Method and system for uniformly planning and allocating distributed resources of combustion chamber of solid engine

Abstract

The invention discloses a solid engine combustion chamber distributed resource unified planning and allocation method and system. Firstly, unified modeling is carried out on a complex space-time coupling relation among multiple processes and multiple resources through a time-varying hypergraph and a time extension network; further constructing a four-objective optimization model including completion time, energy consumption, mass loss and distribution robust CVaR risk; adopting Wasserstein distribution robust opportunity constraint to process random disturbance, and ensuring a safety and quality probability threshold value under the condition of uncertain distribution; solving by using a coevolution distribution robust multi-objective optimization algorithm, online calibrating disturbance distribution in combination with digital twinning, and guaranteeing the engineering feasibility of a solution through two-stage feasible region projection; and finally outputting a robust Pareto solution set and an interpretable rescheduling label. According to the method, the problems of low feasible rate and weak risk control of a traditional method under distribution drift are effectively solved, and multi-objective unified optimization of safety, rhythm, energy consumption and quality is realized.

Description

Technical Field

[0001] This invention belongs to the field of production resource planning and scheduling technology, specifically a method and system for unified planning and allocation of distributed resources in a solid rocket motor combustion chamber. Background Technology

[0002] Current continuous loading production lines primarily employ heuristic multi-objective optimization algorithms for scheduling and resource planning, which fail to effectively characterize cross-process resource coupling, risk disturbances, and energy and safety constraints. Particularly in AGV transfer, weighing and mixing, and casting and curing processes, safety and quality fluctuations caused by random disturbances have not been systematically controlled. Existing methods largely rely on static MOPSO or NSGA-II algorithms, lacking robustness and interpretable rescheduling mechanisms. Traditional NSGA-II and MOPSO algorithms have significant limitations in handling distributed drift and mechanistic constraints, including: low feasibility of random solutions; overly strong assumptions about disturbance distribution; and a lack of interpretable rescheduling mechanisms. Specifically, existing technologies have the following shortcomings: 1) Cross-process coupling and safety: The main mixing and pouring gate need to occupy AGV / lifting resources simultaneously, and the cycle time vibration is transmitted to the curing quality and safety margin through temperature control / shear rate; 2) Disconnect between algorithm and model: Heuristic / single-objective approximation is difficult to handle quality and safety probability constraints, makes strong assumptions about the distribution of disturbances, and lacks robustness and auditability against "distribution drift"; 3) Fragile feasible region: Stochastic solutions under multi-resource synchronization and time window constraints are infeasible, and there is a lack of globally consistent projection based on time-extended networks; 4) Lack of mechanism: Energy consumption-temperature rise-fatigue and solidification kinetics are not integrated into the optimization, and are only controlled by empirical thresholds, which makes it difficult to explain "why the rearrangement"; Summary of the Invention

[0003] In view of this, the purpose of this invention is to provide a method and system for unified planning and allocation of distributed resources in solid rocket motor combustors. This method addresses the problem of multi-source heterogeneous resource coordination in continuous propellant production of solid rocket motor combustors by combining hypergraph, chance constraint and multi-objective optimization of distributed bar, and achieving unified allocation of multiple objectives such as safety, energy consumption, quality and cycle time through online calibration with digital twins.

[0004] To achieve the above objectives, the present invention provides the following technical solution: This invention first proposes a method for unified planning and allocation of distributed resources in a solid rocket motor combustion chamber, comprising the following steps: Step 1: Hypergraph Modeling and Temporally Spreading Network Construction: Mapping the multi-source heterogeneous resources and tasks involved in the production line into a time-varying hypergraph Among them, the super-edge This represents the set of multiple resource types that a single task needs to occupy simultaneously; based on the hypergraph, a time-extended network is constructed, discretizing the time dimension into a set of time slots. For each resource Construct nodes and through arc Indicates the time slots between adjacent time slots The occupied or idle state forms a joint constraint representation of the task in the time domain and resource domain; Step 2: Multi-objective optimization modeling: Construct an optimization problem with four objectives: in: Indicates task Completion time; Indicates the total energy consumption of the equipment; Represents the quality loss function; This represents the expected risk of CVaR under the uncertainty set of the Wasserstein distribution; Indicates a task; Indicates control variables; Represents device state variables; This indicates a negative safety margin. Indicates a disturbance; Indicates at confidence level Below, based on distribution family Conditional risk expectation operator; It is a family of fuzzy distributions; Step 3: Chance Constraints and Wasserstein Divide and Bloom Bar Processing: For production disturbance variables Constructing the Wasserstein sphere: in: Represents a family of fuzzy distributions; and Let them represent the true distribution and the empirical distribution, respectively; Forming a robust opportunity constraint: , in: Indicates quality; Indicates the quality threshold; Indicates the safety threshold; This represents the weighting coefficient of the quality constraint; Indicates the weighting coefficient of the safety constraints; Step 4: Solve the problem using the co-evolutionary multi-objective optimization algorithm: The CDRD-MO algorithm is used to solve the problem, and the following core steps are included: Decomposition strategy: using reference vectors The target space is decomposed to construct multiple scalar quantum problems: Dominant archives: Adopted Dominant external archive maintenance non-dominant solution, and adaptive adjustment based on archive density. value; Risk perception speed update: Use importance sampling to estimate the risk gradient and update particle velocity or individual variation direction; Feasible region network flow projection: The solution is restored to the feasible region through a two-stage feasible region projection operator; Step 5: Online calibration of the digital twin: By combining real-time production line status data collected by a digital twin system, the disturbance distribution parameters are dynamically updated through Kalman filtering and multi-fidelity correction, and the Wasserstein sphere radius is adjusted accordingly. With risk parameters ; Step Six: Output an interpretable scheduling scheme: Output a robust Pareto solution set and an interpretable rescheduling label vector. By using sparse optimization, bottleneck resources, key tasks, and risk triggers can be identified.

[0005] Furthermore, in step one, the time-varying hypergraph In this context, resource synchronization occupancy constraints are represented as: in: For the task At any moment The decision variable for whether to start execution; For the task At any moment The decision variable for whether to start execution; For the task At any moment Is it allocated to resources? A binary variable; For the task The start time variable; For discrete-time index variables; For continuous-time index variables; For the task The duration; For the task The end time variable; Capacity / mutual exclusion constraints are expressed as: in: For resources The upper limit of capacity or capability; The constraints on the relationship between the process and the pre-process are expressed as follows: in: For the task The set of preceding tasks; For the preceding task The end time variable; The spatiotemporal flow conservation constraint for AGVs is expressed as: in: For at any time From workstation To the workstation Binary decision variables for transferring materials or tasks; For the previous moment From node To the node Material transfer state variables; As the starting node; For the target node; This is the starting node of the previous transfer.

[0006] Furthermore, in step two, the CVaR risk term is constructed using a dual equivalence form: in: The Lipschitz continuity constraint term of the loss function is represented and obtained through the Jacobian spectral radius approximation; The excess loss function represents the smoothing process; Indicates sample Assign task Disturbance Loss function under given conditions; Represents the overall loss function; Indicates the risk cutoff threshold; Indicates the first One perturbation sample; Indicates risk parameters; Represents the radius of the Wasserstein sphere; Indicates the number of samples.

[0007] Furthermore, in step four, the risk gradient is estimated using importance sampling: in: This represents the fourth objective function after the Wasserstein-CVaR correction; Indicates the decision variable The gradient operator; To smooth the step function; This represents an approximate update mapping based on gradient propagation.

[0008] Furthermore, in step four, the solution is repaired to the feasible region using a two-stage feasible region projection operator, including: The first stage, network flow projection, corrects discrete variables that violate resource capacity or timing constraints by solving the minimum cost flow problem on time-extended networks. in: Indicates from node To the node Resource or task traffic; Represents a node With nodes The unit transmission cost or energy consumption coefficient between them; Represents a node Net supply and demand; This represents the total energy consumption or energy objective function of the system. The second stage, SOCP mechanism repair, involves correcting continuous variables that still violate constraints related to temperature rise, energy consumption, or fatigue mechanisms by solving a second-order cone programming problem. in: Represents the linear constraint coefficient matrix; Represents the vector of linear constraint constants; Indicates the first The coefficient matrix of a second-order cone constraint; Represents the translation vector of the second-order cone constraint; The linear direction vector representing the cone constraint; This represents the bias scalar of the second-order cone constraint.

[0009] Furthermore, the mechanistic coupling constraint includes the exothermic kinetic equation and the temperature rise approximation equation for single-batch casting / curing: in: Indicates the activation energy of the reaction; Indicates the reaction progress factor; Indicates the Arrhenius pre-index factor; This represents the rate of heat release per unit volume; This term represents the product of the gas constant and temperature. Indicates the equivalent specific heat capacity; Indicates the system temperature; Indicates the rate of temperature change; Indicates the system power input item; Represents the heat transfer function; Indicates ambient temperature; The definition of the heat release rate; This indicates the enthalpy change of the reaction.

[0010] Furthermore, in step four, the population update in the co-evolutionary multi-objective optimization algorithm adopts a velocity update strategy based on the reference vector: in: This is the updated particle velocity vector; The particle velocity vector before the update; This is the inertia weighting coefficient; and These are individual learning factors; and These are two random numbers that are uniformly distributed in the interval [0,1]. This represents the best historical position of an individual particle. This represents the particle position vector at the current iteration time. This refers to the adaptive learning rate or step size coefficient. For decision variables The gradient operator; To smooth the risk objective function; Dominant archives control the diversity of solution sets. Values ​​are self-annealed based on file density: in: This is the attenuation coefficient.

[0011] Furthermore, in step five, the radius of the Wasserstein sphere... Dynamically updated based on the quantiles of historical perturbation residuals, satisfying the adaptive update law: in: The updated Wasserstein sphere radius; The radius of the Wasserstein sphere before the update; For adaptive adjustment coefficients; 95% quantile; express The disturbance of a moment; This indicates the estimated disturbance value or the smoothed disturbance state.

[0012] Furthermore, in step six, the interpretable rescheduling label vector Represented as: in: Represents the feature mapping function; Indicates the first The decision variable vector for the next iteration; This represents the sparse weight matrix or projected weights. Represents the sparsity regularization coefficient; Representing vectors The L1 norm.

[0013] The present invention also proposes a system for implementing the above-described method for unified planning and allocation of distributed resources in a solid rocket motor combustion chamber, comprising: Data acquisition module: Real-time acquisition of production line temperature, strain, power and AGV position data via OPC-UA or Modbus industrial protocol; Hypergraph Modeling and Time-Scaling Network Module: Used to build and maintain time-varying hypergraph models and time-scaling networks; The Brussels bar optimization module is equipped with a reference vector generation unit. The file maintenance unit and the risk gradient calculation unit are used to execute the CDRD-MO algorithm; Feasible region repair module: integrates a network flow solver and a second-order cone programming solver to perform two-stage feasible region projection; Digital twin module: includes physical layer model, data layer model and fusion calibration unit, used for real-time correction of disturbance distribution; Interpretable rescheduling module: Employs a sparse constraint optimization method to output a set of bottleneck factors in the task-device-time dimension; Visualization module: Used to graphically display the Pareto frontier, risk probability curve, and resource utilization rate.

[0014] The beneficial effects of this invention are as follows: The unified planning and allocation method for distributed resources in solid rocket motor combustion chambers of this invention, through the construction of an integrated technical solution of "hypergraph-distributed bar optimization-digital twin", has achieved the following technical effects in the continuous propellant production scheduling of solid rocket motors: (1) Breakthroughs in performance optimization and robustness: Through unified modeling of hypergraph and time-extended network, the complex spatiotemporal coupling relationship between multiple processes and resources is accurately characterized, reducing resource conflicts and cycle time jitter from the source, and significantly shortening the production cycle time (Makespan); By introducing Wasserstein partial bar optimization, the dependence of traditional optimization on fixed distributed parameters is upgraded to robust control of the "distributed uncertain set", which enables the scheduling scheme to maintain high performance when facing unknown disturbances such as weighing error, temperature control drift, and AGV delay, effectively reducing the tail risk in the worst case and avoiding quality slippage and safety over-limit; (2) Significant improvements have been made in terms of engineering feasibility and physical consistency: The proposed two-stage feasible domain projection mechanism (network flow + SOCP) forces the solution generated by the algorithm to be repaired to the feasible domain that satisfies all process constraints and mechanism equations, which solves the problem of low feasibility of random solutions in traditional algorithms; by embedding physical laws such as solidification dynamics with SOCP hard constraints, the scheduling decision is not only mathematically optimal, but also physically reliable, which significantly improves the engineering feasibility of the scheme. In summary, this invention addresses the problem of multi-source heterogeneous resource coordination in the continuous propellant production of solid rocket motor combustors. It combines hypergraph, chance constraint, and multi-objective optimization with distributed bar, and achieves unified allocation and improvement of multiple objectives such as safety, energy consumption, quality, and cycle time through online digital twin calibration. Attached Figure Description

[0015] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 A schematic diagram of a hypergraph and time-extended network structure; Figure 2 A schematic diagram of the Wasserstein sphere and the tail risk area of ​​CVaR; Figure 3 Here is a flowchart of the CDRD-MO algorithm; Figure 4 The curves are used to verify the convergence and stability of the algorithm. Figure 5 A diagram of the cloud-edge collaborative self-evolutionary learning structure; Figure 6 This is a schematic diagram of the interpretability analysis interface. Detailed Implementation

[0016] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0017] 1. A method and system for unified planning and allocation of distributed resources in solid rocket motor combustion chambers.

[0018] The method for unified planning and allocation of distributed resources in a solid rocket motor combustion chamber according to this embodiment includes the following steps.

[0019] Step 1: Hypergraph modeling and temporally extended network construction.

[0020] The multi-source heterogeneous resources and tasks involved in the production line, including weighing, mixing, casting, AGV transfer, and hoisting, are mapped as time-varying hypergraphs. Among them, the super-edge This represents the set of multiple types of resources that a single task needs to occupy simultaneously; a time-extended network is constructed based on a hypergraph to discretize the time dimension into a set of time slots. For each resource Construct nodes and through arc Indicates the time slots between adjacent time slots The occupied or idle state forms a joint constraint representation of the task in the time domain and resource domain.

[0021] Time-varying hypergraph In this context, resource synchronization occupancy constraints are represented as: in: For the task At any moment The decision variable for whether to start execution; For the task At any moment The decision variable for whether to start execution; For the task At any moment Is it allocated to resources? A binary variable; For the task The start time variable; For discrete-time index variables; For continuous-time index variables; For the task The duration; For the task The end time variable.

[0022] Capacity / mutual exclusion constraints are expressed as: in: For resources The upper limit of capacity or capability.

[0023] The constraints on the relationship between the process and the pre-process are expressed as follows: in: For the task The set of preceding tasks; For the preceding task The end time variable.

[0024] The spatiotemporal flow conservation constraint for AGVs is expressed as: in: For at any time From workstation To the workstation Binary decision variables for transferring materials or tasks; For the previous moment From node To the node Material transfer state variables; As the starting node; For the target node; This is the starting node of the previous transfer.

[0025] Step 2: Multi-objective optimization modeling.

[0026] Construct an optimization problem with four objectives: in: Indicates task Completion time; Indicates the total energy consumption of the equipment; Represents the quality loss function; This represents the expected risk of CVaR under the uncertainty set of the Wasserstein distribution; Indicates a task; Indicates control variables; Represents device state variables; This indicates a negative safety margin. Indicates a disturbance; Indicates at confidence level Below, based on distribution family Conditional risk expectation operator; It belongs to the fuzzy distribution family.

[0027] The CVaR risk term is constructed using a dual equivalent form: in: The Lipschitz continuity constraint term of the loss function is represented and obtained through the Jacobian spectral radius approximation; The excess loss function represents the smoothing process; Indicates sample Assign task Disturbance Loss function under given conditions; Represents the overall loss function; Indicates the risk cutoff threshold; Indicates the first One perturbation sample; Indicates risk parameters; Represents the radius of the Wasserstein sphere; Indicates the number of samples.

[0028] Step 3: Chance constraints and Wasserstein decomposition bar processing.

[0029] For production disturbance variables Constructing the Wasserstein sphere: in: Represents a family of fuzzy distributions; and Let them represent the true distribution and the empirical distribution, respectively; This represents the Wasserstein distance.

[0030] Forming a robust opportunity constraint: , in: Indicates quality; Indicates the quality threshold; Indicates the safety threshold; This represents the weighting coefficient of the quality constraint; This represents the weighting coefficient of the safety constraints.

[0031] Step 4: Solve using the Co-evolutionary Decomposition-Based Multi-Objective Optimization Algorithm (CDRD-MO), including decomposition strategies, Dominant profiles, risk perception speed updates, and feasible domain network flow projection are considered. Specifically, the CDRD-MO algorithm is used for solving this problem, which includes the following core steps.

[0032] (1) Decomposition strategy: using reference vector The target space is decomposed to construct multiple scalar quantum problems: (2) Dominant archives: Adopted Dominant external archive maintenance non-dominant solution, and adaptive adjustment based on archive density. value; use Dominant archives control the diversity of solution sets. Values ​​are self-annealed based on file density: in: This is the attenuation coefficient.

[0033] (3) Risk perception speed update: Use importance sampling to estimate the risk gradient and update the particle velocity or individual variation direction.

[0034] Risk gradients are estimated using importance sampling: in: This represents the fourth objective function after the Wasserstein-CVaR correction; Indicates the decision variable The gradient operator; To smooth the step function; This represents an approximate update mapping based on gradient propagation.

[0035] The population update in the co-evolutionary multi-objective optimization algorithm adopts a velocity update strategy based on the reference vector. in: This is the updated particle velocity vector; The particle velocity vector before the update; This is the inertia weighting coefficient; and These are individual learning factors; and These are two random numbers that are uniformly distributed in the interval [0,1]. This represents the best historical position of an individual particle. This represents the particle position vector at the current iteration time. This refers to the adaptive learning rate or step size coefficient. For decision variables The gradient operator; To smooth the risk objective function.

[0036] (4) Feasible region network flow projection: through a two-stage feasible region projection operator Repair the solution to the feasible region, including: The first stage, network flow projection, corrects discrete variables that violate resource capacity or timing constraints by solving the minimum cost flow problem on time-extended networks. in: Indicates from node To the node Resource or task traffic; Represents a node With nodes The unit transmission cost or energy consumption coefficient between them; Represents a node Net supply and demand; This represents the total energy consumption or energy objective function of the system.

[0037] The second stage, SOCP mechanism repair, involves correcting continuous variables that still violate constraints related to temperature rise, energy consumption, or fatigue mechanisms by solving a second-order cone programming problem. in: Represents the linear constraint coefficient matrix; Represents the vector of linear constraint constants; Indicates the first The coefficient matrix of a second-order cone constraint; Represents the translation vector of the second-order cone constraint; The linear direction vector representing the cone constraint; This represents the bias scalar of the second-order cone constraint.

[0038] Mechanistic coupling constraints include the exothermic kinetic equations and temperature rise approximation equations for single-batch casting / curing: in: Indicates the activation energy of the reaction; Indicates the reaction progress factor; Indicates the Arrhenius pre-index factor; This represents the rate of heat release per unit volume; This term represents the product of the gas constant and temperature. Indicates the equivalent specific heat capacity; Indicates the system temperature; Indicates the rate of temperature change; Indicates the system power input item; Represents the heat transfer function; Indicates ambient temperature; The definition of the heat release rate; This indicates the enthalpy change of the reaction.

[0039] Step 5: Online calibration of the digital twin.

[0040] By combining real-time production line status data collected by a digital twin system, the disturbance distribution parameters are dynamically updated through Kalman filtering and multi-fidelity correction, and the Wasserstein sphere radius is adjusted accordingly. With risk parameters To maintain consistency between the model and the actual production environment.

[0041] Wasserstein sphere radius Dynamically updated based on the quantiles of historical perturbation residuals, satisfying the adaptive update law: in: The updated Wasserstein sphere radius; The radius of the Wasserstein sphere before the update; For adaptive adjustment coefficients; 95% quantile; express The disturbance of a moment; This indicates the estimated disturbance value or the smoothed disturbance state.

[0042] Step Six: Output an interpretable scheduling scheme: Output a robust Pareto solution set and an interpretable rescheduling label vector. By using sparse optimization, bottleneck resources, key tasks, and risk triggers can be identified.

[0043] Interpretable rescheduled label vector Represented as: in: Represents the feature mapping function; Indicates the first The decision variable vector for the next iteration; This represents the sparse weight matrix or projected weights. Represents the sparsity regularization coefficient; Representing vectors The L1 norm.

[0044] This embodiment also proposes a unified planning and allocation system for distributed resources in a solid rocket motor combustor, used to implement the unified planning and allocation method for distributed resources in a solid rocket motor combustor as described above. The system includes a data acquisition module, a hypergraph modeling and time-spreading network module, a sub-Bruker optimization module, a feasible region repair module, a digital twin module, an interpretable rescheduling module, and a visualization module. Specifically, the data acquisition module collects real-time data on production line temperature, strain, power, and AGV position via OPC-UA or Modbus industrial protocols. The hypergraph modeling and time-spreading network module is used to construct and maintain a time-varying hypergraph model and a time-spreading network. The sub-Bruker optimization module is equipped with a reference vector generation unit, The archive maintenance unit and risk gradient calculation unit are used to execute the CDRD-MO algorithm. Specifically, the sub-Bruker optimization module is also equipped with a dedicated risk gradient calculation unit, which uses dual equivalence form and importance sampling method to perform unbiased estimation of the gradient of CVaR risk. The feasible region repair module integrates a network flow solver and a second-order cone programming solver to perform two-stage feasible region projection. The digital twin module includes a physical layer model, a data layer model, and a fusion calibration unit for real-time correction of perturbation distribution. Among them, the fusion calibration unit dynamically corrects temperature control and time delay distribution parameters based on online least squares method. The interpretable rescheduling module adopts a sparse constraint optimization method to output a set of bottleneck factors in the task-device-time dimension. The visualization module is used to graphically display the Pareto front, risk probability curve, and resource utilization.

[0045] 2. Model Building and Reasoning 2.1 Sets and Variables Task Collection Resource collection Time-varying hypergraph Super-edge This means that a single task requires the simultaneous use of multiple types of resources; Time-extended network layer: Discrete time slot For each resource Construct nodes ,arc Indicates in Occupied / Idle; Decision: (1) , indicating task Is it in the time slot? Start; (2) , indicating task In the time slot Does it consume resources? (3) This indicates that the AGV is in the time slot. Is it an arc? (4) Continuous decision-making: temperature control setting Mixing speed .

[0046] 2.2 Objectives and Constraints (Multi-objectives + Opportunity Constraints + DRO) (1) Multi-objective (minimization) in: This indicates a negative safety margin (the smaller the value, the more dangerous it is). This indicates disturbances (weighing error, temperature control drift, AGV delay, etc.); It belongs to the fuzzy distribution family.

[0047] (2) Hypergraph and resource synchronization constraints Time-varying hypergraph In this context, the resource synchronization constraint (one task triggers a hyperedge, simultaneously locking multiple resources) is represented as: in: For the task At any moment The decision variable for whether to start execution; For the task At any moment The decision variable for whether to start execution; For the task At any moment Is it allocated to resources? A binary variable; For the task The start time variable; For discrete-time index variables; For continuous-time index variables; For the task The duration; For the task The end time variable.

[0048] Capacity / mutual exclusion constraints are expressed as: in: For resources The upper limit of capacity or capability.

[0049] The constraints on the relationship between the process and the pre-process are expressed as follows: in: For the task The set of preceding tasks; For the preceding task The end time variable.

[0050] The spatiotemporal flow conservation constraint for AGVs is expressed as: in: For at any time From workstation To the workstation Binary decision variables for transferring materials or tasks; For the previous moment From node To the node Material transfer state variables; As the starting node; For the target node; This is the starting node of the previous transfer.

[0051] (3) Chance constraints and Wasserstein-DRO: The lower bound of the worst distribution probability for strong robust chance constraints can be given by the first-order martingale inequality or by the Cantelli / Chen-Chebyshev explicit conservative linearization; for the linearly separable case, it is transformed into a second-order cone constraint.

[0052] Assume mass With security The threshold is and Introducing opportunity constraints: But the actual distribution Unknown, only known empirical distribution Define the Wasserstein sphere: Upgraded to strong form: , Upgrade "parameter fluctuations" to "distribution uncertainty" with strong robustness.

[0053] (4) CVaR risk objectives and equivalent reconstruction Define tail loss DRO-CvaR is: Theorem 1 (Dual equivalence, given the implementation path): In On a sphere, the expected risk of CVaR for any The upper bound can be written as an empirical term. By multiplying the Lipschitz upper bound, we obtain the dual equivalent form of the CVaR risk term. The key points of the proof are the Kantorovich–Rubinstein duality and the Lipschitz upper bound of the composite function.

[0054] Specifically, if right It is L-Lipschitz, and The radius of the sphere is ,but: in: Represents the disturbance response function; Represents the disturbance response function The Lipschitz constant.

[0055] Will Substituting, we get: The above equation provides a computable closed upper bound, including the empirical mean and the Wasserstein penalty term, estimating Lip as... The upper bound (dual norm) forms a convex problem embedded in the outer multi-objective layer.

[0056] (5) Mechanism coupling (safety-energy consumption-curing kinetics) Taking the exothermic kinetics of single-batch casting / curing as an example: Conversion rate : Approximate to temperature rise: Will Discretization and approximation with a piecewise linear / second-order cone envelope (to avoid non-convexity) yields the energy-temperature-fatigue hard constraint: The above formula links "safety / quality / energy consumption" to process physics, rather than a simple threshold, which can enhance the ability to resist comparison.

[0057] 2.3 CDRD-MO Solver (for each achievable step) (1) Outer layer: decomposition, reference vector and file Generate reference vector (Covering four-objective simplex); Subproblems ,in For multi-objective optimization models ;maintain Dominant external archives Grid side length Annealing (the greater the crowding).

[0058] (2) Inner layer: evaluation of importance and sampling gradient of the bar. For each candidate solution ,calculate: Estimate using the upper bound of the sample gradient (either by norm or Jacobian spectral bound); CVaR subgradient (REINFORCE / indicator function smoothing): in: To smooth out the temperature step (temperature) ).

[0059] (3) Group update and feasible region projection (key engineering techniques) Particle velocity update strategy (or individual mutation): feasible region projection It includes the following steps: Step A: Pull the binary variable that violates capacity / synchronization back to the nearest feasible corner (greedy repair); Step B: For the AGV path and time window, solve a minimum cost flow problem using a time-extended network, and then correct the solution. ; Step C: If the mechanistic constraints are violated, adjust... and Solve a small-scale SOCP with minimal changes that satisfy the constraints: Projection allows "infeasible solutions" to quickly return to the feasible region, significantly stabilizing convergence and exhibiting engineering reproducibility.

[0060] (4) Archive resampling and adaptive preferences: in the bounded feasible region, Lipschitz, bounded second moment of noisy gradient While maintaining the diversity of archives, the external archives generated by CDRD-MO cover the true Pareto front with probability 1. Neighborhood. Specifically, increase sample density for high-risk and sparse regions in the archive (importance sampling, variance reduction); support online preferences (e-constraint or ASF) to give the production line more real-time weighting based on safety / cycle time. Treat the speed update strategy and minimum modification to meet constraints as a projected stochastic approximation; archive updates satisfy absorption and sparse coverage; importance sampling ensures variance convergence.

[0061] (5) Integrated multi-objective optimization model of energy consumption-cycle time-synchronization To further reflect the coupling relationship between time constraints, energy consumption dynamics, and synchronization cycle during the continuous charging process of a solid rocket motor, this embodiment introduces an energy consumption sensitive factor based on the original multi-objective model. Synchronized with the beat The following comprehensive optimization objectives are established: in: For the first The cycle cost of each process task; For resources In time Power consumption; This refers to the time deviation between each loading station; and These respectively reflect energy consumption sensitivity and cycle time coordination weight.

[0062] Through the , and By implementing adaptive normalized weight control, this embodiment achieves a three-dimensional dynamic balance of "efficiency-energy consumption-synchronization", thereby ensuring the coordination of the continuous charging cycle and the optimal allocation of energy in multi-station operations.

[0063] Furthermore, to enhance the model's robustness to uncertain perturbations, a Distributed Bar Optimization (DRO) structure based on Wasserstein distance is introduced: in: Represented by empirical distribution Centered on, with radius The Wasserstein sphere is used. Kernel density resampling and empirical smoothing can avoid the problem of model non-convergence under extreme perturbations.

[0064] To ensure the convexity of the model in terms of computability, this embodiment introduces a second-order cone constraint (SOCP) for relaxation. The objective function can then be written as: This transforms the nonlinear constraint into an analytical convex cone structure, ensuring solution stability.

[0065] In theory, the above combinatorial problem satisfies the piecewise convexity condition, and therefore can achieve global convergence through the interior point method and the heuristic multi-agent solution framework.

[0066] 3. Case Description Taking a continuous propellant loading production line for a solid rocket motor combustion chamber as an example, it involves the coordinated operation of multiple resources, including main mixing, premixing, casting, AGVs, and hoisting. Through perturbation modeling of symmetry ±1.5%, temperature control ±0.8℃, and AGV delay, the CDRD-MO algorithm is used for multi-objective optimization of the blobs.

[0067] 3.1 Implementation Examples Example 1: Continuous charging production line for solid rocket motor combustion chamber Resources: 2 main mixers, 2 premixers, 2 casting machines, 5 AGVs, 1 hoisting machine; 20–80 batches / day, time trough Δ=1min.

[0068] Disturbance: Weighing error ~ cutoff N(0, 1.5%) 2 ), AGV delay ~LogN(μ,σ) 2 The temperature control drift is a bounded random walk of ±0.8℃.

[0069] Comparison: Baseline-MOPSO, NSGA-II, rule base, and CDRD-MO (including DRO-CVaR and two-stage projection) in this embodiment.

[0070] Indicators: Feasibility rate, CVaR@0.9, Makespan, energy consumption, quality non-conformity rate, Diversity, explanation of trigger hit rate.

[0071] Statistics: Independent replicates 30 times, mean ± standard deviation, Welch t test (α=0.05), Cliff δ effect size, bootstrap interval (B=1000).

[0072] Expected improvements: Feasibility +15~30%, CVaR reduced by 40~60%, Makespan reduced by 8~12%, energy consumption reduced by 5~10%, and explanation trigger ≥90%.

[0073] Example 2: Ablation experiment (without DRO / without opportunity constraint / without mechanism SOCP / without network flow projection) to verify the contribution of mechanism and projection to stability.

[0074] 3.2 Experimental Results Experimental results show that the method in this embodiment achieves robust allocation of resources across processes while improving safety and feasibility by 30%, reducing worst-case distribution CVaR by 55%, shortening cycle time by 10%, and reducing energy consumption by 8%.

[0075] 1) Robustness: Provides upper bound control for CVaR under distribution drift / long tail conditions; importance sampling reduces variance. The archives maintain cutting-edge coverage.

[0076] 2) Feasibility: Two-stage projection significantly improves feasibility and convergence stability; network flow ensures global consistency, and SOCP ensures mechanism feasibility.

[0077] 3) Multi-objective unified improvement: Reduce the rate of quality defects and the probability of safety exceedances without sacrificing cycle time, and reduce the energy consumption per unit batch.

[0078] 4) Explainable: Sparse triggering factors provide evidence of "when / why / why the bottlenecks are rearranged", supporting process traceability and compliance.

[0079] 3.3 Experimental Procedure This embodiment achieves a balance between robustness, interpretability, and engineering feasibility in the multi-objective scheduling of continuous charge production, demonstrating its potential for widespread application. This embodiment achieves closed-loop unification at three levels: model (hypergraph + time-spreading network + DRO chance constraint + mechanistic SOCP), algorithm (CDRD-MO dual reconstruction and two-stage projection), and system (digital twin + interpretable auditing), providing provable... It achieves near-convergence and risk upper bound control, and realizes online scheduling with high feasibility and high robustness in engineering scenarios.

[0080] like Figure 1 As shown, the hypergraph and time-extended network structure are used to describe the interrelationships and constraints among multiple resources, tasks, and time sequences in the continuous propellant loading process of a solid rocket motor combustor. This model abstracts different processes (such as weighing, premixing, master mixing, casting, curing, and AGV transportation) into node sets. The time dimension is indicated by sub-subscripts. Discretization is performed to form a time-extended dynamic network. Horizontal dashed lines represent the state transfer of the same resource in adjacent time periods, i.e., temporal edges, reflecting the continuity and cycle constraints of tasks in the time dimension. Vertical and intersecting solid lines represent resource competition or synchronous coupling relationships between multiple tasks, i.e., hyperedges, used to characterize physical relationships such as occupancy mutual exclusion, cooperative waiting, and energy consumption coupling between mixing vessels and transfer AGVs.

[0081] In the optimization solution, the nodal state variables can be represented as: Where 1 represents the time when the task or resource is at time 1. Activated. The constraint form of the time-spreading network can be written as: in: Indicates control actions (scheduling decisions). This represents random disturbances (such as AGV delays, temperature control fluctuations, etc.). This formula reflects the dynamic transmission of task status over time.

[0082] Super Edge The cost function for the mutual constraints between tasks is defined as follows: in: Indicates time synchronization error; This indicates the cost of energy consumption coordination. This indicates a quality risk caused by synchronization delay; , and This represents the weighting coefficient. This cost function can map the timing coordination and risk management between processes into the optimization objective.

[0083] The advantage of this hypergraph structure lies in its ability to overcome the limitation of traditional directed graph models, which can only describe binary dependencies, and to simultaneously express joint resource occupation, parallel task competition, and multi-dimensional collaborative relationships. When combined with time-extended networks, it enables global temporal modeling of multiple processes and stages, allowing optimization algorithms to achieve a dynamic balance between resource utilization and energy consumption while ensuring stable cycle time.

[0084] In the solution process, the hypergraph-temporal network structure serves as the foundational topology for the CDRD-MO (Co-evolutionary Distributionally Robust Decomposition for Multi-objective Optimization) algorithm, used to construct feasible region projections and risk propagation paths. Through iterative updates of time node states and weighted distribution of hyperedges, the model dynamically adjusts the coupling weights between different resources, ensuring the feasibility and robustness of optimal scheduling under perturbation conditions. This structure not only possesses a clear physical interpretation but also provides topological support for subsequent Wasserstein-DRO constraints and SOCP projections, serving as a crucial intermediate layer for achieving cloud-edge collaborative optimization.

[0085] like Figure 2 As shown, in constructing a multi-objective optimization model for distributed resource planning and allocation, this embodiment adopts a Distributed Robust Optimization (DRO) mechanism based on Wasserstein distance to model the uncertainty of the input distribution in order to cope with random disturbances and uncertainties in the production process. It also achieves explicit control of losses in the worst-case scenario through CVaR (Conditional Value at Risk) tail risk region constraints.

[0086] The circular boundaries in the figure represent empirical distributions. Centered on, with radius The Wasserstein ball is defined as follows: in: This represents the first-order Wasserstein distance, used to measure the difference between the true distribution and the empirical distribution in terms of probabilistic quality transfer. Parameters The robust radius represents the degree of conservatism of the model towards unknown disturbances: a smaller radius indicates a more robust model. Offers more aggressive performance optimizations, while larger This enhances the defense against extreme perturbations. Within the Wasserstein sphere, the model no longer assumes that the perturbation follows a single fixed distribution, but rather that it occurs over all conditions that satisfy... We perform worst-case expectation optimization on the distribution set to obtain the distributed target: in: Let be the loss function, representing the production scheduling scheme. In random perturbation Performance deviations (such as exceeding cycle time limits, energy consumption fluctuations, or uneven temperature).

[0087] The shaded area in the figure represents the tail risk region of CVaR, which is the region where the loss distribution exceeds a certain confidence level. At a certain point (e.g., the 95th percentile), the system enters a high-risk state. Its mathematical definition is: in: This represents the quantile of the loss distribution. This metric measures the average value of the loss after it exceeds the quantile threshold, reflecting the "tail vulnerability" of the system under extreme perturbations. This embodiment proposes a quantile-bar tail risk control framework (Wasserstein-DRO-CVaR) by combining the Wasserstein sphere with the CVaR risk function. The optimization problem is transformed into: in: This is the risk weighting coefficient, which controls the trade-off between expected performance and tail robustness.

[0088] The core idea of ​​this embodiment is to simultaneously minimize average loss and tail risk in multi-objective scheduling, thereby ensuring that the production system not only operates efficiently under normal conditions but also possesses stability and safety margin under extreme disturbances (such as equipment failure, abnormal temperature control, AGV blockage, etc.). This is achieved by introducing the Wasserstein radius adaptive update law: The model can dynamically adjust its robustness level according to actual disturbances, realizing a robust optimization mechanism of "risk perception-self-adjustment".

[0089] therefore, Figure 2 This not only visually demonstrates the geometric meaning of the bibliometric constraint in probability space, but also reveals the crucial role of CVaR in risk management: the former defines the "uncertainty boundary," while the latter characterizes the "high-risk tail." Together, they enable the production scheduling system for solid rocket motor combustors to maintain optimal performance and safety control in complex environments such as data distribution drift and sudden changes in operating conditions.

[0090] like Figure 3 As shown, the CDRD-MO (Co-evolutionary Distributionally Robust Decomposition for Multi-objective Optimization) algorithm flowchart describes the core optimization process in the unified planning and allocation of distributed resources in the solid rocket motor combustor of this embodiment. The entire algorithm is based on a hypergraph-time-spreading network for modeling and uses Wasserstein-DRO (Multi-objective Distributed Robust Optimization) as the core solution method, realizing a closed loop from task modeling to robust solution. After the process starts from the "Start" node, it first enters the hypergraph modeling and time-spreading network construction stage. This stage uses node sets... and hyper-edge set This characterizes the complex coupling relationship between tasks, resources, and time series. The time dimension is discretized into multiple sub-intervals. This forms a temporal expansion network, where each node... Corresponding resources At any moment The state is represented by edges, which indicate task transfer and process constraints. This structure can simultaneously express parallel, mutual exclusion, and cooperative constraints, providing a topological foundation for subsequent multi-objective optimization.

[0091] The second stage involves constructing a multi-objective optimization model, namely: in: Indicates the production cycle (Makespan); Energy consumption; This refers to quality deviation. This stage addresses the Worst-case CVaR Risk. It unifies the representation of performance metrics into vector form and uses Pareto dominance to achieve multi-objective trade-offs, providing a foundation for the algorithm's biblical decomposition.

[0092] The third stage involves opportunity constraints combined with the Wasserstein-DRO mechanism. This stage introduces bilabiality constraints into the model. That is, the true distribution of disturbances With experience distribution The Wasserstein distance does not exceed the set threshold. This constraint ensures that the algorithm still has a feasible solution when faced with distribution drift or extreme perturbations, and transforms the distribution constraint into a linearly solvable form through dual reconstruction. Meanwhile, the chance constraint guarantees system stability at a certain confidence level, meaning that the scheduling result still satisfies the tick and safety constraints at a 95% or 99% confidence level.

[0093] The fourth stage is the mechanistic SOCP hard constraint embedding (Second-Order Cone Programming). In this stage, multiple physical mechanisms such as thermo-mechanical-fluidic processes are transformed into second-order cone constraints, such as temperature gradients, energy balance, or thermal stress limits. This process embeds real-world mechanistic information into the optimization framework, achieving a fusion from data-driven to mechanistic constraints, ensuring the optimization results have physical consistency and interpretability.

[0094] like Figure 3 As shown, the fifth stage's diamond-shaped decision box " The question mark (?) indicates a robustness test for Wasserstein bars. This is performed when the Wasserstein distance is less than the robust radius threshold. When the condition is met, it indicates that the optimal solution has met the robust feasibility requirement in the probability space. At this point, the algorithm terminates and outputs the optimal scheduling scheme. If the condition is not met, the algorithm returns to the previous step and performs joint optimization of chance constraints and mechanistic projection again until convergence.

[0095] Overall, the evolution path of the CDRD-MO algorithm is as follows: Modeling → Multi-objective decomposition → Sub-Brow bar constraints → Mechanism projection → Robust verification → Convergence output.

[0096] The main features of this algorithm include: (1) Co-evolutionary mechanism: Parallel solution of multi-objective sub-problems, global search achieved through information sharing; (2) DRO-based decomposition: Wasserstein-DRO is used to control the shift of the uncertain distribution; (3) Mechanism embedding and SOCP repair: Ensure that the optimization results conform to the physical constraints of thermo-mechanical-fluid coupling; (4) Convergence self-check: through Determine the robust feasible region. Therefore, Figure 3 This embodiment intuitively demonstrates the hierarchical optimization logic of the algorithm: from hypergraph modeling to solving the sub-Brubars, and then to physical mechanism repair and robustness testing, forming a convergent, interpretable, and implementable multi-objective sub-Brubars optimization closed-loop process.

[0097] like Figure 4 As shown, the convergence and stability of the CDRD-MO (Co-evolutionary Distributionally Robust Decomposition for Multi-objective Optimization) algorithm proposed in this embodiment have been verified in the problem of unified planning and allocation of distributed resources in solid rocket motor combustion chambers. The horizontal axis represents the number of iterations, the left side of the vertical axis represents the comprehensive fitness function value, and the right side represents the CVaR tail risk index. The black dashed line represents the trend of the comprehensive fitness of the algorithm under multi-objective optimization, and the blue dashed line represents the CVaR tail risk curve under the same iteration conditions. It can be seen that in the initial stage (the first 20 iterations), both the fitness value and the CVaR value of the algorithm show a rapid downward trend, indicating that the evolutionary driving force of individuals is strong in the early search process, and the group quickly approaches the Pareto front. Subsequently (the 20th–50th iterations), the rate of decrease in fitness gradually slows down, indicating that the algorithm transitions from the exploration stage to the convergence stage, the diversity among individuals decreases, and the evolutionary search begins to finely adjust around the local optimum. After approximately 50 iterations, Fitness stabilized at around 125 and CVaR stabilized below 145, indicating that the algorithm had reached a balance between multi-objective convergence and risk robustness. Theoretically, the convergence of the CDRD-MO algorithm can be described by the following expected error bounds: in: For the first The solution of the next iteration This is the optimal solution. For learning rate, Let be the perturbation variance. This equation shows that the expected error of the algorithm gradually converges to zero with increasing iterations, and the perturbation term has a limited impact on overall stability. Furthermore, the Wasserstein-DRO mechanism employed by the algorithm ensures the consistency of the objective function gradient under different perturbation distributions, and its Lipschitz continuity constraint is: This makes the input disturbance Even when drift occurs, the optimization process still converges smoothly. Notably, the steady decrease in the CVaR (Conditional Value at Risk) index reflects the role of the biblical bar constraint in risk control. Traditional multi-objective algorithms (such as NSGA-II and MOPSO) typically exhibit CVaR fluctuations or rebounds in the later stages of iteration, while this embodiment introduces a Wasserstein distance constraint into the objective function. By limiting the variation of the perturbation distribution to a controllable range, the risk of tail distribution is effectively reduced. The smooth monotonicity of the CVaR curve in the figure indicates that the system still has high robustness when facing extreme perturbations, and the stability of the optimized solution is significantly better than that of traditional algorithms. In addition, through repeated experiments (N=30), the CDRD-MO algorithm can achieve a feasibility rate of over 95% within 100 iterations in all experiments, indicating that the algorithm not only converges rapidly but also has strong adaptability to initial value selection and sample fluctuations. This stability comes from the algorithm's "co-evolution mechanism," that is, information exchange is achieved between global search and local correction through dual reconstruction and SOCP projection, so that the solution space can maintain asymptotic convergence characteristics in different dimensions.

[0098] Overall, Figure 4 The three key features of the algorithm in this embodiment were verified: (1) fast convergence: the fitness curve decreases monotonically and stabilizes after 50 iterations; (2) risk robustness: the tail risk of CVaR continues to decrease and the fluctuation amplitude is <2%; (3) global stability: a consistent convergence trend can be obtained under different perturbation conditions. The results prove that the CDRD-MO algorithm proposed in this embodiment has good convergence, robustness and repeatability under multi-objective and distributed uncertainty conditions, providing a reliable theoretical and algorithmic basis for the safe and efficient scheduling of the solid rocket motor combustion chamber propellant production line.

[0099] like Figure 5As shown, the cloud-edge collaborative two-stage projection structure proposed in this embodiment is used to realize feasible domain repair and mechanism consistency correction in the distributed resource optimization process. This structure is one of the core modules of the CDRD-MO algorithm, used to dynamically constrain the solution space after multi-objective optimization search, so that the solution simultaneously satisfies the Wasserstein-DRO constraint and the Somatic Physical Constraint (SOCP). The horizontal axis represents the time cost (unit: seconds), and the vertical axis represents the name of each stage. The light yellow bars in the figure correspond to the four stages in sequence: "candidate solution generation", "temporal extended network flow projection", "SOCP mechanism repair" and "feasible solution output". The first stage, "candidate solution generation", is the set of multi-objective non-dominated solutions generated by the CDRD-MO algorithm in the global search stage. By encoding the task timing and resource dependencies through the hypergraph-temporal network structure, several possible scheduling schemes are generated. This stage has a relatively small time cost (approximately 0.2 seconds) and mainly includes objective function evaluation and perturbation sampling operations.

[0100] The second stage, "Time-Expanded Network Flow Projection," ensures consistency between the time series and resource capacity constraints. Specifically, it transforms potential time-series overlaps, resource conflicts, or tick violation issues in the optimization results into a Minimum Cost Flow (MCF) problem, which is then solved as follows: This stage implements adjustments and time window corrections for globally feasible flows. It takes approximately 1.4 seconds, accounting for about 35% of the total computation time. Its output is a structurally consistent, deadlock-free time-series mapping matrix, providing input for subsequent mechanistic constraint repair.

[0101] The third stage, "SOCP mechanism repair," is used to correct the solution for multi-physics consistency, provided that the time constraints are already met. This process employs Second-Order Cone Programming (SOCP) for solution: The constraint terms describe the coupling mechanism between the temperature field, energy balance, and stress tolerance. The introduction of SOCP constraints ensures that each feasible solution is not only numerically feasible but also satisfies the thermo-mechanical-fluid boundary conditions at the physical level. This stage takes approximately 2.1 seconds and is the main computational part of the entire projection process.

[0102] The final stage, "feasible solution output," is used to complete the final solution verification and result feedback within the cloud-edge collaborative architecture. Edge devices (such as Jetson Xavier NX) quickly evaluate the stability and confidence of the projection results using a lightweight verification model and synchronize updates with the cloud scheduler. When Wasserstein distance... When all SOCP constraints are satisfied, the result is determined to be a feasible solution and output for execution.

[0103] From an overall performance perspective, the cumulative time for time-extended network flow projection and SOCP mechanism repair accounts for approximately 80% of the total optimization time, but their contribution to feasibility repair exceeds 90%. The advantages of this phased structure are: (1) Layered collaboration: the cloud is responsible for solving global constraints and evaluating distributed bars, while the edge is responsible for real-time mechanism correction and feasibility judgment; (2) Distributed computation: time complexity is reduced through task splitting, making the algorithm scalable in multi-device environments; (3) Interpretable results: the time and performance indicators of each stage are traceable, facilitating scheduling, diagnosis, and optimization of industrial-grade systems. In summary, Figure 5 This paper visually demonstrates the crucial role of the two-stage projection proposed in the "cloud-edge collaborative optimization" architecture. It not only improves the feasibility and robustness of the scheduling solution but also ensures the physical reliability and real-time implementability of the results, providing key algorithmic support for the highly reliable propellant production of solid rocket motor combustion chambers.

[0104] like Figure 6 As shown, the interpretability analysis module proposed in this embodiment reveals the contribution and risk trigger strength of each process step in the overall performance optimization by visually analyzing the internal characteristics of the multi-objective optimization results. The horizontal axis represents the production process (weighing, premixing, master mixing, casting, AGV), and the vertical axis represents the corresponding trigger strength, with a value range of 0 to 1. The height of each bar reflects the degree of influence of the process on the overall system fluctuation or performance risk. Among them, the casting process has the highest trigger strength (0.9), followed by AGV transfer (0.7) and premixing (0.6), while master mixing (0.5) and weighing (0.3) have relatively lower trigger strengths.

[0105] The core idea of ​​interpretability analysis lies in extracting key processes affecting the fluctuations of the multi-objective function through joint sensitivity decomposition of the Wasserstein-DRO (Divided Broken Bar Optimization) model and SOCP (Socially Independent Programming Conformity) mechanism constraints. Its basic mathematical expression is: in: Indicates the first The perturbation variables of each process affect the objective function; Sensitivity; This represents the disturbance factor corresponding to the process (such as temperature deviation, viscosity fluctuation, AGV delay, etc.). By calculating and normalizing the partial derivatives of each process disturbance with respect to the system performance indicators, the relative proportion of the trigger intensity can be obtained.

[0106] In implementation, the system employs an interpretability mechanism based on gradient-weighted attribution. By hierarchically tracking the iterative process of the CDRD-MO algorithm, it extracts the marginal contribution of each step's features to the target improvement in each optimization round. This method differs from traditional black-box optimization algorithms by integrating the model's internal attention mechanisms (attention weights) with the perturbation sensitivity matrix. Explicit decoupling allows the influencing factors of each process to be quantified and visualized independently.

[0107] The results in the figure show that the trigger intensity of the casting stage is as high as 0.9, indicating that it dominates the overall risk propagation. This is mainly due to the high sensitivity of the casting process to temperature control, viscosity stability, and curing uniformity; even slight deviations can cause quality fluctuations or cycle time delays. The trigger intensities for AGV transfer and premixing are 0.7 and 0.6 respectively, indicating that material conveying and the initial mixing stage have a significant impact on system cycle time and energy consumption; disturbances in these two stages mainly manifest as delays, path congestion, and uneven mixing viscosity. The trigger intensities for the main mixing and weighing stages are relatively low, indicating that they are more controllable within the overall scheduling system and have limited disturbance effects.

[0108] Furthermore, the heatmap construction is not only used to explain the importance of each stage, but can also be further used for risk visualization and decision-making. The system, under a cloud-edge collaborative architecture, will trigger intensity vectors. The data is then sent back to the cloud-based risk monitoring module and combined with the Wasserstein radius dynamic update law: To achieve adaptive adjustment of system robustness. When the trigger strength of a certain process exceeds a threshold (e.g.) The system will automatically adjust the allocation weights, reducing the scheduling priority of the process or increasing the energy consumption tolerance, thereby achieving dynamic risk mitigation. This "interpretable-controllable-verifiable" mechanism breaks through the "black box" limitation of traditional optimization algorithms, giving the optimization results clear physical semantics and engineering guidance significance. By associating interpretable indicators with mechanistic variables, this invention achieves a closed-loop mapping from sub-bar optimization to risk saliency identification, enabling real-time identification of potential bottleneck processes and high-risk nodes in the production system.

[0109] In conclusion, Figure 6The key achievements of the interpretability module of this invention are demonstrated: (1) Quantifying the impact: calculating the process trigger intensity based on gradient sensitivity and attention weight; (2) Identifying bottlenecks: clarifying the dominant role of high-trigger links (pouring, AGV, premixing) on ​​system performance; (3) Guiding scheduling: realizing risk perception and robust self-adjustment through trigger intensity feedback. This module provides a reliable basis for system decision-making, enabling the distributed drug delivery production line to have real-time diagnosis and dynamic risk control capabilities in complex disturbance environments.

[0110] As shown in Table 1, this embodiment sets five key experimental parameters when verifying the performance of the algorithm for unified planning and allocation of distributed resources in solid rocket motor combustors. These parameters cover measurement error, transportation delay, temperature control fluctuation, risk confidence level, and Wasserstein radius. This parameter system comprehensively reflects the multi-source uncertainty characteristics of the production line and their impact on the robustness of the optimization model, providing a unified benchmark for subsequent algorithm stability, risk control, and feasibility analysis.

[0111] First, weighing error This represents the level of random disturbance in the raw material weighing process. Solid propellant batching typically employs high-precision electronic scales or vibratory weighing systems, but slight errors can occur due to factors such as equipment resolution, ambient temperature, and particle adhesion. These errors follow a truncated normal distribution. By limiting the upper and lower bounds, the global impact of unreasonable outliers on the system can be avoided. The introduction of weighing error is mainly used to test the algorithm's sensitivity to input uncertainty and the stability of its solution under parameter fluctuations.

[0112] Secondly, AGV latency ( This study simulates the communication and scheduling delays of an automated material handling system (AGV) under complex production cycles. The delay distribution of AGVs operating between multiple workstations is often skewed due to factors such as path planning, traffic congestion, and node waiting; therefore, a lognormal distribution is used for modeling. This disturbance term directly affects time synchronization and resource contention between tasks and is a key random variable in the time-extended network model. By introducing AGV delay disturbances into the model, the robust scheduling capability of the CDRD-MO algorithm under temporal uncertainties can be evaluated.

[0113] Third, temperature fluctuations This invention is used to characterize the temperature drift during the mixing and casting stages. Because the rheological properties and solidification rate of the combustion chamber slurry are extremely sensitive to temperature, even slight fluctuations can cause viscosity changes and uneven flow. To closely approximate actual working conditions, this invention employs a bounded random walk model to describe the temperature variation: in: The model assumes small-amplitude random perturbations. In dynamic simulations, this model ensures that temperature fluctuations have physical continuity and a controllable range, providing the temperature field input for subsequent SOCP (Self-Constraint of Temperature) mechanisms.

[0114] Fourth, risk confidence level It is a key parameter in the CVaR risk control model, used to determine the cutoff threshold for tail distribution. Its mathematical definition is: in: These are the quantiles of the loss distribution. When When the value is 0.9, the model focuses on the worst-case 10% risk scenario, i.e., the average loss of the system under extreme perturbations. By adjusting... The value can balance conservatism and optimal performance: higher. Enhances risk defense capabilities, but may reduce energy efficiency; lower This improves performance but increases system vulnerability. This embodiment selects... It represents the optimal compromise between safety and efficiency, based on experience.

[0115] Finally, the Wasserstein radius The "uncertainty boundary" characterizes the Distributed Bar Optimization (DRO) model. It is defined as the empirical distribution. With the true distribution Maximum permissible offset at first-order Wasserstein distance: The value of is dynamically adjusted through an adaptive update law: To achieve a risk self-regulation mechanism based on perturbation observation. (Larger) The smaller the value, the more robust the model becomes, but the more conservative it becomes. The value makes the model more agile but more susceptible to distribution drift. In the experiment... The value varies within the range of 0.05-0.10, balancing robustness and computational efficiency.

[0116] In summary, the five parameters in Table 1 together constitute the basic scenario for system simulation and optimization. Weighing error and AGV delay represent operational-level disturbances, temperature control fluctuations reflect physical-level uncertainties, and risk confidence and Wasserstein radius embody the robust control mechanism at the algorithm level. Mathematically, they correspond to the noise term, delay constraint, mechanistic boundary, and bibloc domain in the model, respectively, enabling the optimization algorithm to maintain interpretability and controllability under multi-level disturbance conditions.

[0117] This parameter configuration table serves not only as the input benchmark for the experimental design but also as the basis for subsequent performance comparisons in Table 2. Figure 4 – Figure 6 The logical premise of the validation curve ensures the reproducibility and statistical validity of the experimental results.

[0118] As shown in Table 2, the CDRD-MO algorithm proposed in this embodiment was systematically compared with two mainstream multi-objective optimization algorithms, MOPSO (Multi-Objective Particle Swarm Optimization) and NSGA-II (Non-dominated Sorting Genetic Algorithm II), in the task of unified planning and allocation of distributed resources in solid rocket motor combustors. Evaluation metrics included feasibility rate, tail risk index CVaR@0.9, production makespan, and energy consumption. The data in the table show that the algorithm in this embodiment exhibits significant advantages in all four core dimensions, verifying its comprehensive superiority under complex perturbation and multi-constraint conditions.

[0119] First, regarding feasibility rate, CDRD-MO achieves a feasible solution ratio of 94.5%, a 16.1% improvement over MOPSO and a 13.3% improvement over NSGA-II. This result demonstrates that the algorithm in this embodiment can more effectively maintain the physical and logical feasibility of solutions under complex mechanistic constraints and distribution drift conditions. Traditional algorithms generate solutions solely through random or Pareto-based crossover and mutation, while this invention introduces a two-stage correction mechanism of time-extended network flow projection and SOCP mechanism repair in each iteration, dynamically maintaining the solution space within the feasible region boundary. This projection-repair strategy effectively avoids the algorithm getting trapped in invalid or unexecutable regions, significantly improving global feasibility.

[0120] Secondly, the CVaR@0.9 (Conditional Value at Risk) metric measures the worst-case expected loss of the system under extreme perturbations and is a key indicator for evaluating the risk robustness of scheduling strategies. MOPSO and NSGA-II have CVaR values ​​of 4.62 and 3.98, respectively, while CDRD-MO has only 2.15, representing a risk reduction of approximately 45%–53%. This result stems from the Wasserstein-DRO partial robustness constraint introduced into the algorithm, which controls the empirical distribution. With the true distribution Wasserstein distance: This mechanism achieves explicit constraints on distribution drift. It makes the optimization results statistically robust to unobserved perturbations, thereby significantly reducing tail risk.

[0121] Third, in terms of production takt time (Makespan), CDRD-MO reduces the total production time to 60.9 minutes, a reduction of 10.7% and 5.6% compared to MOPSO and NSGA-II, respectively. This takt time optimization benefits from the algorithm's "hypergraph-temporally extended network structure" modeling method. This model considers the temporal interlocking and synchronization relationships between multiple processes in resource scheduling. By introducing a "takt time constraint + network flow projection" strategy in multi-objective optimization, it can dynamically balance resource conflicts between tasks, reduce waiting and idle time, and achieve optimal overall takt time.

[0122] Fourth, in terms of energy consumption, CDRD-MO's unit energy consumption is 92.4 kWh, a 10.7% reduction compared to MOPSO and a 6.4% reduction compared to NSGA-II. This is attributed to the algorithm explicitly including the energy consumption function f2(x) in the optimization objective and introducing energy conservation and heat balance equations into the SOCP mechanism constraints. By applying joint energy consumption and risk constraints during the optimization process, CDRD-MO can automatically suppress energy fluctuations while ensuring cycle time and quality, achieving optimal energy efficiency.

[0123] From an overall trend perspective, the CDRD-MO algorithm achieves comprehensive optimization of "high feasibility, low risk, short cycle time, and low energy consumption" in four indicators, demonstrating the following three major technical advantages: (1) Enhanced robustness of the distribution: Through Wasserstein-DRO constraints and adaptive robust radius update mechanism, stable control of the perturbation distribution drift is achieved; (2) Mechanism consistency guarantee: Through SOCP hard constraint embedding, the optimization solution satisfies the physical boundary of thermo-mechanical-fluid coupling, improving the executability and credibility of the solution; (3) Global convergence and energy efficiency balance: Co-evolution and opportunity constraint mechanism ensure that the algorithm dynamically balances multiple objectives, taking into account both cycle time and energy consumption optimization.

[0124] In summary, Table 2 demonstrates the significant performance improvement of the algorithm in this embodiment compared to traditional multi-objective optimization methods. CDRD-MO not only outperforms MOPSO and NSGA-II in numerical metrics, but also achieves breakthroughs in theoretical architecture and interpretability, providing a new, efficient, robust, and engineering-feasible paradigm for multi-objective optimization of sub-Brukers in complex mechanism-constrained manufacturing systems.

[0125] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for unified planning and allocation of distributed resources in a solid rocket motor combustion chamber, characterized in that: Includes the following steps: Step 1: Hypergraph Modeling and Temporally Spreading Network Construction: Mapping the multi-source heterogeneous resources and tasks involved in the production line into a time-varying hypergraph Among them, the super-edge This represents the set of multiple resource types that a single task needs to occupy simultaneously; based on the hypergraph, a time-extended network is constructed, discretizing the time dimension into a set of time slots. For each resource Construct nodes and through arc Indicates the time slots between adjacent time slots The occupied or idle state forms a joint constraint representation of the task in the time domain and resource domain; Step 2: Multi-objective optimization modeling: Construct an optimization problem with four objectives: in: Indicates task Completion time; Indicates the total energy consumption of the equipment; Represents the quality loss function; This represents the expected risk of CVaR under the uncertainty set of the Wasserstein distribution; Indicates a task; Indicates control variables; Represents device state variables; This indicates a negative safety margin. Indicates a disturbance; Indicates at confidence level Below, based on distribution family Conditional risk expectation operator; It is a family of fuzzy distributions; Step 3: Chance Constraints and Wasserstein Divide and Bloom Bar Processing: For production disturbance variables Constructing the Wasserstein sphere: in: Represents a family of fuzzy distributions; and Let them represent the true distribution and the empirical distribution, respectively; Forming a robust opportunity constraint: ， in: Indicates quality; Indicates the quality threshold; Indicates the safety threshold; This represents the weighting coefficient of the quality constraint; Indicates the weighting coefficient of the safety constraints; Step 4: Solve the problem using the co-evolutionary multi-objective optimization algorithm: The CDRD-MO algorithm is used to solve the problem, and the following core steps are included: Decomposition strategy: using reference vectors The target space is decomposed to construct multiple scalar quantum problems: Dominant archives: Adopted Dominant external archive maintenance non-dominant solution, and adaptive adjustment based on archive density. value; Risk perception speed update: Use importance sampling to estimate the risk gradient and update particle velocity or individual variation direction; Feasible region network flow projection: The solution is restored to the feasible region through a two-stage feasible region projection operator; Step 5: Online calibration of the digital twin: By combining real-time production line status data collected by a digital twin system, the disturbance distribution parameters are dynamically updated through Kalman filtering and multi-fidelity correction, and the Wasserstein sphere radius is adjusted accordingly. With risk parameters ; Step Six: Output an interpretable scheduling scheme: Output a robust Pareto solution set and an interpretable rescheduling label vector. By using sparse optimization, bottleneck resources, key tasks, and risk triggers can be identified.

2. The method for unified planning and allocation of distributed resources in a solid rocket motor combustion chamber according to claim 1, characterized in that: In step one, the time-varying hypergraph In this context, resource synchronization occupancy constraints are represented as: in: For the task At any moment The decision variable for whether to start execution; For the task At any moment The decision variable for whether to start execution; For the task At any moment Is it allocated to resources? A binary variable; For the task The start time variable; For discrete-time index variables; For continuous-time index variables; For the task The duration; For the task The end time variable; Capacity / mutual exclusion constraints are expressed as: in: For resources The upper limit of capacity or capability; The constraints on the relationship between the process and the pre-process are expressed as follows: in: For the task The set of preceding tasks; For the preceding task The end time variable; The spatiotemporal flow conservation constraint for AGVs is expressed as: in: For at any time From workstation To the workstation Binary decision variables for transferring materials or tasks; For the previous moment From node To the node Material transfer state variables; As the starting node; For the target node; This is the starting node of the previous transfer.

3. The method for unified planning and allocation of distributed resources in a solid rocket motor combustion chamber according to claim 1, characterized in that: In step two, the CVaR risk term is constructed using a dual equivalent form: in: The Lipschitz continuity constraint term of the loss function is represented and obtained through the Jacobian spectral radius approximation; The excess loss function represents the smoothing process; Indicates sample Assign task Disturbance Loss function under given conditions; Represents the overall loss function; Indicates the risk cutoff threshold; Indicates the first One perturbation sample; Indicates risk parameters; Represents the radius of the Wasserstein sphere; Indicates the number of samples.

4. The method for unified planning and allocation of distributed resources in a solid rocket motor combustion chamber according to claim 3, characterized in that: In step four, the risk gradient is estimated using importance sampling: in: This represents the fourth objective function after the Wasserstein-CVaR correction; Indicates the decision variable The gradient operator; To smooth the step function; This represents an approximate update mapping based on gradient propagation.

5. The method for unified planning and allocation of distributed resources in a solid rocket motor combustion chamber according to claim 1, characterized in that: In step four, the solution is repaired to the feasible region using a two-stage feasible region projection operator, including: The first stage, network flow projection, corrects discrete variables that violate resource capacity or timing constraints by solving the minimum cost flow problem on time-extended networks. in: Indicates from node To the node Resource or task traffic; Represents a node With nodes The unit transmission cost or energy consumption coefficient between them; Represents a node Net supply and demand; This represents the total energy consumption or energy objective function of the system. The second stage, SOCP mechanism repair, involves correcting continuous variables that still violate constraints related to temperature rise, energy consumption, or fatigue mechanisms by solving a second-order cone programming problem. in: Represents the linear constraint coefficient matrix; Represents the vector of linear constraint constants; Indicates the first The coefficient matrix of a second-order cone constraint; Represents the translation vector of the second-order cone constraint; The linear direction vector representing the cone constraint; This represents the bias scalar of the second-order cone constraint.

6. The method for unified planning and allocation of distributed resources in a solid rocket motor combustion chamber according to claim 5, characterized in that: The mechanistic coupling constraints include the exothermic kinetic equation and the temperature rise approximation equation for single-batch casting / curing: in: Indicates the activation energy of the reaction; Indicates the reaction progress factor; Indicates the Arrhenius pre-index factor; This represents the rate of heat release per unit volume; This term represents the product of the gas constant and temperature. Indicates the equivalent specific heat capacity; Indicates the system temperature; Indicates the rate of temperature change; Indicates the system power input item; Represents the heat transfer function; Indicates ambient temperature; The definition of the heat release rate; This indicates the enthalpy change of the reaction.

7. The method for unified planning and allocation of distributed resources in a solid rocket motor combustion chamber according to claim 1, characterized in that: In step four, the population update in the co-evolutionary multi-objective optimization algorithm adopts a velocity update strategy based on the reference vector: in: This is the updated particle velocity vector; The particle velocity vector before the update; This is the inertia weighting coefficient; and These are individual learning factors; and These are two random numbers that are uniformly distributed in the interval [0,1]. This represents the best historical position of an individual particle. This represents the particle position vector at the current iteration time. This refers to the adaptive learning rate or step size coefficient. For decision variables The gradient operator; To smooth the risk objective function; Dominant archives control the diversity of solution sets. Values ​​are self-annealed based on file density: in: This is the attenuation coefficient.

8. The method for unified planning and allocation of distributed resources in a solid rocket motor combustion chamber according to claim 1, characterized in that: In step five, the Wasserstein sphere radius Dynamically updated based on the quantiles of historical perturbation residuals, satisfying the adaptive update law: in: The updated Wasserstein sphere radius; The radius of the Wasserstein sphere before the update; For adaptive adjustment coefficients; 95% quantile; express The disturbance of a moment; This indicates the estimated disturbance value or the smoothed disturbance state.

9. The method for unified planning and allocation of distributed resources in a solid rocket motor combustion chamber according to claim 1, characterized in that: In step six, the interpretable rescheduling label vector Represented as: in: Represents the feature mapping function; Indicates the first The decision variable vector for the next iteration; This represents the sparse weight matrix or projected weights. Represents the sparsity regularization coefficient; Representing vectors The L1 norm.

10. A system for implementing the method for unified planning and allocation of distributed resources in a solid rocket motor combustion chamber as described in any one of claims 1-9, characterized in that: include: Data acquisition module: Real-time acquisition of production line temperature, strain, power and AGV position data via OPC-UA or Modbus industrial protocol; Hypergraph Modeling and Time-Scaling Network Module: Used to build and maintain time-varying hypergraph models and time-scaling networks; The Brussels bar optimization module is equipped with a reference vector generation unit. The file maintenance unit and the risk gradient calculation unit are used to execute the CDRD-MO algorithm; Feasible region repair module: integrates a network flow solver and a second-order cone programming solver to perform two-stage feasible region projection; Digital twin module: includes physical layer model, data layer model and fusion calibration unit, used for real-time correction of disturbance distribution; Interpretable rescheduling module: Employs a sparse constraint optimization method to output a set of bottleneck factors in the task-device-time dimension; Visualization module: Used to graphically display the Pareto frontier, risk probability curve, and resource utilization rate.

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