CN112465391A - Distributed intelligent factory supply task allocation method based on game theory - Google Patents

Distributed intelligent factory supply task allocation method based on game theory Download PDF

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CN112465391A
CN112465391A CN202011456251.2A CN202011456251A CN112465391A CN 112465391 A CN112465391 A CN 112465391A CN 202011456251 A CN202011456251 A CN 202011456251A CN 112465391 A CN112465391 A CN 112465391A
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董晨
熊乾程
洪祺瑜
陈震亦
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Fuzhou University
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    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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Abstract

The invention relates to a distributed intelligent factory supply task allocation method based on a game theory, which comprises the following steps: calculating and decomposing the current supply tasks to obtain the position of each task and the number information of the required supply robots; establishing a task allocation model of supply problems in an intelligent factory; based on a greedy selection strategy, generating supply robot partitions meeting the requirements of the number of the current tasks; and a Nash balance concept of a game theory is applied to seek a balance solution for task division, so that the distribution quality is further improved. The invention can effectively improve the distribution efficiency and optimize the distribution result.

Description

Distributed intelligent factory supply task allocation method based on game theory
Technical Field
The invention relates to the technical field of intelligent factory supply task allocation, in particular to a distributed intelligent factory supply task allocation method based on a game theory.
Background
As the core of industry 4.0, intelligent factories aim to construct manufacturing-oriented cyber-physical systems, and by integrating cyber-physical systems with physical entities, self-organized production of machines, materials, and products in factories is achieved, multi-robot systems have been widely integrated in smart manufacturing to improve profitability and competitiveness in the past few years due to high speed, precision, and cost effectiveness in repetitive work, and successful application of multi-robot systems in transportation, assembly, and transportation has emerged, how to reasonably divide tasks for multi-robot systems in manufacturing, and balancing efficiency and cost has become a hot point of research.
At present, the research of task allocation methods in intelligent factories is mainly divided into two categories:
the task allocation based on the market method is essentially a process of simulating human auction activities, an algorithm process is just like an auction, auction houses acquire bidding information of all bidders, target objects are sold to the bidders with the highest bidding price, and the final result should ensure the maximum benefits of all bidders and the auction houses as far as possible. Huang et al propose a distributed robot collaborative task allocation mechanism in an intelligent factory based on an auction algorithm, and consider the distance between a heterogeneous robot and a task and the matching degree between the robot capability and the task to perform task division; baroudi et al propose a task allocation algorithm based on dynamic multi-objective auction, design a new utility function by integrating three indexes of task completion quality, load balance and running distance of a robot, and verify the effectiveness of the algorithm in a real scene. However, when the task allocation method based on the market method works, each system operates independently, the strain capacity is poor, most tasks are executed by only a single robot, and resources cannot be utilized to the maximum extent.
The task allocation of the cleaning robot of the power plant to the cleaning work of the solar cell panel is realized based on the task allocation algorithm of the swarm intelligence and the improved ant colony algorithm provided by Qin Xinzhu and the like; lee et al use a multi-objective genetic algorithm NSGA-II to optimize time, energy and cost attributes for emergency management problems in intelligent plants, and allocate resources for emergency management service multi-robot systems. However, these algorithms are slow in convergence speed and face the problem of being prone to fall into local optima.
Although there has been much research on multi-robot systems for various manufacturing stages in an intelligent factory, multi-robot cooperative task allocation in the production material supply stage is still rare, and the flexibility and scalability of the entire automated load transfer robot system remain to be a problem in the face of ever changing demands.
Disclosure of Invention
In view of this, the present invention provides a distributed intelligent factory supply task allocation method based on a game theory, which can effectively improve allocation efficiency and optimize allocation results.
The invention is realized by adopting the following scheme: a distributed intelligent factory supply task allocation method based on game theory specifically comprises the following steps:
calculating and decomposing the current supply tasks to obtain the position of each task and the number information of the required supply robots;
establishing a task allocation model of supply problems in an intelligent factory;
based on a greedy selection strategy, generating supply robot partitions meeting the requirements of the number of the current tasks;
and a Nash balance concept of a game theory is applied to seek a balance solution for task division, so that the distribution quality is further improved.
Further, the establishing of the task allocation model of the supply problem in the intelligent plant specifically includes:
the design utility U and the cost function cost are used for reflecting the execution effect of the supply robot on the assigned tasks and the consumption of the execution tasks on the robot, and the calculation formula is as follows:
Figure BDA0002829330410000031
Figure BDA0002829330410000032
in the formula, xijIndicating robot riFor task tjM represents the number of supply robots, CjIndicating the execution of task tjThe number of supply robots required;
Figure BDA0002829330410000033
respectively represent robots riAnd task tjD represents a distance function for calculating two coordinates, length and width correspond to the length and width of the factory, and epsilon is a constant greater than zero;
according to the designed utility and cost function, a supply task optimization model is established, the cost of the robot executing the corresponding task is minimized while the utility sum is maximized, and the calculation formula is as follows:
Figure BDA0002829330410000034
Figure BDA0002829330410000035
Figure BDA0002829330410000036
xij∈{0，1} i＝1，…，mj＝1，…，n (3)
where m, n represent the number of provisioning robots and tasks, constraint (1) requires that each task be assigned a provisioning robot that satisfies the number requirements, constraint (2) specifies that a provisioning robot intelligently execute a task at the same time, and constraint (3) xijE {0,1} represents robot riFor task tjIf the execution is 1, otherwise it is 0;
defining an in-plant supply task allocation solution that maximizes total revenue pi*The concrete formula is as follows:
π*＝argmax profit(π)；
and satisfies the following conditions: u (Pi)*)＝MAX_UTILITY；
In the formula, the profit (pi) represents the total profit of the supply task allocation, and is expanded into: the prefix (pi) ═ U (pi) -Cost (pi), MAX _ utiity is the maximum UTILITY sum of tasks, expanded as:
Figure BDA0002829330410000041
further, the division of the supply robot for generating the demand of meeting the current quantity of each task based on the greedy selection strategy is specifically as follows:
defining a provisioning robot preference matrix B for performing a task Tm×n＝(bij) The current idle supply robot firstly calculates respective preference of all current executable tasks as a quotation and sends a message to a task point, and the calculation formula is as follows:
Figure BDA0002829330410000042
in the formula, bijShows a supply robot riFor executing task tjPreference between bijThe higher the supply robot riThe more inclined to perform task tj；
The working platform selects the supply robot for executing the task from high to low according to the number of robots required by the task, and the working platform sets S to be { S ═ S1,...,Sj,...Sn,Sn+1Assign a set for the supply robot task, where SjRepresenting a task tjIs assigned to a set of supply robots, j ∈ [1, n ]]，Sn+1A set of robots representing tasks not currently assigned;
confirming the distribution condition of the supply tasks, if one robot is distributed to a plurality of tasks, the supply robot selects the task with the highest preference to execute, updates the task matching set, and returns the preference matrix of the supply robot for defining the execution task T again for the defaults of other tasks until the distribution requirements of the robots in all sets are met to obtain a supply task distribution conditionNew supply robot task division set S ═ { S ═ S1,...,Sj,...Sn,Sn+1And entering the next stage to obtain a balance solution of task division.
Further, the Nash balance concept of the game theory is used for seeking a balance solution for task division, and the specific steps for further improving the distribution quality are as follows:
s41: partitioning a set S ═ S with disjoint supply robot tasks1,...,Sj,...Sn,Sn+1Recording task division of task-supplying robot, set SjSatisfies the following conditions: i Sj|＝Cj，j∈[1，n](ii) a By collections
Figure BDA0002829330410000051
Representing the task execution utility of each of the provisioning robot task allocation sets, wherein
Figure BDA0002829330410000052
Representation set SjFor task tjEffect of execution of (1), PSUMThe overall effect of the current task division is shown, and the calculation formula is as follows:
Figure BDA0002829330410000053
Figure BDA0002829330410000054
step S42: the supply robot exchanges preference information for the current distributed task with other robots in the factory through self broadcasting, and in the communication process, the supply robot executes the supply task tiRobot rpAnd performing the provisioning task tjRobot rqIf present, if present
Figure BDA0002829330410000055
The swapping robot currently allocates tasks, updates the task partition set S, and returns to step S41, repeating this operation until no task partitions are madeAnd changed again until changed.
The invention also provides a distributed intelligent factory provisioning task allocation system based on game theory, which comprises a memory, a processor and computer program instructions stored on the memory and capable of being executed by the processor, and when the computer program instructions are executed by the processor, the method steps as described above can be realized.
The present invention also provides a computer readable storage medium having stored thereon computer program instructions executable by a processor, the computer program instructions when executed by the processor being capable of performing the method steps as described above.
Compared with the prior art, the invention has the following beneficial effects: according to the method, robots with the corresponding quantity requirements are divided for each task according to the fitness between each robot and each task by using a greedy selection strategy, so that the rapid distribution of supply tasks is realized, and the distribution efficiency is improved; and each robot seeks a Nash equilibrium solution for task division through information interaction among individuals, and further optimizes the distribution result.
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FIG. 1 is a schematic flow chart of a method according to an embodiment of the present invention.
FIG. 2 is a pseudo code diagram of an initial task partitioning algorithm according to an embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As shown in fig. 1, the embodiment provides a distributed intelligent factory provisioning task allocation method based on a game theory, which specifically includes the following steps:
calculating and decomposing the current supply tasks to obtain the position of each task and the number information of the required supply robots;
establishing a task allocation model of supply problems in an intelligent factory;
based on a greedy selection strategy, generating supply robot partitions meeting the requirements of the number of the current tasks;
and a Nash balance concept of a game theory is applied to seek a balance solution for task division, so that the distribution quality is further improved.
In this embodiment, the establishing of the task allocation model for the supply problem in the intelligent plant specifically includes:
the design utility U and the cost function cost are used for reflecting the execution effect of the supply robot on the assigned tasks and the consumption of the execution tasks on the robot, and the calculation formula is as follows:
Figure BDA0002829330410000071
Figure BDA0002829330410000072
in the formula, xijIndicating robot riFor task tjM represents the number of supply robots, CjIndicating the execution of task tjThe number of supply robots required;
Figure BDA0002829330410000073
respectively represent robots riAnd task tjD represents a distance function for calculating two coordinates, length and width correspond to the length and width of the factory, and epsilon is a constant greater than zero;
according to the designed utility and cost function, a supply task optimization model is established, the cost of the robot executing the corresponding task is minimized while the utility sum is maximized, and the calculation formula is as follows:
Figure BDA0002829330410000074
Figure BDA0002829330410000075
Figure BDA0002829330410000076
xij∈{0，1} i＝1，…，mj＝1，…，n (3)
where m, n represent the number of provisioning robots and tasks, constraint (1) requires that each task be assigned a provisioning robot that satisfies the number requirements, constraint (2) specifies that a provisioning robot intelligently execute a task at the same time, and constraint (3) xijE {0,1} represents robot riFor task tjIf the execution is 1, otherwise it is 0;
defining an in-plant supply task allocation solution that maximizes total revenue pi*The concrete formula is as follows:
π*＝argmax profit(π)；
and satisfies the following conditions: u (Pi)*)＝MAX_UTILITY；
In the formula, the profit (pi) represents the total profit of the supply task allocation, and is expanded into: the prefix (pi) ═ U (pi) -Cost (pi), MAX _ utiity is the maximum UTILITY sum of tasks, expanded as:
Figure BDA0002829330410000081
in this embodiment, the division of the supply robot that generates the demand for meeting the number of each task based on the greedy selection policy is specifically:
defining a provisioning robot preference matrix B for performing a task Tm×n＝(bij) The current idle supply robot firstly calculates respective preference of all current executable tasks as a quotation and sends a message to a task point, and the calculation formula is as follows:
Figure BDA0002829330410000082
in the formula, bijShows a supply robot riFor executing task tjPreference between bijThe higher the supply robot riThe more inclined to perform task tj；
The working platform selects the supply robot for executing the task from high to low according to the number of robots required by the task, and the working platform sets S to be { S ═ S1,...,Sj,...Sn,Sn+1Assign a set for the supply robot task, where SjRepresenting a task tjIs assigned to a set of supply robots, j ∈ [1, n ]]，Sn+1A set of robots representing tasks not currently assigned;
confirming the distribution situation of the supply tasks, if one robot is distributed to a plurality of tasks, selecting the task with the highest preference by the supply robot to execute, updating the task matching set, returning the supply robot preference matrix for defining the execution task T again for the default of other tasks until the robot distribution requirements of all sets are met, and obtaining a new supply robot task division set S ═ { S ═ S { (S) }1,...,Sj,...Sn,Sn+1And entering the next stage to obtain a balance solution of task division.
In this embodiment, the nash balance concept using the game theory seeks a balance solution for task division, and further improving the distribution quality specifically includes:
s41: partitioning a set S ═ S with disjoint supply robot tasks1,...,Sj,...Sn,Sn+1Recording task division of task-supplying robot, set SjSatisfies the following conditions: i Sj|＝Cj，j∈[1，n](ii) a Use the albumCombination of Chinese herbs
Figure BDA0002829330410000091
Representing the task execution utility of each of the provisioning robot task allocation sets, wherein
Figure BDA0002829330410000092
Representation set SjFor task tjEffect of execution of (1), PSUMThe overall effect of the current task division is shown, and the calculation formula is as follows:
Figure BDA0002829330410000093
Figure BDA0002829330410000094
step S42: the supply robot exchanges preference information for the current distributed task with other robots in the factory through self broadcasting, and in the communication process, the supply robot executes the supply task tiRobot rpAnd performing the provisioning task tjRobot rqIf present, if present
Figure BDA0002829330410000095
The swapping robot currently allocates the task, updates the set of task partitions S, and returns to step S41, repeating this operation until the task partitions are no longer changed.
The present embodiment also provides a distributed smart factory provisioning task allocation system based on game theory, comprising a memory, a processor and computer program instructions stored on the memory and executable by the processor, which when executed by the processor, enable the implementation of the method steps as described above.
The present embodiments also provide a computer readable storage medium having stored thereon computer program instructions executable by a processor, the computer program instructions, when executed by the processor, being capable of performing the method steps as described above.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing is directed to preferred embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow. However, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention.

Claims (6)

1. A distributed intelligent factory supply task allocation method based on game theory is characterized by comprising the following steps:
calculating and decomposing the current supply tasks to obtain the position of each task and the number information of the required supply robots;
establishing a task allocation model of supply problems in an intelligent factory;
based on a greedy selection strategy, generating supply robot partitions meeting the requirements of the number of the current tasks;
and a Nash balance concept of a game theory is applied to seek a balance solution for task division, so that the distribution quality is further improved.
2. The distributed intelligent factory supply task allocation method based on the game theory as claimed in claim 1, wherein the establishing of the intelligent factory supply problem task allocation model specifically comprises:
the design utility U and the cost function cost are used for reflecting the execution effect of the supply robot on the assigned tasks and the consumption of the execution tasks on the robot, and the calculation formula is as follows:
Figure FDA0002829330400000011
Figure FDA0002829330400000012
in the formula, xijIndicating robot riFor task tjM represents the number of supply robots, CjIndicating the execution of task tjThe number of supply robots required;
Figure FDA0002829330400000013
respectively represent robots riAnd task tjD represents a distance function for calculating two coordinates, length and width correspond to the length and width of the factory, and epsilon is a constant greater than zero;
according to the designed utility and cost function, a supply task optimization model is established, the cost of the robot executing the corresponding task is minimized while the utility sum is maximized, and the calculation formula is as follows:
Figure FDA0002829330400000014
Figure FDA0002829330400000021
Figure FDA0002829330400000022
xij∈{0，1} i＝1，…，m j＝1，…，n (3)
where m, n represent the number of provisioning robots and tasks, constraint (1) requires that each task be assigned a provisioning robot that satisfies the number requirements, constraint (2) specifies that a provisioning robot intelligently execute a task at the same time, and constraint (3) xijE {0,1} represents robot riFor task tjIf the execution is 1, otherwise it is 0;
defining an in-plant supply task allocation solution that maximizes total revenue pi*The concrete formula is as follows:
π*＝argmax profit(π)；
and satisfies the following conditions: u (Pi)*)＝MAX_UTILITY；
In the formula, the profit (pi) represents the total profit of the supply task allocation, and is expanded into: the prefix (pi) ═ U (pi) -Cost (pi), MAX _ utiity is the maximum UTILITY sum of tasks, expanded as:
Figure FDA0002829330400000023
3. the distributed intelligent factory supply task allocation method based on the game theory as claimed in claim 1, wherein the division of the supply robot generating the supply robot meeting the requirements of the number of the current tasks based on the greedy selection strategy is specifically as follows:
defining a provisioning robot preference matrix B for performing a task Tm×n＝(bij) The current idle supply robot firstly calculates respective preference of all current executable tasks as a quotation and sends a message to a task point, and the calculation formula is as follows:
Figure FDA0002829330400000031
in the formula, bijShows a supply robot riFor executing task tjPreference between bijThe higher the supply robot riThe more inclined to perform task tj；
The working platform selects the supply robot for executing the task from high to low according to the number of robots required by the task, and the working platform sets S to be { S ═ S1，...，Sj，...Sn，Sn+1Assign a set for the supply robot task, where SjRepresenting a task tjIs assigned to a set of supply robots, j ∈ [1, n ]]，Sn+1A set of robots representing tasks not currently assigned;
confirming the distribution of the supply tasks, and if one robot is distributed to a plurality of tasks, selecting the task with the highest preference to execute by the supply robotUpdating the task matching set, returning the default of other tasks to define the preference matrix of the supply robot for executing the task T again until the robot distribution requirements of all sets are met, and obtaining a new supply robot task division set S ═ S { (S)1，...，Sj，...Sn，Sn+1And entering the next stage to obtain a balance solution of task division.
4. The method for distributing the tasks supplied by the distributed intelligent factory based on the game theory as claimed in claim 1, wherein the Nash equilibrium concept of the game theory is applied to seek a balanced solution for the task division, and the further improvement of the distribution quality specifically comprises:
s41: partitioning a set S ═ S with disjoint supply robot tasks1，...，Sj，...Sn，Sn+1Recording task division of task-supplying robot, set SjSatisfies the following conditions: i Sj|＝Cj，j∈[1，n](ii) a By collections
Figure FDA0002829330400000032
Representing the task execution utility of each of the provisioning robot task allocation sets, wherein
Figure FDA0002829330400000035
Representation set SjFor task tjEffect of execution of (1), PSUMThe overall effect of the current task division is shown, and the calculation formula is as follows:
Figure FDA0002829330400000033
Figure FDA0002829330400000034
step S42: the provisioning robot exchanges preference information for the currently assigned task with other robots within the factory through its own broadcast,during communication, for executing a provisioning task tiRobot rpAnd performing the provisioning task tjRobot rqIf present, if present
Figure FDA0002829330400000041
The swapping robot currently allocates the task, updates the set of task partitions S, and returns to step S41, repeating this operation until the task partitions are no longer changed.
5. A distributed intelligent factory provisioning task allocation system based on game theory, comprising a memory, a processor and computer program instructions stored on the memory and executable by the processor, the computer program instructions when executed by the processor being capable of implementing the method steps of any of claims 1 to 4.
6. A computer-readable storage medium, having stored thereon computer program instructions executable by a processor, the computer program instructions, when executed by the processor, being capable of carrying out the method steps according to any one of claims 1 to 4.
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