Multi-condition path planning method based on M-PCA model

Abstract

The invention discloses a multi-condition path planning method based on M-PCA. The method comprises the following steps: constructing a starting point data set, an order data set, a traffic data set and a road network data set; constructing an M-PCA model with the lowest cost as a target function by using the comprehensive data set in combination with a search strategy of a heuristic algorithm; and setting three constraint conditions including time constraint, single carrier load constraint and total load capacity constraint for path planning through an M-PCA model, and then solving to obtain the optimal path planning. A heuristic algorithm is utilized to take various transportation requirements as different constraint conditions, and the constraint conditions are converted into corresponding KKT conditions to constrain a transportation target and solve an optimal solution, so that an optimal distribution path can be dynamically planned under the constraint conditions of cost, time and the like, the distribution efficiency is improved, and the transportation time and cost are reduced.

Description

Technical Field

[0001] The present invention relates to intelligent logistics and supply chain optimization, and in particular to a multi-condition path planning method based on an M-PCA model. Background Art

[0002] Traditional logistics models face urgent challenges when dealing with the transportation of such fruits and vegetables, primarily difficulties in effectively controlling costs and shortening transportation times while ensuring product quality. It is worth noting that the traditional supply chain distribution model distributes orders based on administrative regions, but this model is less applicable to the delivery of fruit and vegetable orders. However, fruit and vegetable orders have high timeliness and freshness requirements. Therefore, based on relevant technologies, a new distribution route planning method is needed. This model can generate different distribution plans based on different actual distribution conditions, thereby more effectively adapting to the particularities of the fruit and vegetable supply chain and achieving goals such as cost reduction and timeliness optimization. Summary of the Invention

[0003] The purpose of this invention is to provide a multi-condition path planning method based on the M-PCA model to generate different delivery plans for different constraints, improve the accuracy of delivery results, and expand the application scenarios of path planning.

[0004] In order to solve the above problems, the present invention provides a multi-condition path planning method based on M-PCA, comprising: constructing a comprehensive data set, wherein the data set includes a starting point data set, an order data set, a traffic data set, and a road network data set; using the comprehensive data set combined with a heuristic algorithm search strategy to construct an M-PCA model with minimum cost as the objective function; and using the M-PCA model to set three constraints for path planning, including time constraints, single vehicle load constraints, and total load constraints, and then solving the problem to obtain the optimal path planning.

[0005] In addition, a comprehensive data set combined with a heuristic algorithm search strategy is used to construct an M-PCA model with the minimum cost as the objective function, including: defining constraints and objective functions, where the constraints include equality constraints and inequality constraints, and the constraint-related data are obtained from the comprehensive data set; combining the constraints with the Lagrange multiplier method to transform the objective function; combining the constraints with the corresponding KKT conditions to generate the corresponding KKT conditions; and combining the KKT conditions, the transformed objective function and the constraints as the M-PCA model.

[0006] In addition, equality constraints include: the start and end point conditions must exist, and the path starts from the specified start point and ends at the specified end point; inequality constraints include: time constraints, single vehicle load constraints, and total load constraints.

[0007] Additionally, time constraints include:

[0008]

[0009] Among them, T i is the longest transportation time of vehicle i, indicating that the corresponding order must be shipped within T i Delivery within 12 hours, Time(x i ) represents the actual transportation time of vehicle i;

[0010] The load constraints for a single vehicle include:

[0011]

[0012] Among them, Weigt i is the maximum load of vehicle i, L(x i ) is the actual load capacity of a single vehicle i;

[0013] Total load constraints include:

[0014]

[0015] Where D is the total freight volume, and n and i are integers greater than or equal to 1.

[0016] In addition, the objective function is transformed using the Lagrange multiplier method in combination with the constraint conditions, including:

[0017] Define the Lagrange function Lagrange, where the Lagrange function includes the original objective function and the Lagrange multiplier associated with each constraint, and the Lagrange multiplier includes λ i 、μ i 、ν;

[0018] λ i Corresponding to the load constraint of a single vehicle 0≤L(x i )≤Weigt i ;

[0019] μ i Corresponding to the time constraint Time(x i )≤T i ;

[0020] ν corresponds to the total load constraint

[0021] At this time, the Lagrangian function is:

[0022]

[0023] in Represents the original objective function of minimum cost.

[0024] In addition, the corresponding KKT conditions are generated in combination with the constraints, including:

[0025] Generate gradient conditions:

[0026]

[0027] in, Represents the result of gradient operation;

[0028] Generate the original feasibility conditions:

[0029]

[0030] Generate dual feasibility conditions:

[0031] λ i ,μ i ≥0

[0032] ν≥0

[0033] Generate complementary slackness conditions:

[0034] λ i (weight i -L(x i ))=0

[0035] μ i (T i -Time(x i ))=0

[0036]

[0037] In addition, the M-PCA model includes:

[0038]

[0039] subject to:

[0040]

[0041] ν≥0

[0042]

[0043] Compared with the existing technology, the present invention has the following significant effects: by utilizing the heuristic algorithm, a multi-condition path planning method based on M-PCA is proposed, which takes multiple transportation demands as different constraints, and converts the constraints into corresponding KKT conditions to constrain the transportation goals and seek the optimal solution. It can reasonably dispatch transportation resources, freely combine transportation modes, and dynamically plan the optimal distribution path under the constraints of cost, time, etc., improve distribution efficiency, reduce transportation time and cost, realize intelligent task allocation and resource allocation, ensure the efficient collaboration of the two, and improve overall distribution efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a flow chart of a multi-condition path planning method based on an M-PCA model according to one embodiment of the present invention;

[0045] Figure 2 A Jiangsu Province route map according to an embodiment of the present invention;

[0046] Figure 3 A path map of the Yangtze River Delta according to one embodiment of the present invention;

[0047] Figure 4 A route map of the three northeastern provinces according to one embodiment of the present invention. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, each embodiment of the present invention will be described in detail below with reference to the accompanying drawings. However, it will be understood by those skilled in the art that in each embodiment of the present invention, many technical details are provided to enable the reader to better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical solutions claimed in this application can be implemented. The division of the following embodiments is for convenience of description and should not constitute any limitation on the specific implementation of the present invention. The various embodiments can be combined with each other and referenced to each other under the premise that there is no contradiction.

[0049] One embodiment of the present invention relates to a multi-conditional path planning method based on the cheapest arc path combined with a metaheuristic algorithm (M-PCA) model, which can be applied to a computing terminal such as a computer. In this embodiment, a comprehensive dataset is first constructed, including a starting point dataset, an order dataset, a traffic dataset, and a road network dataset. An M-PCA model is then constructed using the comprehensive dataset combined with a heuristic algorithm search strategy. The M-PCA model sets constraints for the path planning and solves the problem to obtain the optimal path plan. By utilizing a heuristic algorithm and considering multiple constraints, a multi-conditional path planning scheme based on M-PCA is proposed. This scheme can rationally dispatch transportation resources, freely combine transportation modes, and dynamically plan optimal delivery routes under constraints such as cost and time. This scheme improves delivery efficiency, reduces transportation time and cost, and enables intelligent task allocation and resource allocation, ensuring efficient collaboration between the two, thereby enhancing overall delivery efficiency. The following describes the implementation details of the multi-conditional path planning method based on the M-PCA model according to one embodiment of the present invention. The following implementation details are provided for ease of understanding and are not required for implementation.

[0050] Taking the supply of peaches in Yangshan, Wuxi as an example, this paper conducts research to construct a corresponding model to better solve the problems of seasonality, regionality, vulnerability and high timeliness in the transportation of such fruits and vegetables.

[0051] In this embodiment, if Figure 1 As shown in step 101, a comprehensive data set is constructed, wherein the data set includes a starting point data set, an order data set, a traffic data set, and a road network data set.

[0052] Specifically, to address the current issues of insufficient diversity and sample size in logistics and distribution datasets, this implementation constructs multiple comprehensive datasets, including a starting point dataset, an order dataset, a traffic dataset, and a road network dataset. These datasets can not only be used to build and verify the performance of the M-PCA model, but can also serve as reliable data for other researchers to solve similar transportation problems.

[0053] The starting points in the starting point dataset are divided into warehouses and airports. Warehouses are used for material storage, and airports are used for long-distance transportation. We collected latitude and longitude data for multiple warehouses and airports to provide starting point data for the model.

[0054] The order data in the order dataset is divided into B-end and C-end. The B-end corresponds to regional dealers, and the C-end corresponds to ordinary customers. The B-end has a large shipping volume, and the C-end has a large number of orders.

[0055] The transportation resources in the traffic dataset include trucks and airplanes. Trucks are divided into 4.2-meter trucks, 7.5-meter trucks, 9.6-meter trucks, and 13.5-meter trucks, and their speed, cost, load capacity, and carbon emissions vary. Aircraft are divided into freighters, bulk cargo planes, and drones. Freighters and bulk cargo planes differ only in their load capacity. Drones, as short-distance delivery tools, are characterized by high cost, high speed, and strong flexibility.

[0056] The road network dataset includes real road network data from various provinces. The data is obtained from the OSM public map data service platform, which has a fast data update frequency. The data in the dataset accurately maps the road network data to the street level, which enables the constructed M-PCA model to have better performance.

[0057] In step 102, an M-PCA model is constructed using a comprehensive data set combined with a heuristic algorithm search strategy.

[0058] Specifically, an M-PCA model is constructed using a comprehensive data set combined with a heuristic algorithm search strategy, including: defining constraints and objective functions, wherein the constraints include equality constraints and inequality constraints, and constraint-related data are obtained from a comprehensive data set; transforming the objective function using the Lagrange multiplier method based on the constraints; generating corresponding KKT conditions based on the constraints; and combining the KKT conditions, the transformed objective function, and the constraints as the M-PCA model.

[0059] The equality constraints include: the start and end conditions must exist, and the path starts from the specified start point and ends at the specified end point. The starting point set can be set as: S = {s1, s2, ..., s n}; End point set: D = {d, d2, ..., d n}.

[0060] Inequality constraints include: time constraints, single vehicle load constraints, and total load constraints.

[0061] Time constraints: Ensure that the required shipping time is within acceptable limits.

[0062]

[0063] Among them, T i is the maximum transportation time of vehicle i. The order must be placed within T i Delivery within 1 hour; Time(x i ) is the actual transportation time of vehicle i, which depends on the route chosen; n is the number of nodes.

[0064] Single vehicle load constraint: Ensure that the load of each vehicle does not exceed its maximum carrying capacity and is at least equal to the amount of cargo it carries in the mission.

[0065]

[0066] Among them, Weigt i is the maximum load of vehicle i, L(x i ) is the actual load of vehicle i, and the specific value depends on the planned route.

[0067] Total load constraint: The total load must be greater than or equal to the total cargo volume, ensuring that the total load of all vehicles is at least equal to the total cargo demand.

[0068]

[0069] Where D is the total cargo volume.

[0070] According to the above constraints, the objective function of minimum transportation cost can be obtained as follows:

[0071]

[0072] The constraints are:

[0073]

[0074] In an example, we can assume that there are two vehicles, x1 and x2, involved in a transport. We set T1 and T2 for each vehicle to 10 hours and 15 hours, respectively; Weigt1 and Weigt2 for each vehicle to 100 tons and 150 tons, respectively; and the total freight volume, D, to 150 tons. We can then obtain the cost function for this transport:

[0075] f(x)=5×Distance(x1)+8×Distance(x2)

[0076] Where f(x) is the transportation cost, 5 and 8 are the unit cost coefficients of the two vehicles, and Distance(x1) and Distance(x2) are the distances traveled by the two vehicles. It should be noted that the unit cost coefficient represents the cost coefficient of vehicle transportation. In this implementation, the unit cost coefficient represents the cost per kilometer of cargo transported by a vehicle, including vehicle maintenance costs, traffic congestion costs, and cargo damage costs. In actual scenarios, different unit cost coefficients can be obtained for different transportation situations.

[0077] From this, we can construct the original objective function and constraints for the minimum cost:

[0078] Original objective function:

[0079]

[0080] Time constraints:

[0081] Time(x1)≤10,Time(x2)≤15

[0082] Single vehicle load constraints:

[0083] 0≤L(x1)≤100, 0≤L(x2)≤150

[0084] Total load capacity constraints:

[0085] D≤L(x1)+L(x2), D=200

[0086] After obtaining the objective function and constraints of minimum transportation cost, the Lagrange multiplier method is used to transform the objective function of minimum transportation cost. Specifically, it includes:

[0087] Define the Lagrange function Lagrange, where the Lagrange function includes the objective function of minimum transportation cost and the Lagrange multiplier associated with each constraint:

[0088] λ i Corresponding to the load constraint of a single vehicle 0≤L(x i )≤Weigt i ;

[0089] μ i Corresponding to the time constraint Time(x i )≤T i ;

[0090] ν corresponds to the total load constraint

[0091] At this time, the Lagrangian function is:

[0092]

[0093] In an example, the Lagrangian function can be expressed as:

[0094]

[0095] After obtaining the Lagrangian function, the corresponding KKT conditions are generated in combination with the constraints. Specifically, the generated KKT conditions include:

[0096] Generates a gradient condition, which requires that the gradient of the Lagrangian with respect to the decision variables be zero. This means that at the optimal point, the gradient of the objective function must be canceled by the linear combination of the gradients of the constraint functions. This condition ensures that within the range of feasible solutions, there is no direction in which the objective function can be further improved.

[0097] Gradient conditions:

[0098]

[0099] in, represents the result of gradient operation,

[0100] Generate the original feasibility conditions and ensure that the decision variables satisfy the three constraints. This means that at the optimal point, all defined constraints must be satisfied.

[0101] Original feasibility conditions:

[0102]

[0103] Generate the dual feasibility condition, which requires that all Lagrange multipliers must be nonnegative. This is related to the "direction" of the constraint (i.e., "greater than or equal to" or "less than or equal to"). This condition ensures the feasibility of the dual problem, so that the solution to the dual problem is related to the solution to the primal problem.

[0104] Dual feasibility conditions:

[0105] λ i ,μ i ≥0

[0106] ν≥0

[0107] Generates a complementary slackness condition where, for each inequality constraint, either the corresponding Lagrange multiplier is zero, or the constraint function is exactly on the bound (i.e., the constraint is "tight"). This means that if a constraint does not reach the bound, the corresponding Lagrange multiplier should be zero, and vice versa. This condition helps simplify the problem because it reduces the number of variables that need to be considered.

[0108] Complementary slackness conditions:

[0109] λ i (weight i -L(x i ))=0

[0110] μ i (T i -Time(x i ))=0

[0111]

[0112] The KKT conditions, the objective function of the minimum transportation cost after transformation and the constraints are combined as the M-PCA model.

[0113] The specific model is as follows:

[0114] Objective function:

[0115]

[0116] Constraints:

[0117]

[0118] ν≥0

[0119]

[0120] After the M-PCA model is obtained, step 103 is performed to set constraints on the path planning using the M-PCA model and then solve the problem to obtain the optimal path planning.

[0121] In one example, you can set the load of a single vehicle:

[0122] (L(x1)=90) tons, (L(x2)=110) tons (total load satisfies (D=200) tons).

[0123] Initial driving distance:

[0124] (Distance(x1)=100) kilometers, (Distance(x2)=120) kilometers.

[0125] The transportation cost at this time is:

[0126] f(x) = 5 × 100 + 8 × 120 = 500 + 960 = 1460 unit cost

[0127] Then set the constraints.

[0128] Time constraints:

[0129] Assume (Time(x1)=9) hours, (Time(x2)=14) hours, and satisfy the single vehicle load constraints of (9≤10) and (14≤15):

[0130] Vehicle 1: (L(x1)=90≤100) tons

[0131] Vehicle 2: (L(x2)=110≤150) tons

[0132] Total load capacity constraints:

[0133] L(x1)+L(x2)=90+110=200≥200

[0134] After that, Lagrangian optimization and KKT condition constraints are performed to gradually optimize the minimum transportation cost. At this time, the corresponding path is the optimal path planning.

[0135] In an example, when the delivery area is Jiangsu Province, the optimal route planning corresponding to the minimum transportation cost is as follows:

[0136] (1) Path planning

[0137] Table 1 Route planning in Jiangsu Province

[0138]

[0139] Figure 2 For Jiangsu Province route planning, through Figure 2 From Table 1, we can see that in Jiangsu Province, 44 orders were divided into 4 delivery routes, of which three routes were in Figure 2 The remaining path is too short and only one order is processed, so Figure 2 Not shown. Additionally, green markers on the path in the figure represent customers, whose information is stored in the order dataset; red markers represent warehouses, whose information is stored in the starting dataset. In this embodiment, the maximum route distance is 1056 km, the maximum route cost is 7392 yuan, and the maximum route travel time is 21.12 hours. From the perspectives of cost and time, the path planning scheme for Jiangsu Province can be evaluated, concluding that it has low cost and short travel time.

[0140] (2) Traffic resource statistics

[0141] Table 2 Statistics of transportation resources in Jiangsu Province

[0142]

[0143]

[0144] From Table 2, we can see that the route planning for Jiangsu Province uses a total of three trucks with a load capacity of 3000KG and one truck with a load capacity of 12000KG.

[0145] (3) Route statistics

[0146] Table 3 Route statistics in Jiangsu Province

[0147]

[0148] Table 3 shows that for Jiangsu Province, the total cost of route planning is 14,382 yuan, and the delivery time for all orders is 21.12 hours. Other reference values include total distance, total load, and total number of orders processed.

[0149] In an example, when the delivery area is Heilongjiang Province, the optimal route planning corresponding to the minimum transportation cost is as follows: (1) Route planning

[0150] Table 4 Route planning in Heilongjiang Province

[0151]

[0152] Table 4 shows that in Heilongjiang Province, 16 orders were divided into 2 routes for delivery. Among them, the longest route distance is 1360 km, the maximum route cost is 6800 yuan, and the maximum route driving time is 22.67 hours. From the two dimensions of cost and time, the route planning scheme in Heilongjiang Province can be evaluated, and the conclusion is that the cost is low and the time is short.

[0153] (2) Traffic resource statistics

[0154] Table 5 Statistics of transportation resources in Heilongjiang Province

[0155] Vehicle (3000KG) Vehicle (12000KG) Vehicle (18000KG) Vehicle (30,000 kg) Use quantity 2 0 0 0

[0156] Table 5 shows that two trucks with a load capacity of 3000 kg were used for route planning in Jiangsu Province.

[0157] (3) Route statistics

[0158] Table 6 Statistics of routes by different modes of transportation in Heilongjiang Province

[0159] Transportation Cost (yuan) Time (H) Distance (km) airplane 1147 4.14 1764 truck 9740 22.67 1948

[0160] Table 7 Total statistics of routes in Heilongjiang Province

[0161]

[0162] Tables 6 and 7 show that the total cost of route planning for the three northeastern provinces is 10,887 yuan, of which air freight costs 1,147 yuan and land freight costs 9,760 yuan. The delivery time for all orders is 26.81 hours, of which air freight time is 4.14 hours and land freight time is 22.67 hours. Other reference values include total distance, total load, and total number of orders processed.

[0163] In an example, when the delivery area is the Yangtze River Delta, the optimal route planning corresponding to the minimum transportation cost is as follows:

[0164] (1) Route planning

[0165] Table 8 Yangtze River Delta route planning

[0166]

[0167]

[0168] Figure 3 Describes the Yangtze River Delta route planning, through the above Figure 3 From Table 8, we can see that in the Yangtze River Delta, 123 orders were divided into 4 delivery routes, corresponding to Figure 3There are four color paths, among which the longest route distance is 1647KM, the largest route cost is 11529 yuan, and the longest route driving time is 32.94 hours. From the two dimensions of cost and time, the path planning scheme in the Yangtze River Delta region can be evaluated, and the conclusion is that the cost is lower and the time is longer.

[0169] (2) Traffic resource statistics

[0170] Table 9 Statistics of transportation resources in the Yangtze River Delta

[0171] Vehicle (3000KG) Vehicle (12000KG) Vehicle (18000KG) Vehicle (30,000 kg) Use quantity 1 5 0 0

[0172] (3) Route statistics

[0173] Table 10 Statistics of Yangtze River Delta routes

[0174]

[0175] Tables 9 and 10 show that for the Yangtze River Delta, the total cost of route planning is 41,914 yuan, and the time required to deliver all orders is 32.94 hours. Other reference values include total distance, total load, and total number of orders processed.

[0176] In an example, when the delivery area is the three northeastern provinces, the optimal route planning corresponding to the minimum transportation cost is as follows: (1) Route planning

[0177] Table 11 Route planning for the three northeastern provinces

[0178]

[0179] Figure 4 Describes the path planning of the three northeastern provinces, through Figure 4 As shown in Table 11, in the three northeastern provinces, 51 orders were divided into three delivery routes, corresponding to Figure 4 There are three color paths, among which the maximum route distance is 2067KM, the maximum route cost is 10335 yuan, and the maximum route driving time is 34.45H. From the two dimensions of cost and time, we can evaluate the path planning scheme in the three northeastern provinces and draw the conclusion that the cost is medium and the time is long.

[0180] (2) Traffic resource statistics

[0181] Table 12 Statistics of transportation resources in the three northeastern provinces

[0182] Vehicle (3000KG) Vehicle (12000KG) Vehicle (18000KG) Vehicle (30,000 kg) Use quantity 3 0 0 0

[0183] Table 12 shows that three trucks with a load capacity of 3,000 kg were used for route planning in the three northeastern provinces.

[0184] (3) Route statistics

[0185] Table 13 Statistics of routes by different modes of transportation in the three northeastern provinces

[0186] Transportation Cost (yuan) Time (H) Distance (km) airplane 5333 3.42 1462 truck 26975 34.45 5395

[0187] Table 14 Statistics of routes in the three northeastern provinces

[0188]

[0189] Tables 13 and 14 show that the total cost of route planning for the three northeastern provinces is 32,307 yuan, of which air freight costs are 5,333 yuan and land freight costs are 26,975 yuan. The delivery time for all orders is 37.88 hours, of which air freight time is 3.42 hours and land freight time is 34.45 hours. Other reference values include total distance, total load, and total number of orders processed.

[0190] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited thereto. Various changes that can be made within the scope of knowledge possessed by technicians in the relevant technical field without departing from the spirit of the present invention are all within the scope of protection of the claims of the present invention.

[0191] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A multi-condition path planning method based on M-PCA, characterized in that: include: Constructing a comprehensive data set, wherein the data set includes a starting point data set, an order data set, a traffic data set, and a road network data set; Using the comprehensive data set combined with a heuristic algorithm search strategy to construct an M-PCA model with minimum cost as the objective function; The M-PCA model is used to set three constraints for path planning, including time constraint, single vehicle load constraint, and total load constraint, and then solves to obtain the optimal path planning.

2. The multi-condition path planning method based on M-PCA according to claim 1, characterized in that: The method of using the comprehensive data set in combination with a heuristic algorithm to construct an M-PCA model with minimum cost as the objective function includes: defining constraint conditions and an objective function, wherein the constraint conditions include equality constraints and inequality constraints, and the constraint condition-related data are obtained from the comprehensive data set; In combination with the constraint conditions, the objective function is transformed using the Lagrange multiplier method; Generate corresponding KKT conditions based on the constraint conditions; The KKT condition, the transformed objective function and the constraint condition are combined as the M-PCA model.

3. The multi-condition path planning method based on M-PCA according to claim 2, characterized in that: The equality constraints include: the start and end conditions must exist, and the path starts from the specified start point and ends at the specified end point; The inequality constraints include: time constraints, single vehicle load constraints, and total load constraints.

4. The multi-condition path planning method based on M-PCA according to claim 3, characterized in that: The time constraints include: Among them, T i is the longest transportation time of vehicle i, indicating that the corresponding order must be shipped within T i Delivery within 12 hours, Time(x i ) represents the actual transportation time of vehicle i; The load constraints for a single vehicle include: Among them, Weigt i is the maximum load of vehicle i, L(x i ) is the actual load capacity of a single vehicle i; The total load capacity constraints include: Where D is the total freight volume, and n and i are integers greater than or equal to 1.

5. The multi-condition path planning method based on M-PCA according to claim 4, characterized in that: The transforming of the objective function by using the Lagrange multiplier method in combination with the constraint conditions includes: Define the Lagrangian function Lagrange, wherein the Lagrangian function includes the original objective function and the Lagrangian multiplier associated with each constraint, and the Lagrangian multiplier includes λ i 、μ i 、ν; λ i Corresponding to the single vehicle load constraint 0≤L(x i )≤Weigt i ; μ i Corresponding to the time constraint Time(x i )≤T i ; ν corresponds to the total load constraint At this time, the Lagrangian function is: in Represents the original objective function of minimum cost.

6. The multi-condition path planning method based on M-PCA according to claim 5, characterized in that: The corresponding KKT conditions are generated in combination with the constraints, including: Generate gradient conditions: in, Represents the result of gradient operation; Generate the original feasibility conditions: Generate dual feasibility conditions: l i ,m i ≥0 ν≥0 Generate complementary slackness conditions: λ i (weight i -L(x i ))=0 μ i (T i -Time(x i ))=0 7. The multi-condition path planning method based on M-PCA according to claim 6, characterized in that: The M-PCA model includes:

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