Multi-target multi-robot fruit tree picking task allocation method
By combining the random neighborhood search method of genetic algorithm, task allocation in multi-robot systems is optimized, the problem of uneven task allocation is solved, system efficiency is improved and energy consumption is reduced.
Patent Information
- Application Number
- CN202510589982.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-08
- Publication Date
- 2025-08-15
AI Technical Summary
In the existing multi-robot system, the task allocation method ignores the complexity and characteristics of the task, resulting in unbalanced work of the robot and affects the system efficiency.
A multi-objective multi-robot fruit tree picking task allocation method is adopted, combined with the random neighborhood search method of genetic algorithm, and the task allocation process is optimized through task sequence optimization, task balance mechanism, adjacent task optimization and population-based task allocation mechanism.
The efficiency of collaborative work of multiple robots is improved, energy consumption costs are reduced, and the reasonable allocation and balance of tasks are achieved.
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Figure CN120494389A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of path planning, and in particular relates to a multi-target multi-robot fruit picking task allocation method. Background Art
[0002] In recent years, with the continuous advancement of planting technology and agricultural mechanization, agricultural production has gradually developed towards a more intelligent and efficient direction. The widespread application of smart agricultural technologies has significantly increased crop yields. my country, as a major agricultural country with vast arable land resources, has been a major driving force behind this trend. According to Henan Province's agricultural development plan, the area of high-quality orchards in the province is expected to reach 15 million acres by 2025, laying a solid foundation for further agricultural development.
[0003] However, labor shortages in agriculture have become a pressing issue. Despite significant progress in agricultural mechanization over the past few decades, the production of high-value crops such as apples, pears, and peaches still relies heavily on manual labor. With China's accelerating urbanization, a large number of rural workers have migrated to cities, resulting in a gradual decline in the agricultural labor supply. Furthermore, with the changing global economic landscape, agricultural labor costs are rising, and the agricultural sector is facing increasing economic pressure, leaving significant uncertainty about the future labor supply.
[0004] Research has shown that the harvesting process requires significant manual labor, accounting for the majority of the overall labor involved in fruit tree management. To address this issue, researchers have been working to develop effective solutions to reduce reliance on manual labor. Fruit harvesting research has made significant progress in recent years, with the goal of automating the harvesting process through technological means, thereby reducing labor requirements and improving production efficiency.
[0005] The rise of agricultural robots has provided new insights into addressing this issue. In recent years, numerous research teams, both domestically and internationally, have proposed various robot prototypes for fruit-picking and tested them in various experimental environments. These robots can replace manual labor in identifying, sorting, and harvesting fruit. Consequently, the concept of multi-robot systems has emerged. In orchards, using multiple robots to collaborate not only improves operational efficiency but also reduces the bottlenecks faced by a single robot when handling large-scale tasks. The advantage of multi-robot systems lies in their ability to achieve parallel processing of tasks through task allocation and collaboration mechanisms, significantly improving the overall system's operational efficiency. However, effective task allocation and scheduling within multi-robot systems remains a major challenge in current research.
[0006] In existing multi-robot systems, task allocation is typically based on the physical distance between the robot and the task, or on simple task classification. However, this random task allocation approach ignores the complexity and characteristics of tasks, and the workloads of different tasks can vary significantly. Relying solely on the distance between robots and tasks can lead to some robots being overworked while others remain idle, significantly impacting the efficiency of the entire system.
[0007] Therefore, in a multi-robot system, optimizing the allocation of tasks becomes crucial for improving harvesting efficiency and reducing operating costs. By thoroughly analyzing task characteristics and integrating them with the robots' current state and capabilities, more intelligent task scheduling can be achieved while maximizing system efficiency. For example, different tasks may require varying amounts of time and energy. Therefore, task allocation requires consideration not only of the distance between the robot and the task, but also of factors such as task priority, urgency, and workload. Summary of the Invention
[0008] In order to solve the above problems, the present invention proposes a multi-objective multi-robot fruit tree picking task allocation method, which combines the random neighborhood search method of genetic algorithm to improve the efficiency of multiple robots working together while reducing energy consumption costs.
[0009] The technical solution adopted in the present invention is:
[0010] A multi-target multi-robot fruit picking task allocation method includes the following steps:
[0011] S1, number each mature fruit tree and record its coordinates;
[0012] S2, initialize the sequence number of the fruit tree tasks included in each trip;
[0013] S3, uses the task sequence optimization method to optimize the order of tasks included in each trip;
[0014] S4, uses the task balancing mechanism to optimize the most time-consuming journey;
[0015] S5, uses the adjacent task optimization mechanism to optimize trips with similar travel routes;
[0016] S6, uses a population-based task allocation method to assign all journeys to multiple robots;
[0017] S7, perform environmental selection on all assigned tasks to obtain a set of non-dominated solutions;
[0018] S8, the allocation results in all solutions are evaluated using the hypervolume metric.
[0019] Furthermore, the specific steps of S2 are:
[0020] S21, cluster all the fruit tree tasks to be completed according to the number of robots using K-means;
[0021] S22, in each cluster, divide each trip according to the yield of the fruit trees, the distance and the load of the robot;
[0022] S23, divide the redundant tasks into other clusters and merge them with the tasks of other clusters into one trip, until all tasks are arranged into multiple trips.
[0023] Furthermore, the specific steps of S3 are:
[0024] S3, uses the task sequence optimization method to optimize the order of tasks included in each trip. The specific steps include:
[0025] S31, obtaining the serial numbers of the fruit trees included in a trip;
[0026] S32, shuffle the order of these serial numbers and obtain a new serial number;
[0027] S33, set the population size to 10;
[0028] S34, evaluate the energy consumption if the robot completes the tasks according to the order of tasks in each sequence:
[0029]
[0030] Where k represents the number of trees to be picked in a trip, y j represents the position of the j-th fruit tree, load represents the load of the robot after completing the j-th picking task; weight is the robot's own weight, which is a fixed constant;
[0031] S35, the corresponding task with low energy consumption is taken as the current optimal sequence, recorded as sequence best;
[0032] S36, cross the best sequence with another sequence, first randomly select two positions in the vector from one of the parents, copy them to the corresponding positions in the child, and then fill the remaining elements from the other parent into the blank positions in the child, thus obtaining two new sequences;
[0033] S37, repeat steps S34-S36 until the number of sequences obtained reaches the population size;
[0034] S38, change the next trip to be optimized, and repeat steps S31-S37 until all trips are optimized.
[0035] Furthermore, the specific steps of S4 are:
[0036] S41, add an empty journey;
[0037] S42, find the trip T1 with the highest energy consumption among all current trips and record its energy consumption P1;
[0038] S43, placing some tasks in the trip with the highest energy consumption into the empty trip; the specific steps include:
[0039] S431, record the journey with high energy consumption as Td, and record the journey with low energy consumption as Tx;
[0040] S432, recording the sum of energy consumption of the two trips Ph1;
[0041] S434, after placing the first task in Td to the last task in Tx, two new trips Tdx and Txx are obtained;
[0042] S435, re-evaluate the sum of the energy consumption of the two trips Ph2;
[0043] S436, if Ph2 is less than or equal to Ph1, then replace the value of Ph1 with the value of Ph2, and replace Td and Tx with Tdx and Txx respectively, and repeat steps S434-S436;
[0044] S437, if Ph2 is greater than Ph1, the original Td, Tx and Ph1 are still used;
[0045] S438, after placing the last task in Td to the last task in Tx, two new trips Tdx and Txx are obtained;
[0046] S439, re-evaluate the sum of the energy consumption of the two trips, Ph2;
[0047] S440, if Ph2 is less than or equal to Ph1, then replace the value of Ph1 with the value of Ph2, and replace Td and Tx with Tdx and Txx respectively, and repeat steps S438-S440, otherwise terminate the operation of S43;
[0048] S44, using the task sequence optimization method to optimize the task order in the two trips respectively;
[0049] Furthermore, the specific steps of S5 are:
[0050] S51, calculate the average coordinates of all tasks in each trip;
[0051] S52, randomly select a trip Ts;
[0052] S53, find the trip Tj with the nearest average coordinate;
[0053] S54, evaluate the sum of the energy consumption of these two trips and record it as P3;
[0054] S55, places some tasks from the trip with the highest energy consumption into the empty trip;
[0055] S56, uses the task sequence optimization method to optimize the task order in these two trips respectively;
[0056] S57, evaluate the sum of the energy consumption of these two trips and record it as P4;
[0057] S58, if P4 is less than or equal to P3, use the newly obtained two trips to replace the old two trips;
[0058] S59, repeat steps S51-S68 ten times.
[0059] Furthermore, the specific steps of S6 are:
[0060] S61, number each trip;
[0061] S62, randomly generate two sequences containing these numbers, where the order of the numbers in the two sequences is different;
[0062] S63, record the number of robots as r, divide the first sequence into r parts, and each part contains a random number of robots;
[0063] S64, calculating the total time for a robot to complete all journeys in each portion, where the total time is equal to the total moving distance divided by the average speed, where the average speed is set as a fixed constant;
[0064] S65, determining which robot takes the longest time to complete all journeys, and recording its time Time;
[0065] S66, repeat steps S63-S65 ten times, and select the portioning method with the smallest time among the ten times for the first sequence;
[0066] S67, similarly, perform S63-S66 operations on the second sequence;
[0067] S68, performing a crossover operation on the two sequences, the principle is the same as S36, and obtaining two new sequences;
[0068] S69, repeating the operations S63-S69 ten times to obtain a sequence with the minimum Time and the allocation result of this sequence.
[0069] The beneficial effects produced by the present invention are:
[0070] 1. Task sequence optimization method is used to adjust the order of tasks in each journey to ensure smooth transition between tasks and reduce unnecessary travel time;
[0071] 2. The task optimization mechanism fills empty trips and reduces the workload of trips with heavy workloads through reasonable task transfer, thereby balancing the energy consumption and time of each trip;
[0072] 3. The adjacent task optimization mechanism further improves the quality of the solution by optimizing the task structure between adjacent journeys to prevent excessive dispersion of tasks;
[0073] 4. The population-based task allocation mechanism is used to assign the obtained multiple trips to the existing robots. BRIEF DESCRIPTION OF THE DRAWINGS
[0074] Figure 1 is a flow chart of the method of the present invention;
[0075] Figure 2 This is the crossover principle diagram of S36 in the present invention. DETAILED DESCRIPTION
[0076] The present invention will be further described below with reference to the accompanying drawings.
[0077] like Figure 1 As shown, the present invention is a multi-target multi-robot fruit tree picking task allocation method, comprising the following steps:
[0078] S1, number each mature fruit tree and record its coordinates.
[0079] S2, initialize the sequence number of the fruit picking tasks included in each trip. The specific steps include:
[0080] S21, cluster all fruit picking tasks to be completed according to the number of robots using K-means:
[0081] S211, determine cluster centers: first randomly select r initial cluster centers, where r is equal to the number of robots;
[0082] S212, assign samples: assign each data point to the nearest centroid, thus forming r clusters;
[0083] S213, update the centroid: recalculate the centroid of each cluster, that is, calculate the mean of all sample points in each cluster and use the mean as the new centroid;
[0084] S214, repeated iteration: repeat the steps of allocating samples and updating the centroid until the centroid no longer changes or the set maximum number of iterations is reached.
[0085] S22, in each cluster, divide each trip according to the yield of the fruit trees, the distance and the load of the robot: use the enumeration method to further cluster the fruit trees according to the distance of the picking task, so that the sum of all fruit tree tasks in each cluster does not exceed the load of the robot.
[0086] S23, divide the redundant picking tasks into other clusters and merge them with the tasks of other clusters into one trip until all tasks are arranged into multiple trips.
[0087] S3, uses the task sequence optimization method to optimize the order of tasks included in each trip. The specific steps include:
[0088] S31: Get the serial numbers of the fruit trees included in a trip. This serial number is a sequence of serial numbers from S2. Due to load constraints, S2 divides all fruit and vegetable picking tasks into multiple trips. The order of picking tasks in each trip is optimized one by one.
[0089] S32, shuffle the order of these serial numbers and obtain a new serial number;
[0090] S33, set the population size to 10;
[0091] S34, evaluate the energy consumption if the robot completes the tasks according to the order of tasks in each sequence:
[0092]
[0093] Where k represents the number of trees to be picked in a trip, y j represents the position of the j-th fruit tree, load represents the load of the robot after completing the j-th picking task; weight is the robot's own weight, which is a fixed constant;
[0094] S35, the corresponding task with low energy consumption is taken as the current optimal sequence, recorded as sequence best;
[0095] S36, cross the best sequence with another sequence. The crossover principle is as follows Figure 2 As shown, first randomly select two positions in the vector from one of the parents, copy them to the corresponding positions of the child, and then fill the remaining elements of the other parent into the blank positions of the child in sequence, thus obtaining two new sequences;
[0096] S37, repeat steps S34-S36 until the number of sequences obtained reaches the population size;
[0097] S38, change the next trip to be optimized, and repeat steps S31-S37 until all trips are optimized.
[0098] S4, uses the task balancing mechanism to optimize the most time-consuming journey; the specific steps include:
[0099] S41, add an empty journey;
[0100] S42, find the trip T1 with the highest energy consumption among all current trips and record its energy consumption P1;
[0101] S43, placing some tasks in the trip with the highest energy consumption into the empty trip; the specific steps include:
[0102] S431, record the journey with high energy consumption as Td, and record the journey with low energy consumption as Tx;
[0103] S432, recording the sum of energy consumption of the two trips Ph1;
[0104] S434, after placing the first task in Td to the last task in Tx, two new trips Tdx and Txx are obtained;
[0105] S435, re-evaluate the sum of the energy consumption of the two trips Ph2;
[0106] S436, if Ph2 is less than or equal to Ph1, then replace the value of Ph1 with the value of Ph2, and replace Td and Tx with Tdx and Txx respectively, and repeat steps S434-S436;
[0107] S437, if Ph2 is greater than Ph1, the original Td, Tx and Ph1 are still used;
[0108] S438, after placing the last task in Td to the last task in Tx, two new trips Tdx and Txx are obtained;
[0109] S439, re-evaluate the sum of the energy consumption of the two trips, Ph2;
[0110] S440, if Ph2 is less than or equal to Ph1, then replace the value of Ph1 with the value of Ph2, and replace Td and Tx with Tdx and Txx respectively, and repeat steps S438-S440, otherwise terminate the operation of S43;
[0111] S44, the same task sequence optimization method as S3 is used to optimize the task sequences in the two trips respectively;
[0112] S45, evaluate the sum of the energy consumption of these two trips and record it as P2;
[0113] S46, determining the magnitude relationship between P1 and P2;
[0114] S47, if P1 is less than or equal to P2, split T1 according to the above method and repeat steps S41-S47;
[0115] S48: If P1 is greater than P2, stop step S4.
[0116] S5, using the adjacent task optimization mechanism to optimize trips with similar routes; the specific steps include:
[0117] S51, calculate the average coordinates of all tasks in each trip;
[0118] S52, randomly select a trip Ts;
[0119] S53, find the trip Tj with the nearest average coordinate;
[0120] S54, evaluate the sum of the energy consumption of these two trips and record it as P3;
[0121] S55, placing some tasks in the trip with the highest energy consumption into the empty trip, the process is similar to S43;
[0122] S56, uses the task sequence optimization method to optimize the task order in these two trips respectively;
[0123] S57, evaluate the sum of the energy consumption of these two trips and record it as P4;
[0124] S58, if P4 is less than or equal to P3, use the newly obtained two trips to replace the old two trips;
[0125] S59, repeat steps S51-S68 ten times.
[0126] S6, using a population-based task allocation method to assign all journeys to multiple robots; the specific steps include:
[0127] S61, number each trip;
[0128] S62, randomly generate two sequences containing these numbers, where the order of the numbers in the two sequences is different;
[0129] S63, record the number of robots as r, divide the first sequence into r parts, and each part contains a random number of robots;
[0130] S64, calculating the total time for a robot to complete all journeys in each portion, where the total time is equal to the total moving distance divided by the average speed, where the average speed is set as a fixed constant;
[0131] S65, determining which robot takes the longest time to complete all journeys, and recording its time Time;
[0132] S66, repeat steps S63-S65 ten times, and select the portioning method with the smallest time among the ten times for the first sequence;
[0133] S67, similarly, perform S63-S66 operations on the second sequence;
[0134] S68, performing a crossover operation on the two sequences, the principle is the same as S36, and obtaining two new sequences;
[0135] S69, repeating the operations S63-S69 ten times to obtain a sequence with the minimum Time and the allocation result of this sequence.
[0136] S7, perform environmental selection on all assigned tasks to obtain a set of non-dominated solutions;
[0137] S8, the allocation results in all solutions are evaluated using the hypervolume metric.
[0138] To further illustrate the superiority of the present invention in solving multi-objective multi-robot task allocation, Table 1 shows the results obtained by the present invention and some excellent multi-robot task allocation algorithms, Multi-objective Discrete ArtificialBee Colony (MODABC), Non-dominated Sorting Genetic Algorithm-Ⅱ (NSGA-Ⅱ) and Multi-objective Evolutionary Algorithm based on Decomposition (MOEA / D), on the generated orchard multi-robot task allocation test set.
[0139] Table 1 Comparison of the optimal times achieved by experimental results of datasets
[0140]
[0141] The examples provide experimental results on a generated test set of orchard multi-objective, multi-robot task allocation problems. These problems vary in difficulty, including greenhouses ranging in size from 50×50 to 70×70 square meters, containing 625, 900, and 1225 fruit trees, respectively. The fruit tree maturity rate in each scenario was set to 0.8. Therefore, each combination of the number of fruit trees and their maturity represented a different test problem to evaluate the algorithm's task allocation performance under different work scenarios and task difficulties. The number of evaluations in the experiment was set to 10,000, and the population size was set to 10. To avoid the influence of randomness on the experimental results, each algorithm was run 10 times for each test problem. The evaluation results were metrically evaluated using hypervolume. Table 1 shows the number of problems for which each algorithm achieved optimal results in each test problem scenario. By comparison, it can be seen that the method proposed in the present invention demonstrates superior optimization performance in solving multi-objective, multi-robot task allocation. Specifically, regardless of the test problem scenario, the number of optimal results obtained was greater than the number of optimal results obtained by other algorithms.
[0142] In summary, the present invention can effectively handle the multi-objective multi-robot task allocation problem by combining the random neighborhood search method with the genetic algorithm, and provide decision makers with a series of ideal compromise solutions.
[0143] A number of multi-objective evolutionary algorithms have been designed and widely recognized for their effectiveness in solving multi-objective problems. However, to solve more complex problems, the structure of existing multi-objective optimization algorithms has also become more complex. Therefore, it is necessary to improve the performance of algorithms without significantly increasing their complexity to broaden their application. Since single-objective optimization algorithms are less complex than multi-objective optimization algorithms, a hybrid framework of single-objective and multi-objective optimization algorithms can achieve better performance and lower complexity.
[0144] This paper combines variable neighborhood search theory with a population-based approach to propose a randomized neighborhood search method combined with a genetic algorithm to solve the multi-target, multi-robot task allocation problem in an orchard scenario. Experiments and analysis demonstrate the effectiveness and superiority of this algorithm. The algorithm's problem-solving capabilities are influenced by a variety of methods and mechanisms, including a clustering-based task initialization method, a task sequence optimization method, a task balancing mechanism, a neighboring task optimization mechanism, and a population-based task allocation mechanism.
[0145] Although the above describes the specific embodiments of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without any creative work are still within the scope of protection of the present invention.
Claims
1. A multi-target multi-robot fruit picking task allocation method, characterized in that: The following steps are involved: S1, number each mature fruit tree and record its coordinates; S2, initialize the sequence number of the fruit tree tasks included in each trip; S3, uses the task sequence optimization method to optimize the order of tasks included in each trip; S4, uses the task balancing mechanism to optimize the most time-consuming journey; S5, uses the adjacent task optimization mechanism to optimize trips with similar travel routes; S6, uses a population-based task allocation method to assign all journeys to multiple robots; S7, perform environmental selection on all assigned tasks to obtain a set of non-dominated solutions; S8, the allocation results in all solutions are evaluated using the hypervolume metric.
2. The multi-target multi-robot fruit picking task allocation method according to claim 1 is characterized in that: The specific steps of S2 are: S21, cluster all the fruit tree tasks to be completed according to the number of robots using K-means; S22, in each cluster, divide each trip according to the yield of the fruit trees, the distance and the load of the robot; S23, divide the redundant tasks into other clusters and merge them with the tasks of other clusters into one trip, until all tasks are arranged into multiple trips.
3. The multi-target multi-robot fruit picking task allocation method according to claim 1, characterized in that: The specific steps of S3 are: S3, uses the task sequence optimization method to optimize the order of tasks included in each trip. The specific steps include: S31, obtaining the serial numbers of the fruit trees included in a trip; S32, shuffle the order of these serial numbers and obtain a new serial number; S33, set the population size to 10; S34, evaluate the energy consumption if the robot completes the tasks according to the order of tasks in each sequence: Where k represents the number of trees to be picked in a trip, y j represents the position of the j-th fruit tree, load represents the load of the robot after completing the j-th picking task; weight is the robot's own weight, which is a fixed constant; S35, the corresponding task with low energy consumption is taken as the current optimal sequence, recorded as sequence best; S36, cross the best sequence with another sequence, first randomly select two positions in the vector from one of the parents, copy them to the corresponding positions in the child, and then fill the remaining elements from the other parent into the blank positions in the child, thus obtaining two new sequences; S37, repeat steps S34-S36 until the number of sequences obtained reaches the population size; S38, change the next trip to be optimized, and repeat steps S31-S37 until all trips are optimized.
4. The multi-target multi-robot fruit picking task allocation method according to claim 1, characterized in that: The specific steps of S4 are: S41, add an empty journey; S42, find the trip T1 with the highest energy consumption among all current trips and record its energy consumption P1; S43, placing some tasks in the trip with the highest energy consumption into the empty trip; the specific steps include: S431, record the journey with high energy consumption as Td, and record the journey with low energy consumption as Tx; S432, recording the sum of energy consumption of the two trips Ph1; S434, after placing the first task in Td to the last task in Tx, two new trips Tdx and Txx are obtained; S435, re-evaluate the sum of the energy consumption of the two trips Ph2; S436, if Ph2 is less than or equal to Ph1, then replace the value of Ph1 with the value of Ph2, and replace Td and Tx with Tdx and Txx respectively, and repeat steps S434-S436; S437, if Ph2 is greater than Ph1, the original Td, Tx and Ph1 are still used; S438, after placing the last task in Td to the last task in Tx, two new trips Tdx and Txx are obtained; S439, re-evaluate the sum of the energy consumption of the two trips, Ph2; S440, if Ph2 is less than or equal to Ph1, then replace the value of Ph1 with the value of Ph2, and replace Td and Tx with Tdx and Txx respectively, and repeat steps S438-S440, otherwise terminate the operation of S43; S44, use the task sequence optimization method to optimize the task sequences in the two trips respectively.
5. The multi-target multi-robot fruit picking task allocation method according to claim 1, characterized in that: The specific steps of S5 are: S51, calculate the average coordinates of all tasks in each trip; S52, randomly select a trip Ts; S53, find the trip Tj with the nearest average coordinate; S54, evaluate the sum of the energy consumption of these two trips and record it as P3; S55, places some tasks from the trip with the highest energy consumption into the empty trip; S56, uses the task sequence optimization method to optimize the task order in these two trips respectively; S57, evaluate the sum of the energy consumption of these two trips and record it as P4; S58, if P4 is less than or equal to P3, use the newly obtained two trips to replace the old two trips; S59, repeat steps S51-S68 ten times.
6. The multi-target multi-robot fruit picking task allocation method according to claim 1, characterized in that: The specific steps of S6 are: S61, number each trip; S62, randomly generate two sequences containing these numbers, where the order of the numbers in the two sequences is different; S63, record the number of robots as r, divide the first sequence into r parts, and each part contains a random number of robots; S64, calculating the total time for a robot to complete all journeys in each portion, where the total time is equal to the total moving distance divided by the average speed, where the average speed is set as a fixed constant; S65, determining which robot takes the longest time to complete all journeys, and recording its time Time; S66, repeat steps S63-S65 ten times, and select the portioning method with the smallest time among the ten times for the first sequence; S67, similarly, perform S63-S66 operations on the second sequence; S68, performing a crossover operation on the two sequences, the principle is the same as S36, and obtaining two new sequences; S69, repeating the operations S63-S69 ten times to obtain a sequence with the minimum Time and the allocation result of this sequence.
Citation Information
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