Task allocation method for heterogeneous multi-agent system considering decision preference information

Abstract

The application discloses a kind of heterogeneous multi-agent system task allocation methods considering decision preference information, the method includes defining heterogeneous multi-agent system and the system variable of target attack;Task allocation model is constructed according to system variable;And task allocation model includes multi-source objective function matrix and corresponding constraint condition set;Objective function grouping mechanism based on decision preference information is constructed, and the objective function corresponding to the multi-source objective function matrix in task allocation model is grouped to obtain the task allocation model after grouping;Based on the constructed task allocation model, strategy is solved, and the task allocation result of heterogeneous multi-agent system to the target attack is obtained after grouping the task allocation model is solved.This application solves the problem that the existing task allocation model does not fully consider the decision preference, the decision preference information such as task stage change, and the model lacks pertinence;When solving high-dimensional multi-objective optimization problem, the algorithm has high computational complexity and low running efficiency.

Description

Technical Field

[0001] This invention relates to the field of cooperative control and optimization technology for multi-agent systems, and in particular to a task allocation method for heterogeneous multi-agent systems that considers decision preference information. Background Technology

[0002] Multi-agent systems, as a new type of intelligent equipment platform, are characterized by flexibility, high efficiency, and low cost, and are widely used in logistics distribution, environmental monitoring, emergency rescue, and other fields. Multi-agent systems (such as aerial robots, ground robots, and surface robots) have become an important means of performing tasks, transportation, and collaborative processing in modern complex missions. Task allocation is one of the key issues in the collaborative work of multi-agent systems. Its essence is to rationally allocate tasks to each agent under constraints to maximize overall efficiency, which belongs to a complex multi-objective optimization problem.

[0003] Existing task allocation methods mainly include mixed-integer linear programming models, multiple traveling salesman models, and cooperative task allocation models. Among these methods, multi-objective genetic algorithms are widely used due to their strong scalability and low computational complexity. However, existing technologies have the following shortcomings: 1. The task allocation model does not fully consider decision-making preferences, changes in task stages, and other decision preference information. The model lacks specificity and does not meet the needs of actual applications. 2. When solving high-dimensional multi-objective optimization problems, the algorithm has high computational complexity, low running efficiency, poor convergence, and a large amount of redundancy in the solution set, which increases the decision-making burden. Summary of the Invention

[0004] This invention provides a task allocation method for heterogeneous multi-agent systems that considers decision preference information, in order to overcome the above-mentioned technical problems.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows: A method for task allocation in a heterogeneous multi-agent system that considers decision preference information includes the following steps: S1: Defines the system variables for the heterogeneous multi-agent system and the target; Furthermore, the system variables include at least the set of heterogeneous multi-agent systems, the set of target individuals, the number of heterogeneous multi-agent system types, the number of multi-agent systems of each type, the value vector of each type of multi-agent system, the number of weapons carried by each type of multi-agent system, the value vector of the weapons carried by each type of multi-agent system, the value vector of the target individuals, the allocation matrix for allocating targets to heterogeneous multi-agent systems, and the number of a certain type of multi-agent system required to attack any target; S2: Construct a task allocation model based on the system variables; Furthermore, the task allocation model includes a multi-source objective function matrix and corresponding constraint set for task allocation models that maximize target value gain, minimize flight distance, minimize task completion time, minimize threat level, minimize resource consumption, and minimize platform type consumption. S3: Construct a target function grouping mechanism based on decision preference information, group the target functions corresponding to the multi-source target function matrix in the task allocation model, and obtain the grouped task allocation model; S4: Based on the constructed task allocation model solution strategy, solve the grouped task allocation model and obtain the task allocation results of the heterogeneous multi-agent system for the strike target.

[0006] Furthermore, the multi-source objective function matrix mentioned in S2 includes the objective function for maximizing target value gain, the objective function for minimizing flight distance, the objective function for minimizing mission completion time, the objective function for minimizing threat level, the objective function for minimizing weapon resource consumption, and the objective function for minimizing the consumption of multiple intelligent agent system types. And the objective function that maximizes the target value return for:

[0007] In the formula: express Multi-agent systems for attacking targets Its destructive power; Indicates attack on the The goal requires The number of multi-agent systems; Indicates the first The value vector of each target individual; Indicates the number of heterogeneous multi-agent system types; Indicates the number of targets; The objective function for minimizing the range of motion for:

[0008] In the formula: express Multi-agent systems for attacking targets Total voyage; The objective function for minimizing task completion time for:

[0009] In the formula: Indicates the number of heterogeneous multi-agent systems; express The multi-agent system completes the strike on the target. Total time of the attack; The objective function that minimizes the degree of threat for:

[0010] In the formula: express Multi-agent system attack targets Risks; express Value vector of multi-agent systems; The objective function of minimizing weapon resource consumption for:

[0011] In the formula: express The number of weapons carried by a multi-agent system; express The value vector of a multi-agent system carrying weapons; The objective function of minimizing the consumption of the multi-agent system type for:

[0012] In the formula: Indicates the target of attack The number of types of multi-agent systems required.

[0013] Furthermore, the set of constraints described in S2 includes constraints on the number of multi-agent systems, constraints on the number of systems allocated, and constraints on the travel distance; The number constraint of the multi-agent system for: ; In the formula: express The number of multi-agent systems; The system allocation quantity constraint for:

[0014] In the formula: Indicate the target The upper limit on the number of agents allocated to a multi-agent system; The sailing distance constraint for:

[0015]

[0016] In the formula: express The risk of multi-agent systems attacking targets; Indicates the task radius; This represents the distance from the target point to the starting point of the last task in a multi-agent system. express The maximum range of a multi-agent system.

[0017] Furthermore, the construction method of the objective function grouping mechanism based on decision preference information in S3 specifically includes the following steps: S31: Define the state set and ; This represents important weight information for the objective function; This represents the unimportant weight information of the objective function; and a decision set is given. and ; They represent the objective function respectively. Perform PSO, BND, and NEG decisions. ; Definition Note They respectively represent when the objective function Weight information is When, implement Risk-value in three decision-making scenarios; definition They respectively represent when the objective function Weight information is When, implement Risk-value in three decision-making scenarios; Note Describe the objective function Through equivalence classes The depiction belongs to the state The conditional probability; denoted as Describe the objective function Through equivalence classes The depiction belongs to the state The conditional probability, and ; S32: Obtain implementation based on S31 The expected costs corresponding to the three decisions are:

[0018]

[0019]

[0020] In the formula: Each represents implementation The expected costs of the three decisions; S33: Based on the Bayesian decision minimum risk criterion, three decision rules containing threshold forms are obtained according to the expected cost: P: If ,but ;Right now ; B: If ,but ;Right now

[0021] N: If ,but ;Right now

[0022] In the formula: Indicates the design threshold and ;

[0023] S34: Group the objective functions corresponding to the multi-source objective function matrix in the task allocation model according to the three decision rules, and obtain the grouped task allocation model. And labeled as group P, group B and group N respectively, and satisfying ; These represent the number of objective functions in each group; This represents the total number of objective functions in the task allocation model.

[0024] Furthermore, the specific solution strategy for the task allocation model constructed in S4 is as follows: Choose an appropriate solution strategy based on the number of objective functions in the grouped task allocation model: That is, delete the groups with zero objective function values ​​as redundant groups; For groups with a single objective function, a single-objective optimization algorithm is used to solve the task allocation model after the grouping; and the single-objective optimization method includes, but is not limited to, the GA genetic algorithm. For groups with more than one objective function, the improved NSGA-Ⅲ algorithm is used to solve the task allocation model after the grouping.

[0025] Furthermore, the improved NSGA-Ⅲ algorithm is specifically as follows: S41: Define the combination of heterogeneous multi-agent systems corresponding to tasks assigned to any target as a population individual to obtain the initial population. ; S42: For the initial population The subpopulation is generated using random selection, simulated binary crossover, and polynomial mutation operations. And the initial population With the subpopulation The population size is and the initial population With subpopulation Merge into a population of size population ; S43: A non-dominated sorting method based on Pareto dominance, which sorts the population Divided into several different non-dominated layers And from the non-dominated layer Start by adding all individuals from each non-dominated layer to a new population that is initially empty, and define the target population size of the new population as N. If we add the first After the population of individuals in the non-dominated layer reaches a size of N, the new population is then confirmed as the population. The next generation of population ; If we add the first After removing individuals from the non-dominated layer, if the new population size is greater than N, then retain the previous individuals. After the population of individuals in the non-dominated layer is reached, continue with steps S44 to S48 to proceed from the first... From the individuals in the non-dominated layer of the population, select the remaining individuals that make the new population size reach N, and then obtain the population. The next generation of population ; S44: Based on the orthogonal boundary crossing algorithm, on a pre-defined regularized M-dimensional hyperplane, according to the... Each non-dominated layer of the population generates several reference points evenly. S45: Use a scalarization function to obtain the target value corresponding to each individual in the population, at the... The projection values ​​along the target direction are obtained; and the individual values ​​of various populations are obtained in the 1st dimension. The maximum projection value along the target direction is determined by taking the population individual corresponding to the minimum value among the maximum projection values ​​as the first... The extreme point in the target direction is expressed as:

[0026] In the formula: Indicates extreme points; Represents the population individuals after translation transformation The corresponding number Dimensional objective function value; Represents the weight vector; S46: Obtained from S45 The extreme points are used to obtain the normalized individual target value:

[0027] In the formula: Represents individuals in a population The corresponding number Dimensional objective function value; Represents the normalized population individuals The corresponding number Dimensional objective function value; ; This indicates a normalization operation; Represents the intercept vector; S47: Obtain the normalized target space based on S46, and within the normalized target space, determine the distance from individual populations. Recent reference line The corresponding reference point is defined as the point relative to the population individual. The associated reference points; and the reference line is the straight line connecting the ideal point set in the M-dimensional hyperplane with each reference point. S48: Based on the small-scale mirror preservation operation, according to the associated reference point, ... Individuals in the non-dominated layer perform population selection until the new population reaches the target population size N; S49: The next generation population As a Pareto non-dominated solution set, and based on the non-dominated solution set fusion rule, the final non-dominated solution set is obtained; and the final non-dominated solution set is the final combination result of the heterogeneous multi-agent system assigned to the task corresponding to the strike target.

[0028] Furthermore, the method for constructing the non-dominated solution set fusion rule described in S49 is as follows: S491: Let For the objective function set and ;Will Defined as the solution space of the objective function set; Defined as the Pareto non-dominated solution set of the objective function set; Divided into Group … ; … If each of these is taken as the corresponding Pareto non-dominated solution set, then the set... There exists a subset of nondominated solutions to the Pareto nondominated solution set. ; S492: The decision preference information of each objective function group in the grouped task allocation model is ranked as follows: Then for two solutions on the Pareto non-dominated solution set and judge Is it superior to The specific judgment method is as follows: like Then confirm Superior Furthermore, no further comparisons will be made sequentially. … and … The relationship between them; like and Then confirm Superior Furthermore, no further comparisons will be made sequentially. … and … The relationship between them; And so on, until... … Then confirm Superior ; S493: Based on S491 to S492, the non-dominated solution set fusion rule corresponding to the task planning model is obtained as follows: Define the Pareto nondominated solution sets corresponding to groups P, B, and N as follows: , as well as Then the set There exists a subset of non-dominated solutions to the Pareto non-dominated solution set as follows: ; By using non-dominated solution subsets The search returned all solutions superior to the above. Solution The set ;gather This is the final non-dominated solution set after fusion.

[0029] This invention provides a task allocation method for heterogeneous multi-agent systems that considers decision preference information, with the following beneficial effects: (1) Enhanced model targeting: Construct a target function grouping mechanism based on decision preference information, group the target functions corresponding to the multi-source target function matrix in the task allocation model, and obtain the grouped task allocation model. That is, by incorporating decision preference information through three-way decision, the task allocation model is more in line with actual needs and the decision complexity is reduced.

[0030] (2) Improved algorithm performance: Based on the task allocation model solution strategy, the grouped task allocation model is solved and the task allocation results of the heterogeneous multi-agent system for the target are obtained. That is, the improved NSGA-III algorithm is superior to the traditional algorithm in terms of convergence, solution set distribution and running efficiency, and is suitable for high-dimensional multi-objective optimization problems. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0032] Figure 1 The flowchart below illustrates the task allocation method for heterogeneous multi-agent systems that takes into account decision preference information, as described in this invention. Figure 2 This is the core block diagram of the objective function grouping mechanism based on decision preference information in this embodiment; Figure 3 This is a schematic diagram of the reference point mechanism for the three-dimensional target in this embodiment; Figure 4 This is a graph showing the characteristic results of the C value of group EXP1 in this embodiment; Figure 5 This is a graph showing the characteristic results of the C value of group EXP2 in this embodiment; Figure 6 This is a graph showing the characteristic results of the C value of group EXP3 in this embodiment; Figure 7 This is a graph showing the characteristic results of the S-value of group EXP1 in this embodiment; Figure 8This is a graph showing the characteristic results of the S-value of group EXP2 in this embodiment; Figure 9 This is a graph showing the characteristic results of the S-value of group EXP3 in this embodiment. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] This embodiment provides a task allocation method for heterogeneous multi-agent systems that considers decision preference information. Task allocation modeling and solving are crucial steps in generating task capabilities for heterogeneous multi-agent systems, significantly improving system task efficiency and ensuring task completion quality. The method described in this embodiment first proposes a decision preference information processing strategy based on three-branch decision theory, addressing the specificity and complexity of the task allocation problem in heterogeneous multi-agent systems. This forms a task allocation model for heterogeneous multi-agent systems that considers decision preference information. Second, an improved NSGA-III algorithm for novel extreme point selection methods is proposed, and the fusion rules for non-dominated solution sets are redefined. Finally, simulations are conducted for real-world task scenarios, validating the effectiveness and adaptability of the method from multiple perspectives and in stages. Simulation results show that the task allocation model for heterogeneous multi-agent systems that considers decision preference information is more consistent with actual tasks. The improved NSGA-III algorithm exhibits better convergence performance, distribution performance, and operational efficiency compared to the SPEA2 and NSGA-III algorithms during model solving. This method can more effectively model and solve the task allocation problem in heterogeneous multi-agent systems. Figure 1 As shown, the specific steps include: S1: Define the system variables for the heterogeneous multi-agent system and the target; where in this embodiment, they are defined as follows: A heterogeneous multi-agent system participates in the task, requiring... To strike enemy targets, the corresponding problem variables, i.e., the system variables, include at least a set of heterogeneous multi-agent systems. The set of detected target individuals The number of heterogeneous multi-agent system types The number of each type of multi-agent system Value vector of each type of multi-agent system The number of weapons carried by each type of multi-agent system The value vector of weapons carried by each type of multi-agent system Value vector of the target individual The allocation matrix for assigning targets to heterogeneous multi-agent systems, that is... Each enemy target is assigned The allocation matrix for a heterogeneous multi-agent system is: The number of multi-agent systems of a certain type required to attack any target, i.e., the number of attacks on the nth target. The goal requires The number of multi-agent systems is ; In order to avoid loss of generality, the following basic assumptions are made in this embodiment: (1) Multi-agent systems and enemy targets can be treated as point masses, without considering their physical size differences and changes in motion posture; (2) The initial positions of the multi-agent system and enemy targets are fixed and randomly distributed within the battlefield area; (3) The heterogeneity of multi-agent systems is reflected in the types of multi-agent platforms and the quantity and value of the weapons they carry. The above elements must be completely consistent for similar multi-agent systems. S2: Construct a task allocation model based on the system variables; Furthermore, the task allocation model includes a multi-source objective function matrix and corresponding constraint set for task allocation models that maximize target value gain, minimize flight distance, minimize task completion time, minimize threat level, minimize resource consumption, and minimize platform type consumption. Specifically, in this embodiment, the ultimate goal of task allocation in a heterogeneous multi-agent system is to maximize the overall task efficiency. Task efficiency can generally be represented by multiple objective functions. Considering the particularity and complexity of the task allocation problem in a heterogeneous multi-agent system, a heterogeneous multi-agent system task allocation objective function matrix is ​​formed. The multi-source objective function matrix includes the objective function for maximizing target value gain, the objective function for minimizing flight distance, the objective function for minimizing mission completion time, the objective function for minimizing threat level, the objective function for minimizing weapon resource consumption, and the objective function for minimizing the consumption of multiple agent system types. And the objective function that maximizes the target value return for:

[0035] In the formula: express Multi-agent systems for attacking targets Its destructive power; Indicates attack on the The goal requires The number of multi-agent systems; Indicates the first The value vector of each target individual; Indicates the number of heterogeneous multi-agent system types; Indicates the number of targets; The objective function for minimizing the range of motion for:

[0036] In the formula: express Multi-agent systems for attacking targets Total voyage; The objective function for minimizing task completion time for:

[0037] In the formula: Indicates the number of heterogeneous multi-agent systems; express The multi-agent system completes the strike on the target. Total time of the attack; The objective function that minimizes the degree of threat for:

[0038] In the formula: express Multi-agent system attack targets Risks; express Value vector of multi-agent systems; The objective function of minimizing weapon resource consumption for:

[0039] In the formula: express The number of weapons carried by a multi-agent system; express The value vector of a multi-agent system carrying weapons; The objective function of minimizing the consumption of the multi-agent system type for:

[0040] In the formula: Indicates the target of attack The number of types of multi-agent systems required.

[0041] In this embodiment, the objective function for task allocation in the heterogeneous multi-agent system includes maximizing target value gain, minimizing travel distance, minimizing task completion time, minimizing threat level, minimizing weapon resource consumption, and minimizing platform type consumption. Specifically, the maximizing target value gain function evaluates the target value acquired during task execution, encouraging the multi-agent system to attack high-value targets; the minimizing travel distance function evaluates the total travel distance traversed by the multi-agent system during task execution, encouraging it to attack nearby targets; the minimizing task completion time function evaluates the unit time taken by the multi-agent system to complete the task, encouraging it to improve strike efficiency; the minimizing threat level function evaluates the total threat level experienced by the multi-agent system, encouraging it to navigate along safe routes; the minimizing weapon resource consumption function evaluates the value of weapon resources consumed by the multi-agent system in completing the task, encouraging it to prioritize the consumption of low-value weapons when attacking targets; and the minimizing multi-agent system type consumption function evaluates the number of multi-agent system types used to complete the task, encouraging similar multi-agent systems to form an alliance to coordinate attacks on targets.

[0042] Based on the task requirements, the task allocation of heterogeneous multi-agent systems needs to consider not only basic constraints such as resource quantity constraints, but also practical constraints such as travel distance constraints; the set of constraints described in this embodiment includes constraints on the number of multi-agent systems, system allocation quantity constraints, and travel distance constraints. The number constraint of the multi-agent system That is, the number of multi-agent systems participating in the task does not exceed the total number of multi-agent systems of that type, and its expression is: ; In the formula: express The number of multi-agent systems; The system allocation quantity constraint To ensure that any target is attacked by a multi-agent system, and that the multi-agent system does not excessively focus on attacking a single target, its expression is:

[0043] In the formula: Indicate the target The upper limit on the number of agents allocated to a multi-agent system; The sailing distance constraint The range of a multi-agent system is within its mission radius. Within this range, and with a total range not exceeding its own maximum range limit, its expression is:

[0044]

[0045] In the formula: express The risk of multi-agent systems attacking targets; Indicates the task radius; This represents the distance from the target point to the starting point of the last task in a multi-agent system. express The maximum range of a multi-agent system.

[0046] S3: Construct a target function grouping mechanism based on decision preference information, group the target functions corresponding to the multi-source target function matrix in the task allocation model, and obtain the grouped task allocation model; This embodiment also includes the definition of three-branch decision theory: Definition 1: Sequential Information System Defined as a quadruple, where the domain of discourse is... A non-empty finite set of objects; It is a non-empty finite set of attributes. ; It is the set of the value range of all attributes, that is ; Information function, ,definition express In attributes The value of is then... And satisfy the order relation ; Definition 2: Sequential Information System ,concept lower approximate set Approximate set above They are defined as follows:

[0047]

[0048] in, express In attributes Equivalence classes on; Definition 3: Based on subsets The lower and upper approximation sets can divide the universe of discourse into three disjoint regions: the positive region. Boundary domain and negative domain Define it as:

[0049]

[0050]

[0051] The rule representation derived from the elements in the positive domain determines which one belongs to. The rule derived from the elements in the negative domain indicates that it does not belong to... The rules, and the rule representation derived from the boundary domain may belong to... The rules are the basic idea behind the three-way decision theory.

[0052] Specifically, in this embodiment, the objective function grouping mechanism based on decision preference information, i.e., the decision preference information processing strategy based on three-way decision-making, is as follows: S31: If there is a one-to-one correspondence between decision preference information and the weights of the model objective function, then define a state set with two types of states. and ; This represents important weight information for the objective function; This represents the unimportant weight information of the objective function; and a decision set is given. and ; They represent the objective function respectively. Perform PSO, BND, and NEG decisions, and apply the objective function. These are labeled as "Primary Objective", "General Objective", and "Redundant Objective", respectively. ; Since different decisions regarding the objective function will result in different risk costs, we define a notation... They respectively represent when the objective function Weight information is When, implement Risk-value in three decision-making scenarios; definition They respectively represent when the objective function Weight information is When, implement Risk-value in three decision-making scenarios; Note Describe the objective function Through equivalence classes The depiction belongs to the state The conditional probability; denoted as Describe the objective function Through equivalence classes The depiction belongs to the state The conditional probabilities of the two satisfy the complementary relationship of their state sets. ; S32: Obtain implementation based on S31 The expected costs corresponding to the three decisions are:

[0053]

[0054]

[0055] In the formula: Each represents implementation The expected costs of the three decisions; S33: Based on the Bayesian decision minimum risk criterion, three decision rules containing threshold forms are obtained according to the expected cost: P: If ,but ;Right now ; B: If ,but ;Right now

[0056] N: If ,but ;Right now

[0057] In the formula: Indicates the design threshold and ;

[0058] S34: Group the objective functions corresponding to the multi-source objective function matrix in the task allocation model according to the three decision rules, and obtain the grouped task allocation model. And labeled as group P, group B and group N respectively, and satisfying ; These represent the number of objective functions in each group; This represents the total number of objective functions in the task allocation model. In this embodiment, decision preference information is initialized based on the user's subjective characteristics and the characteristics of the task process. The cognitive decision layer and preference organization layer respectively represent the three decision-making processes of the objective function and the flow of decision preference information, such as... Figure 2 As shown; S4: Based on the constructed task allocation model solution strategy, solve the grouped task allocation model and obtain the task allocation results of the heterogeneous multi-agent system for the strike target; The specific solution strategy for the constructed task allocation model is as follows: Choose an appropriate solution strategy based on the number of objective functions in the grouped task allocation model: That is, delete the groups with zero objective function values ​​as redundant groups; For groups with a single objective function, a single-objective optimization algorithm is used to solve the task allocation model after the grouping; and the single-objective optimization method includes, but is not limited to, the GA genetic algorithm. For groups with more than one objective function, an improved NSGA-III algorithm is used to solve the grouped task allocation model. In a specific embodiment, the NSGA-III algorithm, as a novel genetic algorithm, exhibits good adaptability to high-dimensional multi-objective optimization problems, offering advantages in increasing the diversity of the solution space, improving operational efficiency, and reducing computational complexity. Therefore, this embodiment, while retaining the advantages of the NSGA-III algorithm, adaptive improvements are made to address the instability of the normalization process. The improved NSGA-III algorithm is then used to solve groups with more than one objective function in the model. Specifically, the improved NSGA-III algorithm is as follows: S41: Define the combination of heterogeneous multi-agent systems corresponding to tasks assigned to any target as a population individual to obtain the initial population. Specifically, population initialization includes two parts: encoding and generating an initial population. In this embodiment, continuous real number encoding is used for encoding, and a large number of uniformly distributed random individuals that meet the constraints are generated, from which the individuals with the best performance are selected to form the initial population. S42: For the initial population The subpopulation is generated using random selection, simulated binary crossover, and polynomial mutation operations. And the initial population With the subpopulation The population size is and the initial population With subpopulation Merge into a population of size population Specifically, the population is generated randomly. Subpopulations are generated using random selection, simulated binary crossover (SBX), and polynomial mutation. ; and The population size is The two were merged into a population of size . population ; S43: A non-dominated sorting method based on Pareto dominance, which sorts the population Divided into several different non-dominated layers And from the non-dominated layer Start by adding all individuals from each non-dominated layer to a new population that is initially empty, and define the target population size of the new population as N. If we add the first After the population of individuals in the non-dominated layer reaches a size of N, the new population is then confirmed as the population. The next generation of population ; If we add the first After removing individuals from the non-dominated layer, if the new population size is greater than N, then retain the previous individuals. After the population of individuals in the non-dominated layer is reached, continue with steps S44 to S48 to proceed from the first... From the individuals in the non-dominated layer, select the remaining individuals that will make the new population size reach N (in this embodiment, in order to...). choose Each chromosome enters the next iteration, and the non-dominated sorting based on Pareto dominance will... Divided into several different non-dominated layers To build a new population The construction method is from Initially, the solutions of each non-dominated layer are successively added to... until The size equals or the first time greater than If the last non-dominated layer to accept it is the first... So, discard the first layer. The layer and subsequent solutions, and ( The solution in the previous non-dominated layer has been determined and selected as the first solution. The solution in the generation, the remaining individuals need to be from (selected from the middle), and then the population is obtained. The next generation of population ; S44: Based on the orthogonal boundary crossing algorithm, on a pre-defined regularized M-dimensional hyperplane, according to the... In each non-dominated layer, several reference points are uniformly generated from the individuals in the population. Specifically, in this embodiment, the NSGA-III algorithm employs a reference point-based individual selection mechanism to maintain population diversity. This embodiment also uses an orthogonal boundary crossover algorithm to generate reference points, which can achieve regularization... Uniform generation on a 3D hyperplane One reference point; S45: Use a scalarization function to obtain the target value corresponding to each individual in the population, at the... The projection values ​​along the target direction are obtained; and the individual values ​​of various populations are obtained in the 1st dimension. The maximum projection value along the target direction is determined by taking the population individual corresponding to the minimum value among the maximum projection values ​​as the first... The extreme point in the target direction is expressed as:

[0059] In the formula: Indicates extreme points; Represents the population individuals after translation transformation The corresponding number Dimensional objective function value; This represents the weight vector; in this embodiment, for The multidimensional objective optimization problem can be solved using the above formula. At this extreme point, when this When all extreme points are different, a unique [structure] can be constructed. The limiting plane; the distance between the intersection points of the limiting plane with each target axis and the ideal point is the intercept vector of each target axis. In this embodiment, the ideal point is taken as the origin, and the definition of "objective axis" in multi-objective optimization problems is that each objective function corresponds to an independent dimension. Assuming the problem has M objectives (e.g., minimizing cost, maximizing efficiency, and minimizing emissions), the objective space is an M-dimensional space. The "objective axis" refers to the coordinate axes in this M-dimensional space that represent the respective objective functions. For example, for a three-objective optimization problem (M=3), the objective space is three-dimensional, and the three mutually perpendicular coordinate axes are called objective axis 1, objective axis 2, and objective axis 3, corresponding to the values ​​of the first, second, and third objective functions, respectively. The positive direction of each axis represents the direction in which the objective value increases (for minimization problems, it is usually desirable to move in the negative direction). Its role in limit plane and intercept calculation: In the normalization step of the NSGA-III algorithm, the limit plane is constructed to calculate the intercepts on each objective axis, thereby mapping objective values ​​of different dimensions to a unified scale. Construction of the Limit Plane: By selecting extreme points, M extreme points are obtained (each extreme point performs best in a target direction). These M extreme points span an M-dimensional hyperplane, called the Limit Plane. Calculation of the Intercept Vector: The Limit Plane intersects each target axis at a point. The coordinates of this intersection point on that target axis are the intercept of that target axis. For example: in a two-dimensional case (two targets)... and The limiting plane is a straight line, which is perpendicular to... The coordinates of the intersection point of the axes are ( ,0), and The coordinates of the intersection point of the axes are (0, ... ); here and It refers to the intercepts of the two target axes. In three dimensions, the limiting plane is a triangular plane, and its intersections with the three target axes are respectively ( ,0,0)(0, ,0)(0,0, In this embodiment, the intercept reflects the "extreme range" achievable by each objective function in the current population; a larger intercept indicates a wider feasible region for that objective direction; a smaller intercept indicates a more compressed objective direction. This embodiment uses the intercept for normalization, unifying objective values ​​of different orders of magnitude into the [0,1] interval, allowing the subsequent reference point association mechanism to fairly measure the distribution in each objective direction; however, in practical applications, [further issues may arise]. The special case of identical extreme points can create an infinite number of [variables / extremes]. In a 3D limiting plane, a unique intercept vector cannot be determined. The optimization process is difficult to converge. To address this, this embodiment optimizes and improves the extreme point selection method: it prioritizes selecting the individual with the largest target value as the extreme point; if that point has already been selected as the extreme point, it selects the next largest individual as the extreme point, and so on. S46: Obtained from S45 The extreme points combined with the intercept vector To obtain the normalized individual target value, its expression is:

[0060] In the formula: Represents individuals in a population The corresponding number Dimensional objective function value; Represents the normalized population individuals The corresponding number Dimensional objective function value; ; This indicates a normalization operation; Represents the intercept vector; S47: Obtain the normalized target space based on S46, and within the normalized target space, determine the distance from individual populations. Recent reference line The corresponding reference point is defined as the point relative to the population individual. Related reference points, such as Figure 3 As shown; and the reference line is the straight line connecting the ideal point set in the M-dimensional hyperplane with each reference point; S48: Based on the small-scale mirror preservation operation, according to the associated reference point, ... Individuals in the non-dominated layer perform population selection until the new population reaches the target population size N; S49: The next generation population As a Pareto non-dominated solution set, and based on the non-dominated solution set fusion rule, the final non-dominated solution set is obtained; and the final non-dominated solution set is the final combination result of the heterogeneous multi-agent system assigned to the task corresponding to the strike target.

[0061] Specifically, the method for constructing the non-dominated solution set fusion rule in this embodiment is as follows: To address the problem of how to obtain the non-dominated set of all objective functions from each set of non-dominated solution sets in the fusion of non-dominated solution sets, a series of assumptions and theorems are listed below: Assumption 1: The objective function is generalizedly continuous in the solution space, that is, if there are redundant discontinuities or step discontinuities, they can be discussed separately in the space where the objective function is continuous. Assumption 2: The solution space is A bounded closed subspace on space (m-dimensional Euclidean space), i.e. ; Theorem 1: Let For the objective function set and ;Will Defined as the solution space of the objective function set; Defined as the Pareto non-dominated solution set of the objective function set; Divided into Group … ; … If each of these is taken as the corresponding Pareto non-dominated solution set, then the set... There exists a subset of nondominated solutions to the Pareto nondominated solution set. ; Theorem 2: Let the decision preference information of each objective function group in the grouped task allocation model be ranked as follows: Then for two solutions on the Pareto non-dominated solution set and judge Is it superior to The specific judgment method is as follows: like Then confirm Superior Furthermore, no further comparisons will be made sequentially. … and … The relationship between them; like and Then confirm Superior Furthermore, no further comparisons will be made sequentially. … and … The relationship between them; And so on, until... … Then confirm Superior ; Based on the above assumptions and theorems, the non-dominated solution set fusion rules corresponding to the task planning model are obtained as follows: Define the Pareto nondominated solution sets corresponding to groups P, B, and N as follows: , as well as Then the set There exists a subset of non-dominated solutions to the Pareto non-dominated solution set as follows: ; By using non-dominated solution subsets The search returned all solutions superior to the above. Solution The set ;gather This is the final non-dominated solution set after fusion.

[0062] This embodiment also includes the following simulation calculations and result analysis: The simulation calculation was carried out in two stages: (1) The impact of the objective function grouping mechanism based on decision preference information on the solution of the task allocation model of heterogeneous multi-agent system was tested. The solution algorithm in this stage adopted the improved NSGA-III algorithm, and the problem variable was decision preference information; (2) The performance of the improved NSGA-III algorithm in solving the task allocation model of heterogeneous multi-agent system was tested. The comparison algorithm in this stage was the SPEA2 algorithm and the traditional NSGA-III algorithm. The problem was the task allocation model that had incorporated decision preference information.

[0063] Mission Scenario: Assuming a 3D scene with units omitted, the battlefield environment size is 10. 10 10, of which the number of heterogeneous multi-agent systems participating in the task Number of enemy targets to be attacked Number of heterogeneous multi-agent system types The number of each type of multi-agent system is The task radius for each type of multi-agent system is The number of weapons carried by each type of multi-agent system is Three sets of experiments (EXP1, EXP2, and EXP3) were designed. The resource parameters and target parameters of the multi-agent system in each set are shown in Tables 1 and 2, respectively. To standardize the units of measurement, the data in the tables have been normalized. The value of each type of multi-agent system... Value of weapons carried and target value The values ​​of are all in [0,1].

[0064] Table 1. Resource Parameter Values ​​for Multi-Agent Systems

[0065] Table 2. Target Parameter Values

[0066] Parameter settings: In three-way decision theory, the loss function value is generally determined by following these rules. , The basic principle is as follows. In task command and decision-making, if the objective function in the task allocation model is misjudged as "unimportant," that is, if an "unimportant" objective function is judged as a "primary objective," it will result in redundant decision information. The resulting solution set will contain some solutions that do not conform to reality, affecting the decision-making effect. However, in this case, at least the originally "important" objective function still exists in the "primary objective" and has not been lost, thus still meeting the decision-making requirements to a certain extent. If the objective function in the model is misjudged as "important," that is, if an "important" objective function is judged as a "secondary objective" or even a "redundant objective," it will cause information loss. The resulting solution set may only have a small portion that conforms to reality or even completely contradict reality, leading to serious decision-making errors. Therefore, based on the different degrees of loss caused by different decisions, various loss functions are set as shown in Table 4.

[0067] Table 3. Loss Function Specification

[0068] Based on the loss function values ​​set in Table 3, the threshold parameters are obtained. , The three decision rules are shown in Table 4.

[0069] Table 4. Loss Function Specification

[0070] For each experimental group (EXP1, EXP2, EXP3), two types of decision preference information are set as follows: DP1, or decision preference information 1, refers to the weight coefficients corresponding to each objective function in the task allocation model. ; DP2, or Decision Preference Information 2, refers to the weight coefficients corresponding to each objective function in the task allocation model. ; Based on the grouping mechanism of the objective function in the task allocation model, we can know that: For DP1: , , , For DP2: , , , .

[0071] The parameter settings for the solution algorithm in this embodiment are as follows: The initial parameters for the SPEA2 algorithm, the traditional NSGA-III algorithm, and the improved NSGA-III algorithm are set as follows: SPEA2 algorithm: population size =50, Archive set size =50, Termination Algebra =50, crossover probability =0.8, mutation probability =0.05; NSGA-III algorithm, improved NSGA-III algorithm: population size =50, Termination Algebra =50, crossover probability =0.8, mutation probability =0.05; Each example was run 20 times independently on a computer with a Core i5 3.3GHz processor and 4GB of memory, in the Matlab 2013a environment.

[0072] Simulation results and analysis: Three performance metrics—Generation Distance (GD), Inverted Generation Distance (IGD), and Computation Time (CT)—were used to test the impact of the objective function grouping mechanism based on decision preference information on the solution of the task assignment model. The GD metric primarily evaluates the algorithm's performance in approximating the Pareto front; a smaller GD value indicates better approximation. The IGD metric evaluates the overall performance of the Pareto solution set obtained by the algorithm; a smaller IGD value indicates better performance of the Pareto solution set. The CT metric primarily evaluates the algorithm's running efficiency and stability. The improved NSGA-III algorithm was used to solve the task assignment model under different decision preference information (DP1, DP2, and none) in each experimental group (EXP1, EXP2, EXP3). The statistical results (mean and standard deviation) of each performance metric are shown in Table 5.

[0073] Table 5. Loss Function Specification

[0074] The statistical results of each performance index in Table 5 show that: (1) For the GD index, the GD values ​​(mean and standard deviation) obtained under DP1, DP2 and no decision preference information in each group of experiments all showed an increasing trend. This indicates that the Pareto front obtained under DP1 in each group of experiments has good performance, the Pareto front obtained under DP2 has relatively good performance, while the Pareto front obtained under no decision preference information has relatively poor performance.

[0075] (2) Regarding the IGD index, the IGD values ​​(mean and standard deviation) obtained under DP1 conditions in each group of experiments are much smaller than the IGD values ​​(mean and standard deviation) obtained under DP2 and no decision preference information conditions in the experiments. However, the IGD values ​​(mean and standard deviation) obtained under DP2 conditions in each group of experiments are not much different from the GD values ​​(mean and standard deviation) obtained under no decision preference information conditions in the same group. This indicates that the overall performance of the Pareto solution set under DP1 conditions in each group of experiments is the best, while the overall performance of the Pareto solution set under DP1 conditions and no decision preference information conditions is relatively poor.

[0076] (3) Regarding the CT index, the CT values ​​(mean and standard deviation) under the DP1 condition in each group of experiments are significantly smaller than the CT values ​​(mean and standard deviation) under the DP2 and no decision preference information conditions in the same group of experiments. This indicates that the computational efficiency and stability of the algorithm under the DP1 condition are optimal in each group of experiments, while the computational efficiency and stability of the algorithm under the no decision preference information condition are the worst.

[0077] In summary, the above analysis reveals two key points: First, the index values ​​(mean and standard deviation) obtained under DP1 and DP2 conditions in each experimental group are superior to those obtained under conditions without decision preference information. This indicates that the grouping mechanism based on decision preference information allows the optimal solution to converge better to the true Pareto front, significantly improving the convergence of the solution set. This enables the algorithm to converge quickly to the region of interest for the decision-maker, resulting in a more targeted and higher-quality solution set, as well as higher computational efficiency and stability. Second, the Pareto solution set obtained under DP1 conditions is of relatively better quality and converges faster than that under DP2 conditions, and the algorithm's computational efficiency is also relatively higher. This is because although DP2 also considers decision preference information, its decision weight vectors are similar, and the decision preference information is relatively ambiguous, failing to effectively guide the population to evolve towards the decision preference region. In contrast, DP1 has relatively clear decision preference information, providing stronger guidance for the direction of population evolution and resulting in a more significant improvement in model performance.

[0078] Two performance metrics, convergence (C) and spatial distribution (S), were used to test the performance of the improved NSGA-III algorithm. The C metric primarily evaluates the convergence of the obtained Pareto front; a smaller C value indicates better convergence of the approximate Pareto optimal solution. The S metric evaluates the uniformity of the obtained Pareto front distribution; a smaller S value indicates a more uniform distribution of the non-dominated solutions in the target space. The test results show that the decision preference information for DP1 is relatively clear. Based on the principle of typicality of the test conditions, the SPEA2 algorithm, the traditional NSGA-III algorithm, and the improved NSGA-III algorithm were used to solve the task allocation model under DP1 for each experimental group (EXP1, EXP2, EXP3), respectively, to test the performance of the improved NSGA-III algorithm in solving the model. The statistical results of the obtained performance metrics are as follows: Figures 4 to 9 As shown. By Figures 4 to 9 It can be seen that in each experimental group (EXP1, EXP2, EXP3), the improved NSGA-III algorithm in DP1 significantly outperforms the SPEA2 algorithm and the traditional NSGA-III algorithm in both C and S values. This indicates that the improved NSGA-III algorithm obtains approximate Pareto optimal solutions with better convergence and a more uniform distribution in the target space. Therefore, the improved NSGA-III algorithm exhibits good performance when solving task allocation models that consider decision preference information.

[0079] Compared with existing technologies, the method described in this embodiment has significant practical implications for effectively modeling and solving the task allocation problem of heterogeneous multi-agent systems that considers decision preference information. This embodiment, while fully considering the particularity and complexity of the task allocation problem in heterogeneous multi-agent systems, clarifies the objective function matrix and constraint set for task allocation in heterogeneous multi-agent systems. It proposes a decision preference information processing strategy for the task allocation model of heterogeneous multi-agent systems based on three-way decision-making, and reduces the dimensionality of the objective function by grouping the objective function, thus forming a task allocation model for heterogeneous multi-agent systems that considers decision preference information. Furthermore, it adaptively improves the extreme point selection method of the traditional NSGA-III algorithm, standardizes the fusion rules of the non-dominated solution set, and proposes an improved NSGA-III algorithm for novel extreme point selection methods. Finally, the proposed method for modeling and solving the task allocation problem of heterogeneous multi-agent systems that considers decision preference information is simulated and implemented in a real-world task scenario. The effectiveness and adaptability of the method are verified from multiple perspectives and in stages. The verification results show that: (1) The task allocation model of heterogeneous multi-agent system that considers decision preference information has been greatly improved compared with the previous model. The model is more in line with the actual task. The decision preference information incorporated has a good guiding role in the solution range of the model, which can effectively reduce the complexity of decision-making and improve the decision-making efficiency of the commander. (2) The improved NSGA-III algorithm for novel extreme point selection methods has good convergence performance, distribution performance and running efficiency when solving task allocation models that take into account decision preference information.

[0080] (3) High versatility: The method is applicable to multiple fields such as logistics and monitoring, avoids sensitive words, and has wide applicability.

[0081] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A task allocation method for a heterogeneous multi-agent system considering decision preference information, characterized in that, The specific steps include: S1: Defines the system variables for the heterogeneous multi-agent system and the target; Furthermore, the system variables include at least the set of heterogeneous multi-agent systems, the set of target individuals, the number of heterogeneous multi-agent system types, the number of multi-agent systems of each type, the value vector of each type of multi-agent system, the number of weapons carried by each type of multi-agent system, the value vector of the weapons carried by each type of multi-agent system, the value vector of the target individuals, the allocation matrix for allocating targets to heterogeneous multi-agent systems, and the number of a certain type of multi-agent system required to attack any target; S2: Construct a task allocation model based on the system variables; Furthermore, the task allocation model includes a multi-source objective function matrix and corresponding constraint set for task allocation models that maximize target value gain, minimize flight distance, minimize task completion time, minimize threat level, minimize resource consumption, and minimize platform type consumption. S3: Construct a target function grouping mechanism based on decision preference information, group the target functions corresponding to the multi-source target function matrix in the task allocation model, and obtain the grouped task allocation model; S4: Based on the constructed task allocation model solution strategy, solve the grouped task allocation model and obtain the task allocation results of the heterogeneous multi-agent system for the strike target.

2. The task allocation method for a heterogeneous multi-agent system considering decision preference information according to claim 1, characterized in that, The multi-source objective function matrix described in S2 includes the objective function for maximizing target value gain, the objective function for minimizing flight range, the objective function for minimizing mission completion time, the objective function for minimizing threat level, the objective function for minimizing weapon resource consumption, and the objective function for minimizing the consumption of multiple agent system types. And the objective function that maximizes the target value return for: In the formula: express Multi-agent systems for attacking targets Its destructive power; Indicates attack on the The goal requires The number of multi-agent systems; Indicates the first The value vector of each target individual; Indicates the number of heterogeneous multi-agent system types; Indicates the number of targets; The objective function for minimizing the range of motion for: In the formula: express Multi-agent systems for attacking targets Total voyage; The objective function for minimizing task completion time for: In the formula: Indicates the number of heterogeneous multi-agent systems; express The multi-agent system completes the strike on the target. Total time of the attack; The objective function that minimizes the degree of threat for: In the formula: express Multi-agent system attack targets The risks; express Value vector of multi-agent systems; The objective function of minimizing weapon resource consumption for: In the formula: express The number of weapons carried by a multi-agent system; express The value vector of a multi-agent system carrying weapons; The objective function of minimizing the consumption of the multi-agent system type for: In the formula: Indicates the target of attack The number of types of multi-agent systems required.

3. The task allocation method for a heterogeneous multi-agent system considering decision preference information according to claim 2, characterized in that, The set of constraints described in S2 includes constraints on the number of multi-agent systems, constraints on the number of systems allocated, and constraints on the travel distance. The number constraint of the multi-agent system for: ； In the formula: express The number of multi-agent systems; The system allocation quantity constraint for: In the formula: Indicate the target The upper limit on the number of agents allocated to a multi-agent system; The sailing distance constraint for: In the formula: express The risk of multi-agent systems attacking targets; Indicates the task radius; This represents the distance from the target point to the starting point of the last task in a multi-agent system. express The maximum range of a multi-agent system.

4. The task allocation method for a heterogeneous multi-agent system considering decision preference information according to claim 3, characterized in that, The construction method of the objective function grouping mechanism based on decision preference information in S3 includes the following steps: S31: Define the state set and ; This represents important weight information for the objective function; This represents the unimportant weight information of the objective function; and a decision set is given. and ; They represent the objective function respectively. Perform PSO, BND, and NEG decisions. ; Definition Note They respectively represent when the objective function Weight information is When, implement Risk-value in three decision-making scenarios; definition They respectively represent when the objective function Weight information is When, implement Risk-value in three decision-making scenarios; Note Describe the objective function Through equivalence classes The depiction belongs to the state Conditional probability; denoted as Describe the objective function Through equivalence classes The depiction belongs to the state The conditional probability, and ; S32: Obtain implementation based on S31 The expected costs corresponding to the three decisions are: In the formula: Each represents implementation The expected costs of the three decisions; S33: Based on the Bayesian decision minimum risk criterion, three decision rules containing threshold forms are obtained according to the expected cost: P: If ,but ;Right now ; B: If ,but ;Right now N: If ,but ;Right now In the formula: Indicates the design threshold and ; S34: Group the objective functions corresponding to the multi-source objective function matrix in the task allocation model according to the three decision rules, and obtain the grouped task allocation model. And labeled as group P, group B and group N respectively, and satisfying ; These represent the number of objective functions in each group; This represents the total number of objective functions in the task allocation model.

5. A task allocation method for a heterogeneous multi-agent system considering decision preference information according to claim 4, characterized in that, The specific solution strategy for the task allocation model built in S4 is as follows: Choose an appropriate solution strategy based on the number of objective functions in the grouped task allocation model: That is, delete groups with zero objective function values ​​as redundant groups; For groups with a single objective function, a single-objective optimization algorithm is used to solve the task allocation model after the grouping; and the single-objective optimization method includes, but is not limited to, the GA genetic algorithm. For groups with more than one objective function, the improved NSGA-Ⅲ algorithm is used to solve the task allocation model after the grouping.

6. A task allocation method for a heterogeneous multi-agent system considering decision preference information according to claim 5, characterized in that, The improved NSGA-Ⅲ algorithm is specifically as follows: S41: Define the combination of heterogeneous multi-agent systems corresponding to tasks assigned to any target as a population individual to obtain the initial population. ; S42: For the initial population The subpopulation is generated using random selection, simulated binary crossover, and polynomial mutation operations. And the initial population With the subpopulation The population size is and the initial population With subpopulation Merge into a population of size population ; S43: A non-dominated sorting method based on Pareto dominance, which sorts the population Divided into several different non-dominated layers And from the non-dominated layer Start by adding all individuals from each non-dominated layer to a new population that is initially empty, and define the target population size of the new population as N. If we add the first After the population of individuals in the non-dominated layer reaches a size of N, the new population is then confirmed as the population. The next generation of population ; If we add the first After removing individuals from the non-dominated layer, if the new population size is greater than N, then retain the previous individuals. After the population of individuals in the non-dominated layer is reached, continue with steps S44 to S48 to proceed from the first... From the individuals in the non-dominated layer of the population, select the remaining individuals that make the new population size reach N, and then obtain the population. The next generation of population ; S44: Based on the orthogonal boundary crossing algorithm, on a pre-defined regularized M-dimensional hyperplane, according to the... Each non-dominated layer of the population generates several reference points evenly. S45: Use a scalarization function to obtain the target value corresponding to each individual in the population, at the... Projection value along the target direction; And obtain the individuals of various groups in the first The maximum projection value along the target direction is determined by taking the population individual corresponding to the minimum value among the maximum projection values ​​as the first... The extreme point in the target direction is expressed as: In the formula: Indicates extreme points; Represents the population individuals after translation transformation The corresponding number Dimensional objective function value; Represents the weight vector; S46: Obtained from S45 The extreme points are used to obtain the normalized individual target value: In the formula: Represents individuals in a population The corresponding number Dimensional objective function value; Represents the normalized population individuals The corresponding number Dimensional objective function value; ; This indicates a normalization operation; Represents the intercept vector; S47: Obtain the normalized target space based on S46, and within the normalized target space, determine the distance from individual populations. Recent reference line The corresponding reference point is defined as the point relative to the population individual. The associated reference points; and the reference line is the straight line connecting the ideal point set in the M-dimensional hyperplane with each reference point. S48: Based on the small-scale mirror preservation operation, according to the associated reference point, ... Individuals in the non-dominated layer perform population selection until the new population reaches the target population size N; S49: The next generation population As a Pareto non-dominated solution set, and based on the non-dominated solution set fusion rule, the final non-dominated solution set is obtained; and the final non-dominated solution set is the final combination result of the heterogeneous multi-agent system assigned to the task corresponding to the strike target.

7. A task allocation method for a heterogeneous multi-agent system considering decision preference information according to claim 6, characterized in that, The method for constructing the non-dominated solution set fusion rule described in S49 is as follows: S491: Let For the objective function set and ;Will Defined as the solution space of the objective function set; Defined as the Pareto non-dominated solution set of the objective function set; Divided into Group … ; … If each of these is taken as the corresponding Pareto non-dominated solution set, then the set... There exists a subset of nondominated solutions to the Pareto nondominated solution set. ; S492: The decision preference information of each objective function group in the grouped task allocation model is ranked as follows: Then for two solutions on the Pareto non-dominated solution set and judge Is it superior to The specific judgment method is as follows: like Then confirm Superior Furthermore, no further comparisons will be made sequentially. … and … The relationship between them; like and Then confirm Superior Furthermore, no further comparisons will be made sequentially. … and … The relationship between them; And so on, until... … Then confirm Superior ; S493: Based on S491 to S492, the non-dominated solution set fusion rule corresponding to the task planning model is obtained as follows: Define the Pareto nondominated solution sets corresponding to groups P, B, and N as follows: , as well as Then the set There exists a subset of non-dominated solutions to the Pareto non-dominated solution set as follows: ; By using non-dominated solution subsets The search returned all solutions superior to the above. Solution The set ;gather This is the final non-dominated solution set after fusion.

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