Manufacturing task multi-modal optimization method based on ecological niche evaluation indexes

Abstract

The invention discloses a manufacturing task multi-modal optimization method based on ecological niche evaluation indexes. The method is suitable for a multi-workshop part distribution scheduling scene in industrial manufacturing. The method comprises the following steps of: firstly, constructing an optimization model taking minimum vehicle number, total path length and carbon emission as targets, and integrating constraints such as vehicle capacity and time window; further designing an enhanced special congestion distance to evaluate solution set distribution, and constructing an ecological niche evaluation index in combination with a Pareto level; and dynamically adjusting pheromones and heuristic information based on the indexes, and guiding the population to realize multi-objective optimization in a feasible solution space. According to the invention, a diversified solution set with low vehicle number, short path, low carbon emission and high feasibility can be output, and the comprehensive efficiency of a part distribution system is improved.

Description

Technical Field

[0001] The present invention belongs to the fields of intelligent manufacturing and industrial logistics scheduling, and designs a multi-modal optimization method for manufacturing tasks based on niche evaluation indicators, which is applicable to the multi-modal path planning and resource scheduling problems of part distribution in the intelligent manufacturing industry. The aim is to introduce niche technology and an improved multi-objective optimization mechanism to obtain more optimized scheduling schemes for decision-makers to choose while ensuring the diversity of solutions. Background Art

[0002] In the process industry manufacturing environment, part distribution scheduling involves collaborative operations among multiple distribution centers, transfer warehouses and production workshops, and has the characteristics of multi-nodes, multi-constraints and multi-objectives. Traditional scheduling methods often focus on single-objective optimization and are difficult to effectively balance multiple conflicting objectives such as vehicle quantity and total path length while meeting complex constraints such as time windows and vehicle capacity. Although the existing ant colony optimization algorithm has been applied to path planning, when dealing with complex industrial scenario scheduling problems, there are problems such as insufficient diversity of optimized scheduling schemes and room for improvement in path optimization speed, resulting in the inability to quickly provide multiple optimized scheduling schemes. Summary of the Invention

[0003] The purpose of the present invention is to provide a multi-modal optimization method for manufacturing tasks based on niche evaluation indicators, and by designing an enhanced special crowding distance mechanism and a comprehensive niche evaluation indicator, dynamically guide the update of pheromone and heuristic information to achieve rapid optimization of part distribution paths.

[0004] The technical solution of the present invention is as follows:

[0005] Step 1: Determine the optimization objectives and constraints of industrial manufacturing part distribution scheduling:

[0006] Suppose there are K distribution vehicles, 1 distribution center and N - 1 workshops in a certain industrial park, where 0 < K < 100 and 0 < N < 100. The optimization objectives include minimizing the number of vehicles used, minimizing the total driving distance and minimizing the carbon emissions, which are expressed as follows:

[0007] This part distribution scheduling problem takes minimizing the number of vehicles, minimizing the total driving distance and minimizing the carbon emissions as optimization objectives:

[0008]

[0009]

[0010] where x h , h , ij , ij h is a binary decision variable. If vehicle h delivers to workshop j after delivering to workshop i, then x ij hThe value is 1; otherwise, it is 0. Specifically, when i = 0, it indicates that vehicle h departs from the distribution center, and when j = 0, it indicates that vehicle h returns to the distribution center. i,j e represents the distance from workshop i to workshop j; ij This represents the carbon emissions required between workshop i and workshop j.

[0011] The constraints include:

[0012] All vehicles depart from and return from the distribution center:

[0013]

[0014] Where n = {0, 1, 2, ..., N} represents the workshop, and k = {0, 1, 2, ..., K} represents the delivery vehicle.

[0015] All workshops have completed delivery:

[0016]

[0017] Where y i h Let y be a binary decision variable. If vehicle h serves workshop i, then y i h Select 1 if the value is 1, otherwise select 0.

[0018] Each workshop is served by only one vehicle per trip:

[0019]

[0020] The distance between the two workshops is greater than zero.

[0021]

[0022] The distance traveled by each vehicle shall not exceed the maximum travel distance for each vehicle:

[0023]

[0024] Where C represents the vehicle's maximum travel distance;

[0025] Vehicle capacity is limited; total demand must not exceed the maximum load capacity.

[0026]

[0027] Where q i Let Q be the delivery demand of workshop i, and Q be the maximum load capacity of the vehicle.

[0028] Time window constraint: The vehicle must arrive within the customer's requested time window.

[0029]

[0030] Where w i Indicates the delivery time required for workshop i, a ih t represents the time when vehicle h arrives at workshop i. ai and t bi These represent the start and end values ​​of the time window for workshop i, respectively;

[0031] Step 2: Calculate the enhanced special congestion distance:

[0032] Step 2.1 Calculate local density information:

[0033] For a feasible delivery plan that satisfies the conditions in step 1, calculate its local density value in the decision space and target space based on neighborhood delivery plans. First, based on the Pareto ranking of the feasible delivery plan, the plans are divided into different classes; that is, feasible delivery plans in one ranking constitute one class. Second, the neighborhood radius of a feasible delivery plan is set to half the difference between the maximum and minimum values ​​of all delivery plans in the class to which the feasible plan belongs. Finally, the local density is calculated using the inverse distance weighting method, and the local density value of a feasible delivery plan is the sum of the reciprocals of the normalized Euclidean distances between the feasible plan and all its neighboring feasible delivery plans in the corresponding spaces.

[0034]

[0035] Where, d αβ Let d be the Euclidean distance between feasible delivery plans α and β. αβ ≥0, β∈Neighborhood indicates that feasible delivery solution β is a neighborhood feasible delivery solution of feasible delivery solution α;

[0036] When calculating the specific congestion distance index for feasible delivery plan α, the denominator uses the local density value that considers the distance between neighboring delivery plans. The denominator of feasible delivery plan α is defined as the local density value among all neighboring delivery plans.

[0037] Maximum value:

[0038] Denomi(α) = max β∈Neighborhood (d αβ ×Den(α)) (13)

[0039] Step 2.2 Calculate the enhanced special congestion distance component:

[0040] The population is divided into multiple Pareto sets based on non-dominated sorting; for each feasible delivery scheme, its enhanced special congestion distance component (ESCD) in the decision space is calculated. α,x Enhanced Special Congestion Distance Component (ESCD) in Target Space α,f :

[0041]

[0042]

[0043] Where x = {x1, x2, ... x} d Let} be a d-dimensional decision space, where Denomi(α,x) is the value of Denomi(α) in the decision space, calculated using the Euclidean distance and local density in the decision space. p1 and q1 are neighboring points along the x1 direction in the decision space, and p2 and q2 are neighboring points along the x2 direction in the decision space. d and q d It is along x in the decision space d Neighboring points in the direction; Denomi(α,f) is the value of Denomi(α) in the target space, calculated using the Euclidean distance and local density in the target space, f = {f1, f2, ... f}. o Let f1 be an o-dimensional target space, m1 and n1 be neighboring points along the direction f1 in the target space, and m2 and n2 be neighboring points along the direction f2 in the target space. o and n o It is along f in the target space o Adjacent points in the direction;

[0044] Step 2.3 Calculate the enhanced special congestion distance value:

[0045] Calculate the average enhanced special crowding distance (ESCD) of the population in the decision space and the target space; for each delivery scheme, if its ESCD... α,x or ESCD α,f If the value is greater than the corresponding average, the larger value is taken as the final enhanced special congestion distance (ESCD) value for the feasible delivery plan; otherwise, the smaller value is taken.

[0046] Step 3: Constructing niche evaluation indicators:

[0047] Step 3.1 Indicator Definition:

[0048] The Niche Evaluation Index (ENCEI) is a linear weighted average of the Pareto Rank of feasible delivery schemes and the Enhanced Special Crowding Distance (ESCD) value. The calculation formula is as follows:

[0049]

[0050] ESCD max (t)=max α∈Population(t) ESCD(α) (17)

[0051] Here, ω1 and ω2 are two parameters used to adjust the ESCD value and Pareto ranking ratio, and their sum is 1. To prevent the algorithm from converging prematurely when solving the multi-objective delivery problem defined in step 1 and to maintain its exploratory ability, ω1 and ω2 are set to 0.3 and 0.7, respectively. Rank α (t) represents the Pareto rank of the α-th feasible delivery solution in the t-th iteration. max (t) represents the total number of Pareto rankings in the t-th iteration, ESCD α ESCD(t) represents the ESCD value of the α-th feasible delivery plan in the t-th iteration, and ESCDmax(t) represents the maximum value of ESCD in the t-th iteration.

[0052] Step 3.2 Indicator Normalization:

[0053] The ENCEI region is mapped to the [0,1] interval using the max-min normalization method. The normalization formula is as follows:

[0054]

[0055] Step 4: Pheromones Update Strategy Based on Niche Evaluation Indicators

[0056] Step 4.1 Pheromone intensity factor update:

[0057] Based on the normalized niche comprehensive evaluation index ENCEI, the pheromone intensity factor is updated nonlinearly using the Sigmoid function:

[0058]

[0059] Q base This is the base value of the pheromone intensity factor, with a value of 5. This value affects the overall pheromone intensity level, balancing the algorithm's exploration and development behavior within the feasible delivery solution space. α (t) represents the Q value of the α-th feasible delivery scheme in the t-th iteration;

[0060] Step 4.2 Pheromone volatile factor update:

[0061] Based on the normalized niche comprehensive evaluation index ENCEI, the pheromone volatile factor is dynamically adjusted using the hyperbolic tangent function:

[0062]

[0063] Where ρ base The baseline value for the pheromone volatile factor is set at 0.85. A higher volatile rate is used to ensure basic exploration capabilities for unexplored feasible delivery routes;

[0064] Step 5: Adjustment strategy based on heuristic information from niche evaluation indicators:

[0065] By incorporating niche assessment indicators into heuristic information, the adjusted heuristic information calculation formula is as follows:

[0066]

[0067] Where η αβ It is the heuristic information from feasible delivery plan α to feasible delivery plan β at the t-th iteration;

[0068] Step 6: Ant Colony Path Construction and Optimization

[0069] The population selects the next delivery workshop according to the state transition probability formula, and constructs a feasible delivery path under the premise of satisfying all constraints in step 1 (vehicle capacity, time window, path continuity, etc.). This probability is jointly determined by the pheromone concentration and the heuristic information adjusted in step 5. After each generation of the population completes the path construction, the pheromone is updated according to step 4. During the scheme construction process, the constraints defined in step 1 are handled by the feasibility rules to ensure that the generated delivery scheme is always in the feasible region. Iterative execution is carried out until the maximum number of iterations, and the multimodal optimized scheduling path of the manufacturing task is output.

[0070] The innovation of this invention is reflected in:

[0071] This invention proposes a dynamic adjustment strategy based on niche evaluation in the multi-objective vehicle routing problem. The Pareto order of the solution is nonlinearly fused with the ESCD value to form a unified niche evaluation index. In the early stages of evolution, a large number of alternative delivery schemes with significant differences in vehicle usage, travel routes, and carbon emissions are generated. In the later stages of evolution, computational resources are concentrated on optimizing those delivery schemes that have proven to have potential, quickly obtaining multiple high-quality vehicle delivery schemes.

[0072] Special note: This invention designs a multimodal optimization method for manufacturing tasks based on niche evaluation indicators. Any research on scheduling technology that uses the optimization algorithm of this invention should fall within the scope of this invention. Attached Figure Description

[0073] Figure 1 This is the vehicle delivery route map in the optimization results of this invention. Detailed Implementation

[0074] The data sample used in this invention is C102, which belongs to the Solomon dataset. As shown in Table 1, the first to seventh columns represent the workshop number i and the x-coordinate of the workshop location, respectively. i and the vertical coordinate y i The required quantity of parts to be delivered to the workshop, q i Earliest start time t ai, the latest start service time t bi and the service time w i , where the data corresponding to i = 0 is the logistics center information. Table 2 shows the carbon emission data between workshops related to C102. Every three columns form a group of information. The first group (the first to the third columns) contains the workshop number i, the workshop number j, and the carbon emission amount e between these two workshops ij ; similarly, the second group (the fourth to the sixth columns) and the third group (the seventh to the ninth columns) also arrange the data in the order of the workshop number i, the workshop number j, and the carbon emission amount e ij respectively;

[0075] The present invention selects the number of vehicles used in the scheduling process, the total driving distance of the vehicles, and the carbon emission amount as the optimization objectives, and adopts the following technical solutions and implementation steps:

[0076] Step 1 Determine the optimization objectives and constraints of the industrial manufacturing part distribution scheduling:

[0077] Suppose there are K distribution vehicles, 1 distribution center, and N - 1 workshops in a certain industrial park, 0 < K < 100, 0 < N < 100. The optimization objectives include minimizing the number of vehicles used, minimizing the total driving distance, and minimizing the carbon emission amount, which are expressed as follows:

[0078] The part distribution scheduling problem takes minimizing the number of vehicles, minimizing the total driving distance, and minimizing the carbon emission amount as the optimization objectives:

[0079]

[0080] where x ij h is a binary decision variable. If vehicle h delivers to workshop j after delivering to workshop i, then x ij h takes 1; otherwise, it takes 0; in particular, when i = 0, it means that vehicle h departs from the distribution center, and when j = 0, it means that vehicle h returns to the distribution center; c i,j represents the distance from workshop i to workshop j; e ij represents the required carbon emission amount between workshop i and workshop j

[0081] The constraint conditions include:

[0082] All vehicles depart from and return to the distribution center:

[0083]

[0084] where n = {0, 1, 2,..., N} represents the workshops, and k = {0, 1, 2,..., K} represents the distribution vehicles

[0085] All workshops have completed the delivery:

[0086]

[0087] Where y i h Let y be a binary decision variable. If vehicle h serves workshop i, then y i h Select 1 if the value is 1, otherwise select 0.

[0088] Each workshop is served by only one vehicle per trip:

[0089]

[0090] The distance between the two workshops is greater than zero.

[0091]

[0092] The distance traveled by each vehicle shall not exceed the maximum travel distance for each vehicle:

[0093]

[0094] Where C represents the vehicle's maximum travel distance;

[0095] Vehicle capacity is limited; total demand must not exceed the maximum load capacity.

[0096]

[0097] Where q i Let Q be the delivery demand of workshop i, and Q be the maximum load capacity of the vehicle.

[0098] Time window constraint: The vehicle must arrive within the customer's requested time window.

[0099]

[0100] Where w i Indicates the delivery time required for workshop i, a ih t represents the time when vehicle h arrives at workshop i. ai and t bi These represent the start and end values ​​of the time window for workshop i, respectively;

[0101] Step 2: Calculate the enhanced special congestion distance:

[0102] Step 2.1 Calculate local density information:

[0103] For a feasible delivery plan that satisfies the conditions in step 1, calculate its local density value in the decision space and target space based on neighborhood delivery plans. First, based on the Pareto ranking of the feasible delivery plan, the plans are divided into different classes; that is, feasible delivery plans in one ranking constitute one class. Second, the neighborhood radius of a feasible delivery plan is set to half the difference between the maximum and minimum values ​​of all delivery plans in the class to which the feasible plan belongs. Finally, the local density is calculated using the inverse distance weighting method, and the local density value of a feasible delivery plan is the sum of the reciprocals of the normalized Euclidean distances between the feasible plan and all its neighboring feasible delivery plans in the corresponding spaces.

[0104]

[0105] Where, d αβ Let d be the Euclidean distance between feasible delivery plans α and β. αβ ≥0, β∈Neighborhood indicates that feasible delivery solution β is a neighborhood feasible delivery solution of feasible delivery solution α;

[0106] When calculating the specific congestion distance index for feasible delivery plan α, the denominator uses the local density value that considers the distance between neighboring delivery plans. The denominator of feasible delivery plan α is defined as the local density value among all neighboring delivery plans.

[0107] Maximum value:

[0108] Denomi(α) = max β∈Neighborhood (d αβ ×Den(α)) (34)

[0109] Step 2.2 Calculate the enhanced special congestion distance component:

[0110] The population is divided into multiple Pareto sets based on non-dominated sorting; for each feasible delivery scheme, its enhanced special congestion distance component (ESCD) in the decision space is calculated. α,x Enhanced Special Congestion Distance Component (ESCD) in Target Space α,f :

[0111]

[0112] Where x = {x1, x2, ... x} d Let} be a d-dimensional decision space, where Denomi(α,x) is the value of Denomi(α) in the decision space, calculated using the Euclidean distance and local density in the decision space. p1 and q1 are neighboring points along the x1 direction in the decision space, and p2 and q2 are neighboring points along the x2 direction in the decision space. d and q d It is along x in the decision space dNeighboring points in the direction; Denomi(α,f) is the value of Denomi(α) in the target space, calculated using the Euclidean distance and local density in the target space, f = {f1, f2, ... f}. o Let f1 be an o-dimensional target space, m1 and n1 be neighboring points along the direction f1 in the target space, and m2 and n2 be neighboring points along the direction f2 in the target space. o and n o It is along f in the target space o Adjacent points in the direction;

[0113] Step 2.3 Calculate the enhanced special congestion distance value:

[0114] Calculate the average enhanced special crowding distance (ESCD) of the population in the decision space and the target space; for each delivery scheme, if its ESCD... α,x or ESCD α,f If the value is greater than the corresponding average, the larger value is taken as the final enhanced special congestion distance (ESCD) value for the feasible delivery plan; otherwise, the smaller value is taken.

[0115] Step 3: Constructing niche evaluation indicators:

[0116] Step 3.1 Indicator Definition:

[0117] The Niche Evaluation Index (ENCEI) is a linear weighted average of the Pareto Rank of feasible delivery schemes and the Enhanced Special Crowding Distance (ESCD) value. The calculation formula is as follows:

[0118]

[0119] ESCD max (t)=max α∈Population(t) ESCD(α) (38)

[0120] Here, ω1 and ω2 are two parameters used to adjust the ESCD value and Pareto ranking ratio, and their sum is 1. To prevent the algorithm from converging prematurely when solving the multi-objective delivery problem defined in step 1 and to maintain its exploratory ability, ω1 and ω2 are set to 0.3 and 0.7, respectively. Rank α (t) represents the Pareto rank of the α-th feasible delivery solution in the t-th iteration. max (t) represents the total number of Pareto rankings in the t-th iteration, ESCD α ESCD(t) represents the ESCD value of the α-th feasible delivery plan in the t-th iteration, and ESCDmax(t) represents the maximum value of ESCD in the t-th iteration.

[0121] Step 3.2 Indicator Normalization:

[0122] The ENCEI region is mapped to the [0,1] interval using the max-min normalization method. The normalization formula is as follows:

[0123]

[0124] Step 4: Pheromones Update Strategy Based on Niche Evaluation Indicators

[0125] Step 4.1 Pheromone intensity factor update:

[0126] Based on the normalized niche comprehensive evaluation index ENCEI, the pheromone intensity factor is updated nonlinearly using the Sigmoid function:

[0127]

[0128] Q base This is the base value of the pheromone intensity factor, with a value of 5. This value affects the overall pheromone intensity level, balancing the algorithm's exploration and development behavior within the feasible delivery solution space. α (t) represents the Q value of the α-th feasible delivery scheme in the t-th iteration;

[0129] Step 4.2 Pheromone volatile factor update:

[0130] Based on the normalized niche comprehensive evaluation index ENCEI, the pheromone volatile factor is dynamically adjusted using the hyperbolic tangent function:

[0131]

[0132] Where ρ base The baseline value for the pheromone volatile factor is set at 0.85. A higher volatile rate is used to ensure basic exploration capabilities for unexplored feasible delivery routes;

[0133] Step 5: Adjustment strategy based on heuristic information from niche evaluation indicators:

[0134] By incorporating niche assessment indicators into heuristic information, the adjusted heuristic information calculation formula is as follows:

[0135]

[0136] Where η αβ It is the heuristic information from feasible delivery plan α to feasible delivery plan β at the t-th iteration;

[0137] Step 6: Ant Colony Path Construction and Optimization

[0138] The population selects the next delivery workshop according to the state transition probability formula, constructing a feasible delivery route while satisfying all constraints in step 1 (vehicle capacity, time window, path continuity, etc.). This probability is jointly determined by the pheromone concentration and the adjusted heuristic information in step 5. After each generation of the population completes path construction, the pheromone is updated according to step 4. During the scheme construction process, feasibility rules are used to handle the constraints defined in step 1 to ensure that the generated delivery schemes are always in the feasible region. Iterative execution continues until the maximum number of iterations, outputting a set of vehicle delivery schemes that are superior in terms of vehicle number, total path length, and carbon emissions, and satisfy all industrial delivery constraints, as shown in Table 3. Figure 1 As shown, the vehicle delivery plan and vehicle delivery plan diagram are displayed.

[0139] Table 1. R102 Vehicle Route Optimization Data

[0140] Workshop Number Workshop location Workshop location Demand Earliest start time Latest start time of service Service Hours 0 35 35 0 0 230 0 1 41 49 10 0 204 10 2 35 17 7 0 202 10 3 55 45 13 0 197 10 4 55 20 19 149 159 10 5 15 30 26 0 199 10 6 25 30 3 99 109 10 7 20 50 5 0 198 10 8 10 43 9 95 105 10 9 55 60 16 97 107 10 10 30 60 16 124 134 10 11 20 65 12 67 77 10 12 50 35 19 0 205 10 13 30 25 23 159 169 10 14 15 10 20 32 42 10 15 30 5 8 61 71 10 16 10 20 19 75 85 10 17 5 30 2 157 167 10 18 20 40 12 87 97 10 19 15 60 17 76 86 10 20 45 65 9 126 136 10

[0141] Table 2. Carbon Emissions Between Workshops

[0142]

[0143]

[0144] Table 3. Optimal Vehicle Delivery Plan

[0145]

Claims

1. A multimodal optimization method for manufacturing tasks based on niche evaluation indicators, characterized in that, Specifically, it includes the following steps: Step 1: Determine the optimization objectives and constraints of industrial manufacturing part distribution scheduling: Suppose there are K distribution vehicles, 1 distribution center, and N - 1 workshops in an industrial park, where 0 < K < 100 and 0 < N < 100; the optimization objectives include minimizing the number of vehicles used, minimizing the total driving distance, and minimizing carbon emissions, which are expressed as follows: The part distribution scheduling problem aims to minimize the number of vehicles, the total driving distance, and carbon emissions: Where x ij h Let x be a binary decision variable. If vehicle h delivers to workshop i and then delivers to workshop j, then x... ij h The value is 1; otherwise, it is 0. Specifically, when i = 0, it indicates that vehicle h departs from the distribution center, and when j = 0, it indicates that vehicle h returns to the distribution center. i,j e represents the distance from workshop i to workshop j; ij This represents the required carbon emissions between workshop i and workshop j; The constraint conditions include: All vehicles start from and return to the distribution center: Where n = {0, 1, 2,..., N} represents workshops, and k = {0, 1, 2,..., K} represents distribution vehicles; All workshops have completed distribution: Where y i h Let y be a binary decision variable. If vehicle h serves workshop i, then y i h Select 1 if the value is 1, otherwise select 0. Each workshop is served by only one vehicle once: The distance between two workshops is greater than zero: The driving distance of the vehicle does not exceed the maximum driving distance of each vehicle: Where C is the maximum driving distance of the vehicle; Vehicle capacity limit, the total demand does not exceed the load limit: Where q i Let Q be the delivery demand of workshop i, and Q be the maximum load capacity of the vehicle. Time window constraint, the vehicle needs to arrive within the customer - required time window: Where w i Indicates the delivery time required for workshop i, a ih t represents the time when vehicle h arrives at workshop i. ai and t bi These represent the start and end values ​​of the time window for workshop i, respectively; Step 2: Calculate the enhanced special crowding distance: Step 2.1: Calculate the local density information: For the feasible distribution plan satisfying Step 1, calculate its local density value in the decision space and the target space based on the neighborhood distribution plan; first, divide the feasible distribution plans into different classes according to the Pareto rank of the feasible distribution plan, that is, the feasible distribution plans in one rank are a class; second, set the neighborhood radius of the feasible distribution plan as half of the difference between the maximum and minimum values of all distribution plans in the class to which the feasible distribution plan belongs; finally, the local density is calculated using the inverse - distance weighted method, and the local density value of the feasible distribution plan is the sum of the reciprocals of the normalized Euclidean distances between all its neighborhood feasible distribution plans and the feasible distribution plan in the corresponding space: Where, d αβ Let d be the Euclidean distance between feasible delivery plans α and β. αβ ≥0, β∈Neighborhood indicates that feasible delivery solution β is a neighborhood feasible delivery solution of feasible delivery solution α; When calculating the special crowding distance index of the feasible distribution plan α, the denominator uses the local density value considering the distance between neighboring distribution plans; the denominator of the feasible distribution plan α is defined as the maximum value among all neighboring distribution plans: Denomination(a)=max β∈Neighborhood (d αβ ×Den(a)) (13) Step 2.2: Calculate the enhanced special crowding distance component: The population is divided into multiple Pareto sets based on non-dominated sorting; for each feasible delivery scheme, its enhanced special congestion distance component (ESCD) in the decision space is calculated. α,x Enhanced Special Congestion Distance Component (ESCD) in Target Space α,f : Where x = {x1, x2, ... x} d Let} be a d-dimensional decision space, and Denomi(α,x) be the value of Denomi(α) in the decision space, calculated using the Euclidean distance and local density in the decision space. p1 and q1 are neighboring points along the x1 direction in the decision space, and p2 and q2 are neighboring points along the x2 direction in the decision space. d and q d It is along x in the decision space d Neighboring points in the direction; Denomi(α,f) is the value of Denomi(α) in the target space, calculated using the Euclidean distance and local density in the target space, f = {f1, f2, ... f}. o Let f1 be an o-dimensional target space, m1 and n1 be neighboring points along the direction f1 in the target space, and m2 and n2 be neighboring points along the direction f2 in the target space. o and n o It is along f in the target space o The adjacent point in the direction; Step 2.3: Calculate the enhanced special crowding distance value: Calculate the average enhanced special crowding distance (ESCD) of the population in the decision space and the target space; for each delivery scheme, if its ESCD... α,x or ESCD α,f If the value is greater than the corresponding average, the larger value is taken as the final enhanced special congestion distance (ESCD) value for the feasible delivery plan; otherwise, the smaller value is taken. Step 3: Construct the niche evaluation index: Step 3.1: Index definition: The comprehensive niche evaluation index ENCEI is linearly weighted by the Pareto rank Rank of the feasible distribution plan and the enhanced special crowding distance value ESCD, and the calculation formula is: ESCD max (t)=max α∈Population(t) ESCD(α) (17) Here, ω1 and ω2 are two parameters used to adjust the ESCD value and Pareto ranking ratio, and their sum is 1; to prevent the algorithm from converging prematurely when solving the multi-objective delivery problem defined in step 1 and to maintain its exploratory ability, ω1 and ω2 are set to 0.3 and 0.7 respectively; Rank α (t) represents the Pareto rank of the α-th feasible delivery solution in the t-th iteration. max (t) represents the total number of Pareto rankings in the t-th iteration, ESCD α ESCD(t) represents the ESCD value of the α-th feasible delivery plan in the t-th iteration, and ESCDmax(t) represents the maximum value of ESCD in the t-th iteration. Step 3.2: Index normalization: Use the maximum - minimum normalization method to map ENCEI to the interval [0, 1], and the normalization formula is as follows: Step 4: The pheromone update strategy based on the niche evaluation index: Step 4.1: Update the pheromone intensity factor: Based on the normalized comprehensive niche evaluation index ENCEI, non - linearly update the pheromone intensity factor using the Sigmoid function: Q base This is the base value of the pheromone intensity factor, which is 5. This value affects the overall pheromone intensity level, balancing the algorithm's exploration and development behavior in the feasible delivery solution space. α (t) represents the Q value of the α-th feasible delivery scheme in the t-th iteration; Step 4.2: Update the pheromone evaporation factor: Based on the normalized comprehensive niche evaluation index ENCEI, dynamically adjust the pheromone evaporation factor using the hyperbolic tangent function: Where ρ base The baseline value for the pheromone evaporation factor is set at 0.85; a higher evaporation rate is used to ensure basic exploration capabilities for unexplored feasible delivery routes; Step 5: The heuristic information adjustment strategy based on the niche evaluation index: Integrate the niche evaluation index into the heuristic information, and the calculation formula for the adjusted heuristic information is: Where η αβ It is the heuristic information from feasible delivery plan α to feasible delivery plan β at the t-th iteration; Step 6: Ant Colony Path Construction and Optimization The population selects the next delivery workshop according to the state transition probability formula. Under the premise of satisfying all constraints in step 1, namely vehicle capacity, time window and path continuity, a feasible delivery path is constructed. This probability is jointly determined by the pheromone concentration and the heuristic information adjusted in step 5. After each generation of the population completes the path construction, the pheromone is updated according to step 4. During the scheme construction process, the constraints defined in step 1 are handled by the feasibility rule to ensure that the generated delivery scheme is always in the feasible region. Iterative execution is carried out until the maximum number of iterations, and the multimodal optimized scheduling path of the manufacturing task is output.

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