Multi-algorithm conflict elimination fusion method and device based on bayesian neural network

Abstract

The application relates to the technical field of adaptive fusion solving, and discloses a multi-algorithm conflict elimination fusion method and device based on a Bayesian neural network. The method predicts the performance distribution of different algorithms under given task characteristics through a pre-trained Bayesian neural network model, calculates dynamic weights according to the performance distribution, and further dynamically allocates computing power, time and parallel proportion according to the dynamic weights, so that the optimal algorithm combination is automatically selected without manual intervention. The method can automatically adjust the solving strategy in an environment where the task type frequently changes, and effectively reduces the misjudgment caused by experience dependence and fixed thresholds.

Description

Technical Field

[0001] This application relates to the field of adaptive fusion solution technology, and in particular to a multi-algorithm conflict elimination fusion method and apparatus based on Bayesian neural networks. Background Technology

[0002] In intelligent optimization and autonomous decision-making systems, the multi-objective conflict resolution problem is widely found in areas such as resource allocation, task scheduling, path planning, and collaborative control. Its core task is to coordinate resource allocation and task execution under multiple constraints to eliminate conflicts and maximize overall efficiency. Because such problems typically involve discrete variables, nonlinear constraints, multi-objective coupling, and resource scarcity, they are typical NP-hard problems, and traditional algorithms struggle to balance solution speed, optimality, and stability. Current mainstream methods include Integer Linear Programming (ILP), Genetic Algorithms (GA), and Backtracking Algorithms (BT). For ILP, it obtains the global optimum by establishing an accurate linear model, offering advantages such as verifiable solutions and theoretical completeness. However, in large-scale tasks or scenarios with complex constraints, computation time increases exponentially, easily leading to real-time solution failures. For Genetic Algorithms (GA), it achieves global search through population evolution, suitable for nonlinear and high-dimensional problems, but it is highly sensitive to parameters, exhibits significant early convergence problems, and the stability of the solution depends on random initialization. Backtracking and greedy heuristic algorithms have good interpretability and low computational cost, making them suitable for quickly obtaining feasible solutions. However, due to the limitations of heuristic strategies, they are prone to getting trapped in local optima, resulting in insufficient overall performance.

[0003] To integrate the advantages of various algorithms, researchers have proposed a multi-algorithm fusion framework. This typically employs a hierarchical collaboration between ILP, GA, and backtracking algorithms to achieve a three-layer complementarity of "precise—global—heuristic." However, traditional fusion systems still have several shortcomings, specifically: First, algorithm adaptability cannot be automatically learned: Existing systems usually rely on preset rules (such as the number of objectives, the number of solutions, and constraint sparsity) to select algorithms. This "manually triggered" judgment cannot reflect the nonlinear relationships between features. For example, when constraint density is high and scarcity changes, the performance of different algorithms will alternate; a fixed threshold cannot dynamically reflect this trend, leading to delayed or incorrect algorithm selection. The system cannot learn from historical performance or predict the optimal strategy in different scenarios, resulting in significant insufficient adaptability. Second, weight scheduling lacks dynamic feedback: Traditional fusion methods often allocate fixed weights or time budgets before algorithm execution, without considering changes in the actual contribution of the algorithm during execution. If an algorithm performs well early but converges slowly later, the system will still allocate too many resources, resulting in wasted computation. The lack of online feedback based on unit time efficiency gain results in a lack of closed-loop adjustment capability in the fusion process, affecting both the overall convergence speed and the quality of the results.

[0004] There are also issues with the fusion process: fragmented processes and insufficient information sharing. Most multi-algorithm systems run as independent modules, with no interaction between algorithms in terms of data and intermediate results. For example, high-quality individuals generated by GA cannot guide variable boundary optimization in ILP, nor can they be used for backtracking pruning strategies. As a result, each algorithm repeatedly explores similar regions, leading to low resource utilization. The lack of a unified information interaction layer means that the fusion structure is merely simple parallelism or cascading, rather than true collaborative optimization. There is also a lack of uncertainty modeling and risk awareness: existing fusion frameworks measure algorithm performance using only a single metric (such as average efficiency), ignoring the volatility and stability of algorithm outputs. In practical applications, algorithm performance is significantly affected by random initialization, data perturbation, and constraint changes. Without quantifying uncertainty, the system struggles to determine the reliability of current results and cannot promptly switch algorithms or implement backtracking strategies when performance degrades, resulting in insufficient robustness and safety. Furthermore, there is the problem of inefficiency in the initialization phase: genetic algorithms and backtracking algorithms typically start from random or empirical solutions, lacking targeted guidance, leading to extremely low efficiency in the early search phase. ILP solvers also require a considerable amount of time to construct variable relaxation and constraint sets. Due to a lack of learning of problem characteristics and prediction of initial distribution, the algorithm often consumes a large amount of computational resources during the cold start phase, and the overall response speed cannot meet the requirements of real-time decision-making. There is also the problem of the system lacking self-optimization and continuous learning capabilities: traditional frameworks are mostly static structures and lack experience accumulation mechanisms. Each solution starts from scratch, and the characteristics and performance data of historical tasks are not utilized. As task complexity increases, this "memoryless" mechanism struggles to achieve cross-task transfer and self-evolution, resulting in poor system generalization, severe redundant computation, and a gradual decline in long-term operating efficiency.

[0005] It is evident that existing multi-algorithm conflict resolution methods suffer from problems such as reliance on experience in selection, low cold-start efficiency, and lack of uncertainty modeling. Summary of the Invention

[0006] Based on this, this application provides a multi-algorithm conflict elimination and fusion method and apparatus based on Bayesian neural networks to solve the problems existing in the current multi-algorithm conflict elimination methods, such as algorithm selection relying on human experience, lack of feedback in weight scheduling, fragmented fusion process, inability to quantify uncertainty, and lack of self-learning ability.

[0007] In a first aspect, this application provides a multi-algorithm conflict elimination fusion method based on Bayesian neural networks, including:

[0008] Feature extraction and problem modeling are performed on the processor resource allocation conflict elimination problem in the decision system to be solved, and standardized features are obtained. The processor resource allocation conflict elimination problem in the decision system includes making allocation decisions among multiple computing tasks and processors to eliminate processor resource usage conflicts.

[0009] The standardized features are input into the pre-trained main model of the Bayesian neural network to obtain the performance distribution of different algorithms under the conflict elimination problem.

[0010] Calculate the dynamic weights of different algorithms based on the performance distribution;

[0011] The dynamic weights are input into the pre-trained Bayesian neural network hot starter model to perform multi-algorithm collaborative solution and initialization guidance, thereby obtaining the computing power, time and parallel ratio of each algorithm when running in the decision system.

[0012] The optimal algorithm combination is determined based on the computing power, time, and parallelism ratio of each algorithm in order to eliminate processor resource allocation conflicts in the decision system.

[0013] In one embodiment, the step of extracting features and modeling the problem based on the processor resource allocation conflict elimination problem in the decision system to obtain standardized features includes:

[0014] The problem of processor resource allocation conflict elimination in the decision system to be solved can be expressed in the following form:

[0015] target set

[0016] Each goal There is a set of solutions

[0017] plan The required set of resources is The efficiency is ;

[0018] The following resource upper limit constraints exist:

[0019] ;

[0020] in, Representation scheme Should resource k be used? Let k be the upper limit of resource inventory. ∈{0,1} indicates whether the option is selected;

[0021] Extract scene features and construct the feature vector as follows:

[0022] ;

[0023] In the formula, S represents the problem size, R represents the constraint sparsity, SCAR represents the resource scarcity, GAP represents the difference between the current best feasible solution and the theoretical bound, FR represents the proportion of solutions that can satisfy all constraints in the random sampling or heuristic initial solution generation stage, and CS represents the density of conflicts between different objective solutions. Indicates the number of targets. Indicators representing the diversity of candidate solutions;

[0024] The feature vectors are standardized to obtain the standardized features.

[0025] In one embodiment, before inputting the standardized features into the pre-trained main model of a Bayesian neural network to obtain the performance distribution of different algorithms under the conflict resolution problem, the method further includes:

[0026] The specific steps for training the main model of the Bayesian neural network are as follows:

[0027] Historical task sets are collected as training samples, and each sample contains input features Xi and algorithm performance labels. ,in:

[0028] ;

[0029] In the formula, This represents the performance that the integer linear programming algorithm can achieve in solving this historical task. This indicates the performance that the genetic algorithm can achieve in solving this historical task. This indicates the performance that backtracking and greedy heuristic algorithms can achieve in solving this historical task;

[0030] The optimization objective is to maximize the lower bound of the evidence, satisfying the following relationship:

[0031] ;

[0032] in, As a weighted prior, For weighted posterior, Represents the weighted posterior The mathematical expectation, This represents the Kullback-Leibler divergence, used to measure the posterior weighting. With weighted prior The differences between them Represents probability;

[0033] The main model of the Bayesian neural network is trained based on training samples and the optimization objective. During the inference phase, the Bayesian neural network model simultaneously outputs the expected performance achievable within a given time budget. and confidence level of expected performance This is used for subsequent weight calculation and initialization guidance.

[0034] In one embodiment, the step of inputting the standardized features into the pre-trained main model of a Bayesian neural network to obtain the performance distribution of different algorithms under the conflict resolution problem includes:

[0035] The standardized task features X are input into the pre-trained main model of the Bayesian neural network, and the prediction results of different algorithms under the conflict elimination problem to be solved are output as follows:

[0036] ;

[0037] in, The expected performance that can be achieved within a given time budget. Let the confidence level of this expectation be... Indicates a normal distribution. Represents an integer linear programming algorithm. This represents a genetic algorithm. This represents backtracking and greedy heuristic algorithms;

[0038] If the confidence level is insufficient, that is If τ is an empirical threshold, then the expected effectiveness is calculated as follows:

[0039] ;

[0040] In the formula, These are the weighting coefficients. This is a supplementary evaluation function for the performance of algorithm A based on the current task features X;

[0041] The final performance distribution is obtained by combining existing triggering indicators with prediction results.

[0042] In one embodiment, calculating the dynamic weights of different algorithms based on the performance distribution includes:

[0043] With expected performance Using the softmax function as input, the process-level resource weights for integer linear programming, genetic algorithms, and backtracking and greedy heuristic algorithms are obtained as follows:

[0044] ;

[0045] In the formula, This represents the expected performance of an exponential function with base e applied to algorithm A. , This represents the expected performance of an exponential function with base e applied to algorithm B. , , This represents the index or code of different algorithms in the algorithm set {ILP, GA, BT}. Represents an integer linear programming algorithm. This represents a genetic algorithm. This represents backtracking and greedy heuristic algorithms;

[0046] Among them, process-level resource weights are used to allocate CPU time, the number of parallel threads, or the number of allowed iterations;

[0047] Based on uncertainty, the weights for result fusion are defined as follows:

[0048] ;

[0049] In the formula, It is a constant. , Let A and B represent the standard deviation or uncertainty of the predictive performance of Algorithm B, respectively. It is a positive number to prevent the denominator from being zero and to ensure the numerical stability of the formula;

[0050] Introducing the exponential moving average as follows:

[0051] ;

[0052] In the formula, This is the smoothing factor for the exponential moving average, with a value range of (0,1). λ The closer it is to 1, the greater the proportion of historical weights, and the smoother the current weight changes. This represents the process-level resource weights of Algorithm A in the t-th time period;

[0053] Set a minimum value

[0054] In one embodiment, the training data for the hot starter model of the Bayesian neural network consists of: task features X and the corresponding optimal initialization parameters of the algorithm during historical runs. ;

[0055] The optimization objective is:

[0056] ;

[0057] In the formula, Represents the weighted posterior distribution The mathematical expectation, The task feature X and the corresponding algorithm are optimally initialized with parameters from historical runs. For the best initialization parameters predicted, The smoothing factor for the exponential moving average. This represents the Kullback-Leibler divergence, used to measure the posterior weighting. With weighted prior The differences between them;

[0058] The sub-model structure is trained independently for each algorithm;

[0059] The online update steps are as follows: after running, record the difference between the actual convergence trajectory and the prediction, and periodically fine-tune the parameters of the hot starter model.

[0060] In one embodiment, the step of inputting the dynamic weights into a pre-trained Bayesian neural network hot starter model for multi-algorithm collaborative solving and initialization guidance, to obtain the computing power, time, and parallelism ratio of each algorithm during operation in the decision system, includes:

[0061] The genetic algorithm module of the trained Bayesian neural network model outputs the initial population distribution parameters. This is used to guide the sampling process to generate highly fit individuals;

[0062] The backtracking and greedy heuristic algorithm module of the trained Bayesian neural network model outputs a variable priority sequence. and pruning threshold distribution ;

[0063] The integer linear programming algorithm module of the trained Bayesian neural network model is used to predict the probability of tightly constrained sets. And select the initial relaxed set based on the probability of the tightly constrained set;

[0064] Genetic algorithms, backtracking and greedy heuristic algorithms, and integer linear programming algorithms are run in parallel, with resources allocated according to process-level resource weights;

[0065] If the prediction results show that the superiority of a certain algorithm exceeds a set threshold, a set cascading mode is adopted. The set cascading modes include a mode for refining the genetic algorithm to the integer linear programming algorithm and a mode for verifying the backtracking and greedy heuristic algorithm to the integer linear programming algorithm.

[0066] The dynamic feedback during parallel operation is as follows:

[0067] ;

[0068] In the formula, This indicates the feedback results during the runtime. This represents the performance value of algorithm A at time t. This represents the historical best performance value obtained among all algorithms up to time t-1. This represents the time interval, that is, the length of time from time t-1 to time t;

[0069] according to Adjust process-level resource weights in real time for the next cycle.

[0070] In one embodiment, determining the optimal algorithm combination based on the computing power, time, and parallelism ratio of each algorithm includes:

[0071] The multi-objective comprehensive score is calculated based on the output of each algorithm, as follows:

[0072] ;

[0073] in, The evaluation indicators include effectiveness, balance, robustness, timeliness, and interpretability. Represents the k-th evaluation index The weighting coefficient in the overall score;

[0074] The weighted calculation is performed based on the result weights, as follows:

[0075] ;

[0076] In the formula, Weights are used to combine the results. This is a comprehensive score for Algorithm A;

[0077] The solution with the highest comprehensive score is selected as the final solution to obtain the optimal algorithm combination.

[0078] Secondly, this application also provides a multi-algorithm conflict elimination fusion device based on a Bayesian neural network, comprising:

[0079] The feature extraction and problem modeling module is used to extract features and model the processor resource allocation conflict elimination problem in the decision system to be solved, and obtain standardized features; the processor resource allocation conflict elimination problem in the decision system includes making allocation decisions among multiple computing tasks and processors to eliminate processor resource usage conflicts;

[0080] The performance distribution prediction module is used to input the standardized features into the pre-trained main model of the Bayesian neural network to obtain the performance distribution of different algorithms under the conflict elimination problem.

[0081] The dynamic weight calculation module is used to calculate the dynamic weights of different algorithms based on the performance distribution.

[0082] The collaborative solving module is used to input the dynamic weights into the pre-trained Bayesian neural network hot starter model, perform multi-algorithm collaborative solving and initialization guidance, and obtain the computing power, time and parallel ratio of each algorithm when running in the decision system.

[0083] The determination module is used to determine the optimal algorithm combination based on the computing power, time, and parallelism ratio of each algorithm, so as to eliminate processor resource allocation conflicts in the decision system.

[0084] Beneficial effects:

[0085] The aforementioned multi-algorithm conflict elimination and fusion method based on Bayesian neural networks predicts the performance distribution of different algorithms under given task characteristics using a pre-trained master model of the Bayesian neural network. Dynamic weights are calculated based on this performance distribution, and then input into a pre-trained Bayesian neural network hot-starter model for multi-algorithm collaborative solving and initialization guidance. This yields the computational power, time, and parallelism ratio of each algorithm during system operation, automatically selecting the optimal algorithm combination without manual intervention. This enables hot-start and intelligent guidance before algorithm execution, significantly shortening the cold-start phase and improving initial search efficiency. By focusing the search range on high-quality solution regions during solution initiation, convergence is accelerated, blind searches are reduced, and the stability of early solutions is improved, enabling the output of confident initialization parameters, thus achieving predictive initiation. Attached Figure Description

[0086] Figure 1 This is a flowchart of a multi-algorithm conflict elimination and fusion method based on a Bayesian neural network in one embodiment;

[0087] Figure 2 This is a flowchart illustrating the training process of the main model of a Bayesian neural network in one embodiment.

[0088] Figure 3 This is a flowchart illustrating the training and online updating of a hot-starter model of a Bayesian neural network in one embodiment.

[0089] Figure 4 This is a block diagram of a multi-algorithm conflict elimination and fusion device based on a Bayesian neural network in one embodiment. Detailed Implementation

[0090] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0091] It should be understood that this application can be applied to optimization scenarios with multiple objectives, multiple constraints, and resource or solution conflicts. Existing algorithm conflict elimination and fusion methods suffer from problems such as reliance on experience for selection, low cold-start efficiency, and lack of uncertainty modeling. Based on this, this application provides a multi-algorithm conflict elimination and fusion method based on Bayesian neural networks. It integrates five main steps within the same solution framework: feature extraction, Bayesian prediction, dynamic weight calculation and resource allocation, intelligent initialization guidance and multi-algorithm collaborative solution, and result fusion. This enables adaptive scheduling and collaborative optimization of integer linear programming (ILP), genetic algorithm (GA), and backtracking heuristic algorithm, and can solve the problems of algorithm selection relying on experience, low cold-start efficiency, and lack of uncertainty modeling in existing methods.

[0092] Please see Figure 1 The multi-algorithm conflict elimination fusion method based on Bayesian neural networks provided in this application includes:

[0093] Feature extraction and problem modeling are performed on the processor resource allocation conflict elimination problem in the decision system to be solved, and standardized features are obtained. The processor resource allocation conflict elimination problem in the decision system includes making allocation decisions among multiple computing tasks and processors to eliminate processor resource usage conflicts.

[0094] The standardized features are input into the pre-trained main model of the Bayesian neural network to obtain the performance distribution of different algorithms under the conflict elimination problem.

[0095] Calculate the dynamic weights of different algorithms based on the performance distribution;

[0096] The dynamic weights are input into the pre-trained Bayesian neural network hot starter model to perform multi-algorithm collaborative solution and initialization guidance, thereby obtaining the computing power, time and parallel ratio of each algorithm when running in the decision system.

[0097] The optimal algorithm combination is determined based on the computing power, time, and parallelism ratio of each algorithm in order to eliminate processor resource allocation conflicts in the decision system.

[0098] The aforementioned multi-algorithm conflict elimination and fusion method based on Bayesian neural networks predicts the performance distribution of different algorithms under given task characteristics using a pre-trained master model of the Bayesian neural network. Dynamic weights are calculated based on this performance distribution, and then input into a pre-trained Bayesian neural network hot-starter model for multi-algorithm collaborative solving and initialization guidance. This yields the computational power, time, and parallelism ratio of each algorithm during system operation, automatically selecting the optimal algorithm combination without manual intervention. This enables hot-start and intelligent guidance before algorithm execution, significantly shortening the cold-start phase and improving initial search efficiency. By focusing the search range on high-quality solution regions during solution initiation, convergence is accelerated, blind searches are reduced, and the stability of early solutions is improved, enabling the output of confident initialization parameters, thus achieving predictive initiation.

[0099] In one embodiment, feature extraction and problem modeling are performed based on the processor resource allocation conflict resolution problem in the decision system to be solved, resulting in standardized features, including:

[0100] The problem of processor resource allocation conflict elimination in the decision system to be solved can be expressed in the following form:

[0101] target set

[0102] Each goal There is a set of solutions

[0103] plan The required set of resources is The efficiency is ;

[0104] The following resource ceiling (inventory) constraints exist:

[0105] ;

[0106] in, Representation scheme Should resource k be used? Let k be the upper limit of resource inventory. ∈{0,1} indicates whether the option is selected;

[0107] Extract scene features and construct the feature vector as follows:

[0108] ;

[0109] In the formula, S represents the problem size, which in one example can be taken as "number of objectives × number of solutions"; RR represents constraint sparsity, which can be estimated by "number of constraints / number of variables"; SCAR represents resource scarcity, and a typical calculation formula is:

[0110] ;

[0111] in This represents the total resource requirement k for each option;

[0112] DIV represents the diversity index of candidate solutions, which can be estimated by the difference in historical solutions or the number of solution types; GAP represents the difference between the current best feasible solution and the theoretical bound; FR (Feasibility Rate) represents the proportion of solutions that satisfy all constraints during the random sampling or heuristic initial solution generation stage.

[0113] ;

[0114] In the formula, This indicates the number of feasible solutions. Indicates the total number of samples;

[0115] CS (Conflict Strength) represents the intensity of conflict between different objective schemes, and is calculated as follows:

[0116] ;

[0117] In the formula, Let represent the total number of all possible solutions for the i-th objective Ti. This represents the total number of all available solutions for the j-th objective Tj;

[0118] in, CS represents the number of mutually exclusive solutions in terms of resources or timing. The higher the CS, the more severe the conflict and the more complex the problem.

[0119] The feature vectors are standardized to obtain the standardized features.

[0120] Furthermore, after feature standardization, the samples are used as input samples for the Bayesian neural network model; and three algorithm engines are initialized.

[0121] In one embodiment, before inputting the standardized features into the pre-trained main model of a Bayesian neural network to obtain the performance distribution of different algorithms under the conflict resolution problem, the method further includes:

[0122] The main model of the Bayesian neural network is trained, during which the mapping relationship between features and the performance of the three algorithms is learned; for example... Figure 2 As shown, the specific training steps are as follows:

[0123] Historical task sets are collected as training samples, and each sample contains input features Xi and algorithm performance labels. ,in:

[0124] ;

[0125] In the formula, This represents the performance value that the integer linear programming algorithm can achieve on this historical task. This represents the performance value that the genetic algorithm can achieve on this historical task. This represents the performance value that the backtracking and greedy heuristic algorithms can achieve on this historical task;

[0126] The optimization objective is to maximize the lower bound of evidence (ELBO), satisfying the following relationship:

[0127] ;

[0128] in, As a weighted prior, For weighted posterior, Represents the weighted posterior The mathematical expectation, This represents the Kullback-Leibler divergence, used to measure the posterior weighting. with weighted prior The differences between them Represents probability;

[0129] The main model of the Bayesian neural network is trained based on training samples and the optimization objective. During the inference phase, the main model of the Bayesian neural network simultaneously outputs the expected performance achievable within a given time budget. and confidence level of expected performance This is used for subsequent weight calculation and initialization guidance.

[0130] It's worth noting that online relearning is also possible during the training process: after the system runs, new samples can be used for relearning. Periodic feedback updates the model parameters incrementally, enabling self-evolution.

[0131] After training the main model of the Bayesian neural network, the following steps are required:

[0132] The standardized features X are input into the pre-trained main model of the Bayesian neural network, and the prediction results of different algorithms under the conflict elimination problem to be solved are output as follows:

[0133] ;

[0134] in, The expected performance that can be achieved within a given time budget. Let the confidence level of this expectation be... Indicates a normal distribution. Represents an integer linear programming algorithm. This represents a genetic algorithm. This represents backtracking and greedy heuristic algorithms.

[0135] If the confidence level is insufficient, that is If τ is an empirical threshold, then the expected effectiveness is calculated as follows:

[0136] ;

[0137] In the formula, These are the weighting coefficients. This is a supplementary evaluation function for the performance of algorithm A based on the current task features X.

[0138] The final performance distribution is obtained by combining existing triggering indicators with prediction results.

[0139] In this implementation, the main BNN predicts the performance distribution of different algorithms under given task characteristics, and dynamically allocates computing power, time, and parallelism ratio based on expected value and confidence level, thereby automatically selecting the optimal algorithm combination without manual intervention. This method can automatically adjust the solution strategy in environments with frequently changing task types, effectively reducing misjudgments caused by reliance on experience and fixed thresholds.

[0140] Furthermore, based on the prediction results obtained from each algorithm... , The dynamic weight calculation and resource allocation are performed as follows:

[0141] With expected performance Using the softmax function as input, the process-level resource weights (resource-specific) for the three algorithms are obtained as follows:

[0142] ;

[0143] In the formula, This represents the expected performance of an exponential function with base e applied to algorithm A. The purpose is to amplify the performance differences between different algorithms to facilitate weight allocation. This represents the expected performance of an exponential function with base e applied to algorithm B. The purpose is to amplify the performance differences between different algorithms to facilitate weight allocation. , This represents the index or code of different algorithms in the algorithm set {ILP, GA, BT}. Represents an integer linear programming algorithm. This represents a genetic algorithm. This represents backtracking and greedy heuristic algorithms;

[0144] Among them, process-level resource weights are used to allocate CPU time, the number of parallel threads, or the allowed number of iterations. ;

[0145] Based on uncertainty, the weights (based on confidence level) for result fusion are defined as follows:

[0146] ;

[0147] In the formula, It is usually a constant (which can be set to 1), used in the numerator of the weight calculation formula, and plays an adjusting role. , Let A and B represent the standard deviation or uncertainty of the predictive performance of Algorithm B, respectively. It is a very small positive number (such as 1e-8) to prevent the denominator from being zero and to ensure the numerical stability of the formula;

[0148] It is worth explaining that the less uncertain the algorithm is, the greater the weight of its solution in the final result fusion.

[0149] To avoid large fluctuations in weighting, an exponential moving average is introduced as follows:

[0150] ;

[0151] In the formula, This is the smoothing factor for the exponential moving average, with a value range of (0,1). λ The closer it is to 1, the greater the proportion of historical weights, and the smoother the current weight changes. This represents the process-level resource weights of Algorithm A in the t-th time period;

[0152] Set a minimum value This ensures that any algorithm receives at least some resources, preventing the system from losing its ability to explore a particular algorithm for an extended period.

[0153] Furthermore, weight After the calculations are complete, the warm starter model of the Bayesian neural network is invoked to provide initialization guidance for each algorithm, as follows:

[0154] The genetic algorithm module of the trained Bayesian neural network model outputs the initial population distribution parameters. This is used to guide the sampling process to generate highly fit individuals;

[0155] The backtracking and greedy heuristic algorithm module of the trained Bayesian neural network model outputs a variable priority sequence. and pruning threshold distribution This can reduce the depth of backtracking search;

[0156] The integer linear programming algorithm module of the trained Bayesian neural network model is used to predict the probability of tightly constrained sets. And select the initial relaxation set according to the probability of the tight constraint set to improve the convergence speed;

[0157] Genetic algorithms, backtracking and greedy heuristic algorithms, and integer linear programming algorithms are run in parallel, with resources allocated according to process-level resource weights;

[0158] If the prediction results show that a certain algorithm is significantly superior, the set cascading mode is adopted. The set cascading modes include the mode of refining the genetic algorithm to the integer linear programming algorithm, and the mode of verifying the backtracking and greedy heuristic algorithm to the integer linear programming algorithm.

[0159] The dynamic feedback during parallel operation is as follows:

[0160] ;

[0161] In the formula, This indicates the feedback results during the runtime. This represents the performance value of algorithm A at time t. This represents the historical best performance value obtained among all algorithms up to time t-1. This represents the time interval, that is, the length of time from time t-1 to time t;

[0162] according to Adjust process-level resource weights in real time for the next cycle.

[0163] Operational feedback results It is recorded in real time and used for subsequent model updates.

[0164] like Figure 3 As shown, the hot-start model training of the Bayesian neural network is explained below:

[0165] Training data: Task feature X and corresponding optimal initialization parameters of the algorithm in historical runs. ;

[0166] Optimization goal:

[0167] ;

[0168] In the formula, Represents the weighted posterior distribution The mathematical expectation, The task feature X and the corresponding algorithm are optimally initialized with parameters from historical runs. For the best initialization parameters predicted, The smoothing factor for the exponential moving average. This represents the Kullback-Leibler divergence, used to measure the posterior weighting. With weighted prior The differences between them.

[0169] Sub-model structure: GA, BT, and ILP are trained independently respectively;

[0170] Online updates: After running, the difference between the actual convergence trajectory and the prediction is recorded, and the parameters of the hot-start BNN are periodically fine-tuned.

[0171] In this implementation, a warm start and intelligent guidance before algorithm execution can be achieved, significantly shortening the cold start phase and improving initial search efficiency. By utilizing the warm-start BNN sub-model to predict the high-fitness initial population distribution of the genetic algorithm, the priority search order and pruning threshold of the backtracking algorithm, and the tight constraint set of the integer programming algorithm, the search range is focused on the high-quality solution region during solution startup, thereby accelerating convergence, reducing blind searches, and improving the stability of early solutions. This effect arises from the BNN's learning of the historical running trajectory of subtasks, enabling it to output initialization parameters with confidence, achieving "predictive startup."

[0172] Furthermore, the results are integrated and a multi-objective comprehensive evaluation is conducted as follows:

[0173] The multi-objective comprehensive score is calculated based on the output of each algorithm, as follows:

[0174] ;

[0175] in, The evaluation indicators include effectiveness, balance, robustness, and timeliness. Represents the k-th evaluation index The weighting coefficient in the overall score.

[0176] It is worth further explanation that the performance index is the core metric for evaluating the quality of a solution, directly reflecting the degree to which the solution achieves its core task objectives. Its calculation formula is as follows:

[0177] ;

[0178] Let Sij represent the solid effective energy that can be obtained by selecting the target Ti. The variable is denoted as 'n', which has a value of 1 when solution Sij is selected and 0 otherwise; n is the total number of objectives. This represents the total number of schemes corresponding to the objective Ti.

[0179] The resource balance index is used to evaluate the evenness of resource utilization in a solution, avoiding an unhealthy system state where some resources are bottlenecked while others are idle. Its calculation formula is defined as:

[0180] ;

[0181] in, , indicating resources Utilization rate; , where represents the average utilization rate of all resources; K is the total number of resource types.

[0182] Robustness metrics are used to measure the ability of a solution to maintain performance stability when faced with potential disturbances. This invention utilizes the Key Feature Resource Scarcity (SCAR) calculated during the feature extraction stage to indirectly evaluate the robustness of the solution:

[0183] ;

[0184] SCAR (Resource Scarcity) is one of the components of the feature vector X, and its calculation involves the total demand. Both the total inventory Wk and the total inventory are known parameters. This indicator is based on the following logic: the higher the overall scarcity of resources, the smaller the system's elasticity in response to demand fluctuations, and the greater the risk to the robustness of the solution.

[0185] Timeliness metrics are used to evaluate the computational or execution efficiency of solutions to meet real-time requirements in practical applications. The calculation formula uses a saturation function form:

[0186] ;

[0187] in, It is the actual time taken from the generation of solution y to its completion of execution. It is a reference time constant that can be set to the average solution time of historical tasks or the time limit required for the current task.

[0188] The weighted calculation is performed based on the result weights, as follows:

[0189] ;

[0190] In the formula, Weights are used to combine the results. This is a comprehensive score for Algorithm A.

[0191] The solution with the highest comprehensive score is selected as the final solution to obtain the optimal algorithm combination.

[0192] This implementation enables parallel or cascaded collaborative solving of multiple algorithms, with adaptive optimization during operation. The system dynamically adjusts the weights of each algorithm based on real-time feedback of performance improvement per unit time, concentrating computational power on the algorithm path with the highest current gain. Simultaneously, in cascaded mode, GA or BT can generate approximate solutions for further refinement by ILP, thus balancing solution speed and optimal quality. It achieves multi-objective result fusion and controllable trade-offs in output. The system uniformly evaluates the results of different algorithms through a multi-objective synthesis function and combines confidence weighting to form the final fusion scheme, achieving a dynamic balance among performance, equilibrium, robustness, and timeliness. This mechanism ensures that the results of high-confidence algorithms have higher weight in the fusion, significantly improving the reliability and stability of the output scheme. Its advantages stem from the confidence quantification and adaptive fusion mechanism provided by the main BNN, making the fusion strategy both interpretable and predictively reliable.

[0193] In one example, the task feature X and the prediction result can also be included. Actual effectiveness and feedback gain Store the sample set. Periodically perform incremental training on the main Bayesian neural network model and the warm-start Bayesian neural network model to adaptively update the model parameters and complete the self-learning loop.

[0194] In this implementation, online relearning and continuous performance improvement are possible after the results are output. After solving the problem, the system automatically records task characteristics, algorithm predictions, actual performance, and gain changes. New sample increments are added to the training set, and the main BNN and the warm-start BNN are retrained, continuously improving the model's predictive ability and initialization accuracy. This design gives the system self-evolutionary characteristics, allowing it to gradually optimize its performance as tasks accumulate, resulting in more accurate algorithm selection, more robust fusion, and more efficient solving over long-term operation.

[0195] The following is a specific embodiment to verify and describe the above-mentioned multi-algorithm conflict elimination and fusion method based on Bayesian neural networks:

[0196] Example 1: Industrial production scheduling and resource conflict optimization application is as follows:

[0197] This embodiment takes resource scheduling in a smart manufacturing workshop as an example to illustrate the application process of the present invention in multi-constraint industrial scheduling.

[0198] Suppose a manufacturing system needs to complete the processing and assembly of eight types of parts within a limited timeframe, involving six key pieces of equipment (four CNC machine tools and two assembly robotic arms) and several transportation devices. The tasks are constrained by shared equipment, timing dependencies, and processing sequence conflicts. The goal is to maximize overall capacity utilization and minimize operational conflicts while ensuring on-time delivery.

[0199] Step 1: The system reads the task data and extracts features: problem size S=48, constraint sparsity R=0.40, resource scarcity SCAR=0.64, feasibility FR=0.45, conflict density CS=0.42, solution space diversity DIV=0.71, and efficiency gap GAP=0.37. These feature vectors are then input into the main BNN model.

[0200] Step two, the performance distribution of the three main BNN prediction algorithms is as follows:

[0201]

[0202] The system calculates the weights. Determine a parallel scheduling scheme that is GA-led and ILP-assisted.

[0203] Step 3: The BNN is warm-started and outputs the initialization guidance parameters for each algorithm: the GA module obtains a population template for high-utilization jobs, making the initial solution more concentrated in the region with high equipment time matching degree; the ILP module predicts the tight constraint set B={C1,C3,C5}, reducing the constraint space; the BT module outputs a heuristic sorting strategy to prioritize time-critical tasks.

[0204] Step four: GA, ILP, and BT solve in parallel under allocated computing resources, with the system adjusting weights in real time based on the performance gain ΔA every 0.5 seconds. When the GA convergence speed decreases and the ILP refinement efficiency increases, the system automatically allocates more computing power to the ILP module to complete the final optimization. This dynamic adjustment process significantly improves the global efficiency of the solution phase.

[0205] Step five: The fusion module calculates the comprehensive score of each algorithm solution based on the multi-objective synthesis function, and obtains the final scheduling scheme by inversely weighting the scores according to the confidence level. Actual results show that the scheduling scheme generated by the method of this invention outperforms traditional hybrid heuristic methods in terms of equipment utilization, task balance, and latency control. The system also feeds back the batch of task features and result data to the BNN training set to complete the online relearning of the model.

[0206] This embodiment verifies the application effect of the present invention in industrial production scheduling, demonstrating that it can not only quickly generate high-quality scheduling schemes, but also continuously optimize prediction accuracy and fusion effect as operating data accumulates, thus achieving evolvable intelligent scheduling.

[0207] In summary, this invention establishes a multi-algorithm fusion framework based on Bayesian neural networks, enabling intelligent solution and adaptive optimization in complex optimization tasks with multiple objectives, constraints, and resource conflicts. This significantly improves the intelligence, efficiency, and overall robustness of algorithm selection. Furthermore, this invention exhibits significant robustness and feasible solution stability in complex scenarios with high conflict density and low feasibility rates. Through uncertainty modeling of the main BNN and the fusion mechanism of traditional trigger indicators, the system automatically reverts to a conservative strategy when prediction confidence decreases, ensuring the solution process remains stable and maintains a high feasibility rate. The guiding role of the hot-start BNN further enhances the probability of hitting a feasible solution. Therefore, this invention can still output high-quality solutions under extreme constraints.

[0208] This invention ultimately forms a five-step closed-loop system integrating prediction-driven, intelligent guidance, and online learning. In complex conflict resolution tasks, the system can efficiently complete algorithm selection, execution scheduling, dynamic fusion, and continuous optimization, achieving a balance between efficiency, optimality, and interpretability. This method exhibits significant intelligence, adaptability, and scalability, possessing broad engineering application value and promotion potential.

[0209] like Figure 4 As shown, this application also provides a multi-algorithm conflict elimination fusion device based on a Bayesian neural network, comprising:

[0210] The feature extraction and problem modeling module is used to extract features and model the processor resource allocation conflict elimination problem in the decision system to be solved, and obtain standardized features; the processor resource allocation conflict elimination problem in the decision system includes making allocation decisions among multiple computing tasks and processors to eliminate processor resource usage conflicts;

[0211] The performance distribution prediction module is used to input the standardized features into the pre-trained main model of the Bayesian neural network to obtain the performance distribution of different algorithms under the conflict elimination problem.

[0212] The dynamic weight calculation module is used to calculate the dynamic weights of different algorithms based on the performance distribution.

[0213] The collaborative solving module is used to input the dynamic weights into the pre-trained Bayesian neural network hot starter model, perform multi-algorithm collaborative solving and initialization guidance, and obtain the computing power, time and parallel ratio of each algorithm when running in the decision system.

[0214] The determination module is used to determine the optimal algorithm combination based on the computing power, time, and parallelism ratio of each algorithm, so as to eliminate processor resource allocation conflicts in the decision system.

[0215] The aforementioned Bayesian neural network multi-algorithm conflict elimination and fusion device can implement various embodiments of the Bayesian neural network-based multi-algorithm conflict elimination and fusion method and achieve the same beneficial effects, which will not be elaborated here.

[0216] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0217] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A multi-algorithm conflict elimination fusion method based on Bayesian neural networks, characterized in that, include: Based on the processor resource allocation conflict elimination problem in the decision system to be solved, feature extraction and problem modeling are performed to obtain standardized features; The processor resource allocation conflict elimination problem in the decision-making system includes making allocation decisions among multiple computing tasks and processors to eliminate processor resource usage conflicts. The standardized features are input into the pre-trained main model of the Bayesian neural network to obtain the performance distribution of different algorithms under the conflict elimination problem. Calculate the dynamic weights of different algorithms based on the performance distribution; The dynamic weights are input into the pre-trained Bayesian neural network hot starter model to perform multi-algorithm collaborative solution and initialization guidance, thereby obtaining the computing power, time and parallel ratio of each algorithm when running in the decision system. The optimal algorithm combination is determined based on the computing power, time, and parallelism ratio of each algorithm in order to eliminate processor resource allocation conflicts in the decision system. The step of calculating the dynamic weights of different algorithms based on the performance distribution includes: With expected performance Using the softmax function as input, the process-level resource weights for integer linear programming, genetic algorithms, and backtracking and greedy heuristic algorithms are obtained as follows: ； In the formula, This represents the expected performance of an exponential function with base e applied to algorithm A. , This represents the expected performance of an exponential function with base e applied to algorithm B. , , This represents the index or code of different algorithms in the algorithm set {ILP, GA, BT}. Represents an integer linear programming algorithm. This represents a genetic algorithm. This represents backtracking and greedy heuristic algorithms; Among them, process-level resource weights are used to allocate CPU time, the number of parallel threads, or the number of allowed iterations; Based on uncertainty, the weights for result fusion are defined as follows: ； In the formula, It is a constant. , Let A and B represent the standard deviation or uncertainty of the predictive performance of Algorithm B, respectively. It is a positive number; Introducing the exponential moving average as follows: ； In the formula, This is the smoothing factor for the exponential moving average, with a value range of (0,1). λ The closer it is to 1, the greater the proportion of historical weights, and the smoother the current weight changes. This represents the process-level resource weights of Algorithm A in the t-th time period; Set a minimum value .

2. The multi-algorithm conflict elimination and fusion method based on Bayesian neural networks according to claim 1, characterized in that, The process involves feature extraction and problem modeling based on the processor resource allocation conflict resolution problem in the decision system to be solved, resulting in standardized features, including: The problem of processor resource allocation conflict elimination in the decision system to be solved can be expressed in the following form: target set Each goal There is a set of solutions plan The required set of resources is The efficiency is ; The following resource upper limit constraints exist: ； in, Representation scheme Should resource k be used? Let k be the upper limit of resource inventory. ∈{0,1} indicates whether the option is selected; Extract scene features and construct the feature vector as follows: ； In the formula, S represents the problem size, R represents the constraint sparsity, SCAR represents the resource scarcity, DIV represents the diversity index of candidate solutions, GAP represents the difference between the current best feasible solution and the theoretical bound, FR represents the proportion of solutions that can satisfy all constraints in the random sampling or heuristic initial solution generation stage, and CS represents the density of conflicts between different objective solutions. Indicates the number of targets; The feature vectors are standardized to obtain the standardized features.

3. The multi-algorithm conflict elimination and fusion method based on Bayesian neural networks according to claim 1, characterized in that, Before inputting the standardized features into the pre-trained main model of the Bayesian neural network to obtain the performance distribution of different algorithms under the conflict elimination problem, the method further includes: The specific steps for training the main model of the Bayesian neural network are as follows: Historical task sets are collected as training samples, and each sample contains input features Xi and algorithm performance labels. ,in: ； In the formula, This represents the performance that the integer linear programming algorithm can achieve in solving this historical task. This indicates the performance that the genetic algorithm can achieve in solving this historical task. This indicates the performance that backtracking and greedy heuristic algorithms can achieve in solving this historical task; The optimization objective is to maximize the lower bound of the evidence, satisfying the following relationship: in, As a weighted prior, For weighted posterior, Represents the weighted posterior The mathematical expectation, This represents the Kullback-Leibler divergence, used to measure the posterior weighting. with weighted prior The differences between them Represents probability; The main model of the Bayesian neural network is trained based on training samples and the optimization objective. During the inference phase, the Bayesian neural network model simultaneously outputs the expected performance achievable within a given time budget. and confidence level of expected performance This is used for subsequent weight calculation and initialization guidance.

4. The multi-algorithm conflict elimination and fusion method based on Bayesian neural networks according to claim 1, characterized in that, The process of inputting the standardized features into the pre-trained main model of a Bayesian neural network to obtain the performance distribution of different algorithms under the conflict resolution problem includes: The standardized task features X are input into the pre-trained main model of the Bayesian neural network, and the prediction results of different algorithms under the conflict elimination problem to be solved are output as follows: in, The expected performance that can be achieved within a given time budget. Let the confidence level of this expectation be... Indicates a normal distribution. Represents an integer linear programming algorithm. This represents a genetic algorithm. This represents backtracking and greedy heuristic algorithms; If the confidence level is insufficient, that is If the value is less than τ, where τ is an empirical threshold, then the expected effectiveness is calculated as follows: In the formula, These are the weighting coefficients. This is a supplementary evaluation function for the performance of algorithm A based on the current task features X; The final performance distribution is obtained by combining existing triggering indicators with prediction results.

5. The multi-algorithm conflict elimination and fusion method based on Bayesian neural networks according to claim 1, characterized in that, The training data for the hot starter model of the Bayesian neural network consists of: task features X and the corresponding optimal initialization parameters of the algorithm during historical runs. ; The optimization objective is: In the formula, Represents the weighted posterior distribution The mathematical expectation, The task feature X and the corresponding algorithm are optimally initialized with parameters from historical runs. For the best initialization parameters predicted, The smoothing factor for the exponential moving average. This represents the Kullback-Leibler divergence, used to measure the posterior weighting. with weighted prior The differences between them; The sub-model structure is trained independently for each algorithm; The online update steps are as follows: after running, record the difference between the actual convergence trajectory and the prediction, and periodically fine-tune the parameters of the hot starter model.

6. The multi-algorithm conflict elimination and fusion method based on Bayesian neural networks according to claim 1, characterized in that, The process of inputting the dynamic weights into a pre-trained Bayesian neural network warm-starter model for multi-algorithm collaborative solving and initialization guidance, and obtaining the computing power, time, and parallelism ratio of each algorithm in the decision system, includes: The genetic algorithm module of the trained Bayesian neural network model outputs the initial population distribution parameters. This is used to guide the sampling process to generate highly fit individuals; The backtracking and greedy heuristic algorithm module of the trained Bayesian neural network model outputs a variable priority sequence. and pruning threshold distribution ; The integer linear programming algorithm module of the trained Bayesian neural network model is used to predict the probability of tightly constrained sets. And select the initial relaxed set based on the probability of the tightly constrained set; Genetic algorithms, backtracking and greedy heuristic algorithms, and integer linear programming algorithms are run in parallel, with resources allocated according to process-level resource weights; If the prediction results show that the superiority of a certain algorithm exceeds a set threshold, a set cascading mode is adopted. The set cascading modes include a mode for refining the genetic algorithm to the integer linear programming algorithm and a mode for verifying the backtracking and greedy heuristic algorithm to the integer linear programming algorithm. The dynamic feedback during parallel operation is as follows: ； In the formula, This indicates the feedback results during the runtime. This represents the performance value of algorithm A at time t. This represents the historical best performance value obtained among all algorithms up to time t-1. This represents the time interval, that is, the length of time from time t-1 to time t; according to Adjust process-level resource weights in real time for the next cycle.

7. The multi-algorithm conflict elimination and fusion method based on Bayesian neural networks according to claim 1, characterized in that, The process of determining the optimal algorithm combination based on the computing power, time, and parallelism ratio of each algorithm includes: The multi-objective comprehensive score is calculated based on the output of each algorithm, as follows: in, The evaluation indicators include effectiveness, balance, robustness, timeliness, and interpretability. Represents the k-th evaluation index The weighting coefficient in the overall score; The weighted calculation is performed based on the result weights, as follows: In the formula, Weights are used to combine the results. This is a comprehensive score for Algorithm A; The solution with the highest comprehensive score is selected as the final solution to obtain the optimal algorithm combination.

8. A multi-algorithm conflict elimination and fusion device based on Bayesian neural networks, characterized in that, include: The feature extraction and problem modeling module is used to extract features and model problems based on the processor resource allocation conflict elimination problem in the decision system to be solved, and obtain standardized features. The processor resource allocation conflict elimination problem in the decision-making system includes making allocation decisions among multiple computing tasks and processors to eliminate processor resource usage conflicts. The performance distribution prediction module is used to input the standardized features into the pre-trained main model of the Bayesian neural network to obtain the performance distribution of different algorithms under the conflict elimination problem. The dynamic weight calculation module is used to calculate the dynamic weights of different algorithms based on the performance distribution. The collaborative solving module is used to input the dynamic weights into the pre-trained Bayesian neural network hot starter model, perform multi-algorithm collaborative solving and initialization guidance, and obtain the computing power, time and parallel ratio of each algorithm when running in the decision system. The determination module is used to determine the optimal combination of algorithms based on the computing power, time and parallelism ratio of each algorithm, so as to eliminate the processor resource allocation conflict in the decision system; The step of calculating the dynamic weights of different algorithms based on the performance distribution includes: With expected performance Using the softmax function as input, the process-level resource weights for integer linear programming, genetic algorithms, and backtracking and greedy heuristic algorithms are obtained as follows: ； In the formula, This represents the expected performance of an exponential function with base e applied to algorithm A. , This represents the expected performance of an exponential function with base e applied to algorithm B. , , This represents the index or code of different algorithms in the algorithm set {ILP, GA, BT}. Represents an integer linear programming algorithm. This represents a genetic algorithm. This represents backtracking and greedy heuristic algorithms; Among them, process-level resource weights are used to allocate CPU time, the number of parallel threads, or the number of allowed iterations; Based on uncertainty, the weights for result fusion are defined as follows: ； In the formula, It is a constant. , Let A and B represent the standard deviation or uncertainty of the predictive performance of Algorithm B, respectively. It is a positive number; Introducing the exponential moving average as follows: ； In the formula, This is the smoothing factor for the exponential moving average, with a value range of (0,1). λ The closer it is to 1, the greater the proportion of historical weights, and the smoother the current weight changes. This represents the process-level resource weights of Algorithm A in the t-th time period; Set a minimum value .

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