A cluster-oriented multi-agent collaborative task planning method

Abstract

The present invention discloses a cluster-oriented multi-agent collaborative task planning method, comprising: constructing a cruise simulation interaction scenario, determining the data input to the reinforcement learning network model, the reinforcement learning network model is used to output the timing of multiple subtasks, the agent type and the number of agents corresponding to each subtask; converting the output data of the reinforcement learning network model into cruise constraints; performing a branch and bound search for the optimal combination scheme based on the cruise constraints, planning the start and end time of each agent's action, and completing the agent subtask planning. The present invention decouples the task allocation combination problem from the task execution optimization problem to achieve fast 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 agent type and number 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.

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 agent-based task planning often considers how robots can smoothly move from a starting point to a destination within a work environment and search for feasible paths. However, the increasing level of societal intelligence presents more complex requirements for robot task planning. For example, in warehousing and logistics environments, the placement and retrieval of certain items requires the coordination of multiple heterogeneous AGVs, while the aerial transport of heavier cargo requires the collaboration of multiple drones. Furthermore, swarm-oriented cruising missions require not only the cooperative relationships between tasks but also the coupling relationships between tasks, with timing constraints, and the need to consider the functional characteristics of heterogeneous robots. This poses challenges to the widespread application of multi-robot systems.

[0003] Compared to simple path planning, multi-agent collaboration introduces a coupled combinatorial optimization problem. When there are a large number of agents and multiple optimization tasks, especially when task constraints are part of the optimization objective, approaches based on Mixed Integer Linear Programming (MILP) or Linear Temporal Logic (LTL) face dimensionality explosion, making it difficult to quickly find an optimal task allocation solution.

[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, offer good interpretability, but require a complete mathematical description of the task, making constraint modeling difficult. Furthermore, as the number of agents increases, the complexity increases to O(n!), resulting in long computational times. Reinforcement learning algorithms are data-driven, offering manageable time complexity during the forward inference phase. However, they are also uninterpretable. Furthermore, assigning specific tasks to agents requires modeling all agents, resulting in a vast action and state space, making model convergence difficult. 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, task formations are generated, task allocation decision-making agents are constructed, and reinforcement learning algorithms are used to generate plans that include the types and numbers of agents required for each subtask; in the task phase, agent task execution plans are generated that include agent task allocation and execution time.

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

[0007] Build a cruise simulation interaction scenario and determine the data input to the reinforcement learning network model. The reinforcement learning network model is used to output the time sequence of multiple subtasks, the type of agent corresponding to each subtask, and the number of agents.

[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. Subtask execution time constraints include execution duration constraints, earliest execution time constraints, and latest execution time constraints.

[0009] Based on the cruise constraints, a branch and bound search is performed to find the optimal combination solution, plan the start and end time of each agent's action, and complete the agent's subtask planning.

[0010] In conjunction with the first aspect, in certain implementations of the first aspect, the input portion 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 being a feature vector consisting of available agent type, number, and cruise distance, and the subtask information being a vector consisting of subtask type and position; the action mask input includes a cruise target mask and an agent type mask;

[0011] The reinforcement learning network model is used to splice 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 conjunction with the first aspect, in certain 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 from the simulation environment, selects the task with the highest priority, and calculates and plans 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 return the current state and reward value;

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

[0019] 6) A set of {state, action, reward} is called 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 for the reinforcement learning network model, trains it 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 cruise 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 conjunction with the first aspect, in certain 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 step of decision making, which represents the subtasks assigned one by one. At each time step t, a decision on the number and type of agents will be made for a subtask. t ;π(a t |s t ) means in state s t Select strategy a under the conditions 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 award estimate;

[0024] The optimization loss is

[0025]

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

[0027] In conjunction with the first aspect, in certain 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, Represents the mathematical expectation of multiple sampling.

[0030] In conjunction with the first aspect, in certain implementations of the first aspect, performing a branch and bound search for an optimal combination solution based on the cruise constraint condition includes:

[0031] The agent subtasks are allocated based on the branch-and-bound method, and a distributed synchronization strategy is designed based on the partial order relationship. Task collaboration is achieved by combining reachability path search with independence analysis. 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 conjunction with the first aspect, in certain implementations of the first aspect, performing a branch and bound search for an optimal combination solution based on the cruise constraint condition includes:

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

[0034] P=(Ω,≤,≠)

[0035] Where Ω is an element in the set, describing the smallest indivisible 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 must be executed before or at the same time as ω2; ≠:Ω×Ω describes the non-parallel relationship. If ω1≠ω2, then ω1 cannot be executed at the same time as ω2.

[0036] Initialize the current optimal solution J * , optimal value T * And store the set Q of 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 * , optimal value T * .

[0038] In conjunction 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; Its meaning is if Then ω 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 all been allocated in ν;

[0039] All solutions generated by node ν The upper bound of is expressed as: in is the distribution 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 existing technology, 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 achieving 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) Based on 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 multi-agent modeling space in reinforcement learning. 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 described in further detail below with reference to the accompanying drawings and specific embodiments.

[0047] Figure 1 This is a flowchart 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 of input: direct input and action mask input. Direct input includes agent information (such as a feature vector consisting of available agent types, quantities, and cruise distances) and subtask information (such as a vector consisting of subtask types and positions). The agent information and subtask information are respectively extracted using a one-dimensional convolutional network. At the same time, in order to meet the requirements of illegal action shielding and, information such as the cruise target mask and the agent type mask are designed as illegal action shielding identifiers to mask the agent features that do not meet the 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 agent information and subtask information into a vector. It then passes the final state information through a deep Gated Recurrent Unit (GRU) network. Because multi-task decision-making requires multiple steps to complete planning, and these steps are interconnected, decisions based on the order of the cruise tasks require consideration of information from previous and subsequent subtasks. Therefore, the core network uses a GRU network, leveraging its memory capacity to retain as much useful historical information as possible. This helps the deep reinforcement learning algorithm discover key elements of this historical information, establish long-term decision-making relevance, and enable the agent to consider the issue more comprehensively at each step.

[0051] The outputs of the reinforcement learning network model include state-value output and agent-action output. The state-value output uses a value network to calculate state value, which assists 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's decision-making and action.

[0052] The agent action output is a launch task group, consisting of three actions, output in sequence: the cruise target, the agent type, and the number of agents. A single output from the GRU unit determines the required agent combination and cruise sequence for a subtask. If a cruise task involves n subtasks, the reinforcement learning network model can sequentially generate the execution order for these n subtasks, with subtasks outputted earlier by the reinforcement learning network model being executed earlier in time.

[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 from the simulation environment, selects the task with the highest priority, and calculates and plans 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 return the current state and reward value;

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

[0059] 6) A set of {state, action, reward} is called 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 trains the model and updates the model to continue training. If the number of samples is insufficient, the algorithm model and the corresponding environment will continue to interact to generate more samples, starting from step 1).

[0060] The reinforcement learning network model uses the overall success probability of the task as the ultimate 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 shown in the following formula:

[0062]

[0063] Where t is the step of decision making, which represents the subtasks assigned one by one. At each time step t, a decision on the number and type of agents will be made for a subtask. t π(a t |s t ) means in state s t Select strategy a under the conditions 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 away from the old probability distribution. The modified optimization loss is

[0065]

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

[0067] Adding the value function's objective and the policy model's entropy to the objective, the complete objective function becomes:

[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, 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, converts them into the formal language description model of linear temporal logic, and constructs a partially ordered set.

[0072] According to the results of the agent's pre-planning 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 the corresponding subtask execution time and time window constraints. For example, an agent can execute move_b02, 05, and 09. 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, move_b02 has an execution time of 12 time units, the earliest execution time is 60 time units, and the latest execution time is 90 time units. Move_b05 has an execution time of 15 time units, the earliest execution time is 90 time units, and the latest execution time is 110 time units. Move_b09 has an execution time of 14 time units, the earliest execution time is 40 time units, and the latest execution time is 80 time units.

[0077] Based on the plan constraints, a dictionary of subtask requirements is generated. For example, suppose our team has four categories: A, B, C, and D, with five agents in each category distributed across different areas. The types and numbers 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] Specifically, agent subtasks are assigned using a branch-and-bound approach, and a distributed synchronization strategy is designed based on partial ordering. Task coordination is achieved by combining reachability path search with independence analysis. Based on the subtask constraints and formal language descriptions, constraints are incorporated into a branch-and-bound (BnB) search. Viable solutions are randomly sampled, and the optimal combination is searched for with the shortest possible time as the optimization goal. The start and end times of each agent's action are then planned, completing 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 a set of elements and a type of partially ordered relation:

[0085] P=(Ω,≤,≠)

[0086] Where Ω is an element in the set, describing the smallest indivisible subtask and its sequence number in a formal language. ≤:Ω×Ω describes the ordering relationship: for tasks ω1,ω2∈Ω, if ω1≤ω2, then ω1 must start executing before or at the same time as ω2. ≠:Ω×Ω describes the non-parallelism relationship: if ω1≠ω2, then ω1 cannot execute simultaneously with ω2. These two relationships fully describe the logical and temporal relationships inherent in the automaton.

[0087] In this application, a node is defined as: ν = (τ1, τ2, ..., τ N ), where τ Nis the sequence of tasks assigned by the node to agent i. In order to ensure that the tasks satisfy the partial order relation 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. Its meaning is if Then ω h Must be in ω l Start before you start;

[0089] ii) For task assignment to the next expanded node of ν, the parent tasks of the assigned task ω (tasks that are required to start execution before ω) must have been assigned in ν. In addition, each node expansion completes the assignment of a task, that is, assigning it to the corresponding agent according to the task requirements.

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

[0091] When the time budget t is not exceeded: select node ν from the 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 * , optimal value T * .

[0092] All solutions generated by node ν The upper bound of can be expressed as: in is the distribution 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 compare it with the current optimal solution. If the upper bound obtained for 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 above in terms of preferred embodiments, 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: Build a cruise simulation interaction scenario and determine the data input to the reinforcement learning network model. The reinforcement learning network model is used to output the time sequence of multiple subtasks, the type of agent corresponding to each subtask, and the number of agents. 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 include execution duration 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 times of each agent's actions, and complete the agent's subtask planning; 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, number, 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 agent information and subtask information into vectors, and then obtain the final state information through the deep gated recurrent unit (GRU) network; 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, 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.

2. 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 from the simulation environment, selects the task with the highest priority, and calculates and plans 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 return the current state and reward value; 5) If all target decisions have not been completed, jump to step 2) to continue. If all target decisions have been completed, proceed to the next step; 6) A set of {state, action, reward} is called 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 for the reinforcement learning network model, trains it 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.

3. The method according to claim 2, characterized in that The reinforcement learning network model uses the overall success probability of the task as the ultimate optimization goal; 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.

4. The method according to claim 3, characterized in that The network parameter update objective function of the reinforcement learning network model is shown in the following formula: Where t is the step of decision making, which represents the subtasks assigned one by one. At each time step t, a decision on the number and type of agents will be made for a subtask. t ;π(a t |s t ) means in state s t Select strategy a under the conditions 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 award estimate; The optimization loss is in clip(r t (θ),1-∈,1+∈) means that r t (θ) is restricted, and this ratio can only be limited to [1-∈, 1+∈].

5. The method according to claim 4, 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, is the target value function at time t; S[π θ ](s t ) represents the strategy π θ The entropy of the state distribution, Represents the mathematical expectation of multiple sampling.

6. The method according to claim 1, characterized in that The branch and bound search for the optimal combination solution according to the cruise constraint conditions includes: The agent subtasks are allocated based on the branch-and-bound method, and a distributed synchronization strategy is designed based on the partial order relationship. Task collaboration is achieved by combining reachability path search with independence analysis. 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.

7. The method according to claim 6, characterized in that The branch and bound search for the optimal combination solution according to the cruise constraint conditions includes: Subtask timing constraints described in a formal language Construct a partially ordered set P, which is composed of a set of elements and a type of partially ordered relation: P=(Ω,≤,≠) Where Ω is an element in the set, describing the smallest indivisible 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 must be executed before or at the same time as ω2; ≠:Ω×Ω describes the non-parallel relationship. If ω1≠ω2, then ω1 cannot be executed at the same time as ω2. Initialize the current optimal solution J * , optimal value T * And store the set Q of nodes to be searched; 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 * , optimal value T * .

8. The method according to claim 7, 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; Its meaning is if Then ω 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 all been allocated in ν; All solutions generated by node ν The upper bound of is expressed as: in is the distribution 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.

Images