Decision method based on prospect theory and terminal device

Abstract

The application discloses a decision-making method and a terminal device based on a prospect theory, and the method comprises the following steps: constructing multiple combat rings according to attribute information of a reconnaissance node, a command node, an attack node and a target node; acquiring target values of the target node in each combat ring compared with target nodes in other combat rings; determining damage capacity values and closed-loop time values of each combat ring by using the prospect theory; combining the target values to construct a multi-objective optimization model with the damage capacity values and the closed-loop time values as optimization objectives; and solving the multi-objective optimization model to determine a combat ring meeting preset conditions. The decision-making method based on the prospect theory fully considers the preferences of decision-makers, is beneficial to machine recognition of human intentions in intelligent decision-making, and enables the final decision-making result to meet the expectations of the decision-makers and improve satisfaction.

Description

Technical Field

[0001] This invention belongs to the field of combat decision-making technology, specifically relating to a combat loop decision-making method and terminal equipment based on prospect theory for kill nets. Background Technology

[0002] Intelligent warfare achieves highly complex, fast-paced, and large-scale military confrontations through intelligent decision-making technology. Against the backdrop of the rapid advancement of intelligent warfare, the concept of mosaic warfare has been proposed and expanded. In terms of force design, mosaic warfare aims to rapidly and dynamically reorganize combat elements and their roles by decomposing a single multi-task unit into a larger number of smaller, less functional, and more combinable units, thereby forming a complex and efficient adaptive kill network. In terms of command and control, mosaic warfare aims to employ a machine control system to analyze the decision-maker's intentions and provide action plans, thus achieving a decision-making support function. The process by which the kill network exerts its combat capability is essentially the ability of its internal combat entities to form combat loops (a loop starting from the enemy target, passing through friendly equipment (reconnaissance equipment, command and control equipment, and attack equipment), and then returning to the enemy target) against the enemy target. Therefore, the action plans provided to the kill network are for each combat loop formed by each enemy target. This invention uniformly uses the term "combat loop decision" to represent combat loop decision-making for the kill network.

[0003] Many researchers have conducted research on the operational loop, including weapon system combination selection, operational effectiveness assessment, and equipment development planning. Regarding weapon system combination decision-making, Jiang et al. proposed a structure-oriented weapon system combination selection (SWSPS) based on operational loop theory. In operational effectiveness assessment, Jia et al. calculated the operational effectiveness of swarming UAV air combat systems based on the concept of operational loop capabilities. Yang Weisheng et al. further enriched the operational loop theory, evaluating the effectiveness of operational networks under different node attack strategies. In weapon system development planning, Wan et al. proposed an operational loop based on realistic connection rules to mimic the cooperative relationships between weapons in a defense system. Chi et al. proposed a method for evaluating the provision of weapon system operational networks (WSOSCN) based on operational loops. Research on intelligent decision-making within the operational loop is still in its early stages. Chen proposed an operational loop recommendation model based on DQN, and Xia Boyuan conducted research on a series of operational loop recommendation methods for kill networks in mosaic warfare.

[0004] However, previous studies have not considered the unique nature of the "human factor." Although Mosaic Warfare is a "human-machine" system that leverages the combined advantages of humans and machines to complete all decision-making functions, humans remain the core of decision-making and the creative intelligent factor, while machines provide assistance, support, and services to enhance human effectiveness and impact. Therefore, the inherent uncertainty of the decision-maker (subjective uncertainty) is a crucial factor influencing decision-making.

[0005] Current research on decision-making under uncertainty largely relies on expected utility theory, assuming perfectly rational decision-makers. Expected utility theory, from a logical and reasoning perspective, explains how people should act, making it a normative theory. While methodologically sound, expected utility theory overlooks the complexities of bounded rationality. Extensive empirical evidence shows that decision-makers' preferences play a significant role in the decision-making process. Furthermore, current operational decision-making based on expected utility theory, by neglecting the bounded rationality of decision-makers, often results in outcomes that fail to achieve the expected satisfaction. Summary of the Invention

[0006] This invention provides a decision-making method and terminal device based on prospect theory, which solves the technical problem in the prior art that ignores the bounded rationality of decision-makers in combat loop decision-making oriented towards kill nets, resulting in the final decision result failing to achieve the expected satisfaction.

[0007] The first aspect of this invention discloses a decision-making method based on prospect theory, comprising: Based on the attribute information of reconnaissance nodes, command and control nodes, attack nodes, and target nodes, multiple combat rings are constructed; Obtain the target value of a target node in each combat ring compared to target nodes in other combat rings; Prospect theory is used to determine the destructive capability value and closed-loop time value of each of the aforementioned combat loops; Based on the aforementioned target values, a multi-objective optimization model is constructed with the damage capability value and closed-loop time value as optimization objectives; Solve the multi-objective optimization model to determine the combat loop that meets the preset conditions.

[0008] Preferably, obtaining the target value of a target node in each combat ring relative to target nodes in other combat rings specifically includes: The TODIM method is used to determine the target value of a target node in each operational loop relative to target nodes in other operational loops.

[0009] Preferably, the destructive capability value of each combat ring is determined using prospect theory, specifically including: The destructive capability value of each combat ring is determined according to a first formula, which is:

[0010] In the formula, The destructive capability value of the combat ring, It serves as a reference point for destructive power. Actual destructive power Sensitivity to returns, Sensitivity to loss, Risk aversion coefficient for decision-makers This represents the decision-maker's risk preference coefficient; if the decision-maker is risk-taking, then... If the decision-maker is a middle-of-the-road type, then If the decision-maker is conservative, then .

[0011] Preferably, the closed-loop time value of each combat loop is determined using prospect theory, specifically including: The closed-loop time value of each combat loop is determined according to the second formula, which is:

[0012] In the formula, The closed-loop time value of the combat cycle. As a reference point for closed-loop time, Actual closed-loop time, Sensitivity to returns, Sensitivity to loss, Risk aversion coefficient for decision-makers This represents the decision-maker's risk preference coefficient; if the decision-maker is risk-taking, then... If the decision-maker is a middle-of-the-road type, then If the decision-maker is conservative, then .

[0013] Preferably, in conjunction with the target value, a multi-objective optimization model is constructed with the damage capability value and the closed-loop time value as optimization objectives, specifically including: The optimization function of the multi-objective optimization model is determined according to the third formula, which is:

[0014] In the formula, The optimization objective corresponds to the destructive capability value of the combat ring. For the first The target value of each target node, and , The total number of target nodes. For the first From the combat ring where each target node is located, from the equipment To equipment Decision variables, The value can be 0 or 1. =1 indicates the first The operational ring containing each target node includes equipment. To equipment The connecting edges, =0 indicates the first The combat ring containing each target node does not include equipment. To equipment The edges connecting the edges; Indicates from equipment To equipment The quality of the connecting edges, This represents the total number of equipment nodes in the kill network, which includes reconnaissance nodes, command and control nodes, attack nodes, and target nodes. The value of the destructive capability of the combat ring; The optimization objective corresponds to the closed-loop time value of the combat cycle. For the first The target value of each target node, and , The total number of target nodes. For the first From the combat ring where each target node is located, from the equipment To equipment Decision variables, The value can be 0 or 1. =1 indicates the first The operational ring containing each target node includes equipment. To equipment The connecting edges, =0 indicates the first The combat ring containing each target node does not include equipment. To equipment The edges connecting the edges; Indicates equipment The time required to form a combat ring This represents the total number of equipment nodes in the kill network, which includes reconnaissance nodes, command and control nodes, attack nodes, and target nodes. The closed-loop time value of the combat cycle.

[0015] Preferably, the constraints of the multi-objective optimization model are as shown in the fourth formula, which is:

[0016] In the formula, This represents the total number of equipment nodes belonging to the Red Team in the kill network. For the first From the combat ring where each target node is located, from the equipment To equipment Decision variables, The value can be 0 or 1. =1 indicates the first The operational ring containing each target node includes equipment. To equipment The connecting edges, =0 indicates the first The combat ring containing each target node does not include equipment. To equipment The connecting edges.

[0017] Preferably, solving the multi-objective optimization model to determine the combat loop that meets preset conditions specifically includes: The improved NSGA-II algorithm was used to solve the multi-objective optimization model, and a set of Pareto optimal solutions were obtained. The TOPSIS method is used to determine the operational loop that meets the preset conditions from the set of Pareto optimal solutions.

[0018] Preferably, the improved NSGA-II algorithm is used to solve the multi-objective optimization model to obtain a set of Pareto optimal solutions, specifically including: The initial solution for the NSGA-II algorithm for solving the multi-objective optimization model is constructed based on the ant colony algorithm. In the crossover operation of the NSGA-II algorithm, chromosomes corresponding to two combat rings are randomly selected, and then chromosomes are randomly selected from gene loci. One gene locus, allowing two chromosomes to be selected. Crossover operations are performed on each gene locus. In the mutation operation of the NSGA-II algorithm, a chromosome of the combat ring is randomly selected, and then a gene locus is randomly selected. A number of gene loci, causing the chromosome to be in the selected... Mutation is performed on each gene locus, requiring that the mutated gene corresponds to the same equipment type, and the gene locus corresponding to the enemy target is not mutated, to obtain a set of Pareto optimal solutions. in, n The number of enemy targets killed within the net. For crossover probability, This represents the mutation probability.

[0019] Preferably, the step of using the TOPSIS method to determine the operational loop that meets the preset conditions from the set of Pareto optimal solutions specifically includes: The optimal operational loop is determined from the set of Pareto optimal solutions using the TOPSIS method.

[0020] A second aspect of this invention discloses a terminal device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described method.

[0021] Compared with the prior art, the present invention has the following advantages: This invention first describes the combat loop by modeling nodes and edges. Based on this, the target value, damage capability value, and closed-loop time value of the combat loop are evaluated. The target value is evaluated using TODIM (Portuguese: TOmadade Decisão Interativa e Multicritério), while the damage capability value and closed-loop time value are evaluated using value functions in prospect theory. A multi-objective optimization model for damage capability value and closed-loop time value, weighted by target value, is established. Next, an NSACGA-II (Non-dominated Sorting AntColony Genetic Algorithm-II) algorithm is designed to determine the optimal planning solution for the multi-objectives. The Pareto solution set for the multi-objectives is evaluated based on TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution). This invention's combat loop decision-making method for kill nets, based on prospect theory, fully considers the decision-maker's preferences, which is beneficial for machines to recognize human intentions in intelligent decision-making, ensuring that the final decision result meets the decision-maker's expectations and improving satisfaction. Attached Figure Description

[0022] Figure 1 This is a flowchart of a decision-making method based on prospect theory, as described in an embodiment of the present invention. Figure 2 This is a schematic diagram of the combat ring according to an embodiment of the present invention; Figure 3 This is the evaluation index system for the target value in the embodiments of the present invention; Figure 4 This is a flowchart of the NSACGA-Ⅱ algorithm according to an embodiment of the present invention; Figure 5 The chromosome encoding rule in the operational loop decision problem of this invention; Figure 6 This is a diagram illustrating the crossover and mutation operations in an embodiment of the present invention; Figure 7This is a Pareto front plot generated by the algorithm in a specific embodiment of the present invention; Figure 8 This refers to the solution space in a specific embodiment of the present invention; Figure 9 In the figure, (a) is a bar chart of HV for 10 experiments of the three algorithms in a specific embodiment of the present invention; (b) is a box plot of HV for 10 experiments of the three algorithms in a specific embodiment of the present invention. Figure 10 In the figure, (a) is a bar chart of SP for 10 experiments of the three algorithms in a specific embodiment of the present invention; (b) is a box plot of SP for 10 experiments of the three algorithms in a specific embodiment of the present invention. Detailed Implementation

[0023] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are merely illustrative and explanatory of the present invention and should not be construed as limiting the scope of protection of the present invention. All technologies implemented based on the above content of the present invention are covered within the scope of protection intended by the present invention.

[0024] The first aspect of this invention discloses a decision-making method based on prospect theory, such as... Figure 1 The above includes: Step 1: Construct multiple combat rings based on the attribute information of the reconnaissance node, command and control node, attack node, and target node.

[0025] Modern operational cycle theory posits that combat is a cyclical process consisting of Observation, Location, Decision, and Action (OODA). Based on this theory, Tan Yuejin proposed the concept of an operational loop, a closed loop formed by reconnaissance, command and control, and attack entities, along with enemy target entities. Specifically, reconnaissance entities discover enemy targets and transmit relevant information to their own command and control entities. These entities, after detailed analysis, send commands to attack entities, which then launch attacks on the enemy targets. Both sides construct their own operational loops, treating enemy nodes as targets within their own loops. A schematic diagram of an operational loop in combat is shown below. Figure 2 As shown. According to the definition of a combat ring, it is necessary to model the relationships between nodes and the edges between them.

[0026] 1.1 Node Modeling It should be noted that the purpose of this invention is to evaluate the operational loop based on the connections between nodes, and to analyze how to make operational loop decisions based on this. Therefore, in the node modeling process, the focus is on describing the attributes related to evaluating the operational loop. Some node attributes need to be considered by all nodes, such as node location attributes, which are referred to as common attributes in this invention. The common attributes of nodes will be described first, and then the specific attributes of reconnaissance nodes, command and control nodes, attack nodes, and target nodes will be analyzed in detail.

[0027] 1) Public attributes Based on the combat mission, the common attributes of nodes mainly consider the equipment's faction, type, location, closed-loop time, and number of channels, expressed by the formula:

[0028] (1) Faction

[0029] This invention only considers two-sided confrontations and does not consider situations involving multiple parties; therefore, the faction attribute of equipment nodes only includes the red side. (Our side) and the blue side (The enemy).

[0030] (2) Type

[0031] Equipment types are categorized based on the functions of the equipment nodes. According to the definition of the combat cycle, equipment types include four basic types: reconnaissance, command and control, attack, and target acquisition. Reconnaissance equipment (… S These primarily possess functions such as battlefield information acquisition, processing, and transmission, including reconnaissance drones and radar. Command and control equipment ( D Its main function is to receive information from reconnaissance equipment, process the information based on the battlefield situation, and make operational decisions. Since this invention focuses on the impact of human factors on decision-making in the operational cycle, command and control equipment specifically refers to the decision-maker in this invention. Attack equipment ( I Its main tasks include offensive and defensive operations during combat, such as fighter jets, missiles, and electromagnetic interference equipment. From one side's perspective, all of the other side's equipment falls under the category of target equipment. T The unique attributes of different equipment types will be detailed later.

[0032] (3) Location ，

[0033] In actual combat, longitude, latitude, and altitude are used to represent the location information of equipment nodes. However, for the convenience of subsequent calculations, this invention uses Cartesian three-dimensional coordinates to represent the location attributes of the equipment.x , y , z They represent the equipment respectively x coordinate, y coordinates and z coordinate.

[0034] (4) Closed-loop time Unit: seconds The closed-loop time of equipment is the time consumed for equipment nodes to form an operational loop. For reconnaissance equipment nodes, it represents the time to detect a target and transmit the information to command and control equipment nodes; for command and control equipment nodes, it represents the time to process battlefield information, make decisions, and issue operational orders to attack equipment nodes; for attack equipment nodes, it represents the time to receive operational orders from command and control equipment nodes and complete the attack mission.

[0035] (5) Number of channels , unit The number of channels represents the number of equipment nodes that can connect to other equipment nodes. Specifically, it can be divided into four types: reconnaissance channels, command and control channels, attack channels, and communication channels. The number of reconnaissance channels refers to the number of targets a reconnaissance equipment node can simultaneously detect; the number of command and control channels is the number of equipment a command and control equipment node can simultaneously command and control, which is also the number of attack equipment it can simultaneously connect to; the number of attack channels is the number of targets an attack equipment node can simultaneously attack; and communication channels are channels for information sharing between reconnaissance equipment nodes, channels for coordinated command between command and control equipment nodes, and channels for information feedback between reconnaissance equipment nodes and command and control equipment nodes.

[0036] 2) Attributes of reconnaissance nodes The unique attributes of a reconnaissance node include reconnaissance distance and scan path width, expressed by the formula:

[0037] (1) Reconnaissance distance Unit: meter Reconnaissance range is the most important attribute of reconnaissance equipment, indicating the effective range at which it can detect targets. When the distance between the enemy target and the reconnaissance equipment exceeds the reconnaissance range, the equipment cannot detect the enemy target. When the distance between the enemy target and the reconnaissance equipment is less than the reconnaissance range, the equipment can detect the enemy target.

[0038] (2) Scan path width Unit: meter The scan path width is the path distance of each scan by the detector of the reconnaissance equipment.

[0039] 3) Charge node attributes The attributes unique to the accusation node include preferences, which can be expressed by the formula:

[0040] (1) Preference ，

[0041] Preference refers to the decision-making preference attribute of a decision-maker. In decision-centric warfare, the "decision-making" stage of the OODA loop is emphasized, corresponding to the command and control node in the operational loop. Its main function is to receive information from reconnaissance nodes, analyze the battlefield situation, and make operational loop decisions based on its own decision preferences. As mentioned earlier, prospect theory introduces decision preferences into the decision-making process, quantifying these preferences through relevant parameters in the value function and decision weight function. Therefore, in this invention, the decision preference attribute of the command and control node is represented as... Including risk attitude coefficient / Gain / Loss Sensitivity Coefficient / Prospect theory calculates prospect values ​​by assigning fixed decision preference attributes to decision-makers. However, in combat, setting fixed decision preference attributes cannot adequately reflect the flexibility of decision-making. Different decision-makers have different personalities and characteristics; for example, some are more risk-averse, while others tend to be conservative, thus these decision preference attributes will also differ slightly.

[0042] 4) Attack node attributes Attack node-specific attributes include range, firing accuracy, and warhead power, expressed by the formula:

[0043] (1) Range Unit: kilometer Range refers to the effective attack distance of an attack node. When the distance between the enemy target and the attacking equipment is greater than the range, the attacking equipment cannot attack the equipment; when the distance between the enemy target and the attacking equipment is less than the range, the attacking equipment can attack the enemy target.

[0044] (2) Shooting accuracy Unit: meter The firing accuracy of attack equipment is often measured by circular error probability (CEP). It is represented by the probability deviation of a circle drawn with the target as its center. If the probability of the equipment hitting this circle is at least 50%, then the radius of this circle is the probability deviation.

[0045] (3) Warhead power

[0046] The warhead is the final damaging unit for various munitions and missiles, mainly composed of a casing, explosive charge, detonation device, and safety device. The warhead's ability to attack a target can be represented by its inherent warhead yield. For ease of calculation, this invention normalizes the warhead yield at the attack point, with a value ranging from 0 to 1.

[0047] 5) Target node attributes The unique attributes of a target node include cross-sectional area, stealth coefficient, vulnerable area, false alarm survival probability, warning time, and maneuver speed, which are expressed by the following formula:

[0048] (1) Cross-sectional area Unit: square meters The total area of ​​a target that can be detected or attacked under normal conditions is an important factor affecting the detection capability of detection nodes and the damage capability of attack nodes.

[0049] (2) Stealth coefficient

[0050] The stealth coefficient is an indicator of a target node's stealth capability. In actual combat, enemy targets employ various methods of camouflage to reduce the area that can be detected or weaken the effectiveness of reconnaissance, thereby achieving stealth. The stealth coefficient is greater than 1; when the stealth coefficient equals 1, the target node is considered to have no stealth capability.

[0051] (3) Vulnerable area

[0052] Vulnerable area is the area of ​​a target node that is damaged by an attacking node. Different attacking nodes have different warhead powers, and the vulnerable area of ​​a target node varies depending on the warhead power it faces. A larger vulnerable area indicates that the target node is more easily destroyed.

[0053] (4) Probability of survival of false test

[0054] Deception is a general term for various camouflage methods that simulate the exposure of a target and display false phenomena to cause the enemy to make mistakes or oversights. Examples include setting up false targets, spreading false information, and carrying out feints. The probability of survival through deception is the probability that a target node can avoid being detected by enemy reconnaissance equipment by employing deception tactics.

[0055] (5) Warning time Unit: seconds Warning time is the time a target node takes to avoid being detected by reconnaissance equipment or attacked by attack equipment, based on past patterns or observed possible precursors, and to take escape measures to avoid being detected by reconnaissance equipment or attacked by attack equipment, thereby minimizing the damage caused by the harm.

[0056] (6) Speed ​​of movement Unit: km / h Maneuver speed is the speed at which a target node escapes during the early warning process. For a static target, the maneuver speed is 0.

[0057] 1.2 Modeling of Edge Relationships In the operational loop theory, there are relationships between similar equipment and relationships between different equipment. These relationships are essentially the connections between nodes. However, not every two nodes are connected, and these connections are directed. For example, there is no connection between an attack node and a reconnaissance node; there is a connection from a reconnaissance node to a target node, but no connection from a target node to a reconnaissance node.

[0058] Table 1. Types of edges between nodes

[0059] Note: " / " indicates that there is no directed edge relationship between the equipment type in the current row and the equipment type in the current column.

[0060] According to section 1.1, the kill net contains four basic equipment types ( S , D , I , T Therefore, there are a total of 16 potential edge relationships. However, after excluding 9 logically non-existent edge relationships, there are still 7 remaining, as shown in Table 1. Specifically, the edge relationships include the following four types: 1) Reconnaissance of the border A reconnaissance edge describes the reconnaissance relationship (T→S) between a reconnaissance node and a target node, representing the process by which a reconnaissance node acquires, processes, and transmits information about enemy targets. The reconnaissance capability of a reconnaissance edge refers to the ability of a reconnaissance node to detect a target node, and is influenced by the attributes of both the reconnaissance and target nodes. Reconnaissance capability depends on the target node's cross-sectional area and stealth coefficient, the reconnaissance node's reconnaissance range and scan path width, and the distance between the target and reconnaissance nodes. The formula for calculating reconnaissance capability is as follows:

[0061]

[0062] in, and These represent the reconnaissance node and the target node, respectively. Representing reconnaissance nodes Target node detected The ability. It is a reconnaissance node Target node detected The initial distance, The target node speed of movement The target node The warning time, Represents the target node They may use early warning maneuvers to distance themselves from reconnaissance nodes. Representing reconnaissance nodes Reconnaissance range. Parameters With reconnaissance nodes parameter (Related to the performance and reconnaissance principles of different reconnaissance equipment), target node Cross-sectional area Positive correlation, with the target node Stealth coefficient and reconnaissance nodes Scan path width Negative correlation.

[0063] when When the distance between the reconnaissance node and the target node is greater than the reconnaissance distance of the reconnaissance node, the reconnaissance capability is 0. At that time, reconnaissance capability is negatively correlated with the distance between the reconnaissance node and the target node, the survival probability of the target node's deception, the scanning path width of the reconnaissance node, and the stealth coefficient of the target node, and positively correlated with the cross-sectional area of ​​the target node. Furthermore, the target node... False survival probability The higher the level, the lower the reconnaissance node's reconnaissance capability against the enemy target. This indicates that the target node has a very strong ability to make false statements, and the reconnaissance node's reconnaissance capability against the enemy target is 0.

[0064] 2) Communication side The communication edge describes the information sharing relationship (S→S) between reconnaissance nodes, the collaborative command relationship (D→D) between command and control nodes, and the information transmission relationship (S→D, D→S) between reconnaissance nodes and command and control nodes. It is the process of information communication between reconnaissance nodes and command and control nodes. The communication capability of the communication edge is the ability to transmit information between reconnaissance nodes and command and control nodes, which mainly depends on the distance between equipment nodes. The calculation formula is as follows:

[0065] in, and These represent the information sending equipment node and the information receiving equipment node, respectively. Representative node To equipment node The ability to communicate between them. It is a node and nodes Communication distance between them Representative node and nodes The communication capability is zero when the distance between two equipment nodes exceeds the maximum communication distance. When the distance between two equipment nodes is within the maximum communication distance, the communication capability is inversely proportional to the distance between the equipment nodes.

[0066] 3) Accusation of the side The command and control edge describes the command and control relationship (D→I) from the command and control node to the attacking node. It represents the process by which the command and control node processes battlefield situational information, makes operational decisions, and issues operational orders to the attacking node. The command and control capability of the command and control edge is the ability of the command and control node to issue operational orders to the attacking node; essentially, it is still communication between equipment. Therefore, command and control capability and communication capability have the same meaning, and the calculation formula is as follows:

[0067] in, and They represent the accusing node and the attacking node, respectively. It is the node of accusation. and attack nodes The communication capability between them. It should be noted that when a piece of equipment does not have a command and control channel, its command and control capability is zero.

[0068] 4) Attack the edge An attack edge describes the attack relationship (I→T) from an attacking node to a target node. It represents the process by which an attacking node attacks a corresponding enemy target based on operational mission commands received from the command and control node. The attack capability of an attack edge depends on the probability of the attacking node's warhead hitting the target. And the degree of damage to the target under the condition that the warhead hits the target. The formula for calculating attack power is as follows:

[0069] Hit probability is a measure of the likelihood that the warhead of an attacking node will hit an enemy target; it depends on the attacking node's range. and shooting accuracy and the cross-sectional area of ​​the target node The calculation formula is as follows:

[0070] in, and These represent the attacking node and the target node, respectively. Representative attack node Successfully hit the target node The probability of. Representative attack node To the target node The initial distance, Representative attack node range, Represents the target node It may use early warning maneuvers to escape the attack node's range.

[0071] when When the distance between the attacking node and the target node is greater than the attacking node's range, the hit probability is 0. At that time, the target node At the attack node Within range, the probability of hitting is related to the cross-sectional area of ​​the target node. And the shooting accuracy of the attack node related.

[0072] Under the condition of hitting the target, the degree of damage to the target by the warhead depends on the warhead power of the attack point and the vulnerability of the target, where vulnerability is measured by the vulnerable area of ​​the target point, and is expressed by the following formula:

[0073] in, It is a node to be attacked The power of the warhead, The target node Vulnerable area under different warhead yields; Represents the target node At the point of attack The warhead's head yield is The vulnerable area is shown below. It should be noted that, for the sake of ease of research, the conditional damage level of this invention only considers the possibility of damage to the target if the attack node directly hits the target, and only considers the case of a single warhead hitting the target.

[0074] Step 2: Obtain the target value of each target node in each combat ring compared to target nodes in other combat rings.

[0075] The target value encompasses both attribute value and system value. Since the research object of this invention is the kill net, and kill net equipment combinations are diverse, the system value is difficult to obtain. This paper evaluates the target value only from the perspective of attribute value. Combining the description of target node attributes, an evaluation index system for target value can be constructed, such as... Figure 3 As shown.

[0076] Target value evaluation is a multi-attribute decision-making problem, mainly consisting of two parts: first, acquiring decision information, namely attribute weights and attribute values; and second, aggregating decision-makers' preferences and ranking the merits of alternatives. The uncertainty of decision-makers' preferences is the source of the complexity of multi-attribute decision-making problems; therefore, multi-attribute decision-making methods considering decision-makers' psychological behavior have become a research hotspot in the field of decision-making in recent years. Based on prospect theory, Brazilian scholars Gomes and Lima proposed a multi-attribute decision-making method, TODIM (Portuguese: TOmada de Decisão Interativa eMulticritério), which considers decision-makers' psychological behavior. This method, based on prospect theory, constructs pairwise comparisons of the dominance of alternatives according to the different preferences of decision-makers for gains and losses. By aggregating individual dominance to form the overall dominance of each alternative, and comparing and ranking them, it helps decision-makers find a "satisfactory solution" more effectively when facing risky decisions. Therefore, this invention uses the TODIM method to determine the target value of a target node in each operational loop compared to target nodes in other operational loops. The specific steps are as follows: Step 1: Construct the original decision matrix The target node set is The set of indicators is The original decision matrix is ​​then... , Indicate target Corresponding indicators The index value.

[0077] Step 2 Standardize evaluation index values Because different indicators have different dimensions, they cannot be compared directly. Therefore, it is necessary to standardize the indicator values ​​of different dimensions through mathematical transformation, a process known as evaluation indicator standardization. This paper uses the range transformation standardization method to transform the original decision matrix... Transform into a standard decision matrix Quantitative indicators are divided into two categories: benefit-based and cost-based. The standardization methods for benefit-based and cost-based quantitative indicators are given below: For efficiency-type indicators:

[0078] For cost-related indicators:

[0079] Step 3: Determine the indicator weights This paper uses the entropy weight method, a commonly used method in objective weighting, to determine the index weights. The specific calculation steps are as follows: (1) Calculate the information entropy of the index:

[0080] in, ,like Then define

[0081] (2) Determine the entropy weight:

[0082] Calculate the entropy weight for each indicator to obtain the indicator weight vector. .

[0083] Step 4: Calculate the dominance of each indicator. Calculation target In terms of indicators Below the target The dominance is thus obtained, resulting in a dominance matrix under a certain index. ,index The formula for calculating dominance is as follows:

[0084] Consistent with the connotation of the value function in prospect theory, The square root structure used can be considered a special case of the value function, i.e. . Representative indicators The relative weights This represents the reference weight. It is the loss sensitivity coefficient, and The changes result in different shapes for the value function of the foreground theory within the negative quadrant. A smaller value indicates a higher degree of loss aversion among decision-makers. In this paper... With the loss aversion coefficient in the value function equivalence.

[0085] Step 5: Calculate the dominance of all indicators. Calculate the target considering all indicators. Relative to the target Dominance:

[0086] Step 6 Calculate the overall dominance Calculate the objective by taking all objectives into account. The overall dominance of all other objectives is used to rank their value. A higher dominance indicates a higher objective value, as shown in the following formula:

[0087] Step 3: Use prospect theory to determine the destructive capability value and closed-loop time value of each combat loop.

[0088] For a combat ring In other words, , , and If these represent the target node, reconnaissance node, command and control node, and attack node respectively, then... , , and These represent reconnaissance capability, communication capability, command and control capability, and attack capability, respectively. For the entire operational loop, damage capability is an objective evaluation of the loop's own combat capability. It is closely related to the capabilities of its connecting edges; a decrease in the capability of any connecting edge will lead to a decrease in the overall damage capability of the operational loop. Therefore, this paper calculates the operational loop's damage capability based on the multiplication rule, namely:

[0089] Although we have quantitatively characterized the destructive capability of the combat ring, this destructive capability is an objective result, and its value varies from person to person. For example, a combat ring with a destructive capability of 0.5 may meet the operational needs of an adventurous decision-maker, but a conservative decision-maker may need a combat ring with a destructive capability of 0.8 to meet the operational needs. The value of the outcome (consequences) is yet to be determined; that is, quantifying the value of the outcome is the final and most important step in decision-making.

[0090] The most significant difference between the value of an outcome and its actual outcome stems from the fact that people's judgments often rely on reference points, a phenomenon known as reference dependence. When the operational loop's ability to damage the target has reached the decision-maker's psychological expectations (reference point) (similar to a gain, i.e., a successful mission), the decision-maker is risk-averse, and the utility gained from increasing unit damage capability diminishes. Conversely, when the operational loop's ability to damage the target is lower than the decision-maker's psychological expectations (reference point) (similar to a loss, i.e., a failed mission), the decision-maker is risk-seeking, and the utility lost from decreasing damage capability also diminishes. Furthermore, the lower the damage capability is compared to the reference point, the more severe the consequences.

[0091] The value of an outcome determines the decision-maker's preference for that outcome (consequence). Prospect theory uses a value function to represent the decision-maker's preference for objective outcomes. Kahneman and Tversky (1992) provided the value function, the specific form of which is as follows:

[0092] in, Represents the objective result; in this article, it represents destructive capability. The representative reference point is the destructive capability that decision-makers expect to achieve in order to accomplish their combat mission. It is the result Relative to reference point Deviation value; It is a risk attitude coefficient. ,and The larger the value, the more risk-averse the decision-maker is; It is loss sensitivity, if This indicates that decision-makers are more sensitive to losses.

[0093] Based on the above prospect theory, the formula for calculating the destructive capability value of the present invention is as follows:

[0094] In the formula, The destructive capability value of the combat ring, It serves as a reference point for destructive capability, namely, the decision-maker's psychological expectation of destructive capability. Actual destructive power This represents the gain / loss in terms of destructive capability. For a combat ring, the stronger the destructive capability, the better. This represents the benefit of destructive capability, that is, the destructive capability that exceeds the decision-maker's psychological expectations. The loss of destructive capability represents the extent to which the destructive capability falls below the psychological expectations of the target. The value of destructive capability is a characterization of the decision-maker's preference for destructive capability within the operational environment. Sensitivity to returns, For loss sensitivity, if decision-makers are more sensitive to gains than losses, then... , If decision-makers are more sensitive to losses than to gains, then , . Risk aversion coefficient for decision-makers This represents the decision-maker's risk preference coefficient; if the decision-maker is risk-taking, then... If the decision-maker is a middle-of-the-road type, then If the decision-maker is conservative, then .

[0095] The improved value function will The range of possible values ​​has been expanded, the types of decision-makers have been improved, and furthermore, by introducing... This invention incorporates individual sensitivity to gains into the value function. Therefore, it calculates the value of combat ring damage capability based on an improved value function.

[0096] During combat, the formation of a combat loop requires a certain amount of time. The duration from the start of the reconnaissance mission (loop start) to the end of the attack mission (loop termination) is defined as the combat loop closure time. For a combat loop... In other words, , , and If these represent the target node, reconnaissance node, command and control node, and attack node respectively, then... , , These represent the time consumed by the reconnaissance node, command and control node, and attack node to form a closed loop, respectively. The meaning of closed loop time differs for different types of nodes. For a reconnaissance node, it represents the time to detect the target and transmit the information to the command and control node; for a command and control node, it represents the time to process battlefield information, make decisions, and issue combat orders to the attack node; for an attack node, it represents the time to receive combat orders from the command and control node and complete the attack mission. The closed loop time of the combat loop is expressed by the following formula:

[0097] Similar to damage capability, closed-loop time is also an objective result of the operational loop implementation. This invention calculates the value of the operational loop closed-loop time based on an improved value function, serving as a decision-maker's evaluation of the operational loop closed-loop time. The formula for calculating the value of closed-loop time is as follows:

[0098] In the formula, The closed-loop time value of the combat cycle. This serves as a reference point for the closed-loop time, representing the decision-maker's psychological expectation of the closed-loop time. Actual closed-loop time. This represents the gain / loss of closed-loop time. For a combat loop, a shorter closed-loop time is better. This represents the benefit of closed-loop time, meaning the operational loop closed-loop time is shorter than expected. This represents the loss of closed-loop time, meaning the closed-loop time is longer than expected. The value of closed-loop time is a characterization of the decision-maker's preference for the closed-loop time of the operational cycle. Sensitivity to returns, For loss sensitivity, if decision-makers are more sensitive to gains than losses, then... , If decision-makers are more sensitive to losses than to gains, then , . Risk aversion coefficient for decision-makers This represents the decision-maker's risk preference coefficient; if the decision-maker is risk-taking, then... If the decision-maker is a middle-of-the-road type, then If the decision-maker is conservative, then The improved value function will The range of possible values ​​has been expanded, the types of decision-makers have been improved, and furthermore, by introducing... This invention incorporates individual sensitivity to gains into the value function. Therefore, it calculates the value of the operational loop closure time based on an improved value function.

[0099] Step 4: Combining the target value, construct a multi-objective optimization model with damage capability value and closed-loop time value as optimization objectives.

[0100] Assuming the kill net in the red-blue battle contains k One enemy target The Red Team attacks enemy targets sequentially according to their target value. For each enemy target, the Red Team must select a series of equipment from its own arsenal, based on the decision-maker's preferences, to form a combat ring. This creates a combat ring set for each target. The destructive capabilities of the combat ring are combined as follows The closed-loop time set is . and These respectively indicate targets against the enemy. combat ring Its destructive power and closed-loop time.

[0101] The degree of preference for the combat ring is characterized by a value function based on prospect theory. According to the value function, the value of damage capability... and closed-loop time value In other words, the Red Team's decision-makers' operational strategy. The degree of preference is considered. Therefore, the objective of the operational loop decision-making process is to maximize the damage capability value and minimize the closed-loop time value. Since it is impossible to achieve both objectives simultaneously, and damage capability and closed-loop time have different dimensions, they can only be considered as two optimization objectives. This is a typical multi-objective optimization problem, thus requiring research into relevant multi-objective optimization models and algorithms to solve the operational loop decision-making problem.

[0102] Based on the description of the operational environment decision-making problem, this invention constructs the following multi-objective optimization model for operational environment decision-making:

[0103]

[0104] In the formula, The optimization objective corresponds to the destructive capability value of the combat ring. For the first The target value of each target node, and , The total number of target nodes. For the first From the combat ring where each target node is located, from the equipment To equipment Decision variables, The value can be 0 or 1. =1 indicates the first The operational ring containing each target node includes equipment. To equipment The connecting edges, =0 indicates the first The combat ring containing each target node does not include equipment. To equipment The edges connecting the edges; Indicates from equipment To equipment The quality of the connecting edges, This represents the total number of equipment nodes in the kill network, which includes reconnaissance nodes, command and control nodes, attack nodes, and target nodes. The value of the destructive capability of the combat ring; The optimization objective corresponds to the closed-loop time value of the combat cycle. For the first The target value of each target node, and , The total number of target nodes. For the first From the combat ring where each target node is located, from the equipment To equipment Decision variables, The value can be 0 or 1. =1 indicates the first The operational ring containing each target node includes equipment. To equipment The connecting edges, =0 indicates the first The combat ring containing each target node does not include equipment. To equipment The edges connecting the edges; Indicates equipment The time required to form a combat ring This represents the total number of equipment nodes in the kill network, which includes reconnaissance nodes, command and control nodes, attack nodes, and target nodes. The closed-loop time value of the combat cycle.

[0105] The constraints of the multi-objective optimization model for operational loop decision-making are:

[0106]

[0107]

[0108]

[0109] In the formula, This represents the total number of equipment nodes belonging to the Red Team in the kill network. For the first From the combat ring where each target node is located, from the equipment To equipment Decision variables, The value can be 0 or 1. =1 indicates the first The operational ring containing each target node includes equipment. To equipment The connecting edges, =0 indicates the first The combat ring containing each target node does not include equipment. To equipment The connecting edges.

[0110] From constraint (29), we know that A collection of equipment nodes in a kill network. This represents the red team's equipment nodes in the kill web, which contains... k Target nodes (using) l (represented); decision variables are The value ranges from 0 to 1, with 1 indicating that it is aimed at the target. l The combat ring includes equipment To equipment The edges are set to 0 to indicate that they are for the target. l The combat ring does not include equipment To equipment The connecting edges.

[0111] Formula (25) is objective function 1, which means maximizing the weighted total damage capability value of the combat loop for all targets. Wherein, the weights... For the goal value, Represents a node To the node The quality of the connections between them (including reconnaissance capabilities, communication capabilities, command and control capabilities, and attack capabilities). Formula (26) is the objective function 2, which means minimizing the weighted total closed-loop time value of the combat loop for all targets. Among them, the weights For the goal value, Represents a node The time required to form the combat loop. Objective function 1 should be as large as possible to improve the ability to complete combat missions, while objective function 2 should be as small as possible to reduce the risk of target escape or combat loop failure. Formulas (27)-(29) constrain each loop closure from the target... Depart and eventually return to the destination This forms a combat ring.

[0112] Step 5: Solve the multi-objective optimization model to determine the combat loop that meets the preset conditions, specifically including: Step 51: Solve the multi-objective optimization model using the improved NSGA-II algorithm to obtain a set of Pareto optimal solutions.

[0113] Every multi-objective optimization algorithm ultimately generates a Pareto solution set. However, the merits of an algorithm cannot be judged by directly comparing individual Pareto solution sets. Therefore, evaluating the quality of the Pareto solution sets becomes crucial for evaluating the algorithm. To facilitate quantitative comparison of algorithms, this invention uses the following two popular multi-objective optimization algorithm evaluation metrics.

[0114] (1) Hypervolume (HV) The hypervolume value represents the volume of the region in the target space enclosed by the non-dominated solution set obtained by the algorithm and the reference point. A larger hypervolume value indicates better overall performance of the algorithm.

[0115]

[0116] in The size of the solution set, Indicates the first i The hypervolume formed by each solution and the reference point.

[0117] (2) Spacing (SP) The standard deviation of the minimum distance from each solution to all other solutions is calculated to measure the uniformity of the solution set. The smaller the value of this index, the more uniform the solution set.

[0118]

[0119] in The size of the solution set, The distance between consecutive solutions. This represents the average distance.

[0120] Considering the characteristics of the combat-loop decision problem, this invention proposes a modified NSGA-II algorithm structure to adapt to the specific cooperative constraints of the combat-loop decision problem. This invention improves the NSGA-II algorithm in the following two ways: 1) Constructing an initial solution based on the ant colony algorithm. In the combat-loop decision problem, there are many constraints, especially the edge rules of equipment nodes in the combat loop. Therefore, randomly generated initial solutions are not conducive to efficient searching within the feasible region. This invention proposes using the ant colony algorithm to construct the initial population, allowing the algorithm to search directly within the feasible region, reducing search time costs and greatly improving the algorithm's efficiency. 2) Modifying the crossover and mutation operations. Traditional crossover operations randomly select two individuals from the population and pass on superior genes to offspring through the exchange of chromosomes. Traditional mutation operations mainly aim to maintain population diversity. Mutation operations randomly select one individual from the population and mutate one point within that individual to produce a superior individual. However, in the operational loop decision-making problem, directly applying traditional crossover and mutation operations may disrupt the loop structure itself. Therefore, this invention modifies the traditional crossover and mutation operations to adapt them to the operational loop decision-making problem. The NSACGA-Ⅱ algorithm flow is as follows: Figure 4 As shown, the pseudocode is illustrated in Table 2. The improved algorithm will be described in detail later.

[0121] Table 2 NSACGA-II Algorithm

[0122] 1) Encoding rules Since the NSACGA-II algorithm cannot directly process the parameters of the problem space, it is necessary to encode the feasible solutions to the problem as chromosomes in the genetic space. Each combat loop's chromosome consists of five gene positions, representing a combat loop formed by "target → reconnaissance → command and control → strike → target". Assuming the kill net contains n enemy targets, and each enemy target selects one combat loop, then the combat loops for all targets are connected together to form a chromosome of a combat loop scheme, containing a total of 5n gene positions. The chromosome encoding rules in the combat loop decision problem are as follows: Figure 5 As shown.

[0123] 2) Generate the initial population If the initial population is generated randomly on a global scale, a significant amount of time is required to correct the solution, and it is not conducive to efficient searching within the feasible region. Therefore, this invention proposes to construct the initial population using the ant colony algorithm, which greatly improves the efficiency of the algorithm. The main idea of ​​constructing the initial population using the ant colony algorithm is to use pheromones to find paths that satisfy the equipment coordination constraints (target → reconnaissance → command and control → strike → target) specific to the combat cycle. Therefore, the algorithm for generating the initial population based on the ant colony algorithm is shown in Table 3.

[0124] Table 3 Algorithms for generating the initial population

[0125] 3) Crossover and mutation operations This invention designs a genetic operator that ensures the structural stability of the combat ring after crossover and mutation operations. According to chromosome coding rules, a chromosome for a combat ring scheme contains a total of 5n gene loci. During the crossover operation, two chromosomes for combat ring schemes are randomly selected from the population, and then gene loci are randomly selected... One gene locus ( (Assuming a crossover probability), two chromosomes are crossovered at these selected gene positions. This operation ensures that the equipment type at the gene position remains unchanged, thus guaranteeing that the gene order on the chromosome still follows the edge connection rules of the combat ring. In the mutation operation, a chromosome of the combat ring scheme is randomly selected, and then a gene position is randomly selected... One gene locus ( (where is the mutation probability), the chromosome mutates at the selected gene locus, but the mutated gene must correspond to the same equipment type (equipment of the same type is randomly selected from our equipment set for replacement). Furthermore, the gene locus corresponding to the enemy target is not mutated. This improvement to the crossover and mutation operations avoids changes to the edge-connection rules of the combat cycle. The above crossover and mutation operations applicable to combat cycle decision problems are as follows: Figure 6 As shown.

[0126] Step 52: Use the TOPSIS method to determine the operational loop that meets the preset conditions from a set of Pareto optimal solutions, specifically including: The TOPSIS method is used to determine the optimal operational loop from a set of Pareto optimal solutions.

[0127] The NSACGA-II algorithm is used to optimize and solve the multi-pair combat cycle decision problem, ultimately yielding a set of Pareto optimal solutions, i.e., the Pareto front, which is a non-dominated solution set. This invention employs TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution), a ranking method that approximates the ideal solution, to evaluate and filter the Pareto solution set. TOPSIS is a distance-based bipolar reduction method. Its basic principle is to rank the solutions in the non-dominated solution set by comparing their distances to the ideal solution and the negative ideal solution; the solution closest to the ideal solution and furthest from the negative ideal solution is the optimal solution.

[0128] Different targets may have different magnitudes. To avoid the calculated distance favoring a particular target due to large differences in target magnitudes, TOPSIS first normalizes each target. In addition, TOPSIS can incorporate subjective factors, i.e., weighting the normalized targets. If the weights are uncertain, the weights of all targets can be set to be equal. This approach, primarily objective with supplementary subjective factors, greatly improves the applicability of TOPSIS and makes it a general method for reducing non-dominated solution sets. The steps of TOPSIS are as follows: Step 1: Obtain the normalized decision matrix using the vector normalization method; Step 2: Obtain the weighted canonical matrix; Step 3: Determine the ideal solution and the negative ideal solution; Step 4: Calculate the distances from each solution to the ideal solution and the negative ideal solution; Step 5: Calculate how close each solution is to the ideal solution; Step 6: Sort the solutions from highest to lowest based on their proximity.

[0129] A second aspect of this invention discloses a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described method.

[0130] The effectiveness of the method of the present invention is verified below with specific embodiments.

[0131] 1. Case Description The red team has 7 types of equipment, with a total of 60 pieces of equipment. The blue team has 7 types of equipment, with a total of 37 pieces of equipment. The basic attribute settings such as the number of equipment for both the red and blue teams and the number of closed-loop time channels are shown in Tables 4 and 5.

[0132] Table 4 Basic Attribute Settings for Red Team Equipment

[0133] Table 5 Basic Attribute Settings for Blue Team Equipment

[0134] To describe the nodes of the kill net, the attributes of nodes, reconnaissance nodes, command and control nodes, attack nodes, and target nodes need to be characterized by node attributes, as shown in Tables 6 to 10.

[0135] Table 6. Red Team Reconnaissance Node Attribute Settings

[0136] Table 7 Red Team Command Node Attribute Settings

[0137] Table 8. Red Team Attack Node Attribute Settings

[0138] Table 9 Blue Team Target Node Attribute Settings

[0139] Note: F represents the warhead power of the attacking node, and the vulnerable area is a linear function of the warhead power. The larger the slope, the larger the area that is easily damaged, and the more vulnerable the target node is. Furthermore, since B5, B6, and B7 are stationary enemy targets, their speed is zero.

[0140] Table 10 Communication Distance of Red Team Equipment

[0141] 2. Results Analysis The decision information is input into a multi-objective optimization model, and the NSACGA-II algorithm is used for solving the problem. Specific parameter settings are as follows: initial population size is 100, crossover probability is 0.7, mutation probability is 0.02, and maximum number of generations is set to 100. Furthermore, the reference points for damage capability and loop closure time are set to 0.5 and 30, respectively. After parameter settings, the NSACGA-II algorithm proposed in this invention is used to optimize and solve the problem. The Pareto front generated by the algorithm is shown below. Figure 7 As shown.

[0142] The TOPSIS method is then used to rank the Pareto optimal solutions, and finally the operational loop scheme preferred by the decision-maker is selected, with equal weights for both objectives, each being 0.5. The operational loop schemes are shown in Table 11.

[0143] Table 11 Operational Ring Scheme

[0144] 3. Algorithm Comparison To further verify the effectiveness and feasibility of the proposed NSACGA-II algorithm, this invention conducted 10 independent experiments using NSACGA-II, SPEA-II, and NSGA-III algorithms respectively, under the same data conditions. Multi-objective optimization algorithms generate a set of Pareto solutions, making it inconvenient to directly compare the algorithm's performance based on the objective function values ​​of the solutions. Therefore, the performance of the algorithm is analyzed based on the multi-objective evaluation indices HV and SP. The boundary of the Pareto front is considered when calculating HV to determine the reference point. The solution space is as follows: Figure 8 As shown.

[0145] The larger the objective 1 is, the better; the smaller the objective 2 is, the better. Therefore, the solution space boundary in the lower right corner is the Pareto front. Figure 8 It can be determined that the x-coordinate of the Pareto front is not less than 2 and the y-coordinate is not more than 450. Therefore, the reference point of the Pareto front is set as [2, 450].

[0146] The above three algorithms were run 10 times, and the specific data of the generated indicators HV and SP were statistically analyzed. The results are shown in Table 12.

[0147] Table 12 Comparison Results of HV and SP Algorithms

[0148] To provide a more intuitive understanding of the distribution of HV values ​​for each algorithm, bar charts and box plots are created based on the final HV values ​​of the algorithms, such as... Figure 9 As shown. Figure 9 (a) HV bar charts were plotted for 10 experiments of the three algorithms. In each experiment, the first column of the bar chart is the result of the NSACGA-II algorithm, the second column is the result of the SPEA-II algorithm, and the third column is the result of the NSGA-III algorithm. Figure 9 (b) Box plots of HV values ​​from 10 experiments for the three algorithms were drawn. Since a higher HV value is better, from... Figure 9 The distribution obtained by the NSACGA-II algorithm is better. This indicates that the Pareto front generated by the NSACGA-II algorithm is closer to the true Pareto front, and thus performs better in terms of the target value.

[0149] Similarly, to gain a more intuitive understanding of the distribution of SP values ​​for each algorithm, bar charts and box plots are created based on the final SP values ​​of the algorithms, such as... Figure 10 As shown. Figure 10 (a) SP bar charts were plotted for 10 experiments of the three algorithms. In each experiment, the first column of the bar chart is the result of the NSACGA-II algorithm, the second column is the result of the SPEA-II algorithm, and the third column is the result of the NSGA-III algorithm. Figure 10(b) Box plots of SP values ​​from 10 experiments for the three algorithms were drawn. Since smaller SP values ​​are better, from... Figure 10 Based on the above, the NSACGA-II algorithm exhibits the best distribution of SP values. In terms of uniformity, the NSGA-II algorithm still outperforms the SPEA-II algorithm, and is even better than the NSGA-III algorithm.

[0150] Based on the HV and SP metrics, the NSACGA-II algorithm not only generates a Pareto front that is closer to the true Pareto front, but also makes the Pareto front more uniform. In summary, the NSACGA-II algorithm performs better when solving operational cycle decision problems.

[0151] This invention studies a decision-making method for combat loops in kill nets. Based on prospect theory, it fully considers the decision-maker's preferences. We model the combat loop using nodes and edges, and evaluate the target value, damage capability value, and loop closure time value within the combat loop. Based on this, we construct a multi-objective optimization model for combat loop decision-making that considers damage capability value and loop closure time value, and solve this multi-objective optimization problem using the NSACGA-II algorithm based on NSGA-II. The initial solution is constructed using the ant colony algorithm, and the crossover and mutation operations are modified. Compared with other popular multi-objective optimization algorithms (SPEA-II, NSACGA-III), NSACGA-II has better SP values ​​for HV, indicating that the proposed algorithm has superior comprehensiveness and uniformity.

[0152] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention, or modify them into equivalent embodiments, without departing from the scope of the present invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention, without departing from the content of the present invention, should fall within the protection scope of the present invention.

Claims

1. A decision-making method based on prospect theory, characterized in that, include: Based on the attribute information of reconnaissance nodes, command and control nodes, attack nodes, and target nodes, multiple combat rings are constructed; Obtain the target value of a target node in each combat ring compared to target nodes in other combat rings; Prospect theory is used to determine the destructive capability value and closed-loop time value of each of the aforementioned combat loops; Based on the aforementioned target values, a multi-objective optimization model is constructed with the damage capability value and closed-loop time value as optimization objectives; Solve the multi-objective optimization model to determine the combat loop that meets the preset conditions; The destructive capability value of each combat ring is determined using prospect theory, specifically including: The destructive capability value of each combat ring is determined according to a first formula, which is: In the formula, The destructive capability value of the combat ring, It serves as a reference point for destructive power. Actual destructive power Sensitivity to returns, Sensitivity to loss, Risk aversion coefficient for decision-makers This represents the decision-maker's risk preference coefficient; if the decision-maker is risk-taking, then... If the decision-maker is a middle-of-the-road type, then If the decision-maker is conservative, then ; Determining the closed-loop time value for each of the aforementioned operational loops using prospect theory specifically includes: The closed-loop time value of each combat loop is determined according to the second formula, which is: In the formula, The closed-loop time value of the combat cycle. As a reference point for closed-loop time, Actual closed-loop time, Sensitivity to returns, Sensitivity to loss, Risk aversion coefficient for decision-makers This represents the decision-maker's risk preference coefficient; if the decision-maker is risk-taking, then... If the decision-maker is a middle-of-the-road type, then If the decision-maker is conservative, then ; Solving the multi-objective optimization model to determine the operational loop that meets preset conditions specifically includes: The improved NSGA-II algorithm is used to solve the multi-objective optimization model, yielding a set of Pareto optimal solutions, specifically including: The initial solution for the NSGA-II algorithm for solving the multi-objective optimization model is constructed based on the ant colony algorithm. In the crossover operation of the NSGA-II algorithm, chromosomes corresponding to two combat rings are randomly selected, and then chromosomes are randomly selected from gene loci. One gene locus, allowing two chromosomes to be selected. Crossover operations are performed on each gene locus. In the mutation operation of the NSGA-II algorithm, a chromosome of the combat ring is randomly selected, and then a gene locus is randomly selected. A number of gene loci, causing the chromosome to be in the selected... Mutation is performed on each gene locus, requiring that the mutated gene corresponds to the same equipment type, and the gene locus corresponding to the enemy target is not mutated, to obtain a set of Pareto optimal solutions. in, n The number of enemy targets killed within the net. For crossover probability, The mutation probability; The TOPSIS method is used to determine the operational loop that meets the preset conditions from the set of Pareto optimal solutions.

2. The method as described in claim 1, characterized in that, Obtain the target value of a target node in each combat ring relative to target nodes in other combat rings, specifically including: The TODIM method is used to determine the target value of a target node in each operational loop relative to target nodes in other operational loops.

3. The method as described in claim 1, characterized in that, Based on the aforementioned target value, a multi-objective optimization model is constructed with the damage capability value and closed-loop time value as optimization objectives, specifically including: The optimization function of the multi-objective optimization model is determined according to the third formula, which is: In the formula, The optimization objective corresponds to the destructive capability value of the combat ring. For the first The target value of each target node, and , The total number of target nodes. For the first From the combat ring where each target node is located, from the equipment To equipment Decision variables, The value can be 0 or 1. =1 indicates the first The operational ring containing each target node includes equipment. To equipment The connecting edges, =0 indicates the first The combat ring containing each target node does not include equipment. To equipment The edges connecting the edges; Indicates from equipment To equipment The quality of the connecting edges, This represents the total number of equipment nodes in the kill network, which includes reconnaissance nodes, command and control nodes, attack nodes, and target nodes. The value of the destructive capability of the combat ring; The optimization objective corresponds to the closed-loop time value of the combat cycle. For the first The target value of each target node, and , The total number of target nodes. For the first From the combat ring where each target node is located, from the equipment To equipment Decision variables, The value can be 0 or 1. =1 indicates the first The operational ring containing each target node includes equipment. To equipment The connecting edges, =0 indicates the first The combat ring containing each target node does not include equipment. To equipment The edges connecting the edges; Indicates equipment The time required to form a combat ring This represents the total number of equipment nodes in the kill network, which includes reconnaissance nodes, command and control nodes, attack nodes, and target nodes. The closed-loop time value of the combat cycle.

4. The method as described in claim 3, characterized in that, The constraints of the multi-objective optimization model are given in the fourth formula, which is: In the formula, This represents the total number of equipment nodes belonging to the Red Team in the kill network. For the first From the combat ring where each target node is located, from the equipment To equipment Decision variables, The value can be 0 or 1. =1 indicates the first The operational ring containing each target node includes equipment. To equipment The connecting edges, =0 indicates the first The combat ring containing each target node does not include equipment. To equipment The connecting edges.

5. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 4.

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