Industrial manufacturing task intelligent optimization scheduling method considering dual performance

Abstract

The invention provides an industrial manufacturing task intelligent optimization scheduling method considering dual performance, and aims to solve the problem that a plurality of vehicle paths are involved in the industrial manufacturing process and the problem that the driving time of vehicles among factories is uncertain. According to the method, minimization of the use number of vehicles and the total driving distance of the vehicles is taken as an optimization target, a dual-performance decoding strategy is firstly designed, and a continuous solution is converted into a discrete solution which is composed of vehicle scheduling schemes and has optimality and robustness; secondly, two knowledge bases are constructed for each task to be used for storing knowledge related to optimality and robustness in the task evolution process, and finally the optimality and robustness knowledge is migrated from the two knowledge bases of the source task to improve the corresponding performance of the target task. According to the method, the robustness of the scheduling scheme searched by each task under the condition that the driving time is uncertain is improved, the optimality is not lost, and finally the workpiece transportation efficiency is improved.

Description

Technical Field

[0001] The present invention aims at multiple vehicle routing problems existing in the industrial manufacturing process. Considering that the travel time of transport vehicles between factories may be uncertain due to factors such as weather and road conditions, an intelligent optimization scheduling method for industrial manufacturing tasks considering dual performance is designed based on this. Through a decoding strategy considering dual performance and a dual-performance knowledge transfer operation, the algorithm can search for a vehicle scheduling plan that is both optimal and robust for each task. This method belongs to both the field of intelligent information and the field of logistics transportation. Background Art

[0002] In the industrial manufacturing process, the parts required by each factory need to be manufactured by the manufacturing center and then distributed to each factory as needed. Therefore, optimizing the workpiece distribution path of transport vehicles can reduce transportation costs and promote the development of the logistics transportation industry. Traditional vehicle routing optimization methods only consider one task. However, in real life, vehicle routing problems generally do not exist alone. How to efficiently solve multiple vehicle routing problems has become a highly challenging research content. Although the different vehicle routing problems in the industrial manufacturing process serve different factories, they usually have similar ways to solve the scheduling problem. Therefore, a multi-task optimization method can be used to solve multiple vehicle routing problems simultaneously. Among them, the multi-task differential evolution algorithm is a meta-heuristic optimization algorithm with advantages such as strong robustness and fast convergence speed, and is widely used to solve vehicle routing problems. By transferring useful information between tasks, the overall optimization effect of each task can be achieved. However, the travel time between factories may be uncertain due to factors such as weather and road conditions during the vehicle distribution process, resulting in the vehicle scheduling plan searched by the algorithm may be infeasible. To solve this problem, the present invention has broad application prospects in solving multiple vehicle routing problems with uncertain travel times.

[0003] The present invention proposes an intelligent optimization scheduling method for industrial manufacturing tasks considering dual performance. The optimization goal is to minimize the number of vehicles used and the total travel distance of vehicles. By considering a decoding strategy and a knowledge transfer mechanism of optimality and robustness, while improving the convergence performance of each task, the robustness of the searched scheduling plan can be ensured, providing an effective method for searching for a feasible low-cost transportation path under the condition of uncertain vehicle travel time. Summary of the Invention

[0004] The present invention obtains an intelligent optimal scheduling method for industrial manufacturing tasks considering dual performance. This method takes the simultaneous minimization of the number of vehicles used and the total driving distance as the optimization goal, determines the vehicle path optimization model for each task and the driving time perturbation range, and through a decoding strategy and knowledge transfer mechanism that consider both optimality and robustness, it can search for a feasible vehicle scheduling plan for each task under the condition of uncertain driving time, and can improve the workpiece delivery efficiency and reduce the transportation cost.

[0005] The present invention adopts the following technical solutions and implementation steps:

[0006] 1. An intelligent optimal scheduling method for industrial manufacturing tasks considering dual performance, characterized by determining the optimization goal of each scheduling task and the uncertainty of the vehicle driving time, using a multi-task differential evolution algorithm to solve multiple vehicle path problems, improving the optimality and robustness of the discrete solution according to the decoding strategy considering dual performance, and improving the search performance of the algorithm through knowledge transfer, so as to cope with the problem that the solution searched due to the uncertain vehicle driving time is infeasible, and simultaneously achieve the optimal number of vehicles used and the total driving distance, including the following steps:

[0007] Step 1: Determine the optimization goal and constraints of the vehicle path problem with uncertain driving time for each task:

[0008] Assume that there are L tasks, and each task has K max transport vehicles parked at the industrial manufacturing center, which need to serve N factories. The maximum load of each vehicle is Q. The opening time and closing time of the industrial manufacturing center are A and E respectively. Each factory is served by only one transport vehicle. Each vehicle carries the workpiece demand of the factories to be served at the industrial manufacturing center, starts from here, and delivers the required workpieces to each factory in turn according to the service order, and finally returns to the industrial manufacturing center; for each factory to be served, it includes the following attributes: factory number i, the location coordinates of the factory (x i , y i ), the weight q i of the workpieces required by the i-th factory, the expected earliest start service time a i and the expected latest start service time e i of the i-th factory, and the service duration s i of the vehicle at the i-th factory, where i = 0 represents the station; 0 < K max < 50, 0 < N < 150, 0 < Q < 300 kg, 0 < A < 1440, 0 < E < 1440, i = 0,..., N, 0 < x i < 100, 0 < y i < 100, 0 < a i < 1440, 0 < e i<1440, 0 < s i <200;

[0009] Each vehicle routing problem aims to minimize the number of vehicles used and the total driving distance of the vehicles:

[0010] min f1 = K(1)

[0011]

[0012] where f1 and f2 are the two optimization objectives, namely the number of vehicles used and the total driving distance of the vehicles, 0 < K ≤ K max , d ij is the distance between factory i and factory j, i = 0, …, N, j = 0, …, N, i, j = 0 represents the industrial manufacturing center, i, j = 1, …, N represents the factory, x ijk indicates whether the k-th vehicle travels from factory i to factory j, x ijk = 1 means yes, x ijk = 0 means no, k = 1, …, K;

[0013] Each transport vehicle needs to meet the following conditions when delivering workpieces, and each factory has and only has one vehicle for service:

[0014]

[0015] Each transport vehicle starts from the industrial manufacturing center, distributes all workpieces according to the corresponding delivery sequence, and then returns to the industrial manufacturing center:

[0016]

[0017] The sum of the weights of the workpieces required by the factories served by each transport vehicle cannot exceed the maximum load of the vehicle:

[0018]

[0019] The time when each transport vehicle arrives at each factory location should be within the time window required by the factory, and the vehicle should return to the industrial manufacturing center before it closes:

[0020] t i ∈[a i , e i (8)

[0021] t0 ∈ [A, E] (9)

[0022] The time when the vehicle arrives at the next factory location is:

[0023]

[0024] Among them, w i is the waiting time of the transport vehicle at factory i, w i ≥0,s i is the delivery time of the transport vehicle at factory i, It represents the time consumed by the transport vehicle from factory i to factory j, which is:

[0025]

[0026] Among them, δ is the disturbance value of the travel time, which is randomly selected between (-0.25, 0.25), t ij is the fixed travel time of the transport vehicle between factory i and factory j;

[0027] Step 2: Population initialization:

[0028] For task T l The generation scale is N p The initial population, each solution represents a vehicle scheduling plan, when g = 0, task T l The initial population can be expressed as:

[0029]

[0030] in, For task T l The nth solution of the gth generation population, each solution is constructed as follows:

[0031] ① Randomly generate a number from 1 to N l Each natural number in the random vector cus, let i = 1, route j is an empty vector, j=1, N l For task T l Number of factories;

[0032] ② Determine each element cus of the vector cus in turn i Does the required weight of the corresponding factory exceed the remaining load of vehicle j? If not, execute ③, otherwise execute ④;

[0033] ③If route j is an empty vector, then cus i Add directly to route j ; If route j If there is only one element, the factory and customer corresponding to the element are determined according to the following rules: i The corresponding factory access order will be cus i Add to route j ; If route jIf there are more than one element, then judge route in turn according to the following rules j each element in i and the order relationship of cus i until the correct position is found and cus j is added to route

[0034] Suppose the time windows of factory 1 and factory 2 are (a1, b1) and (a2, b2) respectively. Then the access order of these two factories is divided into the following three cases:

[0035] Case 1: a1 < a2, then factory 2 is behind factory 1;

[0036] Case 2: a1 > a2 and b2 - b1 > b1 - a1, then factory 2 is behind factory 1;

[0037] Case 3: a1 > a2 and b2 - b1 <= b1 - a1, then factory 1 is behind factory 2;

[0038] ④ Remove the elements of route from the vector cus j If the vector cus is not empty, let i = 1, j = j + 1, route j is an empty vector, jump to ②. If the vector cus is empty, jump to ⑤;

[0039] ⑤ Concatenate j vectors route into a vector in turn, and insert natural numbers greater than N l to separate them. What is finally obtained is an initial solution composed of the scheduling scheme It can be expressed as:

[0040]

[0041] Step 3 Build a knowledge base of robustness and optimality:

[0042] Step 3.1 Calculate the robustness of each individual in each task:

[0043] The robustness of an individual is the total violation of the time window constraint when the perturbation value takes the maximum value, that is, δ = 0.25. It can be expressed as:

[0044]

[0045] where K is the number of vehicles used in the scheduling scheme corresponding to this individual, and n k is the number of factories to be visited by the k-th vehicle, is the right time window of the j-th factory of the k-th vehicle, is the time when the k-th vehicle arrives at the j-th factory;

[0046] Step 3.2 Calculate the optimality of each individual in each task:

[0047] ① Calculate the domination strength of an individual: For two individuals p and q, if f1(p) ≤ f1(q) and f2(p) ≤ f2(q), it means p dominates q, then the domination strength of p is incremented by 1;

[0048] ② Calculate the robustness of all individuals in this task, and sort them in descending order according to the robustness value, so as to obtain the rank of each individual R ;

[0049] ③ The optimality of an individual is equal to its domination strength plus the rank R , and then the optimality of each individual is sorted in ascending order to obtain the rank F ;

[0050] Step 3.3 Search for the global non-dominated solutions of each task:

[0051] According to the calculated robustness value and optimality value of each individual, for two individuals p and q, if the robustness and optimality of individual p are both better than those of individual q, it means that individual p comprehensively dominates individual q; if an individual in this task is not comprehensively dominated by any other individual, then this individual is called a comprehensive non-dominated solution;

[0052] Step 3.4 Construct the robustness and optimality knowledge bases:

[0053] Create two matrices of size n l *n l , namely the robustness knowledge base and the optimality knowledge base, where the initial value of each element is 0, and n l is the number of factories that task T l needs to serve; then for all the comprehensive non-dominated solutions found in the previous step, if its rank R > rank F , then store its factory access information in the robustness knowledge base, otherwise store it in the optimality knowledge base;

[0054] The way of knowledge storage is: according to the factory access order of the comprehensive non-dominated solution, group them in pairs in order, and add a W to the corresponding elements in the knowledge base. The calculation is as follows:

[0055]

[0056] where g is the current generation, G is the maximum number of generations, and w is a fixed value of 1;

[0057] Step 4 Dual-performance knowledge transfer:

[0058] Step 4.1 Determine two corresponding relationships of factories among tasks:

[0059] ① Calculate the geographical similarity between factory i and factory j in tasks T n and T m where the geographical similarity between factory i and factory j in tasks T

[0060]

[0061] where and are the abscissa and ordinate of factory i in task T n respectively, and and are the abscissa and ordinate of factory j in task T m respectively;

[0062] ② Calculate the time-window similarity between factory i and factory j in tasks T n and T m where the time-window similarity between factory i and factory j in tasks T

[0063]

[0064] where and are the left time-window and right time-window of factory i in task T n respectively, and and are the left time-window and right time-window of factory j in task T m respectively;

[0065] ③ Determine the corresponding relationships of factories in geographical location and time-window for the two tasks respectively, in the following way: Select the factory with the maximum corresponding similarity for each factory in task T m from the factories used in task T n as the one-to-one corresponding relationship;

[0066] Step 4.2 Generate offspring individuals through dual-performance knowledge transfer:

[0067] In each task, N p * rmp offspring individuals are generated by dual-performance knowledge transfer, where rmp is the knowledge transfer rate, with a value of 0.3. Among them, robust knowledge transfer and optimality knowledge transfer each account for half. Knowledge transfer requires the factory corresponding relationships among tasks. When transferring robust knowledge, the time-window corresponding relationship is adopted, and when transferring optimality knowledge, the geographical location corresponding relationship is adopted;

[0068] Taking the transfer of robust knowledge as an example below:

[0069] ① Randomly select a factory in the factory of the current task as the first visited object, denoted as

[0070] ② Find according to the time window correspondence The corresponding factory in the source task, denoted as

[0071] ③ Select the th row in the robustness knowledge base of the source task, and the factory corresponding to the maximum value as The next factory of, denoted as Then select the next factory of in the same way until a sequence composed of all factories in the source task is formed;

[0072] ④ Convert the sequence of the source task constructed in the previous step into a sequence composed of the factories of the current task according to the time window correspondence;

[0073] ⑤ According to the vehicle constraint violation, insert the center point into the sequence of the current task to obtain the final vehicle scheduling plan, that is, the constructed offspring individual;

[0074] The steps of migrating the optimality knowledge are the same as above, only need to change the time window correspondence to geographical location correspondence, and the robustness knowledge base to optimality knowledge base;

[0075] Step 5 generates the offspring population of each task based on the differential evolution of the DE / rand / 1 mutation strategy:

[0076] The remaining N p -N p *rmp offspring individuals of each task are generated through the differential evolution operator:

[0077]

[0078] Among them, is the hth mutant individual of the gth generation of task T i , is The hth parent individual of, and are two parent individuals randomly selected from ; is The offspring of, is The dth dimension component of, is the random number taken by the hth parent in the dth dimension component,

[0079] For the offspring Ascending sorting is performed to obtain the offspring population with integer coding

[0080] Step 6 Environmental selection:

[0081] Calculate the offspring generated by each task for optimality and robustness, and then, together with the parent population sort in descending order according to the optimality value, and each individual obtains a rank Rank F sort in ascending order according to the robustness value, and each individual obtains a rank Rank R Sum the Rank F and Rank R of each individual, then sort in ascending order, and select the top N p individuals as

[0082] Step 7 Judge the algorithm termination condition:

[0083] If g < G, let g = g + 1, and repeat steps 3 - 6. If g = G, the algorithm stops iterating, outputs the non-dominated solution set of each task, and sets all elements representing stations in each solution of each task to 0 to obtain a vehicle scheduling plan with optimality and robustness for each task

[0084] The innovation of the present invention lies in:

[0085] (1) In the vehicle routing problem with uncertain travel times, the present invention designs a decoding strategy considering dual performance. First, based on greedy search, sufficient access points are assigned to each vehicle, and then the time window distribution of each access point is analyzed to adjust the access order of each vehicle, thereby decoding to obtain a vehicle scheduling plan with both optimality and robustness

[0086] (2) In the case of multiple vehicle routing problems with uncertain travel times, the present invention designs a knowledge transfer strategy considering dual performance. First, an optimality and robustness knowledge base is constructed for each task to store the optimality and robustness knowledge in the evolutionary process, and then the performance of the target task is improved by learning the knowledge base of the source task, enabling the algorithm to search for a vehicle scheduling plan with optimality and robustness

[0087] It should be noted particularly that the present invention designs a multi-task differential evolution algorithm considering dual performance, and any research on scheduling technology using the optimization algorithm of the present invention should fall within the scope of the present invention Description of the drawings

[0088] Figure 1 is the vehicle scheduling route map of Task 1 in the optimization result of the present invention

[0089] Figure 2 It is the first vehicle scheduling route map of Task 2 in the optimization result of the present invention

[0090] Figure 3 It is the second vehicle scheduling route map of Task 2 in the optimization result of the present invention Detailed implementation manners

[0091] The data samples of the present invention adopt RC103 and RC105 belonging to the Solomon dataset. As shown in Tables 1 and 2, the first to seventh columns respectively represent the customer number i, the abscissa x of the customer location i and the ordinate y i , the workpiece demand weight q of the factory i , the expected earliest start service time a i , the expected latest start service time e i and the service duration s i , where the data corresponding to i = 0 is the information of the industrial manufacturing center, and the data corresponding to i = 1,..., 100 is the information of the factory. The present invention aims at the two-task vehicle routing problem, where Task 1 uses the RC103 dataset and Task 2 uses the RC105 dataset.

[0092] The present invention takes the number of vehicles used and the total driving distance of the vehicles as the optimization objectives in the scheduling process, and adopts the following technical solutions and implementation steps:

[0093] 1. The specific steps of an intelligent optimization scheduling method for industrial manufacturing tasks considering dual performance are as follows:

[0094] Step 1: Determine the optimization objectives and constraint conditions of the vehicle routing problem with uncertain driving time for each task:

[0095] There are 2 tasks. For each task, 40 transport vehicles are parked at the industrial manufacturing center and need to serve 100 factories. The maximum load of each vehicle is 200. The opening time and closing time of the industrial manufacturing center are 0 and 230 respectively. Each factory is served by only one transport vehicle. Each vehicle carries the workpiece demand of the factories to be served at the industrial manufacturing center, starts from here, and delivers the required workpieces to each factory in sequence according to the service order, and finally returns to the industrial manufacturing center; for each factory to be served, it includes the following attributes: factory number i, the location coordinates of the factory (x i , y i ), the weight q of the workpiece required by the i-th factory i , the expected earliest start service time a of the i-th factory i and the expected latest start service time e i , as well as the service duration s of the vehicle at the i-th factory i , where i = 0 represents the station;

[0096] Each vehicle routing problem aims to minimize the number of vehicles used and the total driving distance of the vehicles:

[0097] min f1 = K (1)

[0098]

[0099] where f1 and f2 are the two optimization objectives, namely the number of vehicles used and the total driving distance of the vehicles, 0 < K ≤ 40, d ij is the distance between factory i and factory j, i = 0, …, 100, j = 0, …, 100, i, j = 0 represents the industrial manufacturing center, i, j = 1, …, 100 represents the factory, x ijk indicates whether the k-th vehicle travels from factory i to factory j, x ijk = 1 means yes, x ijk = 0 means no, k = 1, …, K;

[0100] When each transport vehicle delivers workpieces, it needs to meet the following conditions: each factory is served by exactly one vehicle:

[0101]

[0102] Each transport vehicle starts from the industrial manufacturing center, distributes all workpieces according to the corresponding delivery sequence, and then returns to the industrial manufacturing center:

[0103]

[0104] The sum of the weights of the workpieces required by the factories served by each transport vehicle cannot be greater than the maximum load of the vehicle:

[0105]

[0106] The time when each transport vehicle arrives at each factory location should be within the time window required by the factory, and the vehicle should return to the industrial manufacturing center before it closes:

[0107] t i ∈ [a i , e i (8)

[0108] t0 ∈ [0, 23 (9)

[0109] The time when the vehicle arrives at the next factory location is:

[0110]

[0111] where w i is the waiting time of the transport vehicle at factory i, wi ≥ 0, s i is the delivery time of the transport vehicle at factory i, represents the time consumed for the transport vehicle to travel from factory i to factory j, and this time is:

[0112]

[0113] where δ is the perturbation value of the travel time, which is randomly taken within (-0.25, 0.25), and t ij is the fixed travel time between factory i and factory j for the transport vehicle;

[0114] Step 2 Population initialization:

[0115] For task T l Generate an initial population of size 20. Each solution represents a vehicle scheduling plan. When g = 0, the initial population of task T l can be represented as:

[0116]

[0117] where, is the nth solution of the gth generation population for task T l . The construction method of each solution is as follows:

[0118] ① Randomly generate a random vector cus composed of each natural number from 1 to 100. Let i = 1, and route j be an empty vector, and j = 1;

[0119] ② Successively judge whether the required weight of the factory corresponding to each element cus i of the vector cus exceeds the remaining load capacity of vehicle j. If not, execute ③; otherwise, execute ④;

[0120] ③ If route j is an empty vector, directly add cus i to route j ; if route j has only one element, determine the access order of the factory corresponding to this element and the factory corresponding to cus i and add cus i to route j ; if route j has more than one element, successively judge the order relationship between each element in route j and cus i until the correct position is found and cus i is added to routej , let \(i = i + 1\), then jump to ②;

[0121] Suppose the time windows of Factory 1 and Factory 2 are \((a1, b1)\) and \((a2, b2)\) respectively. Then the visiting order of these two factories is divided into the following three cases:

[0122] Case 1: \(a1 < a2\), then Factory 2 is after Factory 1;

[0123] Case 2: \(a1 > a2\) and \(b2 - b1 > b1 - a1\), then Factory 2 is after Factory 1;

[0124] Case 3: \(a1 > a2\) and \(b2 - b1 <= b1 - a1\), then Factory 1 is after Factory 2;

[0125] ④ Remove the elements of route from the vector cus. If the vector cus is not empty, let \(i = 1\), \(j = j + 1\), route j is an empty vector, jump to ②. If the vector cus is empty, jump to ⑤; j is an empty vector, jump to ②. If the vector cus is empty, jump to ⑤;

[0126] ⑤ Concatenate the j vectors route into a single vector in sequence, inserting natural numbers greater than 100 as intervals between two vectors. What is finally obtained is an initial solution composed of the scheduling scheme It can be expressed as:

[0127]

[0128] Step 3 Build the robustness and optimality knowledge base:

[0129] Step 3.1 Calculate the robustness of each individual in each task:

[0130] The robustness of an individual is the total violation of the time window constraint when the perturbation value takes the maximum value, that is, \(\delta = 0.25\). It can be expressed as:

[0131]

[0132] where K is the number of vehicles used in the scheduling scheme corresponding to this individual, n k is the number of factories to be visited by the k - th vehicle, is the right time window of the j - th factory of the k - th vehicle, is the time when the k - th vehicle arrives at the j - th factory;

[0133] Step 3.2 Calculate the optimality of each individual in each task:

[0134] ① Calculate the domination strength of an individual: For two individuals p and q, if f1(p) ≤ f1(q) and f2(p) ≤ f2(q), it means that p dominates q, then the domination strength of p is incremented by 1;

[0135] ② Calculate the robustness of all individuals in this task, and sort them in descending order according to the robustness value, so as to obtain the rank of each individual R ;

[0136] ③ The optimality of an individual is equal to its domination strength plus the rank R , and then the optimality of each individual is sorted in ascending order to obtain the rank F ;

[0137] Step 3.3 Search for the global non-dominated solutions of each task:

[0138] According to the calculated robustness value and optimality value of each individual, for two individuals p and q, if the robustness and optimality of individual p are both better than those of individual q, it means that individual p comprehensively dominates individual q; if an individual in this task is not comprehensively dominated by any other individual, then this individual is called a comprehensive non-dominated solution;

[0139] Step 3.4 Construct the robustness and optimality knowledge bases:

[0140] Create two matrices of size 100*100, namely the robustness knowledge base and the optimality knowledge base, where the initial value of each element is 0; then for all the comprehensive non-dominated solutions found in the previous step, if its rank R >rank F , then store its factory access information in the robustness knowledge base, otherwise store it in the optimality knowledge base;

[0141] The way of knowledge storage is: according to the factory access order of the comprehensive non-dominated solutions, group them in pairs in order, and add a W to the corresponding elements in the knowledge base. The calculation is as follows:

[0142]

[0143] where g is the current generation, G is the maximum number of evolutionary generations, which is 1000, and w = 1;

[0144] Step 4 Dual-performance knowledge transfer:

[0145] Step 4.1 Determine two corresponding relationships of factories between tasks:

[0146] ① Calculate the geographical similarity between factory i and factory j in task T n and T m

[0147]

[0148] Among them and are the abscissa and ordinate of factory i of task T n respectively, and are the abscissa and ordinate of factory j of task T m respectively;

[0149] ② Calculate the similarity of factories i and j in tasks T n and T m in the time window

[0150]

[0151] Among them and are the left time window and right time window of factory i of task T n respectively, and are the left time window and right time window of factory j of task T m respectively;

[0152] ③ Determine the corresponding relationships of the factories of the two tasks in terms of geographical location and time window respectively, in the following way: sequentially select the factory with the largest corresponding similarity for each factory of task T m from the used factories of task T n as the one-to-one corresponding relationship;

[0153] Step 4.2 Generate offspring individuals through dual-performance knowledge transfer:

[0154] Six offspring individuals are generated by dual-performance knowledge transfer in each task, with half for robustness knowledge transfer and half for optimality knowledge transfer. Knowledge transfer requires the factory correspondence between tasks. For transferring robustness knowledge, the time window correspondence is adopted, and for transferring optimality knowledge, the geographical location correspondence is adopted;

[0155] Take the transfer of robustness knowledge as an example below:

[0156] ① Randomly select a factory in the factories of the current task as the first visiting object, denoted as

[0157] ② Find the corresponding factory of in the source task according to the time window correspondence, denoted as

[0158] ③ Select the in the robustness knowledge base of the source task The factory corresponding to the maximum value in the row is used as the next factory of and then select in the same way the next factory of

[0159] ④ Convert the sequence of source tasks constructed in the previous step into a sequence composed of the factories of the current task according to the time window correspondence relationship;

[0160] ⑤ Insert the center point into the sequence of the current task according to the vehicle constraint violation to obtain the final vehicle scheduling plan, that is, the constructed offspring individual;

[0161] The steps of migrating the optimal knowledge are the same as above, only changing the time window correspondence relationship to the geographical location correspondence relationship, and changing the robust knowledge base to the optimal knowledge base;

[0162] Step 5 Generate the offspring population of each task based on the differential evolution of the DE / rand / 1 mutation strategy:

[0163] The remaining 14 offspring individuals of each task are generated by the differential evolution operator:

[0164]

[0165] Among them, is the h-th mutated individual of task T i in the g-th generation, is the h-th parent individual of and are two parent individuals randomly selected from ; is the offspring of , is the d-th dimensional component of is a random number taken by the h-th parent in the d-th dimensional component,

[0166] Sort the offspring with real number coding in ascending order to obtain the offspring population

[0167] Step 6 Environmental selection:

[0168] Calculate the optimality and robustness of the offspring generated by each task, and then, together with the parent population , sort in descending order according to the optimality value, and each individual obtains the rank Rank F , and sort in ascending order according to the robustness value, and each individual obtains the rank RankR , sum the Rank of each individual F and Rank R , then sort them in ascending order, and select the top 20 individuals as

[0169] Step 7: Judge the algorithm termination condition:

[0170] If g < 1000, let g = g + 1, and repeat steps 3 - 6. If g = 1000, the algorithm stops iterating, outputs the non-dominated solution set of each task, sets all the elements representing the stations in each solution of each task to 0, and obtains the vehicle scheduling plan with optimality and robustness for each task, as shown in Table 3 and Figures 1-3 as shown. Table 3 shows the factory delivery sequence of each task, Figures 1-3 and gives the vehicle scheduling plan diagram of each task.

[0171] Table 1. RC103 Vehicle Routing Optimization Data

[0172]

[0173]

[0174]

[0175] Table 2. RC105 Vehicle Routing Optimization Data

[0176]

[0177]

[0178] Table 3. Optimal Vehicle Scheduling Plan for Each Task

[0179]

[0180]

[0181]

Claims

1. An intelligent optimization scheduling method for industrial manufacturing tasks considering dual performance, characterized in that Determine the optimization objectives of each scheduling task and the uncertainty of vehicle travel time. Use the multi-task differential evolution algorithm to solve multiple vehicle routing problems. Improve the optimality and robustness of discrete solutions according to the decoding strategy considering dual performance, and improve the search performance of the algorithm through knowledge transfer to address the problem that the solutions found are infeasible due to the uncertainty of vehicle travel time, and simultaneously achieve the optimal number of vehicles used and the total travel distance, including the following steps: Step 1. Determine the optimization objectives and constraints of the vehicle routing problem with uncertain travel time for each task: Assume there are L tasks, and each task has K max transport vehicles parked at the industrial manufacturing center, which need to serve N factories. The maximum load of each vehicle is Q. The opening time and closing time of the industrial manufacturing center are A and E respectively. Each factory is served by only one transport vehicle. Each vehicle carries the workpiece requirements of the factories to be served at the industrial manufacturing center, departs from here, and delivers the required workpieces to each factory in sequence according to the service order, and finally returns to the industrial manufacturing center; for each factory to be served, it includes the following attributes: factory number i, the location coordinates of the factory (x i , y i ), the weight q i of the workpieces required by the i-th factory, the expected earliest start service time a i and the expected latest start service time e i of the i-th factory, and the service duration s i of the vehicle at the i-th factory, where i = 0 represents the station; 0 < K max < 50, 0 < N < 150, 0 < Q < 300 kg, 0 < A < 1440, 0 < E < 1440, i = 0, …, N, 0 < x i < 100, 0 < y i < 100, 0 < a i < 1440, 0 < e i < 1440, 0 < s i < 200; The optimization objective of each vehicle routing problem is to minimize the number of vehicles used and the total vehicle travel distance: minf1 = K (1) Among them, f1 and f2 are two optimization objectives, namely the number of vehicles used and the total distance traveled by vehicles, respectively. <K≤K max , d ij is the distance between factory i and factory j, i=0,…,N,j=0,…,N,i,j=0 represents an industrial manufacturing center, i,j=1,…,N represents a factory, x ijk Indicates whether the kth vehicle travels from factory i to factory j, x ijk =1 for yes, x ijk =0 for no, k=1,…,K; When each transport vehicle delivers workpieces, it needs to meet the following conditions: there is exactly one vehicle serving each factory: Each transport vehicle starts from the industrial manufacturing center, distributes all workpieces in the corresponding delivery order, and then returns to the industrial manufacturing center: The sum of the weights of the workpieces required by each factory served by each transport vehicle cannot be greater than the maximum load of the vehicle: The arrival time of each transport vehicle at each factory location should be within the time window required by the factory, and the vehicle should return to the industrial manufacturing center before it closes: t i ∈[a i ,e i ](8)t0∈[A,E](9) The arrival time of the vehicle at the next factory location is: Among them, w i is the waiting time of the transport vehicle at factory i, w i ≥0,s i is the delivery time of the transport vehicle at factory i, It represents the time consumed by the transport vehicle from factory i to factory j, which is: Among them, δ is the disturbance value of the travel time, which is randomly selected between (-0.25, 0.25), t ij is the fixed travel time of the transport vehicle between factory i and factory j; Step 2. Population initialization: For task T l The generation scale is N p The initial population, each solution represents a vehicle scheduling plan, when g = 0, task T l The initial population can be expressed as: in, For task T l The nth solution of the gth generation population, each solution is constructed as follows: ① Randomly generate a number from 1 to N l Each natural number in the random vector cus, let i = 1, route j is an empty vector, j=1, N l For task T l Number of factories; ② Determine each element cus of the vector cus in turn i Does the required weight of the corresponding factory exceed the remaining load of vehicle j? If not, execute ③, otherwise execute ④; ③If route j is an empty vector, then cus i Add directly to route j ; If route j If there is only one element, the factory and customer corresponding to the element are determined according to the following rules: i The corresponding factory access order will be cus i Add to route j ; If route j If there is more than one element in , the route is determined according to the following rules. j Each element in cus i The order relationship until the correct position is found and the cus i Add to route j , let i=i+1, then jump to ②; Suppose the time windows of Factory 1 and Factory 2 are (a1, b1) and (a2, b2) respectively. Then the access order of these two factories is divided into the following three cases: Case 1: a1 < a2, then Factory 2 is behind Factory 1; Case 2: a1 > a2 and b2 - b1 > b1 - a1, then Factory 2 is behind Factory 1; Case 3: a1 > a2 and b2 - b1 <= b1 - a1, then Factory 1 is behind Factory 2; ④Remove route from vector cus j If the vector cus is not empty, let i = 1, j = j + 1, route j If it is an empty vector, jump to ②. If the vector cus is empty, jump to ⑤. ⑤ Connect j route vectors into one vector, insert more than N vectors between the two vectors. l The final result is an initial solution consisting of the scheduling scheme. It can be expressed as: Step 3. Construct a knowledge base of robustness and optimality: Step 3.1 Calculate the robustness of each individual in each task: The robustness of an individual is the sum of the violations of the time window constraints when the perturbation value takes the maximum value, i.e., δ = 0.25, which can be expressed as: Where K is the number of vehicles used in the dispatch plan corresponding to the individual, n k is the number of factories that the k-th vehicle will visit, is the right time window of the jth factory of the kth vehicle, is the time when the kth vehicle arrives at the jth factory; Step 3.2 Calculate the optimality of each individual in each task: ① Calculate the domination strength of an individual: For two individuals p and q, if f1(p) ≤ f1(q) and f2(p) ≤ f2(q), it means that p dominates q, and then the domination strength of p is incremented by 1; ② Calculate the robustness of all individuals in the task and sort them in descending order according to the robustness value, so that the rank of each individual R ; ③The optimality of an individual is equal to its dominance strength plus its rank R , then the optimality of each individual is sorted in ascending order to obtain the rank F ; Step 3.3 Search for the global non-dominated solutions of each task: According to the calculated robustness values and optimality values of each individual, for two individuals p and q, if the robustness and optimality of individual p are both better than those of individual q, it means that individual p comprehensively dominates individual q; if an individual in this task is not comprehensively dominated by any other individual, then this individual is called a globally non-dominated solution; Step 3.4 Construct a knowledge base of robustness and optimality: Create two l *n l The matrices are the robustness knowledge base and the optimality knowledge base, respectively, where the initial value of each element is 0, n l It is task T l The number of factories that need to be served; then for all the fully non-dominated solutions found in the previous step, if their rank R >rank F , then its factory access information is stored in the robustness knowledge base, otherwise it is stored in the optimality knowledge base; The way of knowledge storage is: According to the factory access order of the globally non-dominated solutions, group them in pairs in order, and add a W to the corresponding elements in the knowledge base. The calculation is as follows: where g is the current generation, G is the maximum number of generations, and w is a fixed value of 1; Step 4. Dual-performance knowledge transfer: Step 4.1 Determine two corresponding relationships of factories between tasks: ① Computation task T n and T m The geographical similarity between factories i and j in in and Task T n The horizontal and vertical coordinates of factory i, and Task T m The horizontal and vertical coordinates of factory j; ②Computation task T n and T m The similarity between factory i and factory j in the time window in and Task T n The left time window and the right time window of factory i, and Task T m The left time window and right time window of factory j; ③ Determine the corresponding relationship between the two tasks’ factories in terms of geographical location and time window respectively, by the following method: m The factories used are task T n For each factory, select the corresponding factory with the greatest similarity as a one-to-one correspondence; Step 4.2 Generate offspring individuals through dual-performance knowledge transfer: Each task has N p *rmp offspring individuals are generated by dual-performance knowledge migration. rmp is the knowledge migration rate, which is 0.

3. Robust knowledge migration and optimal knowledge migration each account for half. Knowledge migration requires the factory correspondence between tasks. The migration of robust knowledge adopts the time window correspondence, and the migration of optimal knowledge adopts the geographical location correspondence. Taking the transfer of robustness knowledge as an example: ① Randomly select a factory from the factories of the current task as the first visit object, denoted as ②Find according to the time window correspondence The factory corresponding to the source task is denoted as ③ Select the first robust knowledge base in the source task The factory corresponding to the maximum value in the row is The next factory is Then select in the same way The next factory of the source task is formed until a sequence consisting of all the factories of the source task is formed; ④ Convert the sequence of the source task constructed in the previous step into a sequence composed of the factories of the current task according to the time window correspondence; ⑤ Insert the center points into the sequence of the current task according to the vehicle constraint violation to obtain the final vehicle scheduling plan, that is, the constructed offspring individual; The steps of transferring optimality knowledge are the same as above, only changing the time window correspondence to the geographical location correspondence and changing the robustness knowledge base to the optimality knowledge base; Step 5 Generate the offspring population of each task through differential evolution based on the DE / rand / 1 mutation strategy: The remaining N for each task p -N p *rmp offspring individuals are generated through differential evolution operators: in, It is task T i The h-th mutant individual of the g-th generation, yes The h-th parent individual, and is from Two parents randomly selected from yes The offspring of yes The d-th dimension component of is the random number taken by the h-th parent on the d-th dimension component, F is the scaling factor, with a value of 0.5, C r is the crossover rate, with a value of 0.9; Children encoding real numbers Sort in ascending order to get the integer-coded offspring population Step 6 Environmental selection: Count the children spawned by each task The optimality and robustness of Together, according to the optimality value in descending order, each individual obtains the rank Rank F , sorted in ascending order according to the robustness value, each individual obtains a rank R , the Rank of each individual F and Rank R Sum and sort in ascending order, select the first N p Individuals serve as the initial population for the next generation Step 7 Judge the algorithm termination condition: If g < G, let g = g + 1, and repeat steps 3 - 6. If g = G, the algorithm stops iterating, outputs the non-dominated solution set of each task, and sets all the elements representing the stations in each solution of each task to 0 to obtain the vehicle scheduling plan with optimality and robustness for each task.

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