An Industrial Water Network Optimization Design Method Based on Genetic Algorithm Framework

Abstract

This invention relates to a method for optimizing the design of industrial water supply networks based on a genetic algorithm framework, comprising the following steps: S1 extracting investment cost data for water-using units and pipeline equipment; S2 establishing a mixed-integer nonlinear programming model for industrial water supply network optimization using a general superstructure, analyzing the nonlinear complexity of the mathematical model and identifying key variables; S3 using a genetic algorithm framework for industrial water supply network optimization; S4 optimizing and solving the mixed-integer nonlinear programming model for industrial water supply network optimization, obtaining the optimal solution and design scheme, and recording the optimization solution time and minimizing the total annual cost. This invention improves the optimization efficiency of industrial water supply network design by identifying impurity concentration variables in the mathematical model and developing an efficient genetic algorithm framework.

Description

Technical Field

[0001] This invention relates to the field of optimization design research of industrial water networks, and specifically to an optimization design method for industrial water networks based on a genetic algorithm framework. Background Technology

[0002] Industrial water network optimization design plays a crucial role in chemical industry processes and is an important way to improve water resource utilization efficiency. Matching wastewater flow directions between different water-using units and maximizing cleaning efficiency through wastewater reuse allows limited water resources to be used more efficiently, thereby improving water resource utilization efficiency in industrial processes, reducing water consumption, and saving investment costs. This not only provides strong support for energy conservation and emission reduction in the chemical industry but also helps enterprises minimize operational investment and maximize economic benefits, ultimately achieving the goals of energy conservation and carbon reduction.

[0003] Industrial water network optimization design involves complex mixed-integer nonlinear programming (MINLP) problems. The non-convex and nonlinear nature of the mathematical model leads to difficulties in solving the problem and a tendency to get trapped in local optima. Commonly used industrial water network design methods include pinch analysis and mathematical programming. Pinch analysis is simple to operate and highly practical, but it relies heavily on the designer's experience, cannot simultaneously consider water resource recovery and equipment investment, and often fails to achieve the optimal solution for the network design. Mathematical programming establishes a mathematical model and uses deterministic and stochastic optimization algorithms to optimize the industrial water network. However, deterministic algorithms suffer from combinatorial explosion, time-consuming solutions, and a tendency to get trapped in local optima. Stochastic optimization algorithms rely heavily on human experience, often requiring manual setting of many parameters, which cannot guarantee design quality.

[0004] Currently, the optimization methods for industrial water networks mainly include deterministic algorithms and stochastic optimization algorithms. These two methods have the following two obvious drawbacks:

[0005] (1) The mathematical model of the industrial water network is a complex mixed integer nonlinear programming problem. Local solvers based on deterministic algorithms can only obtain local optimal solutions, while global solvers based on deterministic algorithms usually have convergence problems and are difficult to converge to the global optimal solution in a finite time.

[0006] (2) The mathematical model of industrial water network contains many flow transmission constraints. Developing stochastic optimization algorithms requires the introduction of many penalty functions, which leads to excessively long optimization time. It is difficult to obtain high-quality feasible solutions within a limited time, and the global optimality of feasible solutions and design schemes cannot be guaranteed. Summary of the Invention

[0007] To address the shortcomings of traditional industrial water network optimization methods, the technical problem this invention aims to solve is: to obtain the globally optimal network design scheme by optimizing the industrial water network using a genetic algorithm.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: an industrial water network optimization design method based on a genetic algorithm framework, comprising the following steps:

[0009] S1: Extract relevant data on investment costs for water use units and pipeline equipment, including the unit price of fresh water, annual operating time, equipment investment depreciation factor, impurity content of water use units, upper limit of impurity concentration at the inlet of water use units, upper limit of impurity concentration at the outlet of water use units, and upper limit of concentration of wastewater discharged into the environment.

[0010] S2: A mathematical model for the optimization design of industrial water network is established using a general superstructure. This mathematical model is a mixed integer nonlinear programming model MINLP, which includes formulas (1)-(10).

[0011] Minimizing the total annual cost TAC1 is the objective function of MINLP.

[0012]

[0013] Where fw represents the fresh water usage, in t / h; u 、fwd、fuu u,v ,fuu u,u These represent the flow rates of fresh water to the water-using unit, fresh water to the environmental discharge point, flow rates between water-using units, and water flow rates from the water-using unit to the environmental discharge point, respectively, all in t / h; zfw u zfwd, zfuu u,v zfuu u,u These represent binary integer variables that determine whether the flow of fresh water to the water-using unit exists, binary integer variables that determine whether the flow of fresh water to the environmental discharge point exists, binary integer variables that determine whether the flow between water-using units exists, and binary integer variables that determine whether the water flow from the water-using unit to the environmental discharge point exists. and These represent the annual operating time and the unit price of fresh water, respectively, in h and $ / t; It is the equipment investment depreciation factor, which has no unit; US represents the set of water-using units; The fixed installation cost per unit length of pipeline, expressed in $ / m; The cost per unit length of pipeline is expressed in $ / m. The distance from fresh water to the water-using unit. The distance from fresh water to the environmental discharge point. The distance between water-using units The distance from the water-using unit to the environmental discharge point is in meters.

[0014] Fresh water flow balance constraint equation:

[0015]

[0016] Flow balance constraint equation at the inlet of the water supply unit:

[0017]

[0018] Among them, fu u This indicates the water flow rate entering water-using unit u, in t / h.

[0019] Flow balance constraint equation at the outlet of the water-using unit:

[0020]

[0021] Impurity concentration balance constraint equation at the inlet of the water unit:

[0022]

[0023] Where, cout v This represents the variable in impurity concentration at the outlet of the water-using unit. This indicates the maximum concentration of impurities at the inlet of the water-using unit, all in ppm.

[0024] Mass balance equation for the water unit impurity removal process:

[0025]

[0026] in, This indicates the impurity load of the water-using unit, in kg / h.

[0027] Impurity constraint equations for environmental emission points:

[0028]

[0029] in, The maximum concentration of impurities in wastewater discharged into the environment, expressed in ppm.

[0030] The logical constraint equations for water flow between each unit are as follows:

[0031]

[0032] S3: Output impurity concentration As chromosomes in the genetic algorithm optimization process, the total annual cost obtained is used as the basis for judging the fitness of an individual. The smaller the total annual cost, the higher the fitness of the individual.

[0033] First, set the upper and lower bounds of the outlet impurity concentration, and specify the population size for the genetic algorithm optimization process. Within the population range, randomly generate a set of outlet impurity concentrations as parent chromosomes, and input the parent chromosomes into the constraint model. The constraint model adopts the mixed integer linear programming model (MILP), which includes equations (2)-(4), (8)-(10), and (11)-(14). Then, optimize the constraint model to obtain the annual total cost, and return the obtained annual total cost to the genetic algorithm.

[0034] Crossover mutation is performed on the parent chromosome to obtain the offspring chromosome. The crossover is the random combination of different water-using unit outlet impurity concentrations in the parent chromosome. During the crossover process, perturbation is generated based on the outlet impurity concentration corresponding to the parent chromosome. The solution near the parent chromosome is the mutation.

[0035] Then input the offspring chromosomes into the constraint model to obtain the total annual cost. Select the chromosomes with fitness greater than the preset value from the offspring chromosomes as the parents and perform crossover mutation again to obtain offspring chromosomes. Then input the offspring chromosomes into the constraint model again, and repeat this process until the minimum total annual cost under the current conditions is obtained.

[0036] Minimize the total annual cost (TAC2) as the objective function of the MILP model:

[0037]

[0038] Impurity concentration balance constraint equation at the inlet of the water unit:

[0039]

[0040] Mass balance equation for the water unit impurity removal process:

[0041]

[0042] Constraint equations for impurity concentration at environmental wastewater discharge points:

[0043]

[0044] S4: Record the export impurity concentration corresponding to the minimum annual total cost. The water flow rate and solution time of each unit are used to obtain the globally optimal network design scheme.

[0045] Compared with the prior art, the present invention has at least the following advantages:

[0046] (1) This invention develops a genetic algorithm framework for industrial water network design; the top layer of the algorithm framework uses a genetic algorithm to optimize the impurity concentration at the outlet of the water unit, and the bottom layer of the algorithm framework is a mixed integer linear programming model.

[0047] (2) Compared with commercial nonlinear global solvers, the developed genetic algorithm framework can reduce the optimization solution time; compared with commercial local solvers, the developed algorithm framework can obtain the global optimal solution and design scheme with lower annual total cost, ensuring design quality.

[0048] (3) This invention establishes a constraint model to solve for the minimum annual total cost under given parameter conditions. Then, a genetic algorithm is used to find the optimal outlet impurity concentration under global conditions and solve for the corresponding flow rates between each water-using unit, thus obtaining the globally optimal industrial water network design scheme. Compared with stochastic algorithms and pinch analysis, this invention does not require pre-setting parameters based on experience before solving, reducing the requirements for operators and meeting the design requirements of uncommon industrial water networks. Compared with deterministic algorithms, the genetic algorithm framework proposed in this invention is an intelligent evolutionary method based on a penalty-free mechanism. This method constructs an easy-to-solve mixed-integer linear programming model by randomly generating variable values ​​of impurity concentration at the outlet of the water-using unit. Compared with traditional genetic algorithms, the proposed penalty-free genetic algorithm does not require setting penalty terms, making it easier to search for the globally optimal solution and design scheme, avoiding the problems of combinatorial explosion and excessively long solution time during the solution process, and improving the optimization solution efficiency of industrial water network design. This invention enables the optimization of large-scale industrial water networks that are typically difficult to design, yielding the minimum annual cost, corresponding outlet impurity concentration, and water flow rate of water-using units. This allows for the determination of the optimal value and design of the optimal solution for the industrial water network, thereby improving overall design efficiency and economy. Attached Figure Description

[0049] Figure 1 It is a general superstructure for industrial water network design.

[0050] Figure 2 It is an industrial water network optimization design method based on the genetic algorithm framework.

[0051] Figure 3 This is the genetic algorithm framework of the present invention.

[0052] Figure 4 It is the optimal solution for industrial water network design cases.

[0053] Figure 5 This represents the annual change in the total cost of the genetic algorithm solution process. Detailed Implementation

[0054] The present invention will now be described in further detail.

[0055] See Figure 1 , Figure 2 and Figure 3 An industrial water network optimization design method based on a genetic algorithm framework includes the following steps:

[0056] S1: Extract relevant data on investment costs for water use units and pipeline equipment, including the unit price of fresh water, annual operating time, equipment investment depreciation factor, impurity content of water use units, upper limit of impurity concentration at the inlet of water use units, upper limit of impurity concentration at the outlet of water use units, and upper limit of concentration of wastewater discharged into the environment.

[0057] S2: A mathematical model for the optimization design of industrial water network is established using a general superstructure. This mathematical model is a mixed integer nonlinear programming model MINLP, which includes formulas (1)-(10).

[0058] Minimizing the total annual cost TAC1 is the objective function of MINLP:

[0059]

[0060] Where fw represents the fresh water usage, in t / h; u 、fwd、fuu u,v ,fuu u,u These represent the flow rates of fresh water to the water-using unit, fresh water to the environmental discharge point, flow rates between water-using units, and water flow rates from the water-using unit to the environmental discharge point, respectively, all in t / h; zfw u zfwd, zfuu u,v zfuu u,u These represent binary integer variables that determine whether the flow of fresh water to the water-using unit exists, binary integer variables that determine whether the flow of fresh water to the environmental discharge point exists, binary integer variables that determine whether the flow between water-using units exists, and binary integer variables that determine whether the water flow from the water-using unit to the environmental discharge point exists. and These represent the annual operating time and the unit price of fresh water, respectively, in h and $ / t; It is the equipment investment depreciation factor, which has no unit; US represents the set of water-using units; The fixed installation cost per unit length of pipeline, expressed in $ / m; The cost per unit length of pipeline is expressed in $ / m. The distance from fresh water to the water-using unit. The distance from fresh water to the environmental discharge point. The distance between water-using units The distance from the water-using unit to the environmental discharge point is in meters.

[0061] Fresh water flow balance constraint equation:

[0062]

[0063] Flow balance constraint equation at the inlet of the water supply unit:

[0064]

[0065] Among them, fu u This indicates the water flow rate entering water-using unit u, in t / h.

[0066] Flow balance constraint equation at the outlet of the water-using unit:

[0067]

[0068] Impurity concentration balance constraint equation at the inlet of the water unit:

[0069]

[0070] Where, cout v This represents the variable in impurity concentration at the outlet of the water-using unit. This indicates the maximum concentration of impurities at the inlet of the water-using unit, all in ppm.

[0071] Mass balance equation for the water unit impurity removal process:

[0072]

[0073] in, This indicates the impurity load of the water-using unit, in kg / h.

[0074] Impurity constraint equations for environmental emission points:

[0075]

[0076] in, The maximum concentration of impurities in wastewater discharged into the environment, expressed in ppm.

[0077] The logical constraint equations for water flow between each unit are as follows:

[0078]

[0079] S3: Output impurity concentration As chromosomes in the genetic algorithm optimization process, the total annual cost obtained is used as the basis for judging the fitness of an individual. The smaller the total annual cost, the higher the fitness of the individual.

[0080] First, set the upper and lower bounds of the outlet impurity concentration, and specify the population size for the genetic algorithm optimization process. Within the population range, randomly generate a set of outlet impurity concentrations as parent chromosomes, and input the parent chromosomes into the constraint model. The constraint model adopts the mixed integer linear programming model (MILP), which includes equations (2)-(4), (8)-(10), and (11)-(14). Then, optimize the constraint model to obtain the total annual cost, and return the obtained total annual cost to the genetic algorithm.

[0081] Crossover mutation is performed on the parent chromosome to obtain the offspring chromosome. The crossover is the random combination of different water-using unit outlet impurity concentrations in the parent chromosome. During the crossover process, perturbation is generated based on the outlet impurity concentration corresponding to the parent chromosome. The solution near the parent chromosome is the mutation.

[0082] The offspring chromosomes are then input into the constraint model to calculate the total annual cost. Chromosomes with fitness greater than a preset value are selected as parents and subjected to crossover and mutation again to obtain offspring chromosomes. These offspring chromosomes are then input into the constraint model, and this process is repeated until the minimum total annual cost under the current conditions is obtained. The genetic algorithm framework is as follows: Figure 3 As shown.

[0083] Minimize the total annual cost (TAC2) as the objective function of the MILP model:

[0084]

[0085] Impurity concentration balance constraint equation at the inlet of the water unit:

[0086]

[0087] Mass balance equation for the water unit impurity removal process:

[0088]

[0089] Constraint equations for impurity concentration at environmental wastewater discharge points:

[0090]

[0091] S4: Record the export impurity concentration corresponding to the minimum annual total cost. The water flow rate and solution time of each unit are used to obtain the globally optimal network design scheme. The developed genetic algorithm framework is used to optimize the superstructure mathematical model of the industrial water network design, obtain the globally optimal solution, and record the optimization solution time and the minimum annual total cost.

[0092] Example: An industrial water network optimization design method based on a genetic algorithm framework, the specific steps of which are as follows:

[0093] S1: Extract relevant data on investment costs for water-using units and pipeline equipment, including fresh water unit price, annual operating time, equipment investment depreciation factor, impurity content of water-using units, upper limit of impurity concentration at the inlet of water-using units, upper limit of impurity concentration at the outlet of water-using units, and upper limit of concentration of wastewater discharged into the environment. Data for the water-using units in test cases 1 and 2 are shown in Table 1. The upper limit of impurity concentration in the discharged wastewater is 800.0 ppm for both cases. The equipment investment parameters are as follows: Fwc = 1 $ / t; and Both are 100m.

[0094] Table 1 Input data for test cases

[0095]

[0096] S2: In the case study, a general superstructure is used to establish a mathematical model for the optimization design of industrial water supply networks. This model is a mixed-integer nonlinear programming model (MINLP); the general superstructure is as follows: Figure 1 As shown.

[0097] S3: Develop an industrial water network optimization design method based on a genetic algorithm framework. The steps of this method are as follows: Figure 2 As shown. In this method, the top layer uses a genetic algorithm to randomly generate the impurity concentration at the outlet of the water-using unit. The input is fed into a sub-model, which employs a mixed-integer linear programming (MILP) model. The annual total cost obtained from optimizing the sub-model is then returned to the top-level genetic algorithm to further optimize the impurity concentration at the water-using unit outlet. The genetic algorithm framework is as follows: Figure 3 As shown; the MILP model includes equations (2)-(4), (8)-(10) and (11)-(14).

[0098] S4: Utilize the developed genetic algorithm framework to optimize and solve the superstructure mathematical model of the industrial water network design, obtain the global optimal solution of the industrial water network design, and record the optimization solution time and the minimum annual total cost.

[0099] The developed genetic algorithm was used to optimize the case study, resulting in an industrial water network design scheme that minimizes the total annual cost of $1,712,940.0 / yr. The optimization results are shown in Table 2. The specific industrial water network design scheme is as follows: Figure 4As shown. In Case 1, compared to the optimization result of the local solver (DICOPT) (TAC = 1,820,016.0 USD / yr), the TAC was reduced by 5.88%; compared to the optimization result of the global solver (BARON) (TAC = 1,712,940.0 USD / yr), the genetic algorithm achieved the same TAC (1,712,940.0 USD / yr), but the optimization time was reduced by 36.06%. In Case 2, compared to the optimization result of the local solver (DICOPT) (TAC = 2,154,823.0 USD / yr), the TAC was reduced by 11.54%; compared to the optimization result of the global solver (BARON) (TAC = 1,906,080.0 USD / yr), the genetic algorithm achieved the same TAC (1,906,080.0 USD / yr), but the optimization time was reduced by 36.06%.

[0100] Table 2 Optimization results of test cases

[0101]

[0102] from Figure 5 It is evident that genetic algorithms can quickly find solutions close to the optimal value when minimizing the total annual cost, and rarely get trapped in local optima during the solution process. In addition, genetic algorithms can adjust the population size according to the number of decision variables of the solution objective, thereby optimizing the solution rate while maintaining the solution accuracy.

[0103] Finally, 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 industrial water network optimization design method based on a genetic algorithm framework, specifically including the following steps: S1: Extract relevant data on investment costs for water use units and pipeline equipment, including the unit price of fresh water, annual operating time, equipment investment depreciation factor, impurity content of water use units, upper limit of impurity concentration at the inlet of water use units, upper limit of impurity concentration at the outlet of water use units, and upper limit of concentration of wastewater discharged into the environment. S2: A mathematical model for the optimization design of industrial water network is established using a general superstructure. This mathematical model is a mixed integer nonlinear programming model MINLP, including formulas (1)-(10). Minimizing the total annual cost TAC1 is the objective function of MINLP: Where fw represents the fresh water usage, in t / h; u 、fwd、fuu u,v ,fuu u,u These represent the flow rates of fresh water to the water-using unit, fresh water to the environmental discharge point, flow rates between water-using units, and water flow rates from the water-using unit to the environmental discharge point, respectively, all in t / h; zfw u zfwd, zfuu u,v zfuu u,u These represent binary integer variables that determine whether the flow of fresh water to the water-using unit exists, binary integer variables that determine whether the flow of fresh water to the environmental discharge point exists, binary integer variables that determine whether the flow between water-using units exists, and binary integer variables that determine whether the water flow from the water-using unit to the environmental discharge point exists. and These represent the annual operating time and the unit price of fresh water, respectively, in h and $ / t; It is the equipment investment depreciation factor, which has no unit; US represents the set of water-using units; The fixed installation cost per unit length of pipeline, expressed in $ / m; The cost per unit length of pipeline is expressed in $ / m. The distance from fresh water to the water-using unit. The distance from fresh water to the environmental discharge point. The distance between water-using units The distance from the water-using unit to the environmental discharge point is in meters. Fresh water flow balance constraint equation: Flow balance constraint equation at the inlet of the water supply unit: Among them, fu u This indicates the water flow rate entering water-using unit u, in t / h. Flow balance constraint equation at the outlet of the water-using unit: Impurity concentration balance constraint equation at the inlet of the water unit: Where, cout v This represents the variable in impurity concentration at the outlet of the water-using unit. This indicates the maximum concentration of impurities at the inlet of the water unit, all in ppm; Mass balance equation for the water unit impurity removal process: in, This indicates the impurity load of the water-using unit, in kg / h. Impurity constraint equations for environmental emission points: in, The maximum concentration of impurities in wastewater discharged into the environment, expressed in ppm. The logical constraint equations for water flow between each unit are as follows: S3: Output impurity concentration As chromosomes in the genetic algorithm optimization process, the total annual cost obtained is used as the basis for judging the fitness of an individual. The smaller the total annual cost, the higher the fitness of the individual. Set upper and lower bounds for the outlet impurity concentration, specify the population size for the genetic algorithm optimization process, and first randomly generate a set of outlet impurity concentrations as parent chromosomes within the population range. Input the parent chromosomes into the constraint model, which adopts the mixed integer linear programming model MILP, including equations (2)-(4), (8)-(10) and (11)-(14). Then optimize the constraint model to obtain the annual total cost, and return the obtained annual total cost to the genetic algorithm. Crossing mutation is performed on the parent chromosome to obtain the offspring chromosome. The crossover is the random combination of the outlet impurity concentrations of different water-using units in the parent chromosome. During the crossover process, perturbation is generated based on the outlet impurity concentrations corresponding to the parent chromosome. The solution near the parent chromosome is the mutation. Then input the offspring chromosomes into the constraint model to obtain the total annual cost. Select the chromosomes with fitness greater than the preset value from the offspring chromosomes as the parents and perform crossover mutation again to obtain offspring chromosomes. Then input the offspring chromosomes into the constraint model again, and repeat this process until the minimum total annual cost under the current conditions is obtained. Minimize the total annual cost (TAC2) as the objective function of the MILP model: Impurity concentration balance constraint equation at the inlet of the water unit: Mass balance equation for the water unit impurity removal process: Constraint equations for impurity concentration at environmental wastewater discharge points: S4: Record the export impurity concentration corresponding to the minimum annual total cost. The optimal network design scheme is obtained by calculating the water flow rate and solution time of each unit.

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