A Modeling and Representation Method for Complex Systems Based on Operad and Complex Networks

Abstract

This invention discloses a method for modeling and representing complex systems based on Operand and complex networks. It constructs a network template, decomposes the system into syntactic and semantic levels based on Operand rules, establishes a syntactic model, a semantic model, and a mapping relationship between the two models, forming a core meta-model based on Operand. This core meta-model is then instantiated to establish a complex network model based on Operand. Based on the structural characteristics of the complex network model, an evaluation index system for the capabilities of complex systems is provided. According to the application problem and the evaluation index system, an optimization objective function is constructed. A genetic algorithm is used for the optimal design of the complex system, resulting in an optimal complex network model. This invention solves the problems of difficulty in the elastic response of systems to dynamic and sudden environments due to complexity and dynamic environmental changes, as well as the low accuracy and efficiency of system modeling and representation, providing an optimal representation and design method for complex system modeling.

Description

Technical Field

[0001] This invention relates to a method for modeling and representing complex systems based on Operad and complex networks, belonging to the field of complex system design and modeling. Background Technology

[0002] Modeling and representing complex systems is one of the core challenges in the field of complex system design modeling. Accurate and efficient modeling and representation of complex systems is a prerequisite for the integrated design of large-scale complex systems. Complex system design modeling involves characterizing and describing complex systems during the equipment design process, aiming to predict and evaluate the structure and behavior of complex task systems that span time and space and are constantly changing. Due to the large number of elements and entities in complex systems, and the complex interactions such as dependencies, competition, and correlations between system components and between the system and its environment, special properties such as nonlinearity, emergence, spontaneous order, adaptability, and feedback loops arise. This makes it difficult to describe interaction patterns and influences, and the number of parameters may increase faster than the size of the system. It is impossible to simply understand the entire system as the sum of its individual components based on reductionism, nor can the deterministic properties of the system be effectively inferred from the behavior of the whole. Even with the most advanced technologies, it is difficult to accurately model such complex systems, leading to decreased performance, unexpected problems, and weak adaptability to the environment.

[0003] To overcome this challenge, it is necessary to explore and innovate mathematical methods that can provide a deep understanding of the interactive behavior of system components, offering a unique perspective on system behavior. This would allow for the separation of the system into manageable and reconfigurable parts, supporting analysis at different granular levels and ensuring the system's maintainability and adaptability throughout its lifecycle. Existing modeling and design methods use the static concept of a "playbook," which fails to adequately represent the complexity of the system and cannot accurately model and understand the elements of complex systems. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose a complex system modeling and characterization method based on Operad and complex networks. By constructing a complex network model based on Operad and a complex network capability index system, this invention solves the problems of difficulty in the elastic response of the system to dynamic and sudden environments caused by complexity and dynamic environmental changes, as well as the low accuracy and efficiency of system modeling and characterization. It provides the optimal characterization and design method for complex system modeling and obtains the optimal results for solving application problems.

[0005] The technical solution of this invention is:

[0006] A method for modeling and representing complex systems based on Operad and complex networks, comprising:

[0007] Define the scope of the complex system and the application problem to be solved, provide the structural elements, functional elements and their parameters involved in solving the application problem, and perform formal modeling to form a network template; the structural elements are the subsystems that make up the complex system, and the functional elements are the functions implemented by the subsystems.

[0008] Based on the network template, the system is decomposed into syntactic and semantic levels according to Operad rules, and a syntactic model, a semantic model and the mapping relationship between the two models are established to form a core meta-model based on Operad.

[0009] Instantiate the core meta-model based on Operad to build a complex network model based on Operad;

[0010] Based on the structural characteristics of complex network models, an evaluation index system for the capabilities of complex systems is proposed.

[0011] Based on the application problem and the evaluation index system of complex system capabilities, an optimization objective function is constructed, and a genetic algorithm is used for the optimization design of complex systems, giving the optimal complex network model.

[0012] The advantages of this invention compared to the prior art are:

[0013] This invention combines the advantages of Operad and complex networks. Based on Operad rules, it decomposes the system into syntactic and semantic levels, establishing syntactic and semantic models and the mapping relationship between them, forming a core meta-model based on Operad. This ensures the composability of subsystems and cross-level structural decomposition and model analysis, enabling the decomposition of large-scale problems within the semantic model and solving the problems of low accuracy and efficiency in system modeling and representation. Under the constraints of the Operad framework, it models the structure and function of the system based on complex network templates. By combining the complex network capability index system with the application problem to design and optimize the objective function, it optimizes the complex network, solving the problems of difficulty in elastic response of the system to dynamic and sudden environments due to complexity and dynamic environmental changes, as well as the problems of low accuracy and efficiency in system modeling and representation. Attached Figure Description

[0014] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0015] Figure 1 This is a flowchart of the complex system modeling and representation method based on Operad and complex networks of the present invention.

[0016] Figure 2 This invention provides a modeling and analysis framework based on Operad and complex networks.

[0017] Figure 3 For network template data in this embodiment of the invention, the operator O is specified. Sail ;

[0018] Figure 4 This is a schematic diagram of complex network modeling operations in an embodiment of the present invention;

[0019] Figure 5 This is a complex network diagram of the search and rescue mission system in an embodiment of the present invention. Detailed Implementation

[0020] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] To address the problems of inaccurate characterization and description of complex dynamic systems and low resilience in responding to complex tasks that span multiple time and space and are constantly changing during the integration of complex systems, this invention proposes a complex system modeling and representation method based on Operad theory and complex networks. By introducing Operad theory and complex network technology, this invention improves the complex system modeling method, aiming to find new ways to model and represent complex dynamic systems and to study innovative mathematical architecture schemes to better understand and express the relationships between dynamic systems that span multiple time and space, thereby fundamentally changing system design to achieve a resilient response to dynamic and sudden environments.

[0022] The present invention is as follows Figure 2 As shown, a descriptive framework and model based on Operad and complex networks are constructed. The structure and function of the system are modeled using a complex network template. Components in the system are viewed as nodes in the network, and their interactions are considered as edges. Operad is then used to describe the combinations of these nodes and edges. Based on Operad mapping rules, a syntactic-semantic model is used to separate the complex system, ensuring complementary alignment after model separation. This enables the decomposition of large-scale problems within the semantic model or the gradual improvement of modeling fidelity across models. The invention includes the following steps: Figure 1 As shown:

[0023] Step 1: Determine the scope of the complex system and the problems to be solved, and provide the structural and functional elements involved in solving the application problems of the complex system, as well as the parameters of the structural and functional elements. Structural elements refer to the subsystems that make up the complex system, and functional elements refer to the functions implemented by the subsystems. Then, perform formal modeling to form a network template.

[0024] Step Two: Construct a core meta-model based on Operad, defining the syntactic model, semantic model, and the mapping relationship between the syntactic and semantic models. Based on Operad rules, the system is decomposed into syntactic and semantic levels, establishing a mapping relationship between the syntactic and semantic models. The syntactic level describes the system's syntactic rules and constraints, while the semantic level describes the system's meaning and behavior. The syntactic model models the syntactic rules of structural elements, defining Operad syntactic operator types, including definitions of complex network structure types, complex network node types, and complex network edge types. The semantic model models the semantic relationships between functional elements involved in solving complex system application problems and the constraints of these functional elements. The mapping relationship between the syntactic and semantic models represents the interaction relationships between structural and functional elements in the complex system using mapping functions in Operad, thus ensuring complementary alignment between the models. The mapping relationship determines the interaction rules between structural and functional elements.

[0025] Step 3: Based on the Operad core meta-model, instantiate the Operad model using the system analysis functor, and give a mathematical model of the mapping relationship between syntax and semantics. This realizes the mapping from syntax to semantics of complex systems. The system analysis functor determines whether subsystems can interact or be combined.

[0026] Step 4: Based on the complex network type, complex network node type, and complex network edge type determined in Step 2, instantiate the complex network, determine the connections between nodes according to the system analysis functor, and give the complex network model based on Operad.

[0027] Step 5: Complex systems should have strong adaptability and robustness, and be able to have strong dynamic response capabilities when facing complex scenarios. Based on the structural characteristics of complex network models, a capability evaluation index system for complex systems is given based on task completion capability, system resilience, system elasticity and communication capability.

[0028] Step Six: Solve the application problem of the complex system using a computational model, and construct an optimization objective function based on the application problem and the evaluation index system of the complex system's capabilities. Use a genetic algorithm to optimize the design of the complex system and give the optimal complex network model.

[0029] In step one of the complex system modeling and representation method based on Operad and complex networks described above, it is necessary to determine the scope of the complex system and the problem to be solved, and to provide the structural and functional elements involved in solving the application problem of the complex system, as well as the parameters of the structural and functional elements. Structural elements refer to the subsystems that make up the complex system, and functional elements refer to the functions implemented by the subsystems. Based on the system application scenario and requirements, the structural and functional elements are formally modeled and given as a network template in the form of a JSON file. For example, the entry 'undirected':{'communication':{'port':['cut':……],……}} represents the undirected relationship of communication. If it is necessary to add system types or interactions between types in the network template, this can be achieved by adding relationships between nodes in the network template.

[0030] In step two of the above-mentioned complex system modeling and representation method based on Operad and complex networks, it is necessary to construct a core meta-model based on Operad and provide the mapping relationship between the grammatical model, the semantic model, and the grammatical and semantic models.

[0031] Traditional methods decompose the design of complex systems into composable modules. This approach is well-suited for describing systems with repetitive structures, such as distributed systems, network protocols, and database systems. However, in practice, it is difficult to divide a system into independent composable modules, and it is unsuitable for systems with highly coupled subsystems. Based on Operad rules, this paper decomposes the system into syntactic and semantic levels, establishing a mapping relationship between the syntactic and semantic models. The syntactic level describes the system's syntactic rules and constraints, while the semantic level describes the system's meaning and behavior. The syntactic model models the syntactic rules of structural elements, defining Operad syntactic operator types, including definitions for complex network structure types, complex network node types, and complex network edge types. The semantic model models the semantic relationships between functional elements involved in solving complex system application problems and the constraints of these functional elements. The mapping relationship between the syntactic and semantic models represents the interactions between structural and functional elements in a complex system using Operad mapping functions, ensuring complementary alignment between the models. The mapping relationship determines the interaction rules between structural and functional elements. This method is a crucial step in solving application problems in complex systems. Traditional methods directly model the application problems, system boundaries, and constraints of elements in complex systems, resulting in poor model reusability and requiring a complete redesign if problems arise. This method adds syntactic and semantic modeling of complex system elements within the Operad core metamodel framework, ensuring design accuracy from a syntactic perspective. Simultaneously, it semantically models the system boundaries and constraints that need to be considered when designing complex systems, ensuring the system can solve application problems. This method makes system design more flexible because semantics can be changed while maintaining syntactic integrity. Furthermore, by aligning the semantic models of different subsystems, we can discover their similarities and differences, thereby improving the efficiency of system design and maintenance.

[0032] First, a grammatical model is constructed, defining the grammatical operators (O). Then, structural elements are used to determine the complex network structure type, including whether it is a simple complex network, a multi-layered network, or a hypernetwork. Next, the node types are determined, including node attributes and the types of edges that can be connected. Finally, the edge types are determined, including whether edges are directed or undirected, whether cyclic or parallel edges are allowed, and whether n-way relationships with n>2 (hyperedges) exist.

[0033] Next, a semantic model is constructed, providing a semantic context (Sem, Set, Rel, ...). The semantic context includes categories such as Set, Cat, Ent, Sem, and Rel to describe semantic relationships. Semantic modeling is needed for the interaction relationships between functional elements and the constraints on these elements. For example, in a complex system, the system boundary can be defined as all entities participating in the task, and the relationships between these entities can be constrained in various ways, such as total task time, equipment dependency, and the order in which equipment executes tasks. Semantic modeling is represented using semantic contexts, which can be selected from the following subcategories.

[0034] Set: This subcategory can be used to describe basic algebraic structures such as groups, rings, and fields. Within this subcategory, arrows represent functions between sets, which can be used to describe basic operations in algebraic systems, such as addition, multiplication, and idempotency.

[0035] Cat: This subcategory can be used to describe some basic concepts in category theory, such as functors, natural transformations, limits, etc. In this subcategory, the arrows represent functors between categories, which can be used to describe the structure and relationships between categories.

[0036] Ent: This subcategory can be used to describe relationships between entities, such as the ownership relationship between a person and an object, or the learning relationship between a student and a course. Within this subcategory, arrows represent relationships between entities, which can be used to describe the interactions and dependencies between them.

[0037] Sem: This subcategory can be used to describe semantic relationships between languages, such as translation, interpretation, conversion, etc. Within this subcategory, arrows represent semantic mappings between languages; these mappings can be used to describe the meaning and expression of different languages.

[0038] Rel: This subcategory can be used to describe relationships between relations, such as composition relations, equivalence relations, order relations, etc. Within this subcategory, arrows represent mappings between relations; these mappings can be used to describe the structure and properties of the relations.

[0039] Finally, the mapping relationship between the grammar and semantic models is constructed. This mapping relationship determines the interaction rules between structural and functional elements. It maps the components of a complex system and their interactions to mapping functions between the grammar and semantics in Operad. These mapping functions provide Operad with different ways to combine and design operations to meet different needs and application scenarios. The mapping rules describe how to combine different operations to generate more complex operations, such as associative, commutative, identity, distributive, or idempotent properties. Specific mapping rules include:

[0040] Composition mapping: describes the composition relationship between two components, that is, the output of one component is used as the input of another component.

[0041] Constraint mapping: describes the constraint relationship between components, that is, the output of one component cannot exceed the specified range of another component.

[0042] Mapping composition: describes the compositional relationship between multiple components, that is, multiple components are combined in a certain order to achieve a function.

[0043] Parallel mapping: describes the parallel relationship between multiple components, that is, multiple components running simultaneously to implement a function.

[0044] In step three of the aforementioned complex system modeling and representation method based on Operad and complex networks, it is necessary to instantiate the Operad model using the system analysis functor based on the Operad core meta-model, providing a mathematical model of the mapping relationship between syntax and semantics, thus realizing the mapping of complex systems from syntax to semantics. The system analysis functor determines whether subsystems can interact or be combined. Compared with traditional methods, the system analysis functor mathematically guarantees the complementary alignment after model separation, enabling the decomposition of large-scale problems within the semantic model.

[0045] By constructing system analysis functors and using these mapping functions, we can build a functor from a complex system to an Operad, which maps the components of the complex system and their interactions to Operads and subcategories. The form of the system analysis functor is shown below.

[0046] f:O→Cat

[0047] f represents the name of the system analysis functor, O represents the syntax operator, which is the mathematical representation of the syntax model, and Cat represents the semantic category of the operator mapping, such as the interaction relationship of the system. The system analysis functor implements the mapping relationship from syntax to semantics.

[0048] In step four of the above-mentioned complex system modeling and characterization method based on Operad and complex networks, it is necessary to instantiate the complex network based on the complex network type, complex network node type, and complex network edge type determined in step two, determine the connections between nodes according to the system analysis functor, and give a complex network model based on Operad.

[0049] Compared with traditional methods that can only represent homogeneous nodes and edges, this method uses complex networks to represent structural and functional elements, can model heterogeneous nodes and edges, and the relationships between nodes can be represented by different types of edges. It can also design complex systems through network structure properties.

[0050] Operad describes how, given some basic operations, more complex structures can be built by combining these operations. Different types are represented as nodes, and these are combined into a task flow network using Operad's composition rules. Tasks are defined as edges, and the weights, source nodes, and target nodes of the edges are determined based on factors such as task urgency, type, and resource type. The constraints in step five are transformed into edge constraints. Operad describes the combination of nodes and edges, thus describing the complexity of the entire system.

[0051] Complex network tools are needed to transform Operad rules and syntactic semantic models into nodes and edges in the network.

[0052] D = (V, E, V) * E * )

[0053] V is the set of network nodes, E is the set of directed edges in the network, V * E is a function that describes the attributes of nodes, describing the state of different nodes. * These are link attribute description functions that describe the status of different links.

[0054] The network node set contains four types of nodes: action, decision, task, and goal.

[0055] V = S∪D∪C∪T

[0056] in For the set of action nodes in the network, For the set of decision-making nodes in the network, It is a set of task-type nodes in the network. This is the set of target-type nodes in the network.

[0057] Complex systems are processes in which different equipment systems cooperate with each other, and various information flows interact within the system to ultimately complete a task. The edges between nodes have different attributes depending on the information flow transmitted, and the edges between nodes have different attributes depending on their functions.

[0058] Side e ij =(v i ,v j ),v i ,v j ∈V indicates that there is some kind of relationship between the nodes, where e ij This indicates that different nodes can interact and cooperate.

[0059] In step five of the above-mentioned complex system modeling and characterization method based on Operad and complex networks, a complex system capability evaluation index system based on the structural characteristics of the complex network model is given, which includes the ability to complete tasks, the system's resilience, the system's elasticity, and the communication capability.

[0060] Compared with traditional evaluation indicators and methods, this method analyzes the topology and system of complex networks. Based on the premise that complex systems should have strong adaptability and robustness and strong dynamic response capabilities when facing complex scenarios, it innovatively proposes four types of indicators: task completion capability, system resilience, system elasticity, and communication capability.

[0061] Definition 1: Task completion capability: Task completion capability reflects the processing of target nodes. It is reflected by the number of paths G from action nodes to target nodes. The more paths there are, the stronger the completion capability.

[0062] Definition 2: System resilience: The ability of a system to maintain a certain level of connectivity and resilience when subjected to damage or attack. The natural connectivity of a network reflects the impact of changes in network edges on the network structure, and thus reflects the network's robustness; therefore, it is used to characterize the system's resilience. Mathematically, it can be derived from the characteristic spectrum of the network's adjacency matrix, denoted as...

[0063]

[0064] Where N is the number of network nodes, λ i Let be the i-th eigenvalue of the network adjacency matrix.

[0065] Definition 3: System Resilience: The ability of a system to quickly recover its network structure after being subjected to random or deliberate attacks reflects the system's flexibility and adaptability. This is mainly reflected by the link-to-node ratio and degree distribution; the more links there are, the stronger the ability to cope with node or edge loss.

[0066]

[0067] Where L is the number of links and N is the number of network nodes.

[0068] Definition 4: Communication Capacity: Represented by the average clustering coefficient of a complex network. The average clustering coefficient is the ratio of the actual number of edges to the number of possible edges in the network, reflecting the degree of closeness between nodes. The higher the average clustering coefficient, the closer the connections between nodes and the stronger the communication capacity.

[0069]

[0070] Where C represents communication capacity, N represents the number of network nodes, and E represents the number of actual edges between nodes; k i Let be the degree of the i-th node.

[0071] Ultimately, this method uses the network structure index Ne to measure network structure.

[0072]

[0073] Where w G , w Q w C The weights are respectively the ability to complete tasks, the system's resilience, the system's flexibility, and the communication capabilities.

[0074] In step six of the above-mentioned complex system modeling and characterization method based on Operad and complex networks, a computational model is required to solve the application problem of the complex system. Based on the application problem and the evaluation index system of the complex system's capabilities, an optimization objective function is constructed, and a genetic algorithm is used to optimize the design of the complex system, giving the optimal complex network model.

[0075] (1) Initialization: Set the generation counter t=0, set the maximum generation T, and randomly generate M individuals as the initial population P(0) based on the system boundary and constraints in step five.

[0076] (2) Individual evaluation: Based on the system analysis functor in step five and the complex system capability evaluation index system in step seven, construct the optimization objective function and calculate the fitness of each individual in the population P(t).

[0077] (3) Selection operation: The selection operator is applied to the population. The purpose of selection is to directly pass on optimized individuals to the next generation or to generate new individuals through pairing and crossover and then pass them on to the next generation. The selection operation is based on the fitness evaluation of individuals in the population.

[0078] (4) Crossover operation: Individuals are selected using the binary tournament method, and new offspring individuals are generated by mutation and crossover operations on the selected parent individuals. The crossover operator generates new offspring individuals by exchanging genes at the same locations on the chromosomes of the parent individuals.

[0079] (5) Mutation operation: The mutation operator is applied to the population. That is, the gene values ​​at certain loci of the individual strings in the population are changed. After selection, crossover and mutation operations, the population P(t) is transformed into the next generation population P(t+1).

[0080] (6) Termination condition judgment: If t = T, then the individual with the highest fitness obtained in the evolution process is output as the optimal solution and the calculation is terminated.

[0081] (7) The optimal solution obtained by the genetic algorithm is presented as a complex system modeling and design result in the form of a complex network.

[0082] To further describe and understand the present invention, an embodiment is provided, which designs and models a responsible system for search and rescue (SAR) missions. The system includes rescue tools and vehicles, and the targets to be rescued include people in the water, crew members, and sailboats. The main task is to utilize various tools to carry out rescue operations on the targets.

[0083] Step 1: Determine the set of complex system elements. For search and rescue missions, eight system types were identified for modeling: P = {Port, Cut, Boat, FW, FSAR, Helo, UAV, QD}. Here, Port represents a port, Cut represents a transport aircraft, Boat represents a ship, FW represents a fixed-wing aircraft, FSAR represents a maritime search and rescue aircraft, Helo represents a helicopter, UAV represents a drone, and QD represents a quadcopter. Ships, aircraft, and helicopters can be stationed at ports to transport smaller search and rescue units, such as quadcopters, to the search area.

[0084] The parameters for each element are as follows:

[0085]

[0086]

[0087] Step 2: Determine the modeling and representation framework based on Operad, formally describe the application problem in JSON file format, and construct the network template, core meta-model, and library.

[0088] (1) Constructing a network template requires determining the system types and the interaction methods between them. The system types involved in determining the network template include eight types: P = {Port, Cut, Boat, FW, FSAR, Helo, UAV, QD}. Each type has attributes such as speed and interface, etc. Figure 3 As shown.

[0089] The template for the bearer relationship network is as follows:

[0090]

[0091]

[0092] (2) Constructing the Core-meta Model

[0093] A three-tiered network model was constructed, incorporating morphisms between network operators and encoding mappings for feasible syntactic variables. Specifically, the top two tiers describe a precise mapping from task scheduling (highest) to task planning (middle). The lowest tier, Λ·, provides a coarser level for planning, allowing for search and rescue system design while ignoring tool attributes.

[0094] (3) For search and rescue mission scenarios, how to combine various rescue tools to achieve the rescue plan with the maximum number of rescue targets and the lowest cost within a certain time? To solve this problem, we choose genetic algorithm to select tools and use complex network tools to solve the rescue plan.

[0095] Step 3: Define and select operators to describe the system. Based on the requirements for complex system modeling and the current elements of the complex system, model and represent the complex system for search and rescue missions. Select independent semantic models for modeling, and ensure the alignment between semantic models through Operad's combination rules, thereby designing and analyzing the system.

[0096] Constructing the bearer network operator O Sail The objects of the operation are a list of atomic system types; the operation description carries the system that carries other systems; the carrying operations can be combined to form new carrying relationships. Among them, Operaad O Sail The specific load-bearing relationships are shown in the table below.

[0097] Cut 2 2 2 5 20 100 Boat 2 10 FW 20 FSAR 20 Helo 5

[0098] Tools can be combined into operations f∈O Sail ,like Figure 5 As shown, f places one QD (blue circle) on Cut (green circle) and another QD (blue circle) on Helo (red circle). The constraint template for the combination operation is as follows:

[0099]

[0100]

[0101] Step 4: Use system analysis functors to describe the combinatorial model and interaction relationships of the system (components, architecture).

[0102] Cost analysis functor cost:O Sail →Set. The cost analysis functor primarily uses associative mapping rules to compare the sum of the costs of different components with the cost budget.

[0103] Cost = Tool cost * Number of tools

[0104] Search efficiency analysis function search:O Sail →Set. The search efficiency analysis functor mainly calculates the search efficiency of different components for the rescue target. The mapping rules include parallel mapping rules and composite mapping rules.

[0105] Scanning efficiency E = Search speed * (1 / 3 * PIW scan width of the person who fell into the water + 1 / 3 * CIR scan width of the crew + 1 / 3 * DS scan width of the sailboat).

[0106] Rescue efficiency function save:O Sail →Set. The rescue efficiency analysis functor primarily analyzes the efficiency of transporting a target to a safe location, assuming the target can move at maximum speed during transport.

[0107] Step 5: Complex system element interaction syntax and semantic modeling, modeling the system boundary and element constraints.

[0108] (1) Combine complex system applications with grammatical operations and semantic modeling.

[0109] For the search and rescue problem, semantics are essential for delivering high-volume searches in a timely manner. Given key parameters for each type, such as speed, duration, search efficiency across various objectives and conditions, parent platform, and initial location; and a description of the search environment, such as expected search distribution and environment size; we assume that all platforms must trace their geographic location back to one of a few base locations so that the system can respond from a base, but are organized to support rapid searches. Once a base is selected, the decision problem becomes choosing operations: what to bring (the type of composite system) and how to organize them (what tasks to perform).

[0110] (2) System elements and boundary constraints

[0111] Regarding the elements and boundary constraints of the search and rescue system, we mainly consider the following types of constraints:

[0112] First, there are constraints on the carrying relationships between elements. For example, the number of QDs carried by FW cannot exceed the maximum number of the largest carrying relationship constraint.

[0113] carry i，j ≤max(O Sail )

[0114] Secondly, there is the fuel constraint. Each subject type is subject to fuel constraints, which limit the working time of each subject. The working time of a tool cannot exceed its own maximum working time and the working time of carrying the tool.

[0115] work≤min(max(work i ,...work j )

[0116] Among them work i Specify your maximum working hours, work j This refers to the maximum working time of the portable tool.

[0117] Thirdly, there are constraints on mission execution capabilities: does the tool possess the ability to perform a mission? For example, a QD (Quick Dive) can only be used for reconnaissance and cannot transport a target to a safe location.

[0118] Fourthly, task allocation constraints. Type vector m j This indicates whether each individual participates in the task; the operation vector ∑j represents which tasks are planned in parallel. Assume a task vector ∑j and a source vector m. j The operation, with target m j+1 =m j +M∑j, where M describes the source-goal relationship of the task. Rows in M ​​correspond to tasks, and columns correspond to individuals performing the tasks. The goal-to-source constraint is m. j+1 ≥M s ∑(j+1), where M s The line specifies the requirements for each task. This constraint prevents a single individual from being assigned conflicting tasks or from "remotely transferring" a task to start.

[0119] Step Six: Design and decompose complex systems based on Operad and complex networks, and use computational models to solve application problems of complex systems.

[0120] (1) Modeling complex networks based on Operad rules

[0121] like Figure 4Based on Operad rules, complex systems are modeled and described using complex networks. In the diagram, white nodes represent action nodes, indicating that the node is a tool capable of performing a task; yellow nodes represent target nodes, which in search and rescue missions are the targets to be rescued; blue nodes represent decision nodes, used to control the input-output relationships between different tasks; and green nodes represent task nodes, such as search tasks and rescue tasks in search and rescue missions. The relationships between nodes are abstracted as edges in the complex network. In practical applications, the complex network is instantiated according to the number of different types of nodes, and the network structure is modified according to different needs.

[0122] The network nodes are shown below:

[0123] S={Boat,Cut,FW,FSAR,Helo,UAV,QD}

[0124] D = {CENTRE}

[0125] C = {SEARCH, SAVE}

[0126] T = {PIW, CIR, S}

[0127] The relationships between the edges between the nodes are shown below:

[0128]

[0129] (2) Solve complex system application problems using computational models.

[0130] To address the specific requirements of search and rescue missions, a trade-off analysis is needed between budget, rescue time, and rescue efficiency to achieve the desired search and rescue objectives. To apply this model to automated design synthesis, the algorithm explores the design under relevant constraints based on the parameters in Table 2. Each rescue tool has a cost, operating time, and rescue area per unit time. Here, it is assumed that each rescue tool has a consistent probability of detecting the target, 0.9, meaning that as long as the target is within the scanning area of ​​the tool, the probability of detection is 0.9. The problem then transforms into maximizing rescue efficiency within a given budget and rescue target constraints. However, the rescue capabilities and the number of targets rescued per mission vary among different tools, making the design of the search and rescue system highly complex due to the variability in the distribution of rescued targets.

[0131] Given a search range of 200 nautical miles, the targets to be rescued are randomly distributed within a square area of ​​200 nautical miles. The total cost budget is 420M. The number of the three types of targets to be rescued are 10, 10, and 2 respectively. Determine the search and rescue system with the shortest rescue time. Each entity node has multiple attributes: the number of PIWs carried by the person in the water, the number of CIRs carried by the crew, the number of DSs carried by the sailboat, the scanning efficiency of the PIWs carried by the person in the water, the scanning efficiency of the CIRs carried by the crew, the scanning efficiency of the DSs carried by the sailboat, cost, and working time. If a refueling aircraft is needed for a long distance, the cost doubles while other attributes remain unchanged. Only Helo aircraft are supported for refueling in this scenario. The target (QD) needs to be transported from the port to another location by other types of tools to begin work. Targets exceeding their working time must return to the port to refuel.

[0132] Based on the search efficiency analysis functor, the objective function of the genetic algorithm is determined.

[0133] F = 1 / (Budget - ∑C) i *N i )+∑E i *N i

[0134] Budget is 420M, N i C represents the number of each tool in the solution. i For the cost of each tool in the solution, E i The scanning efficiency of each tool.

[0135] A genetic algorithm fitness function F is constructed based on cost budget and scanning efficiency to generate feasible rescue system solutions.

[0136] Cut 200M 1 Boat 0.5M 1 FW 60M 1 FSAR 72M 2 Helo 9M 1 UAV 0.25M 17 QD 0.015M 148

[0137] According to Operad O Sail The defined carrying relationships involve a large number of QD (Quick Dash) and UAV (Unmanned Aerial Vehicle) vehicles, but their endurance is relatively short. To search over longer distances, they need to be carried to a fixed location by other tools to begin the search. All types of tools can move at maximum speed during transport and at search speed when searching for the target.

[0138] Based on the generated scheme, a complex network is instantiated, and a search and rescue system based on the complex network is constructed. The entire network has a total of 195 nodes and 393 edges.

[0139] There are a total of 171 action-related nodes.

[0140] S={Boat,Cut,FW,FSAR1,FSAR2,Helo,UAV1,...UAV 17 ,QD1,...,QD 148}

[0141] There are 2 task-related nodes.

[0142] C = {SEARCH, SAVE}

[0143] There are 22 target nodes.

[0144] T = {PIW1, ... PIW} 10 ,CIR1,...CIR 10 ,,DS1,DS2}

[0145] The relationships and weights between nodes are determined according to the Operad rules, resulting in a total of 393 edges.

[0146] Complex network analysis shows that, with a budget of 420M and randomly distributed targets, it would take approximately 17.96 hours to complete the rescue of all targets.

[0147] The embodiments described above are merely preferred embodiments of the present invention. Ordinary variations and substitutions made by those skilled in the art within the scope of the technical solution of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for modeling and representing complex systems based on Operand and complex networks, characterized in that, include: Define the scope of the complex system and the application problem to be solved, provide the structural elements, functional elements and their parameters involved in solving the application problem, and perform formal modeling to form a network template; the structural elements are the subsystems that make up the complex system, and the functional elements are the functions implemented by the subsystems. Based on the network template, the system is decomposed into syntactic and semantic levels according to Operad rules, and a syntactic model, a semantic model and the mapping relationship between the two models are established to form a core meta-model based on Operad. Instantiate the core meta-model based on Operad to build a complex network model based on Operad; Based on the structural characteristics of complex network models, an evaluation index system for the capabilities of complex systems is proposed. Based on the application problem and the evaluation index system of complex system capabilities, an optimization objective function is constructed, and a genetic algorithm is used for the optimization design of complex systems, giving the optimal complex network model.

2. The method for modeling and representing complex systems based on Operad and complex networks according to claim 1, characterized in that, Based on the network template, the system is decomposed into syntactic and semantic levels according to Operad rules, establishing a syntactic model, a semantic model, and the mapping relationship between the two models, including: The grammatical hierarchy describes the grammatical rules and constraints of complex systems. Constructing a grammatical model involves modeling the grammatical rules of structural elements, providing Operand grammatical operator types, and defining complex network structure types, complex network node types, and complex network edge types. Semantic levels describe the meaning and behavior of complex systems. Establishing a semantic model involves semantically modeling the interaction relationships and constraints between functional elements involved in solving application problems of complex systems. The mapping relationship between the grammatical model and the semantic model represents the interaction between structural and functional elements in a complex system using mapping functions in Operad, enabling complementary alignment between the models.

3. The method for modeling and representing complex systems based on Operad and complex networks according to claim 2, characterized in that, Building a grammatical model involves modeling the grammatical rules of structural elements, and defining the Operand grammatical operator types, including: Determine the type of complex network structure, which can be one of the following: simple complex network, multilayer network, or hypernetwork. Determine the types of nodes in a complex network, including node attributes and the types of edges they can connect; the nodes are structural elements of a complex system. Determine the edge type of complex networks, including whether the edges are directed or undirected, whether cyclic or parallel edges are allowed, and whether there are n-directed relationships with n>2.

4. The method for modeling and representing complex systems based on Operad and complex networks according to claim 2, characterized in that, Mapping is performed between the grammar model and the semantic model. Mapping rules include composition mapping, restriction mapping, mapping composition, and parallel mapping. A compositional mapping describes the compositional relationship between two structural elements, where the output of one structural element serves as the input of another. Constraint mapping describes the constraint relationships between structural elements, that is, the output of one structural element cannot exceed the specified range of another structural element; Mapping composition describes the composite relationship between multiple structural elements, that is, multiple structural elements are combined in sequence to achieve specific functions; Parallel mapping describes the parallel relationship between multiple structural elements, that is, multiple structural elements run simultaneously to achieve specific functions.

5. The method for modeling and representing complex systems based on Operad and complex networks according to claim 1, characterized in that, Instantiation of the core metamodel based on Operad includes: By instantiating the core meta-model based on Operad using system analysis functors, a mathematical model of the mapping relationship between syntax and semantics is given: f:O→Cat f represents the name of the system analysis functor; O represents the syntax operator, which is the mathematical representation of the syntax model; and Cat represents the semantic category of the operator mapping. By analyzing the functors, we can determine whether the constituent elements can interact or combine.

6. The method for modeling and representing complex systems based on Operad and complex networks according to claim 2, characterized in that, Establish complex network models based on Operad, including: Based on the types of complex networks, nodes, and edges, and according to the results of the system analysis functor determining whether the constituent elements can interact or combine, the connection relationships between nodes are clarified, forming a complex network model based on Operad, including: Complex network nodes are classified according to their actions, decisions, tasks, and goals to establish a network node set: V = S∪D∪C∪T In the formula, S is the set of action nodes in the network, D is the set of decision-making nodes in the network, C is the set of task nodes in the network, and T is the set of target nodes in the network; Use edge e ij =(v i ,v j ),v i ,v j ∈V indicates that there is some kind of connection between the nodes, and the set of all edges obtained constitutes the directed edge set E of the network; where e ij This indicates that different nodes can interact and cooperate. Forming a complex network model D based on Operad: D=(V,E,V * ,E * ) In the formula, V * E is a function that describes the attributes of nodes, describing the state of different nodes. * These are link attribute description functions that describe the status of different links.

7. The method for modeling and representing complex systems based on Operad and complex networks according to claim 1, characterized in that, The capability evaluation index system for complex systems includes the ability to complete tasks, the system's resilience, the system's flexibility, and its communication capabilities. The ability to complete a task reflects the ability to process the target node, and is represented by the number of paths G from the action node to the target node; System resilience reflects the ability of a complex system to maintain connectivity when subjected to damage and attacks; system resilience is represented by the natural connectivity of the network. In the formula, Let λ be the natural connectivity of the network, N be the number of network nodes, and λ be the number of nodes in the network. i Let i be the i-th eigenvalue of the network adjacency matrix; System resilience reflects the ability of a complex system to quickly recover its network structure after being subjected to random or deliberate attacks; system resilience is represented by the link-to-node ratio. In the formula, Q represents the system's resilience, L represents the number of links, and N represents the number of network nodes; Communication capability is represented by the average clustering coefficient of the complex system: Where C represents communication capacity, N represents the number of network nodes, and E represents the number of actual edges between nodes; k i Let be the degree of the i-th node.

8. The method for modeling and representing complex systems based on Operad and complex networks according to claim 7, characterized in that, Based on the evaluation index system for the capabilities of complex systems, the calculation method for evaluating the network structure of complex systems is as follows: Among them, w G , w Q w C These are respectively the ability to complete the mission (G) and the system's resilience. The weights of the system's resilience Q and communication capability C.

9. The method for modeling and representing complex systems based on Operad and complex networks according to claim 1, characterized in that, To address the application problem, an optimization objective function is constructed, and a genetic algorithm is used to design complex systems, including: (1) Initialization: Set the generation counter t=0, set the maximum generation T, and randomly generate M individuals as the initial population P(0) based on the system analysis functor description system combinatorial model and interaction relationship; (2) Individual evaluation: Construct an optimization objective function based on the evaluation index system of complex system capabilities, and calculate the fitness of each individual in the population P(t); (3) Selection operation: Apply the selection operator to the population to directly pass on the optimized individuals to the next generation or generate new individuals through pairing and crossover and then pass them on to the next generation; (4) Crossover operation: The binary tournament method is used to select individuals, and the selected parent individuals are mutated and crossovered to generate new offspring individuals; (5) Mutation operation: Apply the mutation operator to the population, that is, change the gene value on the gene locus of the individual string in the population; (6) Termination condition judgment: After the population P(t) undergoes selection, crossover and mutation operations, the next generation population P(t+1) is obtained. If t = T, the individual with the highest fitness obtained in the evolution process is output as the optimal solution and the calculation is terminated; otherwise, return to step (2) and repeat the calculation process until t = T is satisfied. (7) The optimal solution obtained by the genetic algorithm is given in the form of a complex network to obtain the modeling and design results of the complex system.

10. The method for modeling and representing complex systems based on Operad and complex networks according to claim 1, characterized in that, Formal modeling is performed on functional elements and the relationships between them, and a network template is created in the form of a JSON file.

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