A method for task allocation and reconstruction of a killing net strike based on distribution robust optimization

Abstract

The application discloses a kind of based on distribution robust optimization's killing net strike task allocation and reconstruction method, it is related to killing net field.For the problem of lack of decision robustness under complex confrontation environment, the method includes: first, obtaining combat task demand and strike node resource data;Determine the constraints such as space, load and redundancy, and use fuzzy set to depict the uncertainty of strike node survival probability distribution;By strong duality theory, the distribution robust optimization problem is converted into a general robust optimization model;Dynamic solution is carried out by branch and cut framework, and the optimal allocation scheme under the worst distribution is obtained;At the same time, in the scene of war damage, the task variation threshold constraint is introduced, and the smooth transition of resilience reconstruction and decision is realized.The application gets rid of the dependence on accurate prior probability or probability distribution, improves the theoretical rigor and interpretability of decision, and balances the decision optimality and computational real-time under complex constraints.

Description

Technical Field

[0001] This invention relates to the field of kill nets, and more particularly to a kill net strike task allocation and reconfiguration method based on split-bar optimization. Background Technology

[0002] In modern high-confrontation environments, combat kill networks rely on efficient coordination between combat nodes. Among them, the strike nodes, as the task execution units of the kill network, directly determine the overall effectiveness of the kill network if they can achieve accurate task matching under resource and environmental constraints. The rationality of task allocation for strike nodes has become the key to improving the combat effectiveness of the kill network system.

[0003] Currently, research on the kill network strike layer mainly focuses on structured system modeling and effectiveness evaluation. Related studies often abstract the kill network into a network model composed of nodes and links, achieving a preliminary quantification of the strike layer's capabilities through topology analysis, functional dependency characterization, and static performance evaluation. In the model solution stage, existing technologies mostly transform the above problems into path optimization or constrained resource scheduling problems in graph theory, and solve them using deterministic mathematical programming or machine learning algorithms. However, deterministic programming methods rely on precisely known assumptions, making it difficult to cope with the uncertainties brought about by the high dynamics and intense confrontation in real battlefields, resulting in poor model robustness. While approximate solution methods based on machine learning show potential for handling nonlinear problems, their "black box" nature lacks rigorous theoretical interpretability guarantees, making it difficult to meet the stringent requirements for security and auditability in military decision-making.

[0004] Meanwhile, the Distributed Robust Optimization (DRO) methodology has demonstrated a significant ability to solve complex uncertainty problems in multiple fields. In areas such as financial investment and risk management, supply chain and logistics, and energy and power systems, the DRO method successfully overcomes the bottleneck of traditional optimization methods in handling uncertainty by modeling the uncertainty of parameters as an "Ambiguity Set" or "uncertainty set." It not only eliminates the dependence of stochastic optimization on precise prior probability distributions and does not require the forced assumption of idealized distribution models such as normal or Poisson distributions, but also achieves robust uncertainty characterization based solely on limited historical data, it avoids the shortcomings of traditional robust optimization, such as overly conservative decision-making, inflated costs, and low resource utilization caused by blindly pursuing extreme worst-case scenarios, thus achieving a balance between decision robustness and efficiency.

[0005] The DRO methodology and the task allocation problem in the kill net strike layer are mathematically highly compatible. Kill net strike nodes are affected by enemy countermeasures, battle damage interference, and communication link fluctuations, resulting in non-deterministic distributions of their operational effectiveness parameters. The modeling framework provided by DRO aligns with the uncertainty modeling needs of the kill net strike layer. Currently, neither academia nor industry has systematically introduced the sub-Bruker optimization perspective into kill net node task allocation research. Therefore, those skilled in the art are dedicated to developing a kill net strike task allocation and reconstruction method based on sub-Bruker optimization. The aim is to construct a general analytical framework that not only rigorously characterizes parameter uncertainty under unknown distributions and ensures operational effectiveness under worst-case distributions, but also, by introducing reconstruction stability constraints, enables resilient reconstruction and rapid decision transitions after battle-damaged nodes fail. This provides a highly efficient optimization method with mathematical rigor and decision interpretability for the kill net strike layer in complex adversarial environments. Summary of the Invention

[0006] In view of the above-mentioned shortcomings of the prior art, the technical problems to be solved by the present invention are poor interpretability of results under the influence of parameter uncertainty, slow algorithm convergence, and lack of balance between decision benefits and robustness.

[0007] To achieve the above objectives, this invention provides a kill net strike task allocation and reconstruction method based on split-bar optimization, characterized in that the method includes the following steps:

[0008] Step 1: Obtain the required data and weights of the combat mission, the resource performance parameters of each strike node, and the operational domain matching relationship and distance information between the combat mission and the strike node;

[0009] Step 2: Construct deterministic constraints such as spatial feasibility constraints, task load constraints, and minimum redundancy constraints;

[0010] Step 3: Assume that the survival probability of the working node follows an unknown distribution, and construct a fuzzy set containing the mean, dispersion and extreme value range based on historical data or expert knowledge to characterize the uncertainty of parameter estimation in combat confrontation environment.

[0011] Step 4: Construct an efficiency function weighted by the objective weights, and use the duality principle to transform the original robust optimization problem into a general robust optimization problem with dual variables containing semi-infinite constraints.

[0012] Step 5: Solve the transformed model using a branching and cutting framework. By introducing a dynamic cutting plane to correct the solution space, until the optimality condition is met, the optimal task allocation scheme under the worst distribution is obtained.

[0013] Furthermore, the deterministic constraints in the steps are constructed as follows: spatial feasibility constraints are limited based on the operational domain matching relationship and the coverage radius of the strike nodes; mission load constraints are limited based on the maximum number of missions that can be assigned to each strike node; and minimum redundancy constraints are limited based on the requirement that each target is covered by at least a preset number of working nodes.

[0014] Furthermore, the process of constructing the fuzzy set includes introducing an auxiliary vector to characterize the deviation between the survival probability and the mean, limiting the fluctuation range of the distribution by constraining the expected deviation of the survival probability distribution to be no greater than a preset dispersion, and determining a support set that includes the range of survival probability values ​​and the range of auxiliary variable values.

[0015] Furthermore, the solution mechanism of the branch cutting framework includes: using a dynamic cutting plane mechanism during the branching and bounding process; if the current candidate solution violates the robustness constraint in the subproblem, then the optimal solution of the subproblem is selected to construct a new cutting plane and inject it into the main problem, and the process is iterated until the convergence condition is met.

[0016] Furthermore, the method also includes a task reconstruction step: under the trigger condition that some attack nodes have failed, the system parameters are updated, and the branch cutting algorithm is called again to solve the problem and obtain the optimal task allocation scheme after reconstruction.

[0017] Furthermore, the constraints in the reconstruction step also include threshold limits for the amount of change in task allocation for each strike node, and threshold limits for the total amount of change in the global task allocation scheme, in order to limit the difference between the reconstructed scheme and the original allocation scheme, so as to ensure the stability of the system decision.

[0018] Furthermore, the final task allocation scheme is represented by a binary allocation matrix, where the element values ​​represent the allocation relationship between strike nodes and combat tasks; the allocation matrix is ​​used to generate a visualization image of the mapping relationship between strike nodes and combat tasks.

[0019] Compared with the prior art, the present invention has at least the following beneficial technical effects:

[0020] 1. This invention enhances the resilience of kill networks in complex adversarial environments. By modeling the uncertainties of key parameters such as the survival probability of strike nodes and communication reliability as "ambiguity sets," it eliminates the over-reliance on precise prior probability distributions and achieves robust characterization of parameter fluctuation ranges using only limited historical data. This effectively overcomes the vulnerability of traditional deterministic programming models to sudden environmental changes, significantly enhances the system's decision robustness, and ensures that the strike mission allocation scheme can maintain operational effectiveness even in harsh scenarios.

[0021] 2. This invention achieves a smooth transition and execution stability of mission reconfiguration schemes in battle-damaged scenarios. Addressing the system reconfiguration needs triggered by strike node failures, this invention innovatively introduces global and local task allocation change threshold constraints into the reconfiguration mathematical model, effectively limiting the adjustment range between the reconfiguration scheme and the original allocation scheme. This mechanism overcomes the drastic oscillations in the decision chain caused by a "global overhaul" reconfiguration strategy, preserves the execution inertia of the original resource scheduling plan, ensures the continuity of kill link recovery in time-sensitive warfare, and enables the combat system to achieve rapid response while maintaining a stable command and control architecture.

[0022] 3. This invention achieves theoretical rigor and interpretability of decision-making results. Unlike existing technologies that rely on "black box" algorithms such as deep reinforcement learning for approximate solutions, this invention utilizes duality theory to transform the complex biblical optimization problem into a general robust optimization model, and employs a branch-and-cut framework for solution. It provides theoretical optimality convergence guarantees from a mathematical perspective and endows the task allocation results with clear physical semantics and logical support, making the final strike plan highly auditable and transparent, meeting the stringent requirements of command and decision-making systems for security, controllability, and high-standard decision support.

[0023] 4. This invention achieves an effective balance between decision optimality and computational real-time performance under complex nondeterministic constraints. Through dual transformation, the difficult-to-handle pluripotent optimization problem is simplified into a more easily solvable general robust optimization problem, and the branch-and-cut framework is used to solve it, reducing the computational complexity and resource consumption of the algorithm. This not only ensures the quality of decisions but also improves the system's response speed in time-sensitive environments, effectively overcoming the technical bottleneck of excessive computational overhead in traditional large-scale network scheduling problems under complex constraints. Attached Figure Description

[0024] Figure 1 This is a flowchart of a kill net strike task allocation and reconstruction method based on split-bar optimization proposed in an embodiment of the present invention.

[0025] Figure 2 This is a schematic diagram of the allocation scheme of the kill net strike task allocation and reconstruction method based on the optimization of the split-bars, as proposed in an embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. The present invention can be embodied in many different forms of embodiments, and the scope of protection of the present invention is not limited to the embodiments mentioned herein. Unless otherwise defined, the technical or scientific terms used herein should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains.

[0027] like Figure 1 As shown, one embodiment of the present invention proposes a kill net strike task allocation and reconstruction method based on split-bar optimization. The specific steps of this method include:

[0028] Step 1: Data Acquisition and Analysis

[0029] The system should first acquire combat situation data as input parameters. Specifically, this includes acquiring: the target set. Target weight (Reflecting the target priority determined during the reconnaissance phase), minimum target redundancy requirements ; Strike node set Strike node communication reliability data (Reflecting the probability that each strike node successfully receives command instructions), the maximum mission load capacity of the strike node. Maximum coverage distance of the strike node Operational domain matching matrix Distance matrix ; and prior data on the survival probability of the attacked nodes.

[0030] Step 2: Constructing Deterministic Constraints

[0031] This step constructs a deterministic mathematical boundary for the allocation of attack resources. The deterministic constraints are constructed as follows:

[0032] Spatial feasibility constraints: These are limited based on the operational domain matching relationship and the coverage radius of the strike nodes to ensure the stability of decision variables. Time-strike node For the target It has coverage capabilities.

[0033] Task load constraint: It is limited based on the maximum number of tasks that can be assigned to each strike node, i.e., the maximum task load capacity.

[0034] Minimum redundancy constraint: This constraint is based on the requirement that each target is covered by at least a preset number of working nodes, i.e., the minimum redundancy requirement.

[0035] Step 3: Constructing the fuzzy set of the survival probability distribution of the attacked nodes

[0036] Due to the complex battlefield environment, the actual survival probability of attacking nodes is... Since it is difficult to obtain an accurate probability distribution, this step constructs a distributed fuzzy set. The specific steps are as follows: Based on analysis of expert knowledge, battlefield situation, historical data, etc., the average node survival probability is obtained. Dispersion Minimum value maximum value Based on this information, we then model the distribution of the following fuzzy set pairs:

[0037]

[0038] Among them support set , These are introduced auxiliary vectors used to characterize... and The deviation.

[0039] Step 4: Objective function construction and dualization

[0040] Construct a performance function weighted by the target weights. Its objective function is in the form of:

[0041]

[0042] Using strong duality theory, construct the Lagrangian function The inner minimization problem is transformed into its dual form, thus transforming the original Bruker optimization problem into a general robust optimization problem with semi-infinite constraints. The objective function and constraints of the general robust optimization after the transformation are as follows:

[0043]

[0044] Step 5: Solve using the branching framework.

[0045] After obtaining the general robust optimization problem with semi-infinite constraints, a branch-and-cut framework is used for solving it. The core mechanism is to dynamically introduce a cutting plane during the branch-and-bound process. The specific steps are as follows:

[0046] Take several Possible values ​​generate an initial cutting plane, which, combined with deterministic constraints, forms a preliminary description of the solution space. The branch and bound algorithm is then initiated to spatially partition the discrete variables, searching for potential optimal solutions within subsets of the solution space, ultimately finding candidate solutions that satisfy all constraints. ;make Define the subproblem as Substitute the current candidate solution as a parameter to solve the subproblem. If the parameter is lower... If the condition is met, the algorithm stops; otherwise, a selection is made that... of Construct new constraints, inject the cutting plane into the main problem, search for potential optimal solutions again, and repeat the above process until the algorithm stops.

[0047] Furthermore, this method includes a task reconstruction step: under the trigger condition that some strike nodes have failed, the system parameters are updated, and the branch cutting algorithm is called again to solve the problem, obtaining the optimal task allocation scheme after reconstruction. New constraints can be added to the reconstruction step, including: a threshold limit on the amount of change in task allocation for each strike node (local stability constraint); and a threshold limit on the total amount of change in the global task allocation scheme (global stability constraint). By limiting the reconstructed scheme... Compared with the original allocation plan The degree of difference between them is used to ensure the stability of system decisions.

[0048] The preferred embodiments of the present invention have been described in detail above. It is readily apparent that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without inventive effort. Therefore, all such modifications and variations made by those skilled in the art based on the concept of the present invention and on the existing technology should be within the scope of protection defined by the claims.

Claims

1. A kill net strike task allocation and reconstruction method based on distributed bar optimization, characterized in that, The method includes the following steps: Step 1: Obtain the required data and weights of the combat mission, the resource performance parameters of each strike node, and the operational domain matching relationship and distance information between the combat mission and the strike node; Step 2: Construct deterministic constraints such as spatial feasibility constraints, task load constraints, and minimum redundancy constraints; Step 3: Assume that the survival probability of the working node follows an unknown distribution, and construct a fuzzy set containing the mean, dispersion and extreme value range based on historical data or expert knowledge to characterize the uncertainty of parameter estimation in combat confrontation environment. Step 4: Construct an efficiency function weighted by the objective weights, and use the duality principle to transform the original robust optimization problem into a general robust optimization problem with dual variables containing semi-infinite constraints. Step 5: Solve the transformed model using a branching and cutting framework. By introducing a dynamic cutting plane to correct the solution space, until the optimality condition is met, the optimal task allocation scheme under the worst distribution is obtained.

2. The kill net strike task allocation and reconstruction method based on split-bar optimization as described in claim 1, characterized in that, The deterministic constraints in the steps are constructed as follows: spatial feasibility constraints are limited based on the operational domain matching relationship and the coverage radius of the strike nodes; task load constraints are limited based on the maximum number of tasks that can be assigned to each strike node; and minimum redundancy constraints are limited based on the requirement that each target is covered by at least a preset number of working nodes.

3. The kill net strike task allocation and reconstruction method based on split-bar optimization as described in claim 1, characterized in that, The process of constructing the fuzzy set includes introducing an auxiliary vector to characterize the deviation between the survival probability and the mean, limiting the fluctuation range of the distribution by constraining the expected deviation of the survival probability distribution to be no greater than a preset dispersion, and determining a support set that includes the range of survival probability values ​​and the range of auxiliary variable values.

4. The kill net strike task allocation and reconstruction method based on split-bar optimization as described in claim 1, characterized in that, The solution mechanism of the branch cutting framework includes: dynamically introducing a cutting plane mechanism during the branching and bounding process; if the current candidate solution violates the robustness constraint in the subproblem, the optimal solution of the subproblem is selected to construct a new cutting plane and inject it into the main problem, and the process is iterated until the convergence condition is met.

5. The kill net strike task allocation and reconstruction method based on split-bar optimization as described in claim 1, characterized in that, The method also includes a task reconstruction step: under the trigger condition that some attack nodes have failed, the system parameters are updated, and the branch cutting algorithm is called again to solve the problem and obtain the optimal task allocation scheme after reconstruction.

6. The kill net strike task allocation and reconstruction method based on split-bar optimization as described in claim 5, characterized in that, The constraints in the reconstruction step also include threshold limits on the amount of change in task allocation for each strike node, and threshold limits on the total amount of change in the global task allocation scheme, which are used to limit the difference between the reconstructed scheme and the original allocation scheme to ensure the stability of system decision-making.

7. The kill net strike task allocation and reconstruction method based on split-bar optimization as described in claim 1, characterized in that, The final task allocation scheme is represented by a binary allocation matrix, where the element values ​​represent the allocation relationship between strike nodes and combat tasks; the allocation matrix is ​​used to generate a visualization image of the mapping relationship between strike nodes and combat tasks.

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