Cluster-oriented multi-agent cooperative task planning method

Abstract

The invention discloses a cluster-oriented multi-agent cooperative task planning method, which comprises the steps of constructing a cruise simulation interaction scene, and determining data input to a reinforcement learning network model, the reinforcement learning network model being used for outputting a time sequence of a plurality of sub-tasks, an agent type corresponding to each sub-task and an agent number; converting output data of the reinforcement learning network model into cruise constraint conditions; and performing branch and bound search of an optimal combination scheme according to cruise constraint conditions, planning the action starting time and ending time of each agent, and completing agent sub-task planning. According to the method, a task allocation combination problem and a task execution optimization problem are decoupled, and rapid multi-agent task planning is realized. In the training stage, a task formation is generated, a task allocation decision agent is constructed, and a plan containing the type and number of agents required by each sub-task is generated through a reinforcement learning algorithm; and generating an agent task execution scheme including agent task allocation and execution time in the task.

Description

Technical Field

[0001] The present application relates to the technical field of automatic control and task planning, and in particular to a cluster-oriented multi-agent collaborative task planning method. Background Art

[0002] Traditional intelligent agent task planning problems often consider how robots can smoothly transfer from the starting point to the end point in the working environment and search for feasible paths. However, the increasing level of social intelligence has put forward more complex task requirements for robot task planning. For example, in the warehousing and logistics environment, the placement of certain items requires the cooperation of multiple heterogeneous AGVs, and the air transportation of heavier goods requires the coordination of multiple drones; further, for cluster-oriented cruising tasks, in addition to the cooperative relationship between each task, the coupling relationship between tasks needs to be handled, and there are timing constraints. At the same time, the functional characteristics of heterogeneous robots need to be considered, which brings challenges to the promotion and application of multi-robot systems.

[0003] Compared with simple path planning problems, multi-agent collaboration introduces the coupling of combinatorial optimization problems. When there are a large number of agents and many optimization tasks, especially when task constraints are also part of the optimization goal, methods based on mixed integer linear programming (MILP) or linear temporal logic (LTL) will face the problem of dimensionality explosion, making it difficult to solve a better task allocation solution in a short time.

[0004] Currently, there are two main approaches to task planning: data-driven reinforcement learning and traditional operations research. Traditional operations research methods such as integer programming and linear temporal logic methods have good interpretability, but require a complete mathematical description of the task, and constraint modeling is difficult. As the number of agents increases, the complexity is O(n!), and the computation time is long. Reinforcement learning algorithms are data-driven, and the time complexity is controllable in the forward inference stage, but on the one hand, they are uninterpretable. On the other hand, if specific tasks are assigned to agents, all agents need to be modeled, and the action space and state space will be very large, making it difficult for the model to converge. Summary of the invention

[0005] This application provides a cluster-oriented multi-agent collaborative task planning method, which aims to solve the problem of rapid multi-agent collaborative task allocation, decouple the task allocation combination problem from the task execution optimization problem, and realize rapid multi-agent task planning. In the training phase, a task formation is generated, a task allocation decision-making agent is constructed, and a plan containing the type and number of agents required for each subtask is generated through a reinforcement learning algorithm; in the task, an agent task execution plan containing agent task allocation and execution time is generated.

[0006] In a first aspect, a cluster-oriented multi-agent collaborative task planning method is provided, comprising:

[0007] Construct a cruise simulation interactive scenario and determine the data to be input into the reinforcement learning network model. The reinforcement learning network model is used to output the timing of multiple subtasks, the type of agent and the number of agents corresponding to each subtask.

[0008] Convert the output data of the reinforcement learning network model into cruise constraints, including subtask timing constraints, agent executable subtask constraints, and subtask execution time constraints. The subtask execution time constraints include execution time constraints, earliest execution time constraints, and latest execution time constraints.

[0009] Perform branch and bound search for the optimal combination solution based on the cruise constraints, plan the start and end time of each agent's action, and complete the agent's subtask planning.

[0010] In combination with the first aspect, in some implementations of the first aspect, the input part of the reinforcement learning network model includes direct input and action mask input; the direct input includes agent information and subtask information, the agent information is a feature vector composed of available agent type, quantity, and cruising distance, and the subtask information is a vector composed of subtask type and position; the action mask input includes a cruising target mask and an agent type mask;

[0011] The reinforcement learning network model is used to concatenate the agent information and subtask information into vectors, and then obtain the final state information through the deep gated recurrent unit GRU network.

[0012] In combination with the first aspect, in certain implementations of the first aspect, the output of the reinforcement learning network model includes state value output and agent action output; the state value output uses a value network to calculate the state value to assist in updating the output network; the value network passes the fused feature information through a multi-layer fully connected network MLP and outputs the state value; the agent action output is a launch task group, including three actions output in sequence, namely, the cruise target, the agent type, and the number of agents; the one-step output of the GRU unit determines the agent combination requirement and cruise sequence of a subtask; if the cruise task involves n subtasks, the reinforcement learning network model generates the execution order of the n subtasks in sequence, and the subtask output first by the reinforcement learning network model is earlier in time than the subtask output later.

[0013] In combination with the first aspect, in some implementations of the first aspect, the training process of the reinforcement learning network model includes:

[0014] 1) Constructing task objectives and agent type / state scenarios in the interactive environment;

[0015] 2) The reinforcement learning network model receives state information such as situation information and task information input from the simulation environment, selects the task with the highest priority, and plans and calculates the action;

[0016] 3) The reinforcement learning network model converts the output action into a corresponding plan and executes it, modifying the information in the environment;

[0017] 4) Set the next task as the current goal, and then return the current state and reward value;

[0018] 5) If all target decisions have not been made, jump to step 2) to continue. If all target decisions have been made, proceed to the next step;

[0019] 6) A set of {state, action, reward} is a sample. The samples generated in one round are stored in the algorithm sample pool. The algorithm sample pool uses all samples that meet the requirements as training samples of the reinforcement learning network model, trains them through the deep reinforcement learning algorithm, and updates the model to continue training; if the samples are insufficient, the algorithm model and the corresponding environment will continue to interact from step 1) to generate more samples.

[0020] In combination with the first aspect, in certain implementations of the first aspect, the reinforcement learning network model takes the overall success probability of the task as the final optimization goal; if the intelligent agent completes the cruising task through decision-making, the reward is 1; if all intelligent agents are used but still cannot complete the task, the reward is -1; if all intelligent agents are not fully used but the task is not completed, the reward is -1.

[0021] In combination with the first aspect, in some implementations of the first aspect, the network parameter update objective function of the reinforcement learning network model is as follows:

[0022]

[0023] Where t is the decision step, representing the subtasks assigned one by one. At each time step t, a decision a is made on the number and type of agents assigned to a subtask. t ;π(a t |s t ) means in state s t Choose strategy a under the condition t The probability that π will be updated with the number of iterations, π old Represents the strategy function of the previous iteration; Represents the state (s t ,a t ) under the award estimate;

[0024] The optimization loss is

[0025]

[0026] in clip(r t (θ),1-∈,1+∈) means that r t (θ) is restricted, this ratio can only be restricted to [1-∈, 1+∈].

[0027] In conjunction with the first aspect, in some implementations of the first aspect, the objective function of the reinforcement learning network model is as follows:

[0028]

[0029] in: Where V θ (s t ) is state s t The value function estimation under the condition, V t targ is the target value function at time t; S[π θ ](s t ) represents the strategy π θ The entropy of the state distribution is Represents the mathematical expectation of multiple sampling.

[0030] In combination with the first aspect, in some implementations of the first aspect, performing branch and bound search for an optimal combination solution according to the cruise constraint condition includes:

[0031] Based on the branch and bound method, intelligent agent subtasks are allocated, and a distributed synchronization strategy is designed based on the partial order relationship. The reachability path search and independence analysis are combined to complete task collaboration. According to the subtask constraints and formal language description, the constraints are added to the branch and bound search, and feasible solutions are randomly sampled. The optimal combination solution is searched with the shortest time as the optimization goal.

[0032] In combination with the first aspect, in some implementations of the first aspect, performing branch and bound search for an optimal combination solution according to the cruise constraint condition includes:

[0033] Subtask timing constraints described in formal language Construct a partially ordered set P, which is composed of an element set and a type of partially ordered relation:

[0034] P=(Ω,≤,≠)

[0035] Where Ω is an element in the set, describing the indivisible minimum subtask and its sequence number in the formal language; ≤:Ω×Ω describes the order relationship. For tasks ω1, ω2∈Ω, if ω1≤ω2, then ω1 needs to be executed before ω2 or at the same time as it; ≠:Ω×Ω describes the non-parallel relationship. If ω1≠ω2, then ω1 is not executed at the same time as ω2.

[0036] Initialize the current optimal solution J * , optimal value T * And a set Q storing nodes to be searched;

[0037] When the time budget is not exceeded: select node v from set Q according to the branching method, calculate the upper bound of node v, and update the optimal solution J * and the optimal value T * , expand node v and add child nodes to sequence Q; when the time budget is exceeded: return the optimal solution J * , the optimal value T * .

[0038] In combination with the first aspect, in some implementations of the first aspect, a node is defined as: ν = (τ1, τ2, ..., τ N ), where τ N is the task sequence assigned by the node to agent i, satisfying: For the task assignment of the current node ν, if After allocating task ω1, ω2 is allocated; The meaning is if Then h Must be in ω l Start before starting; for the task allocation of the next expansion node of ν, the parent tasks of the assigned task ω have been allocated in ν;

[0039] All solutions generated by node ν The upper bound of is expressed as: in is the allocation of all subtasks, and its structure is the same as ν. is the time required to complete all subtasks, Record the start time of each subtask; the upper bound algorithm obtains a complete feasible solution through a depth-first search method, and compares it with the current optimal solution. If the upper bound obtained by the current node ν is better than the current optimal solution, the upper bound and the optimal solution are updated.

[0040] Compared with the prior art, the solution provided by this application includes at least the following beneficial technical effects:

[0041] (1) The present invention decouples the problem of combining task requirements from the problem of planning specific agent behaviors, thus realizing agent behavior planning under low-constraint conditions;

[0042] (2) The present invention solves the problem of task requirement analysis through reinforcement learning algorithms and uses machine learning data-driven methods to solve the problem of high complexity of combinatorial optimization problems;

[0043] (3) According to the task requirement constraints output by reinforcement learning, the present invention uses formal method modeling to solve the specific agent task allocation and planning, thereby resolving the problem of large reinforcement learning multi-agent modeling space. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is the algorithm flow chart.

[0045] Figure 2 Schematic diagram of the reinforcement learning network model structure. DETAILED DESCRIPTION

[0046] The present application is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] Figure 1 This is a flow chart of a cluster-oriented multi-agent collaborative task planning method provided by the present invention. The specific steps are as follows.

[0048] Step 1: Build a cruise simulation interaction scenario and determine the data to be input into the reinforcement learning network model. The reinforcement learning network model is used to output the timing of multiple subtasks, the type of intelligent agent corresponding to each subtask, and the number of intelligent agents.

[0049] The reinforcement learning network model structure is as follows Figure 2 As shown. The input part of the feature input network model includes two types: direct input and action mask input. Direct input includes agent information (such as feature vectors composed of available agent types, quantities, and cruise distances) and subtask information (such as vectors composed of subtask types and positions). Agent information and subtask information are respectively extracted using a 1D convolutional network. At the same time, in order to meet the requirements of illegal action shielding and, information such as cruise target mask and agent type mask are designed as illegal action shielding identifiers to mask agent features that do not meet task constraints and narrow the search space. The illegal action shielding identifier serves as the input of the agent action output network.

[0050] The core network of the reinforcement learning network model first concatenates the agent information and subtask information into a vector, and then obtains the final state information through a deep gated recurrent unit (GRU) network. Since planning can only be completed through multiple steps in multi-task decision-making, and there is a connection between the multiple steps, when making decisions according to the order of cruise tasks, it is necessary to consider the previous and subsequent subtask information. Therefore, the core network uses the GRU network, using its memory function to retain as much useful historical information as possible, helping the deep reinforcement learning algorithm to mine the key elements of historical information, establish the relevance of long-term decisions, and enable the agent to consider the problem more comprehensively in each step of decision-making.

[0051] The output of the reinforcement learning network model includes state value output and agent action output. The state value output uses a value network to calculate the state value, which is used to assist in updating the output network. The value network passes the fused feature information through a multi-layer fully connected network (MLP) and outputs the state value. By sharing a deep GRU network with the output network, the value network also considers global information when calculating the value, thereby improving the accuracy of value estimation. The state value is used to guide the agent to make decision actions.

[0052] The agent action output is a launch task group, including three actions output in sequence, namely cruise target, agent type, and agent quantity. One step of the GRU unit output can determine the agent combination requirements and cruise sequence of a subtask. If the cruise task involves n subtasks, the reinforcement learning network model can generate the execution order of the n subtasks in sequence, and the subtask output first by the reinforcement learning network model is earlier in time than the subtask output later.

[0053] The training process of the reinforcement learning network model is as follows.

[0054] 1) Constructing task objectives and agent type / state scenarios in the interactive environment;

[0055] 2) The reinforcement learning network model receives state information such as situation information and task information input from the simulation environment, selects the task with the highest priority, and plans and calculates the action;

[0056] 3) The reinforcement learning network model converts the output action into a corresponding plan and executes it, modifying the information in the environment;

[0057] 4) Set the next task as the current goal, and then return the current state and reward value;

[0058] 5) If all target decisions have not been made, jump to step 2) to continue. If all target decisions have been made, proceed to the next step;

[0059] 6) A set of {state, action, reward} is a sample. The generated samples are stored in the algorithm sample pool. The algorithm sample pool uses all samples that meet the requirements as training samples for the reinforcement learning network model. The deep reinforcement learning algorithm is used for training, and the model is updated to continue training. If the samples are insufficient, the algorithm model and the corresponding environment will continue to interact from step 1 to generate more samples.

[0060] The reinforcement learning network model takes the overall success probability of the task as the final optimization goal. The specific rewards are as follows: if the agent completes the cruise task through decision-making, the reward is 1; if all agents are used but still cannot complete the task, the reward is -1; if all agents are not fully used but the task is not completed, the reward is -1.

[0061] The optimization process is solved using the PPO algorithm. The network parameter update objective function is as follows:

[0062]

[0063] Where t is the decision step, representing the subtasks assigned one by one. At each time step t, a decision a is made on the number and type of agents assigned to a subtask. t π(a t |s t ) means in state s t Choose strategy a under the condition t The probability that π will be updated with the number of iterations, π old Represents the policy function of the previous iteration. Represents the state (s t ,a t ) under the reward estimate.

[0064] Let the variable It represents the ratio of the new and old strategy probabilities. The constraint condition requires that the new strategy probability distribution cannot be too far from the old probability distribution, and the modified optimization loss is

[0065]

[0066] Where clip(r t (θ),1-∈,1+∈) means that r t (θ) is restricted, this ratio can only be restricted to [1-∈, 1+∈].

[0067] Add the target of the value function and the entropy of the policy model to the target, and the complete objective function becomes the following:

[0068]

[0069] in: Where V θ (s t ) is state s t The value function estimation under the condition, V t targ is the target value function at time t. S[π θ ](s t ) represents the strategy π θ The entropy of the state distribution is Represents the mathematical expectation of multiple sampling.

[0070] Step 2: Convert the output data of the reinforcement learning network model into cruise constraints, including subtask timing constraints, agent executable subtask constraints, and subtask execution time constraints (subtask execution time constraints may specifically include execution duration constraints, earliest execution time constraints, and latest execution time constraints).

[0071] That is to say, the agent planning based on linear temporal logic takes the number and type of agents required for each subtask as constraints, transforms them into the formal language description model of linear temporal logic, and constructs a partially ordered set.

[0072] According to the planning results of the agent plan, the logical relationship between subtasks is formally modeled. For example, there are 10 subtask goals, among which the 5 subtasks move_b06-10 need to be executed first, and then move_b01-05 can be executed. The subtask timing constraints It can be described in formal language as follows:

[0073]

[0074] A capability dictionary is maintained for each agent, which contains executable subtasks and corresponding subtask execution time and time window constraints. For example, an agent can execute move_b02, 05, and 09, and its dictionary information is as follows:

[0075] {'move_b02':[12,[60,90]],'move_b05':[15,[90,110]],'move_b09':[14,[40,80]]}

[0076] Among them, the execution time of move_b02 is 12 time units, the earliest execution time is 60 time units, and the latest execution time is 90 time units. The execution time of move_b05 is 15 time units, the earliest execution time is 90 time units, and the latest execution time is 110 time units. The execution time of move_b09 is 14 time units, the earliest execution time is 40 time units, and the latest execution time is 80 time units.

[0077] According to the plan constraints, a dictionary of subtask requirements is generated. For example, it is assumed that our side has four categories: A, B, C, and D, and each category has 5 agents distributed in different areas. The types and quantities of agents required for the subtasks are shown in Table 1.

[0078] Table 1

[0079]

[0080]

[0081] Step 3: Perform branch and bound search for the optimal combination solution based on the cruise constraints, plan the start and end time of each agent's action, and complete the agent subtask planning.

[0082] In other words, the agent subtasks are allocated based on the branch and bound method, and the distributed synchronization strategy is designed based on the partial order relationship; the reachability path search and independence analysis are combined to complete the task collaboration. According to the subtask constraints and formal language description, the constraints are added to the branch and bound (Branch and Bound, BnB) search, and the feasible solutions are randomly sampled. The optimal combination solution is searched with the shortest time as the optimization goal, and the start and end time of each agent action are planned to complete the agent subtask planning.

[0083] The input of the branch-and-bound task allocation algorithm is a partially ordered set P and a search time budget t. The output of the branch-and-bound task allocation algorithm is the current optimal task allocation solution J and the task execution time T. The execution order of the branch-and-bound task allocation algorithm is as follows:

[0084] First, according to the subtask timing constraints described in formal language Construct a partially ordered set P, which is composed of an element set and a type of partially ordered relation:

[0085] P=(Ω,≤,≠)

[0086] Among them, Ω is an element in the set, which describes the indivisible minimum subtask and its sequence number in the formal language; ≤:Ω×Ω describes the order relationship. For tasks ω1, ω2∈Ω, if ω1≤ω2, then ω1 needs to be executed before ω2 or at the same time as it; ≠:Ω×Ω describes the non-parallel relationship. If ω1≠ω2, then ω1 cannot be executed at the same time as ω2. These two relationships can fully describe the logical relationship and temporal relationship contained in the automaton.

[0087] In this application, a node is defined as: ν = (τ1, τ2, ..., τ N ), where τ Nis the task sequence assigned by the node to agent i. In order to ensure that the tasks satisfy the partial order relationship during the assignment process, the following two regulations are formulated:

[0088] i) For the task allocation of the current node ν, if Then ω2 will be assigned only after task ω1 is assigned. The meaning is if Then h Must be in ω l Start before you start;

[0089] ii) For the task allocation of the next expansion node of ν, the parent tasks of the assigned task ω (the tasks that are required to be executed before ω) must have been allocated in ν. In addition, each expansion of a node will complete the allocation of a task, that is, it will be allocated to the corresponding agent according to the task requirements.

[0090] Initialize the current optimal solution J * , optimal value T * And a set Q of nodes to be searched is stored.

[0091] When the time budget t is not exceeded: select node ν from set Q according to the branching method, calculate the upper bound of node ν, and update the optimal solution J * and the optimal value T * , expand node v and add child nodes to sequence Q; when time budget t is exceeded: return the optimal solution J * , the optimal value T * .

[0092] All solutions generated by node ν The upper bound of can be expressed as: in is the allocation of all subtasks, and its structure is the same as ν. is the time required to complete all subtasks, The start time of each subtask is recorded. The upper bound algorithm will quickly obtain a complete feasible solution through a depth-first search method, and will compare it with the current optimal solution. If the upper bound obtained by the current node ν is better than the current optimal solution, the upper bound and the optimal solution will be updated.

[0093] Although the present invention is disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be based on the scope defined by the claims of the present invention.

Claims

1. A cluster-oriented multi-agent collaborative task planning method, characterized in that: include: Construct a cruise simulation interactive scenario and determine the data to be input into the reinforcement learning network model. The reinforcement learning network model is used to output the timing of multiple subtasks, the type of agent and the number of agents corresponding to each subtask. Convert the output data of the reinforcement learning network model into cruise constraints, including subtask timing constraints, agent executable subtask constraints, and subtask execution time constraints. The subtask execution time constraints include execution time constraints, earliest execution time constraints, and latest execution time constraints. Perform branch and bound search for the optimal combination solution based on the cruise constraints, plan the start and end time of each agent's action, and complete the agent's subtask planning.

2. The method according to claim 1, characterized in that The input part of the reinforcement learning network model includes direct input and action mask input; direct input includes agent information and subtask information. Agent information is a feature vector composed of available agent type, quantity, and cruising distance, and subtask information is a vector composed of subtask type and position; action mask input includes cruising target mask and agent type mask; The reinforcement learning network model is used to concatenate the agent information and subtask information into vectors, and then obtain the final state information through the deep gated recurrent unit GRU network.

3. The method according to claim 2, characterized in that The output of the reinforcement learning network model includes state value output and agent action output; the state value output uses a value network to calculate the state value to assist in updating the output network; the value network outputs the state value after passing the fused feature information through a multi-layer fully connected network MLP; the agent action output is a launch task group, including three actions output in sequence, namely the cruise target, agent type, and number of agents; the one-step output of the GRU unit determines the agent combination requirement and cruise sequence of a subtask; if the cruise task involves n subtasks, the reinforcement learning network model generates the execution order of the n subtasks in sequence, and the subtask output first by the reinforcement learning network model is earlier in time than the subtask output later.

4. The method according to claim 1, characterized in that: The training process of the reinforcement learning network model includes: 1) Constructing task objectives and agent type / state scenarios in the interactive environment; 2) The reinforcement learning network model receives state information such as situation information and task information input from the simulation environment, selects the task with the highest priority, and plans and calculates the action; 3) The reinforcement learning network model converts the output action into a corresponding plan and executes it, modifying the information in the environment; 4) Set the next task as the current goal, and then return the current state and reward value; 5) If all target decisions have not been made, jump to step 2) to continue. If all target decisions have been made, proceed to the next step; 6) A set of {state, action, reward} is a sample. The samples generated in one round are stored in the algorithm sample pool. The algorithm sample pool uses all samples that meet the requirements as training samples of the reinforcement learning network model, trains them through the deep reinforcement learning algorithm, and updates the model to continue training; if the samples are insufficient, the algorithm model and the corresponding environment will continue to interact from step 1 to generate more samples.

5. The method according to claim 4, characterized in that The reinforcement learning network model takes the overall success probability of the task as the final optimization goal; if the agent completes the cruising task through decision-making, the reward is 1; if all agents are used but still cannot complete the task, the reward is -1; if all agents are not fully used but the task is not completed, the reward is -1.

6. The method according to claim 5, characterized in that The network parameter update objective function of the reinforcement learning network model is as follows: Where t is the decision step, representing the subtasks assigned one by one. At each time step t, a decision a is made on the number and type of agents assigned to a subtask. t ;π(a t |s t ) means in state s t Choose strategy a under the condition t The probability that π will be updated with the number of iterations, π old Represents the strategy function of the previous iteration; Represents the state (s t ,a t ) under the award estimate; The optimization loss is in clip(r t (θ),1-∈,1+∈) means that r t (θ) is restricted, this ratio can only be restricted to [1-∈, 1+∈].

7. The method according to claim 6, characterized in that The objective function of the reinforcement learning network model is as follows: in: Where V θ (s t ) is state s t The value function estimation under the condition, V t targ is the target value function at time t; S[π θ ](s t ) represents the strategy π θ The entropy of the state distribution is Represents the mathematical expectation of multiple sampling.

8. The method according to claim 1, characterized in that: The branch and bound search for the optimal combination solution according to the cruise constraint condition includes: Based on the branch and bound method, intelligent agent subtasks are allocated, and a distributed synchronization strategy is designed based on the partial order relationship. The reachability path search and independence analysis are combined to complete task collaboration. According to the subtask constraints and formal language description, the constraints are added to the branch and bound search, and feasible solutions are randomly sampled. The optimal combination solution is searched with the shortest time as the optimization goal.

9. The method according to claim 8, characterized in that The branch and bound search for the optimal combination solution according to the cruise constraint condition includes: Subtask timing constraints described in formal language Construct a partially ordered set P, which is composed of an element set and a type of partially ordered relation: P=(Ω,≤,≠) Where Ω is an element in the set, describing the indivisible minimum subtask and its sequence number in the formal language; ≤:Ω×Ω describes the order relationship. For tasks ω1, ω2∈Ω, if ω1≤ω2, then ω1 needs to be executed before ω2 or at the same time as it; ≠:Ω×Ω describes the non-parallel relationship. If ω1≠ω2, then ω1 is not executed at the same time as ω2. Initialize the current optimal solution J * , optimal value T * And a set Q storing nodes to be searched; When the time budget is not exceeded: select node ν from set Q according to the branching method, calculate the upper bound of node ν, and update the optimal solution J * and the optimal value T * , expand node v and add child nodes to sequence Q; when the time budget is exceeded: return the optimal solution J * , the optimal value T * .

10. The method according to claim 9, characterized in that The node is defined as: ν=(τ1,τ2,…,τ N ), where τ N is the task sequence assigned by the node to agent i, satisfying: For the task assignment of the current node ν, if After allocating task ω1, ω2 is allocated; The meaning is if Then h Must be in ω l Start before starting; for the task allocation of the next expansion node of ν, the parent tasks of the assigned task ω have been allocated in ν; All solutions generated by node ν The upper bound of is expressed as: in is the allocation of all subtasks, and its structure is the same as ν. is the time required to complete all subtasks, Record the start time of each subtask; the upper bound algorithm obtains a complete feasible solution through a depth-first search method, and compares it with the current optimal solution. If the upper bound obtained by the current node ν is better than the current optimal solution, the upper bound and the optimal solution are updated.

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