Intelligent multi-objective optimization method for solving infeasible solutions of complex chemical process industry processes

Abstract

This invention relates to an intelligent multi-objective optimization method for solving infeasible solutions in complex chemical process industrial applications. This method uses a classification model to screen infeasible solutions and performs targeted mutations to increase the likelihood of transforming infeasible solutions into feasible ones. The method uses classification as a data-driven model to accurately identify specific infeasible solutions and perform targeted mutations. Differentiated mutation operators are used for different types of solutions to ensure that the mutation direction matches the characteristics of the solution. For specific infeasible solutions, uniform mutation is used, constrained by the variable range of Pareto solutions, to correct the solution to the feasible region. This avoids the waste of traditional methods by generating high-quality Pareto solutions early on and avoids local convergence. Validated in dual-tower side-stream extractive distillation and four-tower extractive distillation systems, this method not only significantly improves computational efficiency, reducing optimization time by 35.3% and 20.8% respectively, but also outperforms widely used genetic methods.

Description

Technical Field

[0001] This invention relates to the fields of chemical process systems engineering and intelligent optimization technology, specifically a multi-objective optimization method for mixed integer nonlinear programming (MINLP) problems in complex chemical process industrial processes, and particularly to an intelligent multi-objective optimization method for solving infeasible solutions in complex chemical process industrial processes. Background Technology

[0002] Complex chemical processes, as one of the most important separation technologies, are widely used in industries such as petrochemicals, pharmaceuticals, and fine chemicals. Due to the significant thermal energy consumption of phase transformation operations, complex chemical processes account for a substantial proportion of total industrial energy consumption. With rising energy costs and increasingly prominent environmental issues, the optimal design of complex chemical processes is crucial for improving energy efficiency, reducing investment and operating costs, and minimizing carbon emissions. Despite their significant industrial value, complex chemical processes exhibit complex behavior, are controlled by highly nonlinear models (such as thermodynamic models), and involve both continuous and discrete optimization variables. Therefore, their optimization naturally falls under the category of mixed-integer nonlinear programming (MINLP) problems, which are challenging to solve. Although various deterministic methods have been developed, their performance heavily relies on good initial guesses and often fails to guarantee global optimality in highly nonconvex cases.

[0003] Metaheuristic methods (MHAs), inspired by natural phenomena, have become a research hotspot for solving complex non-convex MINLP problems. These methods typically treat the optimization task as a black box, focusing only on the input-output relationship, making them well-suited for optimizing complex systems such as complex chemical processes and industrial processes. Among metaheuristic methods, genetic methods (GA) have been widely applied to chemical process optimization due to their robustness and outstanding global search capabilities; moreover, this method is highly flexible and scalable, applicable to various complex chemical processes such as extractive distillation, pressure swing distillation, and reactive distillation, and can simultaneously consider multiple objectives such as energy consumption and economic efficiency. However, traditional genetic methods face many practical challenges when applied to the optimization of complex chemical processes and industrial processes, the most prominent being the frequent generation of infeasible solutions. For infeasible solutions that violate explicit variable constraints, penalty functions or constraint handling techniques have been developed to effectively guide the search toward the feasible region. However, a large number of infeasible solutions originate from convergence failures in process simulation, and effective strategies for handling such infeasible solutions are rarely studied. Convergence failures are mainly caused by improper setting of process variables, which often exhibit strong correlations. Although these solutions are marked as infeasible, many of them still have significant potential to become feasible after minor modifications. However, repeatedly generating and evaluating these infeasible solutions consumes substantial computational resources, reducing optimization efficiency. Therefore, there is an urgent need to develop specialized methods to identify and utilize potentially infeasible solutions, avoiding ineffective evaluations, and thereby improving the overall performance of genetic methods in optimizing complex chemical processes in industrial processes. Summary of the Invention

[0004] In view of the above-mentioned problems in the existing technology, the technical problem to be solved by the present invention is: how to deal with infeasible solutions generated during the optimization process.

[0005] To address the aforementioned technical problems, this invention employs the following technical solution: An intelligent multi-objective optimization method for resolving infeasible solutions in complex chemical process industrial processes. This method integrates data-driven approaches and differential mutation correction strategies to discover potentially infeasible solutions among numerous infeasible solutions and performs targeted mutations to guide the search toward a feasible, high-performance region. The method includes the following steps:

[0006] S1: Based on the NSGA-II framework, set the population size W, crossover operator, and initial number of iterations. At the same time, construct a Pareto solution database to store Pareto feasible solutions generated during the iteration process. The Pareto solution database is initially empty.

[0007] S2: For complex chemical process industrial processes, determine the objective function and B optimization variables.

[0008] S3: Initiate a multi-objective optimization method to generate an initial parent population, where each optimization variable is treated as a gene, and all optimization variables form a chromosome, which in turn constitutes an individual.

[0009] S4: Divide all individuals in the initial parent population into constraint-violation solutions and constraint-satisfaction solutions based on whether they satisfy the constraints. Evaluate the constraint-satisfaction solutions and take the solutions that can make the process mechanism model corresponding to the complex chemical process converge as feasible solutions, and the rest as infeasible solutions.

[0010] S5: Crossover, using the crossover operator to crossover all feasible solutions in the initial parent population.

[0011] S6: Training dataset construction involves fusing feasible solutions from the initial parent population with Pareto solutions from the Pareto solution database to form the training dataset. ,in Let i be the i-th optimization variable. The training dataset is the label for the i-th optimization variable. Feasible solutions from the initial parent population and Pareto solution Together, they form a system where all Pareto solutions are labeled 0, while other feasible solutions are labeled 1.

[0012] judge Check if there is an infeasible solution. If so, proceed to the next step; otherwise, proceed to S13.

[0013] S7: Use D to train the classification model and continuously update the classification model parameters according to the loss function. When the loss function no longer changes, the training ends and the trained classification model is obtained.

[0014] S8: Input the infeasible solutions obtained in S4 into the trained classification model, and output the non-dominated level of each infeasible solution. Set the label of all infeasible solutions with a non-dominated level of 1 to 0, and set the label of the remaining infeasible solutions to 1.

[0015] Define all infeasible solutions with a non-dominance level of 1 as special infeasible solutions, and determine whether a special infeasible solution exists. If it exists, proceed to the next step; otherwise, proceed to S13.

[0016] S9: Calculate the difference between the b-th gene in each particular infeasible solution and the b-th gene in all Pareto solutions, then sum all the differences to obtain the mutation scalar corresponding to the b-th gene. Choose the gene corresponding to the maximum value among the B mutation scalars as the mutant gene.

[0017] S10: Specifies the boundary of the mutation, representing the maximum value of the mutated gene in all Pareto solutions. and minimum value This serves as the boundary for mutations.

[0018] S11: For the kth special infeasible solution When performing mutations, the weight of the mutated gene is set to 1, and the weight of all other genes is set to 0. The mutated gene is within the interval... Uniform mutation is performed inside, and after mutation... Obtained from the uniform catastrophe operator according to the formula:

[0019]

[0020] in, Indicates the first Minimum value of mutated genes, Indicates the first The maximum value of the mutated gene. Randomly generated within the interval [0,1], following a uniform distribution. ~U[0,1]), where K represents the number of special infeasible solutions.

[0021] S12: Mutate all K special infeasible solutions.

[0022] S13: Apply polynomial mutation to the Pareto feasible solution and other feasible solutions in the initial parent population after crossover to obtain the offspring population.

[0023] S14: Merge the offspring population with the initial parent population to obtain a merged population. Apply the NSGA-II non-dominated ranking method to the merged population to obtain the non-dominated level of each individual. Select individuals with a non-dominated level of 1.

[0024] When the number of selected individuals Q > W, the selected individuals are taken as the new generation population;

[0025] When the number of selected individuals When W, the crowding degree is calculated for all individuals with a non-dominance level other than 1, and the crowding degree is sorted in descending order. The individuals corresponding to the top WQ crowding degrees are selected, and the individuals with a non-dominance level of 1 and the individuals corresponding to the top WQ crowding degrees are merged into a new generation of population.

[0026] S15: Update the initial parent population with the new generation population, and update the Pareto solution database with individuals whose non-dominance level is 1 as new Pareto solutions. Then return to S5 until the maximum number of iterations is reached, and output the final Pareto solution database.

[0027] As an improvement, the S2 complex chemical process industrial process is a dual-tower side-stream extractive distillation system. Through degree-of-freedom analysis, its optimization variables include: the total number of trays in both towers. and Feeding positions of the two towers and The number of trays extracted from the side stream in the EDC (Entrainer Discharge Center) , Entrainer flow rate and the reflux ratio of EDC ;in and The first variable is continuous, while the others are discrete; total annual cost (TAC) and greenhouse gas emissions based on carbon dioxide. As the objective function.

[0028] As an improvement, the S2 complex chemical process industrial process is a four-tower side-stream extractive distillation system. Through degree-of-freedom analysis, its optimization variables include: the total number of trays in the four towers. , , , and The position of the feed plates of the four towers , , , and The position of the feed plate for entrained agents in the EDC tower Entrainer flow rate And the reflux ratios of EDC, PDC and SRC. , , and Total Annual Cost (TAC) and Greenhouse Gas Emissions Based on Carbon Dioxide The process system index PRI is used as the objective function.

[0029] As an improvement, the classification model in S7 is a Gaussian process classification model.

[0030] Compared with the prior art, the present invention has at least the following advantages:

[0031] (1) The present invention proposes an intelligent multi-objective optimization method for solving infeasible solutions in complex chemical process industrial processes. It integrates data-driven approaches with targeted mutation correction strategies to discover potentially infeasible solutions among numerous infeasible solutions, guiding the search towards a feasible high-performance region. In this invention, effective solutions are used as the training dataset to construct a classification model. This model is used to classify infeasible solutions, classifying them into infeasible solutions of the same type as Pareto solutions. Then, targeted mutation is performed. This process can discover potentially infeasible solutions among numerous infeasible solutions and transform them into effective solutions as much as possible. This allows them to serve as high-quality priors to guide subsequent iterative searches towards a feasible high-performance region.

[0032] (2) The method of the present invention develops a multi-objective optimization framework that integrates the identification-correction strategy, which is adapted to complex chemical process industrial processes of different complexities. It is implemented in Python, can be reproduced by personnel in the relevant technical field, and is easy to implement in industrial applications.

[0033] (3) The performance of the proposed framework was verified in side-flow dual-tower extractive distillation (SS-DCED) and four-tower extractive distillation (FCED) systems. This optimized framework not only significantly improves computational efficiency, reducing optimization time by 35.3% and 20.8% respectively, but also outperforms widely used genetic methods. Overall, this multi-objective dynamic improved direct distillation control framework provides an efficient and computationally resource-saving solution for optimizing complex distillation processes. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0035] Figure 2 A schematic diagram for identifying special infeasible solutions.

[0036] Figure 3 This is a schematic diagram of the directional mutation of the present invention.

[0037] Figure 4 This is a schematic diagram of the results of the dual-tower side-line extraction distillation in Example 1 of this invention.

[0038] Figure 5Figure 1 shows the comparison results between the traditional method and the method of the present invention in Example 1. Figure (a) shows the Pareto solutions obtained by the traditional multi-objective optimization method after 50, 100, and 200 generations. Figure (b) shows the Pareto solutions obtained by the method of the present invention after 50, 100, and 200 generations. Figure (c) shows the number of iterations corresponding to each Pareto optimal solution when the traditional multi-objective optimization method appears during the optimization of Example 1. Figure (d) shows the number of iterations corresponding to each Pareto optimal solution when the method of the present invention appears during the optimization of Example 1.

[0039] Figure 6 This is a schematic diagram of the four-tower extraction and distillation results in Example 2 of this invention.

[0040] Figure 7 Figure 2 shows the comparison results between the traditional method and the method of the present invention in Example 2. Figure (a) shows the Pareto solutions obtained by the traditional multi-objective optimization method after 50, 100, and 200 generations. Figure (b) shows the Pareto solutions obtained by the method of the present invention after 50, 100, and 200 generations. Figure (c) shows the number of iterations corresponding to each Pareto optimal solution when the traditional multi-objective optimization method appears during the optimization of Example 1. Figure (d) shows the number of iterations corresponding to each Pareto optimal solution when the multi-objective optimization method of the present invention appears during the optimization of Example 1. Detailed Implementation

[0041] The present invention will now be described in further detail.

[0042] This invention proposes an intelligent multi-objective optimization method for solving infeasible solutions in complex chemical process industrial processes, such as... Figure 1 As shown in the diagram, this framework accelerates convergence towards the optimal design by identifying infeasible solutions with characteristics similar to high-performance solutions. Specifically, this invention first trains a surrogate model to distinguish between feasible and infeasible solutions, and then identifies potential high-performance candidate solutions from the set of infeasible solutions based on this model. The entire process is as follows: Figure 2 As shown in Figure S9; then, the optimization variables that need to undergo mutation are obtained through the method shown in S9, and then the range of Pareto solutions is used as the mutation interval to realize the directional uniform mutation strategy. This process is as follows: Figure 3 As shown in the diagram. This strategy reduces ineffective exploration of infeasible regions and concentrates computational resources on finding high-quality solutions within the feasible region.

[0043] An intelligent multi-objective optimization method for solving infeasible solutions in complex chemical process industrial applications integrates data-driven and differential mutation correction strategies. It mines potentially infeasible solutions from numerous infeasible solutions and performs targeted mutations to guide the search toward a feasible, high-performance region. The method includes the following steps:

[0044] S1: Based on the NSGA-II framework, set the population size W, crossover operator, and initial number of iterations. At the same time, construct a Pareto solution database to store Pareto feasible solutions generated during the iteration process. The Pareto solution database is initially empty.

[0045] S2: For complex chemical process industrial processes [such as two-tower side-stream extractive distillation or four-tower side-stream extractive distillation], determine the objective function and B optimization variables.

[0046] S3: Initiate a multi-objective optimization method [The multi-objective optimization method adopts existing methods, such as the Non-dominated Sorting Genetic Algorithm II (NSGA-II), to generate an initial parent population, where each optimization variable is treated as a gene, and all optimization variables form a chromosome, which is an individual; evaluate the feasibility of each individual, and distinguish between individuals corresponding to feasible solutions and individuals corresponding to infeasible solutions.

[0047] S4: All individuals in the initial parent population are categorized into constraint-violation solutions and constraint-satisfaction solutions based on whether they meet the constraints. Constraint-satisfaction solutions are evaluated, and those that enable the convergence of the process mechanism model corresponding to the complex chemical process are considered feasible solutions; otherwise, they are considered infeasible solutions. This invention primarily focuses on targeted modifications to infeasible solutions.

[0048] S5: Crossover, using the crossover operator to crossover all feasible solutions in the initial parent population.

[0049] S6: Training dataset construction involves fusing feasible solutions from the initial parent population with Pareto solutions from the Pareto solution database to form the training dataset. ,in Let i be the i-th optimization variable. The training dataset is the label for the i-th optimization variable. Feasible solutions from the initial parent population and Pareto solution Together, they form a whole; all Pareto solutions are labeled 0, while other feasible solutions are labeled 1; (The last part, "judging," is a separate, unrelated statement and doesn't need a direct translation.) Check if there is an infeasible solution. If so, proceed to the next step; otherwise, proceed to S13.

[0050] S7: Use D to train the classification model and continuously update the classification model parameters according to the loss function. When the loss function no longer changes, the training ends and the trained classification model is obtained.

[0051] S8: Input the infeasible solutions obtained in S4 into the trained classification model, and output the non-dominated level of each infeasible solution. Set the label of all infeasible solutions with a non-dominated level of 1 to 0, and set the label of the remaining infeasible solutions to 1.

[0052] Define all infeasible solutions with a non-dominance level of 1 as special infeasible solutions, and determine whether a special infeasible solution exists. If it exists, proceed to the next step; otherwise, proceed to S13.

[0053] S9: Calculate the difference between the b-th gene in each particular infeasible solution and the b-th gene in all Pareto solutions, then sum all the differences to obtain the mutation scalar corresponding to the b-th gene. Choose the gene corresponding to the maximum value among the B mutation scalars as the mutant gene.

[0054] S10: Specifies the boundary of the mutation, representing the maximum value of the mutated gene in all Pareto solutions. and minimum value This serves as the boundary for mutations.

[0055] S11: For the kth special infeasible solution When performing mutations, the weight of the mutated gene is set to 1, and the weight of all other genes is set to 0. The mutated gene is within the interval... Uniform mutation is performed inside, and after mutation... Obtained from the uniform catastrophe operator according to the formula:

[0056]

[0057] in, Indicates the first Minimum value of mutated genes, Indicates the first The maximum value of the mutated gene. Randomly generated within the interval [0,1], following a uniform distribution. ~U[0,1]), where K represents the number of special infeasible solutions. Note that the distillation process involves both continuous and discrete variables, and data differences must be considered. For the remaining solutions, a polynomial mutation implementation using standard methods is employed for compilation.

[0058] S12: Mutate all K special infeasible solutions.

[0059] S13: Apply polynomial mutation to the Pareto feasible solution and other feasible solutions in the initial parent population after crossover to obtain the offspring population.

[0060] S14: Merge the offspring population with the initial parent population to obtain a merged population. Apply the NSGA-II non-dominated ranking method to the merged population to obtain the non-dominated level of each individual. Select individuals with a non-dominated level of 1.

[0061] When the number of selected individuals Q > W, the selected individuals are taken as the new generation population.

[0062] When the number of selected individuals When W, the crowding degree is calculated for all individuals with a non-dominance level other than 1, and the crowding degree is sorted in descending order. The individuals corresponding to the top WQ crowding degrees are selected, and the individuals with a non-dominance level of 1 and the individuals corresponding to the top WQ crowding degrees are merged into a new generation of population.

[0063] S15: Update the initial parent population with the new generation population, and update the Pareto solution database with individuals whose non-dominance level is 1 as new Pareto solutions. Then return to S5 until the maximum number of iterations is reached, and output the final Pareto solution database.

[0064] Specifically, the S2 complex chemical process industrial process is a dual-tower side-stream extractive distillation system. Through degree-of-freedom analysis, its optimization variables include: the total number of trays in both towers. and Feeding positions of the two towers and The number of trays extracted from the side stream in the EDC (Entrainer Discharge Center) , Entrainer flow rate and the reflux ratio of EDC ;in and The first variable is continuous, while the others are discrete; total annual cost (TAC) and greenhouse gas emissions based on carbon dioxide. As the objective function.

[0065] Specifically, the S2 complex chemical process industrial process is a four-tower side-stream extractive distillation system. Through degree-of-freedom analysis, its optimization variables include: the total number of trays in the four towers. , , , and The position of the feed plates of the four towers , , , and The position of the feed plate for entrained agents in the EDC tower Entrainer flow rate And the reflux ratios of EDC, PDC and SRC. , , and Total Annual Cost (TAC) and Greenhouse Gas Emissions Based on Carbon Dioxide Using the process system index PRI as the objective function, compared with the dual-tower side-stream extractive distillation, there are more optimization objectives and the distillation structure is more complex. This is used to verify that the present invention is effective in optimizing more complex processes.

[0066] Specifically, the classification model in S7 is a Gaussian process classification model. [By using Gaussian process classification as the data-driven model, special infeasible solutions are accurately identified and directionally mutated. Differentiated mutation operators are used for different types of solutions to ensure that the mutation direction matches the characteristics of the solution. For special infeasible solutions, uniform mutation (UMO) is used, with the mutation range determined by the variable interval of the Pareto solution, and directional mutation corrects the solution to the feasible region. This avoids the waste of traditional methods, generates high-quality Pareto solutions early on, and avoids local convergence.]

[0067] The prediction process is as follows:

[0068] A multi-class classification strategy for infeasible solutions is implemented by employing a one-vs-rest (OVR) strategy. This is achieved by introducing the latent function of the Gaussian process prior. The formula is as follows:

[0069]

[0070] The distribution is completely determined by the mean function. and kernel function The description is as follows: The mean function is set to 0, and the kernel function is defined as shown in the following formula:

[0071]

[0072] The Radial Basis Function (RBF, also known as the quadratic exponential kernel) is used as the kernel function. Here, ||·|| represents the Euclidean distance; c and l are hyperparameters of the Gaussian kernel, determining how the Gaussian process interpolates the training data. Finally, the posterior distribution of the latent function is derived through Laplace approximation to obtain the probability prediction. The Sigmoid function is used as the compression function σ(z) to convert the latent function output into a classification probability in the interval [0,1].

[0073] Experimental content and results

[0074] Example 1: To verify the effectiveness of the method of the present invention, a distillation process was designed and tested. Thermodynamic properties were calculated using the NRTL model. All methods were implemented in Python, which has powerful third-party scientific computing libraries such as NumPy and Scikit-Learn. The experiment was conducted on a computer equipped with a 12th generation Intel Core i5-12500 processor and 16GB of memory. The example used was a side-stream dual-tower extractive distillation (SS-DCED) process with triethylamine (Et3N) as an intermediate-boiling-point azeotropic solvent to separate methanol-toluene azeotropes. This process consists of two towers: a side-stream extractive distillation tower (EDC) and a solvent recovery tower (SRC). Toluene with a purity ≥99% was obtained from the bottom of the EDC tower, methanol with a purity ≥99% was obtained from the top of both the EDC and SRC towers, and triethylamine, the extractant with a purity ≥99%, was obtained from the bottom of the SRC tower and recycled back to the EDC tower.

[0075] The optimization variables include the total number of trays in the two towers ( , ), the feeding positions of the two towers ( , ), the number of trays extracted from the side stream in the EDC with entrained agents ( , ), entrainer flow rate ( ) and the EDC reflux ratio ( ). Among them, variables and One variable is continuous; all other variables are discrete. Total annual cost (TAC) and greenhouse gas emissions based on carbon dioxide (CO2) are also included. The objective function is shown in the following formula:

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[0083] The SS-DCED was optimized using both standard methods and the method proposed in this invention. The maximum number of generations in the optimization process was set to 200, and the population size was 50. Details of the objective function evaluation calculation method are shown in Tables 1 and 2.

[0084] Table 1. Formulas and parameters related to TAC calculation

[0085]

[0086] Table 2 Carbon Dioxide Emissions (GGE) CO2 ) Calculation of relevant formulas and parameters

[0087]

[0088] The comparison results show that, compared with NSGA-II, the total annual cost (TAC) of the obtained Pareto solution is lower than that of CO2 power generation efficiency. All significantly decreased [see] Figure 5 (a) Figure 5 (b) indicates that the multi-objective optimization method used in this invention has superior optimization performance. In terms of optimization efficiency, the multi-objective optimization method used in this invention can quickly select high-quality solutions in the early stages of optimization iteration. Specifically, the performance of the solution obtained by the multi-objective optimization method used in this invention in the 100th generation is already better than the solution obtained by NSGA-II in the 200th generation, indicating that the method can converge to the high-performance solution region more quickly. Figure 5 c. Figure 5 d [Yes, there are two small diagrams below ab, which represent cd. This diagram is not available.] Further comparison was made of the timing of the Pareto optimal solution's appearance during the optimization process for the two methods. NSGA-II first obtained a Pareto solution in generation 143, while the multi-objective optimization method used in this invention obtained a Pareto solution in generation 62, 81 generations earlier than NSGA-II. This result confirms that, through the directed mutation correction mechanism, the multi-objective optimization method used in this invention can quickly obtain high-performance solutions, ultimately yielding a better set of Pareto optimal solutions. To analyze the process performance corresponding to the proposed multi-objective optimization method used in this invention, the TOPSIS method was used to screen an equilibrium solution from the Pareto front to achieve a trade-off between the two objectives. Table 3 summarizes the process variables and objective function values ​​of this equilibrium solution and the optimal solution in the literature.

[0089] Table 3. Comparison of the equilibrium solution obtained based on the multi-objective optimization method of this invention with the optimal solution of the traditional NSTA-II SS-DCED process.

[0090]

[0091] The comparison results show that the total annual cost (TAC) of the solution obtained by the multi-objective optimization method used in this invention is 0.6719 × 10⁻⁶. 6 USD / year, CO2 power generation efficiency ( The efficiency was 0.7448 tons / hour, which is 7.06% and 2.26% lower than the optimal solution in the literature, respectively. This result confirms that the multi-objective optimization method used in this invention can significantly improve process performance. Figure 4 A process flow diagram of SS-DCED after the multi-objective optimization method adopted in this invention is presented.

[0092] In terms of computation time, NSGA-II requires 22.4 hours to complete the optimization, while the multi-objective optimization method adopted in this invention only requires 14.5 hours, reducing the computation time by 35.3%. In summary, the multi-objective optimization method adopted in this invention can achieve better optimization performance with lower computational cost, and can identify Pareto solutions in the early stage of optimization, fully demonstrating the optimization efficiency of the method and its ability to quickly discover high-performance solutions.

[0093] Example 2: Four-tower extractive distillation system. This example corresponds to a more complex distillation system with an increased number of decision variables and objective functions. This system is a four-tower extractive distillation (FCED) process using dimethyl sulfoxide (DMSO) as a heavy entrainer to purify ethyl acetate (EtAC) and methanol (MeOH) from wastewater. The FCED process consists of a pre-concentration tower (PC), an extractive distillation tower (EDC), a product distillation tower (PDC), and a solvent recovery tower (SRC). Water (purity ≥99.9 mol%) is obtained from the bottom of the PC tower and the top of the SRC tower; EtAC (purity ≥99.9 mol%) is obtained from the top of the EDC tower; MeOH (purity ≥99.9 mol%) is obtained from the top of the PDC tower; and the entrainer DMSO is collected from the bottom of the SRC tower and recycled back to the EDC. The feed stream flow rate was set at 100 kmol / h, and its composition was 5 mol% methanol (MeOH), 5 mol% ethyl acetate (EtAC), and 90 mol% water. Decision variables included the total number of trays in the four columns (i.e.,...). , , , and ), the feed plate positions of the four towers (i.e. , , , and ), the location of the feed plate for the entrainer in the EDC tower ( ), entrainer flow rate ( ), and the reflux ratios of EDC, PDC, and SRC ( , , and These variables were all determined through degrees of freedom analysis. , , , and One variable is continuous, and the rest are discrete. Except for Total Annual Cost (TAC) and... Furthermore, the Process Route Index (PRI) was introduced as an additional objective function, thus forming a three-objective optimization task. PRI integrates factors such as calorific value, fluid density, pressure, and flammability, and can be used to assess process safety indicators. It has been widely used in the safety analysis of extractive distillation. A higher PRI value means a higher explosion risk and a lower safety level; conversely, a lower PRI value represents a higher intrinsic safety.

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[0104] Similarly, both NSGA-II and the multi-objective optimization method proposed in this paper were applied to the optimization of the FCED process, with a maximum number of iterations set to 200 generations and a population size of 50. Figure 6 The optimal four-tower extractive distillation (FCED) process flow diagram obtained for MO-DIDC.

[0105] like Figure 7 As shown in (a) and (b), the Pareto optimal solution obtained by the multi-objective optimization method of this invention exhibits superior process performance compared to the results obtained by NSGA-II. Furthermore, the multi-objective optimization method of this invention can obtain high-performance solutions more quickly, finding the first Pareto solution in the 96th iteration, 20 iterations earlier than NSGA-II. Figure 7 (c) and (d). Furthermore, NSGA-II took 20.6 hours to complete the optimization, while the multi-objective optimization method used in this invention reduces the computation time to 16.3 hours, a time saving of 20.8%.

[0106] The improvement is smaller than in Case 1, mainly because the distillation process and optimization problems involved in Case 1 are relatively simple, such as... Figure 7 As shown in (c) and (d), high-quality solutions can be identified in the early stages of the optimization iteration. In contrast, the optimization problem in Example 2 is more complex and has stronger solution space constraints, resulting in a slightly lower speedup than in Example 1.

[0107] The equilibrium solution among the three objectives was selected using the TOPSIS method, as shown in Table 4. The equilibrium solution obtained by MO-DIDC has an annual total cost (TAC) of 0.5638 × 10⁻⁶. 6 With CO2 emissions of $ / a, GGE_CO2 is 0.5477 t / h, and the process route index PRI is 4.5292, representing reductions of 5.88%, 3.27%, and 6.41%, respectively. Even in such a complex process, the MO-DIDC framework proposed in this paper still exhibits superior optimization performance.

[0108] Table 4. Comparison of the equilibrium solution obtained by the multi-objective optimization method adopted in this invention with the optimal solution of the FCED process of traditional NSTA-II.

[0109]

[0110] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. An intelligent multi-objective optimization method for solving infeasible solutions in complex chemical process industrial processes, characterized in that, Includes the following steps: S1: Based on the NSGA-II framework, set the population size W, crossover operator, and initial number of iterations. At the same time, construct a Pareto solution database to store Pareto feasible solutions generated during the iteration process. The Pareto solution database is initially empty. S2: For a complex chemical process industrial process, determine the objective function and B optimization variables; S3: Initiate the multi-objective optimization method to generate the initial parent population, where each optimization variable is a gene, and all optimization variables form a chromosome, which in turn constitutes an individual. S4: Divide all individuals in the initial parent population into constraint violation solutions and constraint satisfaction solutions according to whether they meet the constraints. Evaluate the constraint satisfaction solutions and take the solutions that can make the process mechanism model corresponding to the complex chemical process industrial process converge as feasible solutions, otherwise they are infeasible solutions. S5: Crossover, using the crossover operator to crossover all feasible solutions in the initial parent population; S6: Training dataset construction involves fusing feasible solutions from the initial parent population with Pareto solutions from the Pareto solution database to form the training dataset. ,in Let i be the i-th optimization variable. The training dataset is the label for the i-th optimization variable. Feasible solutions from the initial parent population and Pareto solution Together, they form a whole, with all Pareto solutions labeled 0 and other feasible solutions labeled 1. judge If an infeasible solution exists, proceed to the next step; otherwise, proceed to step S13. S7: Use D to train the classification model and continuously update the classification model parameters according to the loss function. When the loss function no longer changes, the training ends and the trained classification model is obtained. S8: Input the infeasible solutions obtained in S4 into the trained classification model, and output the non-dominated level of each infeasible solution. Set the label of all infeasible solutions with a non-dominated level of 1 to 0, and set the label of the remaining infeasible solutions to 1. Define all infeasible solutions with a non-dominance level of 1 as special infeasible solutions, and determine whether there are special infeasible solutions. If there are, proceed to the next step; otherwise, proceed to S13. S9: Calculate the difference between the b-th gene in each particular infeasible solution and the b-th gene in all Pareto solutions, then sum all the differences to obtain the mutation scalar corresponding to the b-th gene. Select the gene corresponding to the maximum value among the B mutation scalars as the mutant gene; S10: Specifies the boundary of the mutation, representing the maximum value of the mutated gene in all Pareto solutions. and minimum value As a mutation boundary; S11: For the kth special infeasible solution When performing mutations, the weight of the mutated gene is set to 1, and the weight of all other genes is set to 0. The mutated gene is within the interval... Uniform mutation is performed inside, and after mutation... Obtained from the uniform catastrophe operator according to the formula: in, Indicates the first Minimum value of mutated genes, Indicates the first The maximum value of the mutated gene. Randomly generated within the interval [0,1], following a uniform distribution. ~U[0,1]), where K represents the number of special infeasible solutions; S12: Mutate all K special infeasible solutions; S13: Apply polynomial mutation to the Pareto feasible solution and other feasible solutions in the initial parent population after crossover to obtain the offspring population; S14: Merge the offspring population with the initial parent population to obtain a merged population. Apply the NSGA-II non-dominated sorting method to the merged population to obtain the non-dominated level of each individual. Select individuals with a non-dominated level of 1: When the number of selected individuals Q > W, the selected individuals are taken as the new generation population; When the number of selected individuals When W, the crowding degree of all individuals with a non-dominance level not equal to 1 is calculated, and the crowding degree is sorted in descending order. The individuals corresponding to the top WQ crowding degrees are selected, and the individuals with a non-dominance level of 1 and the individuals corresponding to the top WQ crowding degrees are merged into a new generation of population. S15: Update the initial parent population with the new generation population, and update the Pareto solution database with individuals whose non-dominance level is 1 as new Pareto solutions. Then return to S5 until the maximum number of iterations is reached, and output the final Pareto solution database.

2. The intelligent multi-objective optimization method for solving infeasible solutions in complex chemical process industrial processes as described in claim 1, characterized in that: The S2 target complex chemical process industrial process is a dual-tower side-stream extractive distillation system. Through degree-of-freedom analysis, its optimization variables include: the total number of trays in both towers. and Feeding positions of the two towers and The number of trays extracted from the side stream in the EDC (Entrainer Discharge Center) , Entrainer flow rate and the reflux ratio of EDC ;in and The first variable is continuous, while the others are discrete; total annual cost (TAC) and greenhouse gas emissions based on carbon dioxide. As the objective function.

3. The intelligent multi-objective optimization method for solving infeasible solutions in complex chemical process industrial processes as described in claim 1, characterized in that: The S2 target complex chemical process industrial process is a four-tower side-stream extractive distillation system. Through degree-of-freedom analysis, its optimization variables include: the total number of trays in the four towers. , , , and The position of the feed plates of the four towers , , , and The position of the feed plate for entrained agents in the EDC tower Entrainer flow rate And the reflux ratios of EDC, PDC and SRC. , , and Total Annual Cost (TAC) and Greenhouse Gas Emissions Based on Carbon Dioxide The process system index PRI is used as the objective function.

4. The intelligent multi-objective optimization method for solving infeasible solutions in complex chemical process industrial processes as described in any one of claims 1-3, characterized in that: The classification model in S7 is a Gaussian process classification model.

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