surrounding islands, greatly increasing the time and risk of distribution activities, and many vulnerabilities of the ship-shore transportation industry have been exposed during the epidemic period. Considering the uncertainty of the marine environment, first, the demand of offshore distribution points is estimated and the risk is detected, and then according to the divided level, the feasibility of the operation of the drone in the island is determined from the economic benefit, human risk factor and environmental impact. Determine and analyze the challenges in local implementation and operation, coordinate the ship and the drone for joint distribution.

[0107] Specifically, in S1, the distribution point classification is performed. By considering the distribution demand of each island in the objective function, the ship-drones cooperative distribution model can preferentially serve the islands with higher demand, increasing the distribution value and providing a strong adaptive solution for the complex island distribution environment. The logistics demand level is divided by using the factor analysis method, and the regional gross domestic product and the urbanization rate of permanent population are selected as the basis for classification. In the factor analysis method, in addition to considering social and economic factors, island-specific indicators such as island area and resident distribution density are also introduced. The steps for dividing the logistics demand level according to the factor analysis method are as follows:

[0108] Step 1: Set the set of ship and drone combined distribution areas as E, and select the set of social and economic indicators as G, so the matrix can be obtained from the logistics-related social and economic data of the distribution area wherein represents the jth logistics demand index data of the ith island.

[0109] Second step: In order to eliminate the dimensional and order of magnitude differences between the indicators of each logistics demand level, the indicator data is standardized to obtain the standardized matrix.

[0110] Third step: Based on the standardized data of logistics demand, the covariance matrix U is constructed. Through the calculation of eigenvalues and eigenvectors of the covariance matrix, the variance contribution rate and cumulative variance contribution rate are obtained. Through numerical analysis of the cumulative contribution rate, the number of factors a required is determined.

[0111] Fourth step: On the basis of the determined number of factors, the factors are rotated and the contribution rate of each factor is redistributed, and the specific expression of each factor is obtained as:

[0112] F a = γ1logi1+ γ2logi2+... + γ b logi b

[0113] Where F a represents the expression of the a-th factor, logi b is the b-th standardized logistics demand indicator data, γ b is the coefficient of the b-th logistics demand indicator.

[0114] Fifth step: The scores of each factor of each distribution island are added to obtain the comprehensive score, and the expression is:

[0115] SC = β1F1+ β2F2+... + β a F a

[0116] Where SC represents the comprehensive score of each island, β a represents the coefficient of the a-th factor; finally, the comprehensive score is sorted from high to low.

[0117] In order to more accurately reflect the relative importance of each island to the overall goal, the concept of weight is introduced. By calculating the proportion of each island score relative to the total score, the relative weight is obtained, which converts the score of each island into the contribution to the overall goal. The advantage of this approach is that it can dynamically adjust the weight of each island according to its actual score, making the model more flexible and adaptable. According to the aforementioned demand level division, the weight of each island is allocated in combination with the demand score: the formula for calculating the total score is:

[0118] SC total = SC1+ SC2+... + SC |S|

[0119] Where SC totalThe sum of the overall scores of the islands for which the entire logistics distribution is performed, SC |s| The overall score of the island denoted by s.

[0120] The formula for calculating the relative weight of each island is then:

[0121]

[0122] where W SC is the relative weight value of each island, |S| is the number of islands for which logistics distribution is performed, SC q is the overall score value of the qth island.

[0123] In the ship-UAV collaborative distribution model, the overall score is assigned as the weight to each distribution point to optimize the distribution value. The distribution value is determined according to the weight and the order of access of the distribution point. The value of each distribution point can be represented by the product of the given weight and the reciprocal of the distribution order. As for the distribution sequence S, if the qth customer point is visited, the weight of this customer point is The distribution value obtained by this customer point can be represented by .

[0124] In this embodiment, the maritime distribution problem is a routing problem considering the series connection of ships and UAVs. The ship serves as a carrier, carrying UAVs and packages, and the UAV is responsible for package distribution. We assume that there is a set of distribution sequences S, for each s i in S, the UAV is launched from the ship, visits S, and then returns to the ship to charge.

[0125] As shown in Figure 4 , the solid line represents the driving path of the ship, the dashed line represents the flight route of the UAV, and the pentagram represents the position where the UAV is launched or returned from the ship.

[0126] The maritime distribution problem is a routing problem considering the series connection of ships and UAVs. This is an extension of the traditional TSP problem. In the traditional TSP, a set of positions and distances between them are given, where each position is visited exactly once and the path eventually returns to the starting point, and the goal is to find the shortest closed path through a specific set of positions.

[0127] In the ship-UAV collaborative delivery model, two types of vehicles are considered: a ship as a carrier, carrying UAVs and packages, and UAVs responsible for package delivery. It is assumed that there is a set of delivery sequences S, for each s in S, the UAV is launched from the ship, visits S, and then returns to the ship to charge. Unlike TSP, the ship-UAV collaborative delivery model allows the UAV and the ship to move independently, but the continuous separation time of the UAV is limited by the battery capacity. The problem aims to find a path in the Euclidean plane that satisfies all target locations being visited by the UAV while minimizing the duration of the entire task and maximizing the value of the delivery. Among them, the variables and parameters mainly involved in the ship-UAV collaborative delivery model can be listed as follows:

[0128] Table 1 Variables and parameters

[0129]

[0130]

[0131] In this embodiment, since the delivery locations on the sea are not fixed:

[0132] (1) Determine the optimal order of visiting each location point s i ∈S drone ;

[0133] (2) For each s i ∈S drone , determine the optimal position to launch the UAV and the optimal position to recover the UAV;

[0134] For the above two problems, the first problem involves discretization, and the second problem involves continuous optimization.

[0135] 1. Second-order cone program for fixed delivery sequence S

[0136] For a fixed delivery sequence S, the following sub-problems need to be solved, denoted as socp(S):

[0137] (1) If i < j, then s i is visited by the UAV before s j ;

[0138] (2) The speed of the UAV does not exceed the maximum speed

[0139] (3) The separation time of the UAV and the ship does not exceed R

[0140] Based on the above description, the optimization objective of the ship-UAV collaborative delivery model is to minimize the total running time of the ship and the UAV jointly visiting customers and maximize the delivery value of each delivery island, where the relative weight of the delivery value of each island is determined according to the weight and visiting order of the delivery points, and the formula is shown. The overall objective function expression is:

[0141]

[0142] Constraint 1:

[0143] Constraint 2:

[0144] Constraint 3:

[0145] Constraint 4:

[0146] Constraint 5:

[0147] Constraint 6:

[0148] Constraint 7: LP0 = orig

[0149] Constraint 8: AP0 = orig

[0150] Constraint 9: LP n+1 = dest

[0151] Constraint 10: AP n+1 = dest

[0152] Constraint 1 ensures that the time for the ship to travel from location AP i to location LP i+1 does not exceed Constraint 2 ensures that the running time for the ship to travel from location LP i to location AP i does not exceed Constraint 3 limits the distance of the UAV from location LP i to location point s i ; Constraint 4 limits the distance of the UAV from location point s i to location AP i ; Constraint 5 ensures that the sum of the flight times of the UAV from location LP i to location point s i and from location point s i to location AP i does not exceed Constraint 6 ensures that the UAV is retrieved within its maximum flight time limit, and constraint 7 indicates that the LP visited by the UAV when i = 0 i is the starting point; constraint 8 indicates that the AP is set when i = 0 i is the point at which the UAV is retrieved after completing the delivery task i is the starting point, and constraint 9 indicates that the LP is set when i = n + 1 n+1 is the path end point; constraint 10 indicates that the AP is set when i = n + 1 n+1 is the path end point.

[0153] In summary, considering the complexity and uncertainty of island logistics distribution, the UAV and ship joint distribution problem is regarded as a series routing problem. The demand level of the distribution points is divided, and the ship-UAV collaborative distribution model prioritizes the islands with higher demand. Considering the characteristics of the launch point and the recovery point of the offshore distribution UAV, the optimal distribution problem of the UAV and the ship is solved through the second-order cone program. The weight-based and visit order-based distribution value optimization strategy is introduced to optimize the selection of offshore distribution points and the distribution strategy, providing a new optimization strategy for island logistics distribution. The main advantages are:

[0154] 1. Improve the distribution value: In this embodiment, the distribution point level is divided by factor analysis, and the distribution value is optimized according to the weight and visit order of the distribution point. In the ship-UAV collaborative distribution model optimized by the GSLS algorithm, the total distribution value reaches 17.448, while the traditional TSP problem model does not consider the optimization of distribution value. This difference highlights the advantages of the collaborative distribution model in resource utilization and value maximization. By accurately calculating the weight of each distribution point, the optimization model not only meets the logistics demand of each island, but also maximizes the economic benefit of the distribution activity, reflecting the high adaptability and practical value in complex island distribution environment.

[0155] 2. Optimize the distribution path and time efficiency: In this embodiment, the greedy sequence with local search (GSLS) algorithm is used to solve the island distribution problem, which significantly optimizes the distribution path and time efficiency. Through comparative experiments, the traditional Traveling Salesman Problem (TSP) model has an average ship navigation distance of 265 kilometers and a total distribution time of 11.35 hours in the application of Zhoushan Islands. However, the ship-UAV collaborative distribution model optimized by the GSLS algorithm reduces the ship navigation distance to 215 kilometers and the total distribution time to 8.66 hours. This result shows that through optimization algorithm, the collaborative distribution model successfully reduces about 18.87% of the ship navigation distance and 23.74% of the distribution time under the premise of ensuring the distribution coverage of all target islands, greatly improving the distribution efficiency.

[0156] 3. Environmental adaptability and safety improvement: Compared with traditional ship-based distribution, the introduction of UAVs significantly improves the environmental adaptability and safety of the distribution system. UAVs can quickly respond to complex and variable marine environments, reducing distribution delays and risks caused by adverse weather, ensuring efficient and safe distribution activities.

[0157] Specific examples:

[0158] In the practical application of this embodiment, the greedy sequence with local search (GSLS) algorithm is chosen to solve the island distribution problem. The main advantage of this algorithm is that it can quickly construct a high-quality initial solution and effectively improve the solution through local search iteration to find an approximate optimal solution. This algorithm not only has high computational efficiency and is suitable for handling large-scale problems, but also has good adaptability, providing practical and feasible distribution path planning while meeting complex operational constraints.

[0159] First, the value of the current sequence is initialized as a TSP solution on the set of positions S∪{orig}. The objective value of the model is continuously optimized by finding better solutions in the neighborhood of the current sequence.

[0160] When finding the optimal access order, the optimal TSP solution may not be the best. Therefore, a neighborhood similar to the current sequence needs to be constructed by modifying the current sequence. We define the neighborhood of any sequence S as Neigh(S). The neighborhood Neigh(S) includes the following types of sequences:

[0161] 1. Two-point exchange: any sequence formed by exchanging s i and s j ;

[0162] 2. One-point exchange: any sequence formed by selecting s i and moving it to another position in the sequence (not before orig or after dest);

[0163] 3. By deleting consecutive substrings s i , s i+1 ,..., s j and reinserting them in reverse order, where i < j.

[0164] After initializing the current sequence S, the following iterative process is performed. First, the objective value is calculated. For each value in the neighborhood neigh(curS), apply the second-order cone program socp to calculate the corresponding model objective value socp(S). If any neighborhood sequence produces a better objective value socp(S') than socp(S), replace S with the neighborhood sequence S' and perform a new iteration. If no neighborhood sequence produces a better solution than S, the algorithm terminates.

[0165] The specific example in the numerical experiment of the embodiment: in order to verify the effectiveness of the ship and unmanned aerial vehicle offshore cooperative distribution model proposed in the embodiment, the embodiment takes an archipelago as the research background, and selects a larger area, port distribution and higher population density inhabited island in the archipelago as the distribution area point.

[0166] In the embodiment, demand index data is obtained. According to a statistical yearbook, the basic situation and social development index of each island are as shown in Table 2.

[0167] Table 2 Demand index data of inhabited islands in the archipelago

[0168]

[0169] The unmanned aerial vehicle selects Matrice 300 series unmanned aerial vehicle, which is a professional unmanned aerial vehicle launched by DJI, which is used for various applications, including logistics, search and rescue, patrol, etc. And meet the requirements of "General Requirements for Civil Unmanned Aerial Vehicle System Logistics Operation Part 1: Island Scene" for unmanned aerial vehicle system, so after selecting Matrice 300 series unmanned aerial vehicle, its main specifications are as shown in Table 3

[0170] Table 3 Specifications of Matrice 300 series unmanned aerial vehicle

[0171]

[0172] According to the statistics of the National Meteorological Information Center, the average weather conditions in the local area are known. According to the historical climate background of the archipelago (taking September as an example), the local historical extreme maximum temperature in September is 36.1℃, the historical average temperature in September is 24.5℃, the historical maximum daily precipitation in September is 127.2mm, and the historical average wind speed in September is 4.3m / s. The selected unmanned aerial vehicle can operate within these parameter ranges and meet the distribution conditions.

[0173] In the embodiment, SPSS software is used for factor analysis to divide the distribution points into grades. First, KMO and Bartlett test is carried out to determine whether it is suitable for factor analysis. According to the KMO statistic shown in Table 4, the KMO statistic is 0.742, which is between 0.7-0.9, indicating that there is a correlation between variables, and the significance value is 0 less than 0.05, which meets the requirements and can be factor analyzed.

[0174] Table 4 KMO and Bartlett test result table

[0175]

[0176] Table 5 Total variance explanation table

[0177]

[0178] The higher the variance explained, the more important the corresponding principal component is, and the weight proportion should be increased accordingly. Figure 5 The scree plot generated according to the degree of explanation of data variation by each principal component is shown. The role of this plot is to determine the number of factor principal components that need to be selected according to the slope of the eigenvalue. It can be observed from the figure that when the third factor is reached, the slope of the broken line tends to be flat. Combined with Table 5, it is confirmed that the number of factor principal components is 3, which contains three larger eigenvalues, 3.592, 1.085 and 0.182 respectively. At the same time, based on the variance contribution rate of each component, we selected the first three factors, and their cumulative contribution rate reached 97.178%. Therefore, the first three principal components can more comprehensively describe the logistics demand of each distribution island.

[0179] The correlation between the original 10 island socio-economic data indicators and the three principal component factors, i.e. the factor loading matrix, can accurately explain the three factors. In the research process, it is found that most factors have a relationship with multiple variables. In order to deal with this relationship, the Kaiser Normalization Maximum Variance Method is used to rotate these factors. Through this process, the factor score coefficients (principal component loadings) contained in each component are calculated, and the specific results are shown in Table 6. These factor score coefficients will be used to calculate the component scores and further obtain the specific expressions of the principal components.

[0180] Table 6 Component Matrix Table

[0181]

[0182] According to the rotated component score coefficient matrix, write the factor expression, let F1, F2, F3 represent the three factors, and according to the factor expression, the three factors can be solved:

[0183] F1 = 0.263 x island area - 0.601 x permanent population (person) + 0.203 x population density + 0.73 x permanent population urbanization rate + 0.571 x regional gross product

[0184] F2 = -0.316 x island area + 0.037 x permanent population (person) + 0.859 x population density + 0.129 x permanent population urbanization rate + 0.154 x regional gross product

[0185] F3 = -0.144 x island area + 1.9 x permanent population (person) - 0.067 x population density - 0.804 x permanent population urbanization rate - 0.457 x regional gross product

[0186] The comprehensive score of each island can be obtained from the comprehensive score expression, and the results are shown in Table 7:

[0187] SC = (0.558 / 0.972) x F1 + (0.257 / 0.972) x F2 + (0.157 / 0.972) x F3

[0188] Table 7 Comprehensive score table

[0189]

[0190] Analysis of experimental results

[0191] Comparison between the traditional TSP problem model and the ship and UAV offshore collaborative distribution model of the present application

[0192] The ship and UAV offshore collaborative distribution model of the present application takes into account the particularity of offshore distribution, i.e. the launch point and recovery point of the UAV are uncertain, and sets constraint conditions to establish a ship-UAV collaborative distribution model. Compared with the traditional TSP problem, it is more in line with the distribution scenario. In the traditional Traveling Salesman Problem (TSP), the ship is responsible for package distribution, and the goal is to find the shortest possible path that covers all distribution points, while each distribution point is only visited once by the ship and finally returns to the starting point. The target values and models produced by the two problem models are obviously different. After solving the ship and UAV offshore collaborative distribution model, the ship-UAV collaborative distribution optimization results are shown in Table 8.

[0193] Table 8 Ship-UAV collaborative distribution optimization results

[0194]

[0195] Table 9 Comparison with the traditional TSP problem model

[0196]

[0197] The delivery network of the ship and UAV offshore collaborative delivery model covers 10 different islands. Considering the geographical distribution of the islands and the complexity of offshore logistics, this number of delivery points reflects a relatively complex logistics network. As shown in Table 9, the total sailing distance of the optimized ship is 215 kilometers. Since only ships are used for delivery in the traditional TSP problem, the ship needs to travel a longer distance to reach the customer point. In the ship-UAV collaborative delivery model, the ship does not need to reach the customer location, but launches a UAV to fly to the customer point and return, so the sailing distance of the ship is smaller than that in the traditional TSP problem model. The total delivery time is 8.66 hours, which includes the transportation time of the ship and the UAV. Since the speed of the UAV is higher than that of the ship, the participation of the UAV reduces the total delivery time by 2.69 compared to the traditional TSP. The delivery value is calculated based on the weight of the delivery point and the access order. The optimization result shows that the total delivery value is 17.448, which indicates that after considering the demand of the islands and the access order, the delivery activity creates a high value. High delivery value means that resources are effectively utilized, maximizing value creation during the delivery process.

[0198] This embodiment takes offshore logistics delivery as the background. Through demand level division, the ship and UAV offshore collaborative delivery model can prioritize service to islands with higher demand. And in view of the uncertainty of offshore UAV landing position, the ship and UAV offshore collaborative delivery model is proposed. By considering the characteristics of offshore delivery, the model can better adapt to island scenarios and optimize the selection of offshore delivery points and delivery strategies. The example analysis shows the potential of the model in improving the efficiency of island delivery and provides a new solution for island logistics delivery.

[0199] The embodiment introduces an innovative ship and unmanned aerial vehicle cooperative distribution model, and aims at island area logistics distribution. The ship and unmanned aerial vehicle cooperative distribution is regarded as a series connection routing problem, the traditional traveling salesman problem (TSP) is successfully converted into a model more in line with the actual demand of marine distribution. The distribution points are accurately classified according to the demand level, and the second-order cone program is used to solve the optimal distribution path problem of the unmanned aerial vehicle and the ship. The application not only minimizes the total running time, but also maximizes the distribution value, significantly improves the distribution efficiency and economic benefit. In the actual application case, the model is solved by using the greedy sequence algorithm (GSLS) of local search, and a high-quality initial solution is effectively constructed, and the optimal solution is approached by iteration improvement. Compared with the traditional TSP model, the ship navigation distance is significantly reduced and the distribution time is effectively shortened in the application of Zhoushan Archipelago, and a higher distribution value is created. Compared with the traditional traveling salesman problem (TSP) model, the ship navigation distance is reduced by about 18.87% and the distribution time is reduced by about 23.74%, and the distribution value is created by 17.448, which shows the advantages of the model in resource utilization and value maximization. The embodiment provides a new idea and method for island area logistics distribution.

[0200] It should be understood that, although Figure 1 The steps in the flowchart of the application are shown in sequence according to the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, the execution of these steps is not strictly limited in sequence, and these steps can be executed in other orders. Moreover, Figure 1 At least part of the steps in the flowchart of the application can include multiple sub-steps or multiple stages, which are not necessarily executed at the same time, but can be executed at different times, and the execution order of these sub-steps or stages is not necessarily sequential, but can be executed in rotation or alternation with at least part of other steps or sub-steps or stages of other steps.

[0201] In one embodiment, a ship and unmanned aerial vehicle cooperative distribution system for marine environment is provided, comprising:

[0202] A level classification module is configured to classify the distribution islands on the sea by factor analysis method, and determine the logistics demand level of each distribution island.

[0203] A model construction module is configured to regard the ship-unmanned aerial vehicle intermodal model problem as a routing problem of series connection of ship and unmanned aerial vehicle according to the logistics demand level of each distribution island, and construct a ship-unmanned aerial vehicle cooperative distribution model.

[0204] A solving module is configured to solve the ship-UAV collaborative distribution model by using a second-order cone program to obtain a ship-UAV collaborative distribution optimization result.

[0205] A distribution module is configured to perform logistics distribution for each distribution island in the sea by the ship-UAV collaborative distribution according to the ship-UAV collaborative distribution optimization result.

[0206] For specific limitations of the ship-UAV collaborative distribution system for the sea environment, refer to the limitations of the ship-UAV collaborative distribution method for the sea environment described above, which will not be repeated here. Each module in the above ship-UAV collaborative distribution system for the sea environment can be realized by software, hardware, and a combination thereof, in whole or in part. The above modules can be embedded in or independent of the processor in the computer device in hardware form, or can be stored in the memory in the computer device in software form, so as to be called and executed by the processor to perform the operations corresponding to each module.

[0207] Each technical feature of the above embodiments can be combined arbitrarily. In order to make the description simple, all possible combinations of each technical feature in the above embodiments are not described, however, as long as the combination of these technical features does not exist contradictory, it should be considered as the scope of the present application.

[0208] The above embodiments only express several implementation manners of the present application, and the description is more specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be pointed out that for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are all within the scope of the present application. Therefore, the scope of the patent of the present application should be subject to the appended claims.

Claims

1. A ship and drone collaborative delivery method for a marine environment, characterized by, The method comprises: Each distribution island on the sea is classified by a factor analysis method to determine the logistics demand level of each distribution island; According to the logistics demand level of each distribution island, a ship-unmanned aerial vehicle (UAV) combined transport model problem is regarded as a routing problem of the ship and the UAV in series, and a ship-UAV collaborative distribution model is constructed; A second-order cone program is used to solve the ship-UAV collaborative distribution model to obtain a ship-UAV collaborative distribution optimization result; According to the ship-UAV collaborative distribution optimization result, each distribution island on the sea is distributed by a ship-UAV collaborative distribution mode. The classification of each distribution island on the sea by the factor analysis method to determine the logistics demand level of each distribution island comprises: Assume that the set of joint delivery areas of ships and drones is E, and the set of selected socioeconomic indicators is G. Therefore, the matrix can be obtained from the logistics-related socioeconomic data of the delivery area in represents the j-th logistics demand indicator data of the i-th island; In order to eliminate the differences in dimension and order of magnitude between various logistics demand level indicators, the logistics demand indicator data is standardized to obtain a standardized matrix; Based on the logistics demand standardized data, a covariance matrix U is constructed, and the eigenvalues and eigenvectors of the covariance matrix are calculated to obtain the variance contribution rate and the cumulative variance contribution rate. The number of required factors a is determined by numerical analysis of the cumulative variance contribution rate. On the basis of the determined number of factors, the factors are rotated, and the contribution rate of each factor is redistributed to obtain the expression of each factor: F a = γ1logi1+ γ2logi2+... + γ b logi b Wherein, F a represents the expression of the a-th factor, logi b is the standardized b-th logistics demand index data, γ b is the coefficient of the b-th logistics demand index; The scores of various factors of each distribution island are added to obtain a comprehensive score, and the expression is: SC = β1F1+ β2F2+... + β a F a where SC denotes the composite score for each island, β a denotes the coefficient of the a-th factor; Finally, the comprehensive scores are sorted in descending order; The ship-UAV combined transport model problem is regarded as a routing problem of the ship and the UAV in series. A ship is used as a carrier to carry unmanned aerial vehicles and packages, and the unmanned aerial vehicles are responsible for package delivery. The ship-unmanned aerial vehicle intermodal model problem is assumed as follows: there is a set of delivery sequences S, for each position point s in S i The unmanned aerial vehicle is launched from the ship, visits S, and then returns to the ship for charging. The unmanned aerial vehicle and the ship are allowed to move independently, but the continuous separation time of the unmanned aerial vehicle is limited by the battery capacity. The expression of the ship-UAV collaborative distribution model is: The objective function is: Constraint 1: Constraint 2: Constraint 3: Constraint 4: Constraint 5: Constraint 6: Constraint condition 7: LP0=orig Constraint condition 8: AP0=orig Constraint 9: LP n+1 = dest Constraint 10: AP n+1 = dest in, Indicates that the drone is moving from position s i Duration on board the ship after returning and before being launched again; Represented as launching from the UAV to the location point s i , until the drone moves from position s i The time it takes to be recovered by the ship after returning; W sc (i) represents the delivery location s i The weight of n is the number of islands that need to be delivered, and constraint 1 is to ensure that the ship is i To location LP i+1 The time does not exceed Constraint 2 is to ensure that the ship is i To location AP i The running time does not exceed Constraint 3 restricts the UAV from position LP i To position s i The constraint 4 is to limit the distance of the UAV from the position s i To location AP i The constraint 5 is to ensure that the UAV is at the position LP i To position s i , and then from position s i To location AP i The total flight time does not exceed Constraint 6 ensures that the drone is retrieved within its maximum flight time limit, and constraint 7 indicates that when i = 0, the LP visited by the drone i is the starting point; constraint 8 means that when i=0, the UAV is at s i The point AP that is retrieved after completing the delivery task i As the starting point, constraint 9 means that when i=n+1, set LP n+1 is the end point of the path; constraint 10 means that when i=n+1, set AP n+1 is the end point of the path; Indicates that the drone is from LP i to s i distance; Indicates that the drone is from s i to AP i The distance between the start and end points is orig and dest respectively.

2. The method of claim 1, wherein, The ship-UAV collaborative distribution model is solved by a second-order cone program. A second-order cone program with a fixed distribution sequence S is used to solve the model. The sub-problem to be solved for the fixed distribution sequence S is expressed as socp(S), which comprises: (1) if i < j, then position point s i was accessed by the drone before position point s j ; (2) The speed of the UAV does not exceed the maximum speed; (3) The separation time of the UAV and the ship does not exceed R.

3. The method of claim 2, wherein, The process of solving the model by the second-order cone program with the fixed distribution sequence S comprises: First, the value of the current distribution sequence S is initialized as a TSP solution on the position S∪{orig} set. The objective value of the ship-UAV collaborative distribution model is continuously optimized by searching for a better solution in the neighborhood of the current fixed distribution sequence S. A neighborhood of a current fixed delivery sequence S is constructed by modifying the current fixed delivery sequence S. The neighborhood of any sequence S is defined as Neigh(S) and includes sequences formed by exchanging s i and s j for any s i and moving it to any other position in the sequence. by deleting consecutive substrings s i , s i+1 ,...,s j and reinserting them in reverse order, where i < j; After initializing the current fixed distribution sequence S, the iteration process is: First, the objective value is calculated. For each value in the neighborhood Neigh(S), the second-order cone program socp is applied to calculate the corresponding model objective value socp(S). If any neighborhood sequence produces a better objective value socp(S') than socp(S), replace S with S' and perform a new iteration. If no neighborhood sequence produces a better solution than S, the algorithm terminates and outputs the ship-UAV collaborative distribution optimization result.

4. A ship and drone coordinated delivery system for use in a marine environment, characterized by, The system comprises: The grade dividing module is configured to divide the delivery islands on the sea into different grades by a factor analysis method, and determine the logistics demand grades of the delivery islands. The model constructing module is configured to construct a ship-UAV collaborative delivery model by regarding the ship-UAV intermodal model problem as a routing problem of the ship and the UAV in series according to the logistics demand grades of the delivery islands. The solving module is configured to solve the ship-UAV collaborative delivery model by using a second-order cone program, and obtain a ship-UAV collaborative delivery optimization result. The delivery module is configured to perform logistics delivery for the delivery islands on the sea by the ship-UAV collaborative delivery according to the ship-UAV collaborative delivery optimization result. The grade dividing module is configured to divide the delivery islands on the sea into different grades by a factor analysis method, and determine the logistics demand grades of the delivery islands. Let the set of distribution areas combined with the unmanned aerial vehicle be E, and the set of social and economic indicators be G. Therefore, the matrix can be obtained from the logistics-related social and economic data of the distribution area wherein represents the jth logistics demand indicator data of the ith island. In order to eliminate the differences in dimension and order of magnitude between the logistics demand level indicators, the logistics demand indicator data is standardized to obtain a standardized matrix. Based on the standardized logistics demand data, a covariance matrix U is constructed, and the variance contribution rate and the cumulative variance contribution rate are obtained by calculating the eigenvalues and eigenvectors of the covariance matrix. The number of required factors a is determined by numerically analyzing the cumulative variance contribution rate. On the basis of the determined number of factors, the factors are rotated, and the contribution rates of the factors are redistributed to obtain the expression of each factor: F a = γ1logi1+ γ2logi2+... + γ b logi b Wherein, F a represents the expression of the a-th factor, logi b is the normalized b-th logistics demand index data, γ b is the coefficient of the b-th logistics demand index; The scores of each factor of each delivery island are added to obtain a comprehensive score, and the expression is: SC = β1F1+ β2F2+... + β a F a where SC denotes the composite score for each island, β a denotes the coefficient of the a-th factor; Finally, the delivery islands are sorted in descending order of the comprehensive score. The ship-UAV collaborative delivery model is expressed as: A ship is taken as a carrier, and an unmanned aerial vehicle and a package are carried, and the ship-unmanned aerial vehicle combined transportation model problem of the unmanned aerial vehicle responsible for package delivery is assumed: there is a set of delivery sequences S, for each position point s in S i The unmanned aerial vehicle is launched from the ship, visits S, and then returns to the ship for charging, and the continuous separation time of the unmanned aerial vehicle and the ship is limited by the battery capacity; Constraint condition 7: LP0=orig The objective function is: Constraint 1: Constraint 2: Constraint 3: Constraint 4: Constraint 5: Constraint 6: Constraint condition 8: AP0=orig ​ Constraint 9: LP n+1 = dest Constraint 10: AP n+1 = dest in, Indicates that the drone is moving from position s i Duration on board the ship after returning and before being launched again; Represented as launching from the UAV to the location point s i , until the drone moves from position s i The time it takes to be recovered by the ship after returning; W sc (i) represents the delivery location s i The weight of n is the number of islands that need to be delivered, and constraint 1 is to ensure that the ship is i To location LP i+1 The time does not exceed Constraint 2 is to ensure that the ship is i To location AP i The running time does not exceed Constraint 3 restricts the UAV from position LP i To position s i The constraint 4 is to limit the distance of the UAV from the position s i To location AP i The constraint 5 is to ensure that the UAV is at the position LP i To position s i , and then from position s i To location AP i The total flight time does not exceed Constraint 6 ensures that the drone is retrieved within its maximum flight time limit, and constraint 7 indicates that when i = 0, the LP visited by the drone i is the starting point; constraint 8 means that when i=0, the UAV is at s i The point AP that is retrieved after completing the delivery task i As the starting point, constraint 9 means that when i=n+1, set LP n+1 is the end point of the path; constraint 10 means that when i=n+1, set AP n+1 is the end point of the path; Indicates that the drone is from LP i to s i distance; Indicates that the drone is from s i to AP i The distance between the start and end points is orig and dest respectively.

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