A long-term multi-agent task allocation method based on a multi-objective hierarchical cultural genetic algorithm

Abstract

The application discloses a long-term multi-agent task allocation method based on a multi-objective multi-level cultural gene algorithm, which is used in a task continuous random arrival scene such as intelligent warehousing. In view of the problems that the existing static method cannot adapt to long-term tasks, the online method is frequently cold started, the historical knowledge is poorly reused, the convergence is slow, and the task period and the agent load balancing are difficult to balance, a double-objective model of minimizing cumulative task period and minimizing load deviation is established; a multi-objective multi-level cultural gene algorithm is designed, multi-strategy initialization, hierarchical population and genetic operation are adopted, adaptive multi-neighborhood and confusion degree pop-up search local search are combined, and the population and historical archives are updated by cooperating with the non-dominated solution sorting, congestion degree calculation and elite reservation strategy. Through the organic combination of the above strategies, the algorithm can realize the collaborative optimization of task response and load balancing without interrupting the system operation.

Description

Technical Field

[0001] This invention relates to the field of multi-agent systems and task scheduling technology, specifically a multi-objective hierarchical cultural gene algorithm for long-term multi-agent task allocation. It is applicable to scenarios such as intelligent warehousing that require continuous task processing, and achieves long-term task allocation with a dual objective of balancing task turnaround time and agent load. Background Technology

[0002] With the rapid iteration of artificial intelligence and autonomous system technologies, multi-agent task allocation has become one of the core supporting technologies for the efficient operation of autonomous systems. Its core essence lies in rationally allocating a series of tasks to multiple agents, and achieving optimal improvement in the overall system performance by optimizing the matching relationship between tasks and agents. For example, in intelligent warehousing, multiple robots need to respond in real time to continuously generated picking and delivery tasks, adjusting their travel paths and task execution order.

[0003] Currently, multi-agent task allocation techniques can be broadly categorized into two types: static task allocation methods and online task allocation methods. Static task allocation methods were the mainstream research direction in the early stages. Their core assumption is that complete information about all tasks is known in advance, and the algorithm completes the allocation of all tasks through a single optimization calculation. Representative methods in this category include multi-objective evolutionary algorithms based on non-dominated sorting (such as NSGA-II and its variants), multi-objective optimization algorithms based on problem decomposition (such as MOEA / D), Pareto genetic algorithms (PGA), and multi-objective greedy algorithms (MOGA). These algorithms, through mechanisms such as non-dominated sorting, crowding calculation, greedy repair, and local refinement, can find Pareto optimal solutions that balance multiple conflicting objectives in offline scenarios. However, due to the strong dependence of static methods on the complete task set, they fail to achieve good results in long-term scenarios where tasks continuously arrive.

[0004] Online task allocation methods have emerged to address scenarios where tasks arrive continuously. These methods do not require prior knowledge of all task information but instead employ an incremental decision-making approach, adjusting the allocation scheme in real time as new tasks arrive. Representative technologies include hierarchical task planners and reinforcement learning-based allocation strategies: hierarchical task planners decompose high-dimensional, complex tasks into multiple low-dimensional sub-tasks and adapt to dynamic changes in tasks through incremental replanning mechanisms; reinforcement learning-based allocation strategies learn the optimal policy for task allocation through continuous interaction between the agent and the environment, achieving online optimization of the allocation scheme. Although these methods can handle streaming task inputs, they reveal significant drawbacks during long-term continuous operation: on the one hand, each new batch of tasks often requires retraining the model or re-executing the entire optimization process, resulting in high computational costs and difficulty in meeting real-time requirements; on the other hand, the lack of a systematic historical knowledge reuse mechanism prevents the effective utilization of high-quality patterns accumulated in previous task allocations, leading to a "cold start" problem with each new batch of tasks, slow optimization convergence speed, and large performance fluctuations and insufficient stability in long-term operation.

[0005] In summary, existing multi-agent task allocation techniques, whether static or online, are insufficient to fully meet the long-term application requirements of "continuous task arrival, multi-objective collaborative optimization, and stable long-term performance improvement." In long-term multi-agent task allocation scenarios, they suffer from prominent problems such as insufficient adaptability, poor multi-objective balancing effect, slow convergence speed, and lack of knowledge reuse. There is an urgent need for a novel multi-agent task allocation method that can specifically address the above-mentioned defects to meet the high requirements of practical applications for task allocation efficiency, stability, and long-term optimization capabilities. Summary of the Invention

[0006] The purpose of this invention is to provide a long-term multi-agent task allocation method based on a multi-objective hierarchical cultural gene algorithm, which aims to solve the problems of frequent cold starts, insufficient balance of multi-objective optimization, lack of historical knowledge reuse, and slow convergence speed in the existing technology in the long-term task allocation scenario, and to achieve efficient long-term optimized task allocation in the scenario of continuous task arrival.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] 1. A long-term multi-agent task allocation method based on a multi-objective hierarchical cultural gene algorithm, characterized by the following steps:

[0009] S1. Problem Modeling: Define a long-term multi-objective, multi-agent task allocation problem, and construct a dual objective function, the first objective function being... The second objective function is to accumulate task turnaround time, which is the total time from task arrival to completion. For agent load balancing, that is, the average deviation between the task load of each agent and the average task load;

[0010] S2. Algorithm Design: Multi-objective hierarchical cultural gene algorithm, the specific steps are as follows:

[0011] S2.1 Define population individuals using integer encoding. Each individual corresponds to a chromosome. The chromosome length is consistent with the current number of tasks. The gene position value represents the agent sequence number assigned to the corresponding task. Based on the population history archive, initialize the population using a multi-strategy fusion method.

[0012] S2.2. Divide the initialized population into two subpopulations using Pareto front sorting, and optimize the two objective functions for each subpopulation accordingly. Perform bidirectional individual migration to achieve knowledge sharing among subpopulations;

[0013] S2.3, Perform improved linear sorting selection and backbone crossover to generate offspring individuals for the two subpopulations respectively;

[0014] S2.4 Optimize the objective function subpopulation Execution task turnover optimization mutation, on the optimization objective function subpopulation Perform load-balanced optimized mutation to generate offspring individuals;

[0015] S2.5, for the population Perform adaptive multi-neighborhood local search on the population. Perform a local search based on perplexity pop-ups to generate offspring individuals;

[0016] S2.6, merge the parent and offspring populations and sequentially perform non-dominated sorting, crowding calculation, elite retention, and update the historical archive. And record archive quality data;

[0017] S2.7 Repeat steps S2.3 to S2.6 until the maximum number of iterations is reached;

[0018] S3. Output task allocation scheme: Decode the long-term multi-agent task allocation scheme from the final non-dominated population set;

[0019] As a preferred embodiment of the present invention, the specific content of the S1 problem modeling is as follows:

[0020] The long-running multi-objective, multi-agent task allocation problem is a continuous task allocation process. Tasks do not have a pre-known complete set, but rather arrive randomly over time, forming an infinite sequence of tasks. Agents must adjust the allocation scheme without interrupting system operation. The goal of this problem is to allocate tasks to all agents over time. The task optimization aims to achieve the following two optimization goals:

[0021] Objective function 1 (minimize task turnaround time): Accumulate time up to the current moment. The turnaround time for all completed tasks is defined as the total time from when a task arrives in the system to when it is fully executed. The calculation formula is as follows:

[0022] ;

[0023] in Deadline The set of tasks that have been reached For the task Completion time, For the task Arrival time;

[0024] Objective function 2 (minimize agent load difference): calculate up to the current time step The degree of load balancing among all agents. Load is defined as the sum of the total number of unexecuted tasks assigned to agents and the total number of tasks currently being executed. The calculation formula is as follows:

[0025] ;

[0026] in The total number of agents. Deadline intelligent agent load capacity, This represents the average load across all agents.

[0027] As a preferred embodiment of the present invention, the multi-strategy fusion initialization operation of the population in S2 specifically includes the following steps:

[0028] S4.1 First, according to the logical order of time, different Each task is numbered;

[0029] S4.2, Use a set of lengths of one-dimensional array Chromosomes, among which Indicates task The allocation of agent serial numbers;

[0030] S4.3 Execute greedy initialization based on task turnaround time: Using the nearest neighbor heuristic strategy, calculate the spatial distance between the pickup location of each task and the current location of all agents, and assign the task to the agent with the closest spatial distance to form the first group of initialization agents;

[0031] S4.4 Execute greedy initialization based on agent load balancing: Based on the load balancing objective, iteratively calculate the current cumulative task load of each agent, and assign each task to the agent with the smallest current cumulative load in turn to form the second group of initialization agents;

[0032] S4.5 Execute migration initialization based on task location: Select the historical non-dominated solutions from the population history archive that are closest to the current task in terms of task pickup and delivery locations, directly inherit the agent allocation relationship of the corresponding task in the historical solution, and construct the third set of initial individuals;

[0033] S4.6 Perform fragment-based migration initialization:

[0034] S4.6.1 If the total number of current tasks is less than a preset threshold, the current chromosome is treated as a single task segment; otherwise, the current chromosome is divided into multiple fixed-length non-overlapping task segments, each task segment constituting a local learning unit.

[0035] S4.6.2 Extract multiple historical task segments with the same length as the current task segment from the optimal solution in the historical archive using a sliding window method;

[0036] S4.6.3. The similarity between the current task segment and the historical task segment is quantified using Euclidean distance. The calculation steps are as follows: For each task in the current task segment and the corresponding task in the historical task segment, extract the pickup location of both tasks. coordinate, Coordinates, calculate the sum of squares of the coordinate differences, take the square root of the sum of squares to get the single-task Euclidean distance, sum the single-task Euclidean distances of all corresponding tasks to get the total distance between the two tasks, the smaller the total distance, the higher the similarity.

[0037] S4.6.4 Select the historical task segment with the smallest total distance (i.e. the highest similarity) and reuse its corresponding agent allocation relationship; for unassigned tasks in the current task segment that are not covered by the historical task segment, randomly assign them to agents without execution conflicts to form the fourth group of initial individuals;

[0038] S4.7 Perform random initialization: For the remaining individuals to be initialized that were not covered by the above steps, randomly assign values ​​within the feasible range of agent numbers to generate randomly initialized individuals;

[0039] S4.8. Merge all the initial individuals generated in steps S4.3 to S4.7 to form the initial population.

[0040] As a preferred embodiment of the present invention, the specific steps of the goal-oriented hierarchical population division and preferential migration mechanism in S2 are as follows:

[0041] S5.1 First, perform a fast non-dominated sort on the initial population to obtain several Pareto fronts. , , , The smaller the frontier index, the better the overall optimization performance of the individual population.

[0042] S5.2 Initialize the cumulative counter This is used to count the number of Pareto fronts with an odd number of individuals, with an initial value set to 0.

[0043] S5.3, for each Pareto front (including) Individuals are divided based on minimizing the task turnaround time according to objective function 1:

[0044] ·like If it is even, extract The optimal objective function 1 Individuals form a subpopulation for task turnaround optimization. The remaining individuals form a subpopulation for load balancing optimization. ;

[0045] ·like If the number is odd, the cumulative counter will be set to odd. Add 1; if If it is an odd number, extract Center front Individuals are categorized The remaining Individuals are categorized ;like If it is even, extract Center front Individuals are categorized The remaining Individuals are categorized ;

[0046] S5.4 During the iteration process, a population selection migration operation is triggered every 5 iterations, specifically as follows:

[0047] S5.4.1 Optimize the task turnover subpopulation All individuals within the population are sorted in ascending order based on the values ​​of objective function 1 (smaller values ​​indicate shorter task turnaround times and better performance); load balancing optimization is applied to the subpopulation. All individuals are sorted in ascending order according to the value of objective function 2 (load balance degree) (the smaller the value, the more balanced the load and the better the performance).

[0048] S5.4.2 Extraction The last individual in the sorted list, i.e., the individual with the worst performance in objective function 1, is replaced with... The individual ranked first in the sorted list is the individual with the best performance in objective function 2; simultaneously extract... The last individual in the sorted list, i.e., the individual with the worst performance in objective function 2, is replaced with... The individual that ranks first in the sorted list is the individual with the best performance in objective function 1.

[0049] As a preferred embodiment of the present invention, the improved linear sorting selection and backbone crossing in S2 are specifically as follows:

[0050] S6.1, to All individuals are sorted in ascending order according to the value of objective function 1; for All individuals are sorted in ascending order according to the value of objective function 2;

[0051] S6.2, Let the subpopulation size be... After sorting, assign a weight of 1 to the individual with the worst fitness and assign a weight of 1 to the individual with the best fitness. If the middle individuals are assigned weights according to their ranking position, then the ranking of the [number]th [item] will be [number]. The probability of an individual choosing a position is: ;

[0052] S6.3. Based on the above selection probabilities, randomly select several individuals from each subpopulation to form a parent set for crossover operations;

[0053] S6.4 Compare the chromosomes of the two parent individuals and find all positions where the gene locus values ​​are the same. The genes corresponding to these positions are the backbone genes. The backbone genes represent the consistent task-agent allocation relationship between the two parents and are directly inherited to the offspring individuals. For the differential genes with different gene locus values ​​in the two parent individuals, randomly select the gene locus value of one of the parents to inherit to the offspring individuals, forming a complete offspring chromosome.

[0054] As a preferred embodiment of the present invention, the mutation operation in S2 that optimizes task turnaround time and agent load balancing is as follows:

[0055] (1) Mutation operation for task turnover optimization: First, randomly select one task as the mutation object, calculate the spatial distance between the pickup location of the task and the current location of each agent, and reassign the task to the agent with the closest spatial distance. If there are multiple agents with equal spatial distance, randomly select one of them.

[0056] (2) Mutation operation for load balancing optimization: First, calculate the current load of all agents. The load is the sum of the tasks assigned to the agents. Select the agent with the largest load as the original agent. Randomly select one task from the task list of the agent as the mutation object. Then select the agent with the smallest load as the target agent. Remove the mutation object task from the task list of the original agent and reassign it to the task list of the target agent.

[0057] As a preferred embodiment of the present invention, the optimized local search operation in S2 for task turnaround time and agent load balancing is as follows:

[0058] (1) Adaptive multi-neighborhood local search operation for task turnaround optimization:

[0059] S7.1 Initialization of the mutated solution Set the maximum number of local search iterations for the current solution. And four neighborhood operators, as follows:

[0060] • Intelligent body exchange operator: from the current solution Randomly select a task sequence for the agent, and then randomly select two tasks from the task sequence to exchange, thus obtaining the neighborhood solution. ;

[0061] • Intelligent body exchange operator: from the current solution Two agents are randomly selected. and The task sequence, in and The task sequence randomly selects one task, swaps two tasks, and obtains the neighborhood solution. ;

[0062] • Intelligent body shift operator: from the current solution Randomly select a task sequence for the agent, and then randomly select a task from the task sequence. Move this task to any position in the task sequence to obtain the neighborhood solution. ;

[0063] • Inter-agent shift operator: from the current solution Two agents are randomly selected. and The task sequence, in The task sequence randomly selects a task and moves that task to... At any position in the task sequence, a neighborhood solution is obtained. ;

[0064] S7.2 Maintaining two neighbor lists and winning neighborhood list , Initialize the data into four sequences of randomly ordered operators, and then apply them sequentially to each individual. The operator in the middle, if the generated neighborhood solution Dominate the current solution ( Better and Better or equal, or Better or equal If it is better, then update. for Add the corresponding operator ;like and If not dominated, then the neighborhood solution is retained with a 50% probability and the operator is added. ;like quilt If the operator is dominant, then discard the operator and retain the one that is dominant. ;

[0065] S7.3, After exhaustion, there is a 75% probability of... Medium sampling operator, with a 25% probability of randomly sampling from four operators, and refilling ;like If empty, reuse the most recently fully filled one. The sorting of operators, when When filling again, you need to clear the space. Neighborhood operators in;

[0066] S7.4 If the current iteration count reaches Then Updated to Output the result; otherwise, increment the iteration count by 1, return to step S7.1, and continue the local search process.

[0067] (2) Local search operation based on confusion pop-up for load balancing optimization:

[0068] S8.1 Initialization of the mutated solution Set the maximum number of local search iterations for the current solution. Calculate the current solution Individual perplexity ( For population size, For indicator functions, hour (Otherwise, it is 0)

[0069] S8.2 Calculate the pop-up rate If random number Then: Calculate the number of tasks for each agent. ( Indicates task Assigned to intelligent agents (otherwise it is 0);

[0070] S8.3 Calculating Gene Perplexity (in , For intelligent agents (Task allocation frequency), filter by task quantity The intelligent agent puts its tasks into a pop-up set. ;

[0071] S8.4, to For each task, calculate its combined cost with all agents (combined cost = spatial distance cost + load increment cost), reassign it to the agent with the lowest combined cost, and update... ;

[0072] S8.5, If the current iteration count reaches Then Updated to Output the result; otherwise, increment the iteration count by 1, return to step S8.1, and continue the local search process.

[0073] As a preferred embodiment of the present invention, the specific steps of the non-dominated sorting strategy, crowding calculation, and elite retention strategy in S2 are as follows:

[0074] S9.1, Non-dominated solution sorting: For each individual in the population, calculate the number of dominated individuals and the set of dominated solutions. Individuals with a number of dominated individuals of 0 are assigned to the first Pareto front. For each individual in the front, decrement the number of dominated solutions they dominate by 1. If the number of dominated solutions becomes 0, assign them to the next front. Iterate in this way until all individuals have completed the Pareto level classification.

[0075] S9.2 Crowding Degree Calculation: Initialize the crowding degree of all individuals to 0. For each objective function, sort the individuals within each Pareto level according to the function value, and set the crowding degree of the first and last boundary individuals after sorting to infinity. For the middle individuals, calculate their crowding degree by the ratio of the difference between the objective function values ​​of their preceding and following individuals to the range of the objective function values.

[0076] S9.3 Elite Preservation: Merge the parent and offspring populations to obtain a merged population. In order of Pareto level from low to high, add all individuals in the new parent population until a certain level cannot accommodate all individuals. Sort the individuals in that level from crowded to low and select individuals in turn to supplement the new parent population, thus completing elite preservation.

[0077] Compared with the prior art, the advantages of the present invention are:

[0078] 1. Multi-strategy fusion initialization strategy: effectively solves the "cold start" problem in long-term scenarios. This invention integrates location-based and fragment-based historical knowledge transfer initialization, reusing high-quality allocation schemes from previous tasks, so that new task batches do not need to start from scratch; at the same time, it combines task turnover greedy, load balancing greedy, and random initialization strategies, which not only significantly improves the quality of initial solutions and algorithm convergence speed, but also fully guarantees population diversity, overcoming the shortcomings of existing online task allocation methods that lack cross-batch knowledge reuse and have high restart overhead in long-term operation.

[0079] 2. Goal-Oriented Hierarchical Population Partitioning and Optimal Migration Mechanism: Existing multi-objective algorithms often use random or simple sorting methods for population partitioning, lacking precise adaptation to the optimization objective. Furthermore, subpopulations lack effective knowledge sharing and are prone to getting trapped in local optima. This invention uses fast non-dominated sorting to divide the population into subpopulations focused on task turnover optimization. With a subpopulation focused on load balancing optimization This ensures that each subpopulation evolves in a targeted manner; during the iteration process, bidirectional migration is triggered every fixed number of times, replacing the worst individual of the other subpopulation with the best individual of the two subpopulations. This achieves both deep optimization of a single objective and promotes knowledge complementarity between subpopulations, avoiding the trap of local optima.

[0080] 3. Target-Customized Local Search Strategy: Existing local search algorithms mostly use a single search logic to process all targets, lacking sufficient targeting for different targets, making it difficult to simultaneously shorten task turnaround time and improve load balancing. This invention provides... An adaptive multi-neighborhood local search is designed, utilizing four operators—intelligent in-body and out-of-body task exchange, shifting, and neighborhood list updating—to efficiently explore the optimization space of task execution order and allocation relationships; The design employs a pop-up local search based on perplexity. By calculating individual and gene perplexity, agents with excessive task concentration are screened, and their tasks are redistributed based on a combination of spatial distance and incremental load cost. This achieves precise load balancing and solves the shortcomings of existing local searches, which suffer from low optimization efficiency and limited effectiveness due to their "one-size-fits-all" approach. Attached Figure Description

[0081] Figure 1 A flowchart for a multi-objective hierarchical cultural gene algorithm;

[0082] Figure 2 This is a schematic diagram of a smart warehouse;

[0083] Figure 3 This is a schematic diagram of the cross-branch structure;

[0084] Figure 4 A schematic diagram of four neighborhood operators;

[0085] Figure 5 A schematic diagram of adaptive multi-neighborhood local search; Detailed Implementation

[0086] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0087] Please see Figure 1 This invention provides an implementation method, taking the task allocation of a certain intelligent warehousing robot as an example:

[0088] This embodiment uses the scheduling of robotic sorting tasks in a large-scale intelligent e-commerce warehouse as an application scenario. Multiple autonomous mobile robots (i.e., intelligent agents) are deployed within the warehouse, and tasks are issued continuously. For example... Figure 2 As shown, tasks such as pickup and delivery requests are incrementally generated and must be completed by agents within the warehouse space while avoiding obstacles. Tasks arrive sequentially over time, represented as an infinite sequence. Each task needs to be delivered from the pickup point to the delivery point, such as... Figure 2 As shown, the first arrow points from the agent to the task's pickup point, and the second arrow points from the task's pickup point to the task's delivery point. Once a task is assigned to an agent, the agent must travel from its current location to the pickup point and then deliver the task to the delivery point.

[0089] The long-run multi-objective multi-agent task assignment problem aims to solve the problem of assigning tasks to all agents in time. The task optimization aims to achieve the following two optimization goals:

[0090] Objective function 1 (minimize task turnaround time): Accumulate time up to the current moment. The turnaround time for all completed tasks is defined as the total time from when a task arrives in the system to when it is fully executed. The calculation formula is as follows:

[0091]

[0092] in Deadline The set of tasks that have been reached For the task Completion time, For the task Arrival time;

[0093] Objective function 2 (minimize agent load difference): calculate up to the current time step The degree of load balancing among all agents. Load is defined as the sum of the total number of unexecuted tasks assigned to agents and the total number of tasks currently being executed. The calculation formula is as follows:

[0094]

[0095] in The total number of agents. Deadline intelligent agent load capacity, This represents the average load across all agents.

[0096] Specifically, when using it:

[0097] 1. Initialize the population: Use a set of lengths... one-dimensional array Chromosomes, among which Indicates task The process involves assigning agent numbers and then performing greedy initialization based on task turnaround time: using a nearest neighbor heuristic, the spatial distance between the pickup location of each task and the current location of all agents is calculated, and tasks are assigned to the agents with the closest spatial distance, forming the first group of initialized individuals; performing greedy initialization based on agent load balancing: based on the load balancing objective, the current cumulative task load of each agent is iteratively calculated, and each task is assigned to the agent with the smallest current cumulative load, forming the second group of initialized individuals; and performing migration initialization based on task location: selecting historical non-dominated solutions from the population history archive that are closest to the current task's pickup and delivery locations. The system directly inherits the agent allocation relationship of the corresponding task in the historical solution to construct the third set of initialized individuals; it performs fragment-based transfer initialization: if the total number of current tasks is less than a preset threshold, the current chromosome is treated as a single task segment; otherwise, the current chromosome is divided into multiple fixed-length non-overlapping task segments, each task segment constituting a local learning unit. Then, from the optimal solution in the population history archive, multiple historical task segments with the same length as the current task segment are extracted using a sliding window method. The similarity between the current task segment and the historical task segment is quantified using Euclidean distance. The calculation steps are as follows: for each task in the current task segment and the corresponding task in the historical task segment, extract the pickup positions of the two tasks. coordinate, The coordinates are calculated, and the sum of squares of the coordinate differences is taken to obtain the single-task Euclidean distance. The single-task Euclidean distances of all corresponding tasks are accumulated to obtain the total distance between the two task segments. The smaller the total distance, the higher the similarity. The historical task segment with the smallest total distance (i.e., the highest similarity) is selected, and its corresponding agent allocation relationship is reused. For unassigned tasks in the current task segment that are not covered by the historical task segment, they are randomly assigned to agents without execution conflicts to form the fourth group of initial individuals. For the remaining uninitialized individuals not covered by the above steps, values ​​are randomly assigned within the feasible range of agent indices to generate random initialized individuals.

[0098] 2. Hierarchical population partitioning and optimal migration mechanism: First, a fast non-dominated sort is performed on the initial population to obtain several Pareto fronts. , , , A smaller frontier index indicates better overall optimization performance of the population, and the cumulative counter is initialized. This is used to count the number of Pareto fronts with an odd number of individuals, with an initial value set to 0; for each Pareto front... (including) Individuals are divided based on minimizing the task turnaround time according to objective function 1:

[0099] ·like If it is even, extract The optimal objective function 1 Individuals form a subpopulation for task turnaround optimization. The remaining individuals form a subpopulation for load balancing optimization. ;

[0100] ·like If the number is odd, the cumulative counter will be set to odd. Add 1; if If it is an odd number, extract Center front Individuals are categorized The remaining Individuals are categorized ;like If it is even, extract Center front Individuals are categorized The remaining Individuals are categorized ;

[0101] During the iteration process, a population selection migration operation is triggered every 5 iterations: the task turnover optimization subpopulation is selected. All individuals within the population are sorted in ascending order based on the values ​​of objective function 1 (smaller values ​​indicate shorter task turnaround times and better performance); load balancing optimization is applied to the subpopulation. All individuals are sorted in ascending order according to the value of objective function 2 (load balancing degree) (the smaller the value, the more balanced the load and the better the performance), and then extracted. The last individual in the sorted list, i.e., the individual with the worst performance in objective function 1, is replaced with... The individual ranked first in the sorted list is the individual with the best performance in objective function 2; simultaneously extract... The last individual in the sorted list, i.e., the individual with the worst performance in objective function 2, is replaced with... The individual that ranks first in the sorted list is the individual with the best performance in objective function 1.

[0102] 3. Improved linear sorting selection and backbone crossover: for All individuals are sorted in ascending order according to the value of objective function 1; for All individuals within the subpopulation are sorted in ascending order according to the values ​​of objective function 2. Let the subpopulation size be... After sorting, assign a weight of 1 to the individual with the worst fitness and assign a weight of 1 to the individual with the best fitness. If the middle individuals are assigned weights according to their ranking position, then the ranking of the [number]th [item] will be [number]. The probability of an individual choosing a position is: Based on selection probability, a number of individuals are randomly selected from each subpopulation to form a parent set for crossover operations. The chromosomes of two parent individuals are compared to identify positions where all gene loci have the same value; these positions correspond to the backbone genes, which represent the consistent task-agent allocation relationship between the two parents and are directly inherited by the offspring individuals. Figure 3 As shown; for differentially expressed genes with different locus values ​​in two parent individuals, the locus value of one parent is randomly selected and inherited by the offspring individual to form a complete offspring chromosome, as shown. Figure 3 As shown;

[0103] 4. Optimized mutation operations for task turnaround time and agent load balancing:

[0104] (1) Mutation operation for task turnover optimization: First, randomly select one task as the mutation object, calculate the spatial distance between the pickup location of the task and the current location of each agent, and reassign the task to the agent with the closest spatial distance. If there are multiple agents with equal spatial distance, randomly select one of them.

[0105] (2) Mutation operation for load balancing optimization: First, calculate the current load of all agents. The load is the sum of the tasks assigned to the agents. Select the agent with the largest load as the original agent. Randomly select one task from the task list of the agent as the mutation object. Then select the agent with the smallest load as the target agent. Remove the mutation object task from the task list of the original agent and reassign it to the task list of the target agent.

[0106] 5. Optimized local search operation for task turnaround time and agent load balancing:

[0107] (1) Adaptive multi-neighborhood local search operation for task turnaround optimization: initialization of the mutated solution Set the maximum number of local search iterations for the current solution. And four neighborhood operators, as follows:

[0108] • Intelligent body exchange operator: from the current solution Randomly select a task sequence for the agent, and then randomly select two tasks from the task sequence to exchange, thus obtaining the neighborhood solution. ,exist Figure 4 (a) represents the swap of 1;

[0109] • Intelligent body exchange operator: from the current solution Two agents are randomly selected. and The task sequence, in and The task sequence randomly selects one task, swaps two tasks, and obtains the neighborhood solution. ,exist Figure 4 (b) is represented as swap 2;

[0110] • Intelligent body shift operator: from the current solution Randomly select a task sequence for the agent, and then randomly select a task from the task sequence. Move this task to any position in the task sequence to obtain the neighborhood solution. ,exist Figure 4 (c) represents displacement 1;

[0111] • Inter-agent shift operator: from the current solution Two agents are randomly selected. and The task sequence, in The task sequence randomly selects a task and moves that task to... At any position in the task sequence, a neighborhood solution is obtained. ,exist Figure 4 (d) represents displacement 2;

[0112] Maintain two neighborhood lists and winning neighborhood list , Initialize the data into four sequences of randomly ordered operators, and then apply them sequentially to each individual. The operator in the middle, if the generated neighborhood solution Dominate the current solution ( Better and Better or equal, or Better or equal If it is better, then update. for Add the corresponding operator ;like and If not dominated, then the neighborhood solution is retained with a 50% probability and the operator is added. ;like quilt If the operator is dominant, then discard the operator and retain the one that is dominant. ; After exhaustion, there is a 75% probability of... Medium sampling operator, with a 25% probability of randomly sampling from four operators, and refilling ;like If empty, reuse the most recently fully filled one. The sorting of operators, when When filling again, you need to clear the space. Neighborhood operators in [the context of the problem].

[0113] The specific execution process is as follows: Figure 5 As shown, firstly, assume that a random number of characters of length 4 are generated. List, such as Figure 5 As shown in (a), from Take the first operator "swap 2" from the middle, and in The neighborhood solution is obtained by performing the "swap 2" operator. ,because Dominate Therefore, Updated to And put the operator "swap 2" into In the list, such as Figure 5 As shown in (b). If Dominate Then the operator "displacement 2" is discarded, such as Figure 5 As shown in (c). Repeat the above process until... Empty (e.g.) Figure 5 (d) As shown, then it is necessary to... The process involves refilling the array by generating a uniformly distributed random number between [0,1]. If the random number is less than 0.75, then... A random operator is selected from the four neighboring operators. If the random number is greater than 0.75, then a random operator is selected from the four neighboring operators (e.g., ...). Figure 5 (e) is shown above. The above process is repeated until... Refilled Cleared (e.g.) Figure 5 (f) shown).

[0114] If the current iteration count reaches Then Updated to Output the result; otherwise, increment the iteration count by 1 and continue the local search process.

[0115] (2) Local search operation based on perplexity popping for load balancing optimization: initialization of the mutated solution Set the maximum number of local search iterations for the current solution. Calculate the current solution Individual perplexity ( For population size, For indicator functions, hour (Otherwise 0), calculate the bounce rate. If random number Then: Calculate the number of tasks for each agent. ( Indicates task Assigned to intelligent agents (Otherwise, it is 0); calculate gene perplexity. (in , For intelligent agents (Task allocation frequency), filter by task quantity The intelligent agent puts its tasks into a pop-up set. ,right For each task, calculate its combined cost with all agents (combined cost = spatial distance cost + load increment cost), reassign it to the agent with the lowest combined cost, and update... If the current iteration count reaches... Then Updated to Output the result; otherwise, increment the iteration count by 1 and continue the local search process.

[0116] 6. Non-dominated solution sorting strategies, crowding calculation, and elite retention strategies:

[0117] (1) Non-dominated solution sorting: For each individual in the population, calculate the number of dominated and the set of dominated solutions. Individuals with a number of dominated solutions of 0 are assigned to the first Pareto front. Traverse each individual in the front and decrement the number of dominated solutions they dominate by 1. If the number of dominated solutions becomes 0, assign them to the next front. Iterate in this way until all individuals have completed the Pareto level classification.

[0118] (2) Crowding degree calculation: Initialize the crowding degree of all individuals to 0. For each objective function, sort the individuals in each Pareto level according to the function value. Set the crowding degree of the first and last boundary individuals after sorting to infinity. For the middle individuals, calculate their crowding degree by the ratio of the difference between the objective function values ​​of their preceding and following individuals to the range of the objective function values.

[0119] (3) Elite retention: Merge the parent population and the offspring population to obtain a merged population. In order of Pareto level from low to high, the entire layer of individuals is incorporated into the new parent population until a certain layer of individuals cannot be accommodated. Sort the individuals in that layer from crowded to small and select individuals in turn to supplement the new parent population to complete the elite retention.

Claims

1. A long-term multi-agent task allocation method based on a multi-objective hierarchical cultural gene algorithm, characterized in that, Specifically, the following steps are included: S1. Problem Modeling: Define a long-term multi-objective, multi-agent task allocation problem, construct a dual objective function, the first of which is the optimization objective function. The second optimization objective function is to accumulate task turnaround time, which is the total time from task arrival to completion. For agent load balancing, that is, the average deviation between the task load of each agent and the average task load; S2. Algorithm Design: Multi-objective hierarchical cultural gene algorithm, the specific steps are as follows: S2.1 Define population individuals using integer encoding. Each individual corresponds to a chromosome. The chromosome length is consistent with the current number of tasks. The gene position value represents the agent sequence number assigned to the corresponding task. Based on the population history archive, initialize the population using a multi-strategy fusion method. S2.

2. Divide the initialized population into two subpopulations using Pareto front sorting, and optimize the two objective functions for each subpopulation. and Perform bidirectional individual migration to achieve knowledge sharing among subpopulations; S2.3, Perform improved linear sorting selection and backbone crossover to generate offspring individuals for the two subpopulations respectively; S2.4 Optimize the objective function subpopulation Execution task turnover optimization mutation, on the optimization objective function subpopulation Perform load-balanced optimized mutation to generate offspring individuals; S2.5, for the population Perform adaptive multi-neighborhood local search on the population. Perform a local search based on perplexity pop-ups to generate offspring individuals; S2.6, merge the parent and offspring populations and sequentially perform non-dominated sorting, crowding calculation, elite retention, and update the historical archive. And record archive quality data; S2.7 Repeat steps S2.3 to S2.6 until the maximum number of iterations is reached; S3. Output task allocation scheme: Decode the long-term multi-agent task allocation scheme from the final non-dominated population set.

2. The long-term multi-agent task allocation method based on a multi-objective hierarchical cultural gene algorithm according to claim 1, characterized in that: The specific details of the S1 problem modeling are as follows: The long-running multi-objective, multi-agent task allocation problem is a continuous task allocation process. Tasks do not have a pre-known complete set, but rather arrive randomly over time, forming an infinite sequence of tasks. Agents must adjust the allocation scheme without interrupting system operation. The goal of this problem is to allocate tasks to all agents over time. The task optimization aims to achieve the following two optimization goals: Objective function 1 (minimize task turnaround time): Accumulate time up to the current moment. The turnaround time for all completed tasks is defined as the total time from when a task arrives in the system to when it is fully executed. The calculation formula is as follows: ； in Deadline The set of tasks that have been reached For the task Completion time, For the task Arrival time; Objective function 2 (minimize agent load difference): calculate up to the current time step The degree of load balancing among all agents. Load is defined as the sum of the total number of unexecuted tasks assigned to agents and the total number of tasks currently being executed. The calculation formula is as follows: ； in The total number of agents. Deadline intelligent agent load capacity, This represents the average load across all agents.

3. The long-term multi-agent task allocation method based on a multi-objective hierarchical cultural gene algorithm according to claim 1, characterized in that: The multi-strategy fusion initialization operation for the population in S2 specifically includes the following steps: S4.1 First, according to the logical order of time, different Each task is numbered; S4.2, Use a set of lengths of one-dimensional array Chromosomes, among which Indicates task The allocation of agent serial numbers; S4.3 Execute greedy initialization based on task turnaround time: Using the nearest neighbor heuristic strategy, calculate the spatial distance between the pickup location of each task and the current location of all agents, and assign the task to the agent with the closest spatial distance to form the first group of initialization agents; S4.4 Execute greedy initialization based on agent load balancing: Based on the load balancing objective, iteratively calculate the current cumulative task load of each agent, and assign each task to the agent with the smallest current cumulative load in turn to form the second group of initialization agents; S4.5 Execute migration initialization based on task location: Select the historical non-dominated solutions from the population history archive that are closest to the current task in terms of task pickup and delivery locations, directly inherit the agent allocation relationship of the corresponding task in the historical solution, and construct the third set of initial individuals; S4.6 Perform fragment-based migration initialization: S4.6.1 If the total number of current tasks is less than a preset threshold, the current chromosome is treated as a single task segment; otherwise, the current chromosome is divided into multiple fixed-length non-overlapping task segments, each task segment constituting a local learning unit. S4.6.2 Extract multiple historical task segments with the same length as the current task segment from the optimal solution in the population history archive using a sliding window method; S4.6.

3. The similarity between the current task segment and the historical task segment is quantified using Euclidean distance. The calculation steps are as follows: For each task in the current task segment and the corresponding task in the historical task segment, extract the pickup location of both tasks. coordinate, Coordinates, calculate the sum of squares of the coordinate differences, take the square root of the sum of squares to get the single-task Euclidean distance, sum the single-task Euclidean distances of all corresponding tasks to get the total distance between the two tasks, the smaller the total distance, the higher the similarity. S4.6.4 Select the historical task segment with the smallest total distance (i.e. the highest similarity) and reuse its corresponding agent allocation relationship; for unassigned tasks in the current task segment that are not covered by the historical task segment, randomly assign them to agents without execution conflicts to form the fourth group of initial individuals; S4.7 Perform random initialization: For the remaining individuals to be initialized that were not covered by the above steps, randomly assign values ​​within the feasible range of agent numbers to generate randomly initialized individuals; S4.

8. Merge all the initial individuals generated in steps S4.3 to S4.7 to form the initial population.

4. The long-term multi-agent task allocation method based on a multi-objective hierarchical cultural gene algorithm according to claim 1, characterized in that: The specific steps of the goal-oriented hierarchical population division and preferential migration mechanism in S2 are as follows: S5.1 First, perform a fast non-dominated sort on the initial population to obtain several Pareto fronts. , , , The smaller the frontier index, the better the overall optimization performance of the individual population. S5.2 Initialize the cumulative counter This is used to count the number of Pareto fronts with an odd number of individuals, with an initial value set to 0. S5.3, for each Pareto front (including) Individuals are divided based on minimizing the task turnaround time according to objective function 1: ·like If it is even, extract The optimal objective function 1 Individuals form a subpopulation for task turnaround optimization. The remaining individuals form a subpopulation for load balancing optimization. ; ·like If the number is odd, the cumulative counter will be set to odd. Add 1; if If it is an odd number, extract Center front Individuals are categorized The remaining Individuals are categorized ;like If it is even, extract Center front Individuals are categorized The remaining Individuals are categorized ; S5.4 During the iteration process, a population selection migration operation is triggered every 5 iterations, specifically as follows: S5.4.1 Optimize the task turnover subpopulation All individuals within the population are sorted in ascending order based on the values ​​of objective function 1 (smaller values ​​indicate shorter task turnaround times and better performance); load balancing optimization is applied to the subpopulation. All individuals are sorted in ascending order according to the value of objective function 2 (load balance degree) (the smaller the value, the more balanced the load and the better the performance). S5.4.2 Extraction The last individual in the sorted list, i.e., the individual with the worst performance in objective function 1, is replaced with... The individual ranked first in the sorted list is the individual with the best performance in objective function 2; simultaneously extract... The last individual in the sorted list, i.e., the individual with the worst performance in objective function 2, is replaced with... The individual that ranks first in the sorted list is the individual with the best performance in objective function 1.

5. The long-term multi-agent task allocation method based on a multi-objective hierarchical cultural gene algorithm according to claim 1, characterized in that: The improved linear sorting selection and backbone crossing in S2 are as follows: S6.1, to All individuals are sorted in ascending order according to the value of objective function 1; for All individuals are sorted in ascending order according to the value of objective function 2; S6.2, Let the subpopulation size be... After sorting, assign a weight of 1 to the individual with the worst fitness and assign a weight of 1 to the individual with the best fitness. If the middle individuals are assigned weights according to their ranking position, then the ranking of the [number]th [item] will be [number]. The probability of an individual choosing a position is: ; S6.

3. Based on the above selection probabilities, randomly select several individuals from each subpopulation to form a parent set for crossover operations; S6.4 Compare the chromosomes of the two parent individuals and find all positions where the gene locus values ​​are the same. The genes corresponding to these positions are the backbone genes. The backbone genes represent the consistent task-agent allocation relationship between the two parents and are directly inherited to the offspring individuals. For the differential genes with different gene locus values ​​in the two parent individuals, randomly select the gene locus value of one of the parents to inherit to the offspring individual, forming a complete offspring chromosome.

6. The long-term multi-agent task allocation method based on a multi-objective hierarchical cultural gene algorithm according to claim 1, characterized in that: The specific mutation operations in S2 that optimize task turnaround time and agent load balancing are as follows: (1) Mutation operation for task turnover optimization: First, randomly select one task as the mutation object, calculate the spatial distance between the pickup location of the task and the current location of each agent, and reassign the task to the agent with the closest spatial distance. If there are multiple agents with equal spatial distance, randomly select one of them. (2) Mutation operation for load balancing optimization: First, calculate the current load of all agents. The load is the sum of the tasks assigned to the agents. Select the agent with the largest load as the original agent. Randomly select one task from the task list of the agent as the mutation object. Then select the agent with the smallest load as the target agent. Remove the mutation object task from the task list of the original agent and reassign it to the task list of the target agent.

7. The long-term multi-agent task allocation method based on a multi-objective hierarchical cultural gene algorithm according to claim 1, characterized in that: The optimized local search operation in S2 for task turnaround time and agent load balancing is as follows: (1) Adaptive multi-neighborhood local search operation for task turnaround optimization: S7.1 Initialization of the mutated solution Set the maximum number of local search iterations for the current solution. And four neighborhood operators, as follows: • Intelligent body exchange operator: from the current solution Randomly select a task sequence for the agent, and then randomly select two tasks from the task sequence to exchange, thus obtaining the neighborhood solution. ; • Intelligent body exchange operator: from the current solution Two agents are randomly selected. and The task sequence, in and The task sequence randomly selects one task, swaps two tasks, and obtains the neighborhood solution. ; • Intelligent body shift operator: from the current solution Randomly select a task sequence for the agent, and then randomly select a task from the task sequence. Move this task to any position in the task sequence to obtain the neighborhood solution. ; • Inter-agent shift operator: from the current solution Two agents are randomly selected. and The task sequence, in The task sequence randomly selects a task and moves that task to... At any position in the task sequence, a neighborhood solution is obtained. ; S7.2 Maintaining two neighbor lists and winning neighborhood list , Initialize the data into four sequences of randomly ordered operators, and then apply them sequentially to each individual. The operator in the middle, if the generated neighborhood solution Dominate the current solution ( Better and Better or equal, or Better or equal If it is better, then update. for Add the corresponding operator ;like and If not dominated, then the neighborhood solution is retained with a 50% probability and the operator is added. ;like quilt If the operator is dominant, then discard the operator and retain the one that is dominant. ; S7.3, After exhaustion, there is a 75% probability of... Medium sampling operator, with a 25% probability of randomly sampling from four operators, and refilling ;like If empty, reuse the most recently fully filled one. The sorting of operators, when When filling again, you need to clear the space. Neighborhood operators in; S7.4 If the current iteration count reaches Then Updated to Output the result; otherwise, increment the iteration count by 1, return to step S7.1, and continue the local search process. (2) Local search operation based on confusion pop-up for load balancing optimization: S8.1 Initialization of the mutated solution Set the maximum number of local search iterations for the current solution. Calculate the current solution Individual perplexity ( For population size, For indicator functions, hour (Otherwise, it is 0) S8.2 Calculate the pop-up rate If random number Then: Calculate the number of tasks for each agent. ( Indicates task Assigned to intelligent agents (otherwise it is 0); S8.3 Calculating Gene Perplexity (in , For intelligent agents (Task allocation frequency), filter by task quantity The intelligent agent puts its tasks into a pop-up set. ; S8.4, to For each task, calculate its combined cost with all agents (combined cost = spatial distance cost + load increment cost), reassign it to the agent with the lowest combined cost, and update... ; S8.5, If the current iteration count reaches Then Updated to Output the result; otherwise, increment the iteration count by 1, return to step S8.1, and continue the local search process.

8. The long-term multi-agent task allocation method based on a multi-objective hierarchical cultural gene algorithm according to claim 1, characterized in that: The specific steps of the non-dominated sorting strategy, crowding calculation, and elite retention strategy in S2 are as follows: S9.1, Non-dominated solution sorting: For each individual in the population, calculate the number of dominated individuals and the set of dominated solutions. Individuals with a number of dominated individuals of 0 are assigned to the first Pareto front. For each individual in the front, decrement the number of dominated solutions they dominate by 1. If the number of dominated solutions becomes 0, assign them to the next front. Iterate in this way until all individuals have completed the Pareto level classification. S9.2 Crowding Degree Calculation: Initialize the crowding degree of all individuals to 0. For each objective function, sort the individuals within each Pareto level according to the function value, and set the crowding degree of the first and last boundary individuals after sorting to infinity. For the middle individuals, calculate their crowding degree by the ratio of the difference between the objective function values ​​of their preceding and following individuals to the range of the objective function values. S9.3 Elite Preservation: Merge the parent and offspring populations to obtain a merged population. In order of Pareto level from low to high, add all individuals in the new parent population until a certain level cannot accommodate all individuals. Sort the individuals in that level from crowded to low and select individuals in turn to supplement the new parent population, thus completing elite preservation.

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