Manufacturing industry value chain collaborative optimization method and device based on dynamic multi-criterion decision analysis

Abstract

The invention discloses a manufacturing industry value chain collaborative optimization method and equipment based on dynamic multi-criterion decision analysis. The method comprises the following steps: defining a value chain collaborative optimization decision problem; obtaining preference information of a decision maker; the method comprises the following steps: associating situation dependence preference of a decision maker with a dynamic decision environment, and describing preference information by using a probability value driven sorting program, so as to construct a preference learning model; deducing parameters of a decision maker dynamic situation preference model based on maximum likelihood estimation, wherein the parameters are used for predicting a value chain collaborative scheme recommendation result; according to continuous new background input, predicting a future preference model of a decision maker and a corresponding sequence of alternative value chain cooperation schemes; and selecting an optimal cooperation scheme according to a sorting result of the alternative value chain cooperation schemes, and carrying out manufacturing industry value chain cooperation optimization. According to the method, the cognitive deviation is reduced by simulating stable and static preference evolution, so that the predicted collaborative scheme recommendation result is more accurate.

Description

Technical Field

[0001] The method relates to the fields of multi-criteria decision making and machine learning, and specifically to a manufacturing value chain collaborative optimization method and device based on dynamic multi-criteria decision analysis. Background Art

[0002] Multi-criteria ranking aims to provide decision makers with recommendations on the ranking of alternatives from best to worst, which are evaluated according to a series of criteria. Such decision problems are prevalent in various fields such as medical diagnosis, supply chain management, ecological planning, renewable energy, and education. The practical significance of ranking has attracted widespread attention in multi-criteria decision analysis (MCDA) and has spawned corresponding methods.

[0003] Despite significant progress in multi-criteria ranking, almost all studies are built on an implicit assumption that decisions are made in a static environment. In other words, decision makers’ preferences for a set of alternatives are assumed to follow a fixed pattern that remains unchanged during the decision process. This, in turn, justifies the inference of static preference models, which are used to make ranking recommendations. However, this approach is insufficient in decision-making environments where decision makers’ preferences may continue to change as the decision environment continues to evolve. For example, in medical diagnosis scenarios, a doctor’s treatment preference for a chronic patient may change as the patient’s condition progresses. In portfolio decisions in financial scenarios, an investment manager’s preferences for risk and return may also change as market conditions fluctuate. Given the prevalence of dynamic decision environments, it is critical to consider decision makers’ preference shifts during the decision process. This highlights the need for a more comprehensive decision aid approach that is able to model decision makers’ changing preferences and thus improve the accuracy of decision recommendations. Summary of the invention

[0004] In view of the above technical deficiencies, this method aims to propose a novel multi-criteria solution ranking method for the collaborative solution recommendation problem in a dynamic multi-base value chain collaborative decision-making environment, in which the decision makers' preferences change with the changes in the environment.

[0005] The value chain collaborative solution recommendation method and device based on dynamic multi-criteria decision analysis is characterized by comprising the following steps:

[0006] S1. Definition of value chain collaborative optimization decision-making problem;

[0007] S2, obtain decision maker preference information;

[0008] S3, constructing a preference learning model by linking the decision maker's context-dependent preferences to the dynamic decision environment and using a probabilistic value-driven ranking procedure to describe the preference information;

[0009] S4. Infer the parameters of the decision maker's dynamic situational preference model based on maximum likelihood estimation to predict the recommendation results of the value chain collaboration plan;

[0010] S5. Predict the decision maker's future preference model and the corresponding ranking of alternative value chain coordination solutions based on continuous new context input;

[0011] S6. Select the best collaborative plan based on the ranking results of the alternative value chain collaborative plans to conduct collaborative optimization of the manufacturing value chain.

[0012] Furthermore, in step S1, a collaborative solution recommendation problem in a dynamic multi-base value chain collaborative decision-making environment is considered. The decision maker's preference is affected by the gradually evolving environment. The goal is to sort a limited set of alternative value chain collaborative solutions to select the best collaborative solution. Formally, A = {a1, ..., a n} represents the set of collaborative alternatives, and assumes that all alternatives are based on m criteria G = {g1,…,g m} to evaluate, let g j (a i ) means a i ∈A in g j ∈G, without loss of generality, assuming that g j (a i ) is larger, a i In g j The better the performance on the dynamic decision environment at each time t, the dynamic decision environment consists of an environment vector containing l observable features To describe, assume that the decision maker's changing preferences are described as the situation-dependent preference model U t (·), t=1,2,…, these models summarize a i ∈A in g j ∈G, thus obtaining a comprehensive score U at each time t t (a i ), since the decision maker's preference related to the environment is time-varying, different rankings π can be obtained on the set of alternatives t ,t=1,2,…, use π t (a i ) means in the sorting π t Option a is given in i ∈A, so that π t (a i )∈{1,…,n}, and denotes the alternatives assigned to position j∈{1,…,n} such that

[0013] Furthermore, in step S2, the decision maker can use the complete order π of the continuous time period t=1,…,T t The goal of this paper is to develop a preference learning method from the provided preference information π 1:T , the preference model U constructed in this way t (·) can be applied to a given unseen environment o at time t′>T t′ Dynamically predict future decision outcomes under the condition π t′ .

[0014] Further, in step S3, the method uses a linear-Gaussian state space model to link the decision maker's preferences related to the collaborative decision-making context with the dynamic collaborative solution recommendation decision environment, wherein the hidden state θ t and the decision maker’s preference model U at time t t (·) is highly correlated, and by t With its previous state θ t-1 And θ t The current decision-making environment t Correlated, according to the Markov process evolving over time, the transition function θ of the linear Gaussian state space model t =f(θ t-1 ,o t )as follows:

[0015] θ t =f(θ t-1 ,o t )=αθ t-1 +(1-α)Ao t +ε t

[0016] Among them, A is the regression coefficient matrix, which is used to connect θ t and t ; ε t is random noise, following a normal distribution with mean vector 0 and diagonal covariance matrix Q, i.e., ε t ~N(0,Q), since it is assumed that the decision maker's preferences evolve gradually and smoothly according to the situation, a hyperparameter α∈[0,1] is used in the model to control the degree of smoothing.

[0017] This method adopts a popular probabilistic model, the Luce model, to define the sorting information π t At each time t given the environment-dependent preference model U t The Luce model assumes that decision makers express their preferences in the following way: The probability of being assigned to the first position is Then the alternative The probability of being assigned to the second position is Continue allocating until a complete sort π is produced t , according to the above generation procedure, with the preference model U t (·) is a complete ordering of conditions π t The probability of can be specified as follows:

[0018]

[0019] In order to summarize the performance of alternatives on multiple criteria according to the decision maker's dynamic preferences, this method uses an additive value function model U related to the environment. t (·) to summarize each alternative a i The performance of ∈A on all criteria is as follows:

[0020]

[0021] Among them, U t (a i ) represents the quantitative decision maker's choice of alternative a at time t i The composite score of perceived attractiveness, u t,j (g j (a i )) is alternative a i In the criteria j The marginal value on the marginal value function u t,j (·) is monotonic, non-decreasing and normalized, so the comprehensive score U t (·) is bounded in the interval [0,1],

[0022] Therefore, the likelihood can be expressed as u t Rephrase as follows:

[0023]

[0024] Then, in order to transform the preference vector u t With hidden state θ t =(θ t,1 ,…,θ t,γ ) T In connection, the softmax transformation can be used as follows:

[0025]

[0026] Please note that θ t with u t With the same dimension γ, the above formula ensures that the Gaussian variable θ t to the parameter vector u defined on a (γ-1)-dimensional simplex t conversion.

[0027] Furthermore, in step S4, the method uses the maximum likelihood estimation method to infer the model parameters and the generation process. This task can be expressed as the following optimization problem:

[0028]

[0029] in represents the maximum likelihood estimate of the parameter λ = (Q, A, θ0), L(π 1:T |λ) represents the likelihood P(π 1:T ∣o 1:T ,λ,α) represents the likelihood, and the Monte Carlo method can be used to obtain an unbiased likelihood approximation, and then the stochastic gradient descent algorithm is applied to obtain the maximum likelihood estimate. The inferred parameters can be used to predict the ranking results of collaborative solutions in future scenarios.

[0030] The maximum likelihood estimation problem can be formulated as follows:

[0031]

[0032] Where LL(π 1:T |λ)=logL(π 1:T |λ), C>0 is a hyperparameter used in LL(π 1:T ∣λ) and Ω(U t ), the regularization term Ω(U t ) is implemented as the change in the slope of the slice linear marginal value function.

[0033] Furthermore, in step S5, the proposed model can be based on the context vector o that is not seen at time t′>T t′ Predict the decision maker's future preferences and corresponding decision results, let A MLE represents the maximum likelihood estimate of parameter A,

[0034] Hidden state θ t′ and the preference vector u t′ It can be predicted as follows:

[0035] θ t′ =αθ t′-1 +(1-α)A MLE o t′

[0036] u t′ =softmax(θ t′ )

[0037] Then the decision maker's preference model at time t′>T can be predicted as

[0038]

[0039] According to the predicted comprehensive value A i ∈A sorted from best to worst, we can get the most likely decision result π t′ , thereby obtaining the ranking results of alternative value chain collaboration solutions that meet the decision makers' preferences in a dynamic environment.

[0040] Further, in step S6, the decision result π is obtained according to the prediction of the collaborative solution decision model. t′ , select the alternative value chain collaboration plan with the highest priority as the best collaboration plan.

[0041] Furthermore, an electronic device is provided, characterized in that it comprises a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to execute the value chain optimization method as described in any one of claims 1 to 7.

[0042] This method has the following beneficial effects and advantages:

[0043] 1. This method establishes a collaborative solution recommendation model framework based on probabilistic graphical models, integrating evolving decision-making situations, dynamic preference models, and probabilistic ranking procedures. The structure of the model is simple and clear, and its meaning is profound, ensuring the transparency and interpretability of the dynamic decision-making process.

[0044] 2. This method introduces a preference learning method in step S3, which combines a state space model to capture the conditional dependence of decision makers' preferences on the changing environment, and a Markov process that links the decision makers' preferences at various decision stages, reflecting the dynamic changes of preferences. This mitigates cognitive bias by simulating a smooth and static preference evolution, thereby making the predicted collaborative solution recommendation results more accurate.

[0045] 3. In step S4, this method uses the reparameterization technique and the Adam optimizer to develop an algorithm for estimating model parameters by maximum likelihood. These technical advances from the field of machine learning ensure computational efficiency when finding the optimal solution to the difficult likelihood function. Therefore, the dynamic situational preference model constructed based on the estimated parameters can be used to recommend future decisions in unknown situations, so that the best solution can be given more quickly in the decision-making scenario of collaborative solution recommendation.

[0046] The proposed method considers scenarios where the decision environment is constantly evolving, leading to changes in preferences for multiple criteria. To be able to handle dynamic decision environments, the method proposes a novel probabilistic preference learning method for multi-criteria ranking. The method aims to build a set of evolving value-based preference models using indirect preference information conditioned on the dynamic decision environment. To this end, the method uses a linear-Gaussian state-space model that describes a probabilistic ranking procedure that generates preference information at different stages of the decision process by linking the underlying time-varying contingent preference model to the evolving decision environment. The method also develops an inference algorithm to estimate the parameters of the model by following the principle of maximizing the likelihood. The computational efficiency of parameter inference is ensured by borrowing and appropriately adapting technological advances in the field of machine learning. Therefore, the parameterized dynamic situational preference model can be used to recommend future decision outcomes in unknown decision situations. In summary, the method aims to solve the problem of predicting the best collaborative solution that meets the individual preferences of decision makers in future scenarios in a dynamic multi-base value chain collaborative decision environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a schematic diagram of the method

[0048] Figure 2 is the model probability graph of this method DETAILED DESCRIPTION

[0049] The present method is further described in detail below in conjunction with specific embodiments, which are intended to explain the present method rather than to limit it.

[0050] like Figure 1 As shown, a multi-base value chain collaborative solution recommendation method and device based on dynamic multi-criteria decision analysis includes the following steps: value chain collaborative optimization decision problem definition, obtaining decision maker preference information, dynamic preference model modeling, model parameter inference, decision maker preference prediction and selection of the best solution.

[0051] 1. Definition of value chain collaborative optimization decision-making problem

[0052] Consider a collaborative solution recommendation problem in a dynamic multi-base value chain collaborative decision-making environment. The decision maker’s preferences are affected by the evolving environment. The goal is to sort a limited set of alternative value chain collaborative solutions and select the best one. Formally, A={a1,…,a n} represents the set of alternative value chain coordination solutions, and assumes that all alternative solutions are based on m criteria G = {g1,…,g m} is evaluated. Let g j (a i ) means a i ∈A in g jWithout loss of generality, assume that g j (a i ) is larger, a i In g j The better the performance is. The dynamic decision environment at each time t consists of an environment vector containing l observable features Assume further that the decision maker’s changing preferences are described by the situation-dependent preference model U t (·), t=1,2,…, these models summarize a i ∈A in g j ∈G, thus obtaining a comprehensive score U at each time t t (a i ). Since the decision maker's preferences related to the environment are time-varying, different rankings π can be obtained on the set of alternatives t ,t=1,2,…. Use π t (a i ) means in the sorting π t Option a is given in i ∈A, so that π t (a i )∈{1,…,n}, and denotes the alternatives assigned to position j∈{1,…,n} such that

[0053] 2. Obtain information about decision makers’ preferences

[0054] The decision maker can use the complete order π of consecutive time periods t = 1, ..., T t The goal of this paper is to develop a preference learning method from the provided preference information π 1:T , the preference model U constructed in this way t (·) can be applied to a given unseen environment o at time t′>T t′ Dynamically predict future decision outcomes under the condition π t′ .

[0055] 3. Dynamic Preference Modeling

[0056] 3.1 Linking context-dependent preferences to dynamic decision environments

[0057] It is assumed that the evolving collaborative decision environment affects the decision maker's context-dependent preferences. A reasonable assumption is that the model representing such preferences evolves smoothly. In order to link the decision maker's context-dependent preferences to the dynamic decision environment, this method uses a linear-Gaussian state space model. In this paper, the hidden state θ t and the decision maker’s preference model U at time tt (·) is highly correlated, and by t With its previous state θ t-1 And θ t The current decision-making environment t is associated with, and evolves over time according to a Markov process. The transition function θ of the linear Gaussian state space model t =f(θ t-1 ,o t )as follows:

[0058] θ t =f(θ t-1 ,o t )=αθ t-1 +(1-α)Ao t +ε t (1)

[0059] Among them, A is the regression coefficient matrix, which is used to connect θ t and t ; ε t is random noise, following a normal distribution with mean vector 0 and diagonal covariance matrix Q, i.e., ε t ~N(0,Q). Since it is assumed that the decision maker's preferences evolve gradually and smoothly according to the situation, a hyperparameter α∈[0,1] is used in the model to control the degree of smoothness. Therefore, the linear-Gaussian state space model not only captures the decision environment o t For the hidden state θ t The influence of the continuous state θ t-1 and θ t The state space model characterizes the static and dynamic patterns of decision makers’ smoothly evolving preferences, thereby alleviating the cognitive bias of decision makers when constructing preference models. t =f(θ t-1 ,o t ), it is obvious that θ t ~N(αθ t-1 +(1-α)Ao t ,Q).

[0060] 3.2 Value-driven probabilistic ranking procedure

[0061] This method adopts a popular probabilistic model, the Luce model, to define the sorting information π t At each time t given the environment-dependent preference model U t The Luce model assumes that decision makers express their preferences in the following way: The probability of being assigned to the first position is Then the alternative The probability of being assigned to the second position is Continue allocating until a complete sort π is produced t According to the above generation procedure, the preference model U t (·) is a complete ordering of conditions π t The probability of can be specified as follows:

[0062]

[0063] In order to summarize the performance of alternatives on multiple criteria according to the decision maker's dynamic preferences, this method uses an additive value function model U related to the environment. t (·) to summarize each alternative a i The performance of ∈A on all criteria is as follows:

[0064]

[0065] Among them, U t (a i ) represents the quantitative decision maker's choice of alternative a at time t i The composite score of perceived attractiveness, u t,j (g j (a i )) is alternative a i In the criteria j The marginal value on . The marginal value function u t,j (·) is monotonic, non-decreasing and normalized, so the comprehensive score U t (·) is bounded in the interval [0,1].

[0066] The decision maker’s true value function model U t (·) is unknown in advance. Therefore, a technique is needed to approximate the true value function model U t (·). Various types of marginal value functions (including linear, piecewise linear, spline, and general monotonic functions) can be used to perform this approximation. For simplicity, this method only considers the case of piecewise linear marginal value functions. Using piecewise linear marginal value functions to approximate the true value function model can be regarded as a nonparametric technique because we do not need to make any assumptions about the form of the true marginal value function. By using piecewise linear marginal value functions for approximation, the true value function model U t (·) can be described as:

[0067]

[0068] Among them, u t is a parameter vector, defined on a γ-dimensional simplex, representing the context-dependent preference model U t(·) intrinsic characteristics; V(a i ) is a feature vector consisting entirely of alternative a i Performance on multiple criteria is determined, in particular, by the decision maker’s dynamic preferences. In other words, the decision maker’s situation-dependent preference model U t (·) is the preference vector u t parameterized. Therefore, the likelihood can be expressed as u t Rephrase as follows:

[0069]

[0070] Then, in order to transform the preference vector u t With hidden state θ t =(θ t,1 ,…,θ t,γ ) T In connection, the softmax transformation can be used as follows:

[0071]

[0072] Please note that θ t with u t With the same dimension γ, the above formula ensures that the Gaussian variable θ t to the parameter vector u defined on a (γ-1)-dimensional simplex t conversion.

[0073] 3.3 Probabilistic Graphical Models and Generative Process

[0074] like Figure 2 As shown, the solid nodes represent the model parameters λ = (Q, A, θ0) and the hyperparameter α, and the blank nodes represent all hidden variables (including ε 1:T ,θ 1:T and u 1:T ), the shaded nodes represent observable data (including environment o 1:T and preference information π 1:T ), and the arrows represent the probabilistic dependencies between nodes. Based on the above affiliation structure, the likelihood of the entire model can be expressed as follows:

[0075]

[0076] Note that the hidden state θ t It can be written recursively using model parameters λ = (Q, A, θ0) and hyperparameters α as follows:

[0077]

[0078] where ε i~N(0,Q). In this way, it can be observed that θt follows some unknown distribution

[0079] P(θ t ∣o 1:t ,A,Q,θ0,α), whose parameters are λ=(Q,A,θ0) and α. However, the distribution P(θ t ∣o 1:t ,A,Q,θ0,α) cannot be solved in closed form.

[0080] 4. Model parameter inference

[0081] This method uses the maximum likelihood estimation method to infer the parameters and generation process of the collaborative solution recommendation decision model. This task can be expressed as the following optimization problem:

[0082]

[0083] in represents the maximum likelihood estimate of the parameter λ = (Q, A, θ0), L(π 1:T |λ) represents the likelihood P(π 1:T ∣o 1:T ,λ,α) represents the likelihood. Since the probability P(θ t ∣o 1:t ,A,Q,θ0,α) has no closed form expression and is therefore included in the likelihood L(π 1:T The integral term in |λ) cannot be calculated analytically. However, we can use the Monte Carlo method to obtain an unbiased likelihood approximation, and then apply the stochastic gradient descent algorithm to obtain the maximum likelihood estimate. Specifically, the integral term ∫P(π t ∣u t )P(θ t ∣o 1:t ,A,Q,θ0,α)dθ t According to formula (11), θ can be randomly selected t Sample (with Expressed) to approximate, that is

[0084]

[0085] It should be noted that although the approximation in Equation (13) may have a higher variance when the covariance matrix Q is large, it provides an unbiased estimate of the likelihood gradient with respect to the parameter λ, which allows the search algorithm to converge to a stationary point. Subsequent experimental results also verify the effectiveness of this approximation method.

[0086] Using the approximation in formula (14), the likelihood L(π 1:T ∣λ) can be reformulated as

[0087]

[0088] By applying the chain rule, the likelihood gradient expressed in formula (16) with respect to the regression coefficient matrix A and the initial state θ0 can be derived. However, the likelihood gradient for the covariance matrix Q cannot be calculated directly because θ in formula (17) t is not deterministically conditional on Q, because ε t ~N(0,Q). To solve this problem, this method uses a reparameterization technique to transform the random variable ε t The equivalent expression is

[0089] ε i =q⊙σ i (18)

[0090] where q is a γ-dimensional vector such that Q = diag(q 2 ), σ i ~N(0,I) is a γ-dimensional random variable, ⊙ represents the Hadamard product. Formula (19) can be reformulated as follows:

[0091]

[0092] The θ in the formula t The determining condition is Q = diag (q 2 ), and θ t The randomness of i ~N(0,I). This method can be used to obtain the covariance matrix Q=diag(q 2 ) is the likelihood gradient of .

[0093] Based on the above analysis, the maximum likelihood estimation problem can be expressed as follows:

[0094]

[0095] Where LL(π 1:T |λ)=logL(π 1:T |λ), C>0 is a hyperparameter used in LL(π 1:T ∣λ) and Ω(U t ) is a trade-off between the regularization term Ω(U t ) is implemented as the change in the slope of the slice linear marginal value function. Note that the hyperparameters of the model include the smoothing coefficient α, the number of subintervals γ j , and the regularization coefficient C. All hyperparameters can be specified through cross-validation.

[0096] This method uses the Adam optimizer to solve the optimization problem in formula (22). This is a state-of-the-art algorithm for solving highly complex non-convex optimization problems. Adam uses a series of innovative computational features such as stochastic gradient descent and adaptive learning rate to ensure minimal memory requirements and fastest convergence when processing data-intensive tasks.

[0097] 5. Decision Makers’ Prediction of Preference

[0098] Finally, the method can be used to predict the unseen context vector o at time t′>T. t′ Predict the decision maker's future preferences and the corresponding multi-criteria scheme ranking results. Let A MLE represents the maximum likelihood estimate of parameter A.

[0099] Hidden state θ t′ and the preference vector u t′ It can be predicted as follows:

[0100] θ t′ =αθ t′-1 +(1-α)A MLE o t′

[0101] u t′ =softmax(θ t′ )

[0102] Then the decision maker's preference model at time t′>T can be predicted as

[0103]

[0104] According to the predicted comprehensive value A i ∈A sorted from best to worst, we can get the most likely decision result π t′ , thereby obtaining multi-criteria ranking results that meet the decision maker's preferences in future scenarios in a dynamic environment.

[0105] 6. Choose the best option.

[0106] The decision result π predicted by the collaborative solution recommendation decision model t′ , select the alternative value chain collaboration plan with the highest priority as the best collaboration plan.

[0107] 7. Computational Experiments

[0108] In order to study the ability of this method and the baseline method to predict the results of scheme ranking in future environments in a dynamic environment, the following experiments were designed and implemented.

[0109] 7.1 Dataset and Experimental Setup

[0110] The experimental analysis is based on the generation of random data and considers the following factors of the problem: the number of alternatives (F1), the number of criteria (F2), the length of the time series (F3), the dimension of the environment vector (F4), and the coefficient that adjusts the decision maker's consistency level (F5). All five factors are directly related to the development of the preference model. For F5, three levels were set: 1.0986, 5.2933, and 12.2060, corresponding to the probability of 0.5, 0.99, and 0.99999 that an alternative a1 with U(a1) = 1 is better than another alternative a2 with U(a2) = 0 according to the decision maker's value function. Table 1 lists the levels of each factor considered in the analysis.

[0111] Table 1 Factor levels considered in the simulation experiment

[0112] factor level <![CDATA[Number of alternatives (F1)]]> 10、15、20 <![CDATA[Number of criteria (F2)]]> 2、4、6 <![CDATA[Length of time series (F3)]]> 5、10、15 <![CDATA[Dimension of the environmental vector (F4)]]> 1、3、5 <![CDATA[Coefficient for adjusting the decision maker's consistency level (F5)]]> 1.0986、5.2933、12.2060

[0113] For each combination of the above five factors in Table 1 (243 combinations), 20 random data sets were simulated and the performance of the alternatives on each criterion was obtained according to the uniform distribution in [0,1]. By considering each combination of the above five factors, a ranking problem instance was constructed and a value function model was randomly generated. To represent the true value system of the decision maker. Specifically, in order to generate an environment vector An environmental feature The derivation process is as follows:

[0114]

[0115] in, is the initial value of the environmental characteristics, r (s) ~U(-1,1) is the environmental change rate. Then, we can get according to formula (23) of the sequence, and according to Get the weight vector w t =(w t,1 ,…,w t,m ) T Finally, each criterion g j The marginal value function of It is simulated in the following way

[0116]

[0117] Among them, c j ≠0 is the parameter that determines the curvature of the marginal value function, which is randomly generated from a uniform distribution in the interval [-10, 10]. Such a procedure can simulate convex or concave marginal value functions, which can reflect different risk attitudes of decision makers.

[0118] Then, using the assumed true preference model Generate preference information and apply the proposed method to build an estimated preference model. Specifically, this method uses the true value function model to calculate the true comprehensive value of a∈A According to the probability value driven ranking procedure in formula (24), the alternatives at each position are determined from best to worst in the following way. For the first position, an alternative is randomly selected from the entire alternative set A, and the probability of each alternative a being selected is Among them, r c is the coefficient used to adjust the decision maker's consistency level, that is, F5; the second position is from set A, Randomly select an alternative from . The probability of each alternative being selected is Continue to assign values ​​until a complete sort π is generated t .

[0119] To quantify the performance of these methods, three ranking quality metrics are used in the experiment: Kendall's τ, ranking difference metric, and ranking consistency metric. This experiment compares the developed dynamic preference learning method with the following two baseline methods:

[0120] 1) UTA method, which is an ordinal regression method that uses linear programming to estimate the parameters of the utility function. It uses the information given by the subjective ranking of a set of stimuli or actions (weak-order comparative judgments) and the multi-criteria evaluation of these actions to evaluate the additive utility function that combines multiple criteria into a composite criterion. The method is implemented using the cvxpy solver;

[0121] 2) The ANN-UTA algorithm uses artificial neural networks (ANNs) to derive the shape of weights and marginal value functions without specifying feature points; the optimization objective is the same as the proposed model.

[0122] Experimental environment and parameter settings: The simulation is run on a server (Intel Xeon Silver 4214CPU 2.20GHz, memory 128G, SSD 480G, 4×RTX 2080Ti 11G), and Python 3.9 is used for data simulation, model inference and result analysis.

[0123] For each simulated problem instance, the experimental data set is divided into two parts. On the one hand, in order to examine the prediction performance of new alternatives, 70% of the alternatives are randomly selected from each alternative set for training the model, and the remaining 30% of the alternatives are used as new alternatives to test the prediction performance. On the other hand, in order to examine the prediction performance in a new environment, the first 70\% of the preference information in the time series is selected for training, and the last 30\% is used as the alternatives in the new environment for testing.

[0124] Regarding model hyperparameters, the range of hyperparameter values ​​is defined here, as well as other hyperparameters involved in the baseline required for successful model training during these model runs. In order to find the best values, cross-validation is performed to verify the ranking quality of different values. Specifically, four hyperparameters are tested:

[0125] 1) Smoothing coefficient α∈{0,0.2,0.5,0.8,1} of the proposed model;

[0126] 2) The number of subintervals γ of the proposed model and UTA method j ∈{1,2,3,4,5};

[0127] 3) Regularization coefficient C∈{0,1,10,100,200} of the proposed model;

[0128] 4) The number of monotone block components of ANN-UTA L∈{10,20,30} - This is the only parameter that needs to be provided with a value before training the method.

[0129] 7.2 Experimental Results

[0130] 7.2.1 Experimental Evaluation of Predicting the Ranking of New Alternatives

[0131] The above three methods are applied to each random dataset to compare the performance in terms of Kendall'sτ, RAM and RDM. The average Kendall'sτ, RAM and RDM values ​​at different levels of each considered factor (F1-F5) are listed in Table 2.

[0132] Table 2 Means and standard deviations of Kendall's τ, RAM, and RDM values ​​for the proposed model, UTA, and ANN-UTA in the new alternative experiments

[0133]

[0134]

[0135] The proposed method outperforms UTA ​​and ANN-UTA under different problem settings. On average, the proposed model obtains Kendall'sτ, RAM, and RDM of 0.655, 0.365, and 0.935, respectively, while UTA obtains 0.635, 0.345, and 0.933, respectively. The three measurements of ANN-UTA are 0.585, 0.306, and 0.929, which are among the lowest values. To verify the statistical significance of the results, a Wilcoxon test was performed. It can be observed from Table 2 that the p-values ​​of the three measurements are less than 0.001. This confirms that the proposed method performs significantly better than UTA on the artificial dataset, and UTA shows stronger performance compared to ANN-UTA, indicating that the proposed method is better able to obtain the solution ranking results that meet the decision maker's preferences in a dynamic decision environment.

[0136] 7.2.2 Experimental evaluation of predicting the ranking of alternatives in new environments

[0137] Since the baseline UTA and ANN-UTA cannot predict alternatives with context vectors in new environments, a multi-layer perceptron (MLP) is developed to predict the decision maker’s preferences based on the inferred preference model derived from UTA and ANN-UTA. This model can transform the current context vector o t With the previous parameter vector u t-1 Combined, output the current parameter vector u t , the predicted value function model U t (·) can be specified using formula (25). The optimization objective of MLP is the same as that of the method proposed in this paper.

[0138] Table 3 shows the average Kendall'sτ, RAM, and RDM values ​​at different levels of the five factors considered. The performance of the three methods shows the same trend as the problem setting changes. Specifically, the best performing method exploits the results obtained by the proposed method. Compared with the case of prediction using new alternatives, the prediction performance of all three methods increases with the increase of time series length (F3) and environment vector dimension (F4). Compared with UTA and ANN-UTA, the proposed method uses a state space model to link environment-related preferences to the dynamic decision environment. In contrast, the two baseline methods combine MLP to consider contextual predictions. When more environmental information is included, all three methods can improve the prediction performance, which is consistent with expectations. In summary, the proposed method has better prediction results in the problem of predicting the ranking of options that meet the decision maker's preferences in future scenarios in a dynamic environment, and can solve such option ranking problems well. Table 3 Mean and standard deviation of Kendall'sτ, RAM, and RDM values ​​of the proposed model, UTA, and ANN-UTA in the new environment experiment

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Claims

1. A collaborative optimization method for manufacturing value chain based on dynamic multi-criteria decision analysis, characterized by The following steps are involved: S1. Definition of value chain collaborative optimization decision-making problem; S2, obtain decision maker preference information; S3, constructing a preference learning model by linking the decision maker's context-dependent preferences to a dynamic decision environment and using a probabilistic value-driven ranking procedure to describe the preference information; S4. Infer the parameters of the decision maker's dynamic situational preference model based on maximum likelihood estimation to predict the recommendation results of the value chain collaboration plan; S5. Predict the decision maker's future preference model and the corresponding ranking of alternative value chain coordination solutions based on continuous new context input; S6. Select the best collaborative plan based on the ranking results of the alternative value chain collaborative plans to conduct collaborative optimization of the manufacturing value chain.

2. The manufacturing value chain collaborative optimization method based on dynamic multi-criteria decision analysis according to claim 1 is characterized by: In step S1, according to the problem of collaborative solution recommendation in a dynamic multi-base value chain collaborative decision-making environment, the decision maker's preference is affected by the gradually evolving environment. The goal is to sort a limited set of alternative value chain collaborative solutions to select the best collaborative solution. Formally, A = {a1, ..., a n } represents the value chain coordination solution set, and assumes that all alternative solutions are based on m criteria G = {g1,…,g m } to evaluate, let g j (a i ) means a i ∈A in g j ∈G, without loss of generality, assuming that g j (a i ) is larger, a i In g j The better the performance on the dynamic decision environment at each time t, the dynamic decision environment consists of an environment vector containing l observable features To describe, assume that the decision maker's changing preferences are described as the situation-dependent preference model U t (·), t=1,2,…, these models summarize a i ∈A in g j ∈G, thus obtaining a comprehensive score U at each time t t (a i ), since the decision maker's preference related to the environment is time-varying, different rankings π can be obtained on the set of alternatives t ,t=1,2,…, use π t (a i ) means in the sorting π t Option a is given in i ∈A, so that π t (a i )∈{1,…,n}, and denotes the alternatives assigned to position j∈{1,…,n} such that 3. The collaborative optimization method for manufacturing value chain based on dynamic multi-criteria decision analysis according to claim 1, characterized in that: In step S2, the decision maker uses the complete order π of the continuous time period t=1,…,T t The goal is to develop a preference learning method from the provided preference information π 1:T , the preference model U constructed in this way t (·) can be applied to a given unseen environment o at time t′>T t′ Dynamically predict future decision outcomes under the condition π t′ .

4. The collaborative optimization method for manufacturing value chain based on dynamic multi-criteria decision analysis according to claim 1, characterized in that: In step S3, a linear-Gaussian state space model is used to link the decision maker's preferences related to the collaborative decision-making context with the dynamic collaborative solution recommendation decision environment, where the hidden state θ t and the decision maker’s preference model U at time t t (·) is highly correlated, and by t With its previous state θ t-1 And θ t The current decision-making environment t Correlated, according to the Markov process evolving over time, the transition function θ of the linear Gaussian state space model t =f(θ t-1 ,o t )as follows: i t =f(θ t-1 ,o t )=αθ t-1 +(1-a)Ao t +e t Among them, A is the regression coefficient matrix, which is used to connect θ t and t ; ε t is random noise, following a normal distribution with mean vector 0 and a diagonal covariance matrix Q, i.e., ε t ~N(0,Q), since it is assumed that the decision maker's preferences evolve gradually and smoothly according to the situation, a hyperparameter α∈[0,1] is used in the model to control the degree of smoothing.

5. The collaborative optimization method for manufacturing value chain based on dynamic multi-criteria decision analysis according to claim 4 is characterized by: A popular probability model Luce model is used to define the sorting information π t At each time t given the environment-dependent preference model U t The Luce model assumes that decision makers express their preferences in the following way: The probability of being assigned to the first position is Then the alternative The probability of being assigned to the second position is Continue allocating until a complete sort π is produced t , according to the above generation procedure, with the preference model U t (·) is a complete ordering of conditions π t The probability of can be specified as follows: According to the decision maker's dynamic preferences, the performance of alternatives on multiple criteria is summarized and an additive value function model U related to the environment is used. t (·) to summarize each alternative a i The performance of ∈A on all criteria is as follows: Among them, U t (a i ) represents the quantitative decision maker's choice of alternative a at time t i The composite score of perceived attractiveness, u t,j (g j (a i )) is alternative a i In the criteria j The marginal value on the marginal value function u t,j (·) is monotonic, non-decreasing and normalized, so the comprehensive score U t (·) is bounded in the interval [0,1], Therefore, the likelihood can be expressed as u t Rephrase as follows: Then, in order to transform the preference vector u t With hidden state θ t =(θ t,1 ,…,θ t,γ ) T In connection, the softmax transformation can be used as follows: θ t with u t With the same dimension γ, the above formula ensures that the Gaussian variable θ t to the parameter vector u defined on a (γ-1)-dimensional simplex t conversion.

6. The manufacturing value chain collaborative optimization method based on dynamic multi-criteria decision analysis according to claim 1 is characterized by: In step S4, the method uses the maximum likelihood estimation method to infer the model parameters and the generation process. This task can be expressed as the following optimization problem: in represents the maximum likelihood estimate of the parameter λ = (Q, A, θ0), L(π 1:T |λ) represents the likelihood P(π 1:T ∣o 1:T ,λ,α) represents the likelihood, and the Monte Carlo method can be used to obtain an unbiased likelihood approximation, and then the stochastic gradient descent algorithm is applied to obtain the maximum likelihood estimate. The inferred parameters can be used to predict the ranking results of collaborative solutions in future scenarios. The maximum likelihood estimation problem can be formulated as follows: Where LL(π 1:T |λ)=logL(π 1:T |λ), C>0 is a hyperparameter used in LL(π 1:T ∣λ) and Ω(U t ), the regularization term Ω(U t ) is implemented as the change in the slope of the slice linear marginal value function.

7. The collaborative optimization method for manufacturing value chain based on dynamic multi-criteria decision analysis according to claim 1, characterized in that: In step S5, the proposed model is based on the context vector o that is not seen at time t′>T t′ Predict the decision maker's future preferences and corresponding decision results, let A MLE represents the maximum likelihood estimate of parameter A, Hidden state θ t′ and the preference vector u t′ It can be predicted as follows: i t′ =θ t′-1 +(1-a)A MLE the t′ u t′ =softmax(θ t′ ) Then the decision maker's preference model at time t′>T can be predicted as According to the predicted comprehensive value A i ∈A sorted from best to worst, we can get the most likely decision result π t′ , thereby obtaining the ranking results of value chain collaboration solutions that meet the decision makers' preferences in a dynamic environment.

8. The collaborative optimization method for manufacturing value chain based on dynamic multi-criteria decision analysis according to claim 1, characterized in that: In step S6, the decision result π is predicted by the value chain collaborative solution recommendation decision model. t′ , select the alternative value chain collaboration plan with the highest priority as the best collaboration plan.

9. An electronic device, characterized in that: It includes a memory and a processor, the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to execute the manufacturing value chain collaborative optimization method as described in any one of claims 1 to 7.

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