Industrial water network optimization design method based on genetic algorithm framework

Abstract

The invention relates to an industrial water network optimization design method based on a genetic algorithm framework. The method comprises the following steps: S1, extracting investment cost data of water units and pipeline equipment; s2, establishing a mixed integer nonlinear programming model of the industrial water network optimization design by adopting a universal superstructure, analyzing the nonlinear complexity in the mathematical model and identifying key variables; s3, using a genetic algorithm framework of industrial water network optimization design; and S4, carrying out optimization solution on the mixed integer nonlinear programming model of the industrial water network optimization design to obtain an optimal solution and a design scheme, and recording optimization solution time and minimum annual total cost. According to the method, the impurity concentration variable of the mathematical model is identified, an efficient genetic algorithm framework is developed, and the optimization solving efficiency of the industrial water network design is improved.

Description

Technical Field

[0001] The invention relates to the research field of optimization design of industrial water networks, and in particular to an optimization design method of industrial water networks based on a genetic algorithm framework. Background Art

[0002] The optimization design of industrial water network plays an important role in the chemical industry process and is an important way to improve the efficiency of water resource utilization. Matching the wastewater flow between different water use units, through wastewater reuse, the limited water resources can play the maximum cleaning efficiency, thereby improving the water resource utilization efficiency of the industrial process, reducing the water resource consumption in the industrial process, saving investment costs, not only can provide strong support for energy conservation and emission reduction in the chemical industry, but also help to minimize the enterprise operation investment and maximize the economic benefits, so as to achieve the goal of energy conservation and carbon reduction.

[0003] The optimization design of industrial water networks involves complex mixed integer nonlinear programming (MINLP) problems. The mathematical model is difficult to solve and easy to fall into local optimality due to its non-convexity and nonlinearity. Commonly used industrial water network design methods include pinch analysis and mathematical programming. The pinch analysis method is easy to operate and practical, but it is highly dependent on the experience of designers. It cannot simultaneously consider water resource recovery and equipment investment, and it is often difficult to achieve the optimal solution for network design. The mathematical programming method optimizes the design of industrial water networks by establishing a mathematical model and using deterministic algorithms and random optimization algorithms. However, deterministic algorithms have problems such as combinatorial explosion, time-consuming solution, and easy to fall into local optimality when solving. The random optimization algorithm is highly dependent on manual experience, usually requires many parameters to be set manually, and cannot guarantee the design quality.

[0004] At present, the optimization methods of industrial water networks mainly include deterministic algorithms and random optimization algorithms. These two methods have the following two obvious defects:

[0005] (1) The mathematical model of the industrial water network is a complex mixed integer nonlinear programming problem. The local solver directly based on the deterministic algorithm can only obtain the local optimal solution, while the global solver based on the deterministic algorithm usually has convergence problems and it is difficult to converge to the global optimal solution within a limited time.

[0006] (2) The mathematical model of the industrial water network contains many flow transfer constraints. The development of a random optimization algorithm requires the introduction of many penalty functions, which results in a long optimization time. It is difficult to obtain a high-quality feasible solution within a limited time, and the global optimality of the feasible solution and the design scheme cannot be guaranteed. Summary of the invention

[0007] In view of the defects of traditional industrial water network optimization methods, the technical problem to be solved by the present invention is: to optimize and solve the industrial water network through a genetic algorithm to obtain a global optimal network design solution.

[0008] In order to solve the above 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 the investment costs of water use units and pipeline equipment, including the unit price of fresh water, annual operating time, equipment investment depreciation factor, impurity content of the water use unit, upper limit of impurity concentration at the inlet of the water use unit, upper limit of impurity concentration at the outlet of the water use unit and upper limit of concentration of wastewater discharged to the environment.

[0010] S2: A general superstructure is used to establish a mathematical model for the optimal design of industrial water networks. This mathematical model is a mixed integer nonlinear programming model MINLP, including formulas (1)-(10).

[0011] The objective function of MINLP is to minimize the total annual cost TAC1.

[0012]

[0013] Where, fw represents the fresh water consumption, in t / h; fw u 、fwd、fuu u,v ,fuu u,u They represent the flow rate of fresh water to the water-using unit, the flow rate of fresh water to the environmental discharge point, the flow rate between water-using units, and the water flow rate from the water-using unit to the environmental discharge point, all in t / h; zfw u 、zfwd、zfuu u,v 、zfuu u,u They respectively represent the binary integer variables for judging whether the flow from fresh water to the water-using unit exists, the binary integer variables for judging whether the flow from fresh water to the environmental discharge point exists, the binary integer variables for judging whether the flow between water-using units exists, and the binary integer variables for judging whether the water flow from the water-using unit to the environmental discharge point exists; and represent the annual operating time and fresh water unit price, in units of h and $ / t, respectively; is the equipment investment depreciation factor, unitless; US represents the set of water use units; is the fixed installation cost per unit length of pipeline, in $ / m; is the purchase cost of pipeline per unit length, in $ / m; is the distance from fresh water to the water-using unit, is the distance from the fresh water to the environmental discharge point, is the distance between water-using units, It is the distance from the water use unit to the environmental discharge point, in meters.

[0014] Fresh water flow balance constraint equation:

[0015]

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

[0017]

[0018] Among them, fu u Represents the water flow entering the water use unit u, in t / h.

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

[0020]

[0021] The impurity concentration balance constraint equation at the inlet of the water unit is:

[0022]

[0023] Among them, cout v Represents the impurity concentration variable at the outlet of the water unit, It indicates the maximum impurity concentration at the inlet of the water unit, and the unit is ppm.

[0024] The mass balance equation of the impurity removal process of the water unit is:

[0025]

[0026] in, Indicates the impurity load of the water use unit in kg / h.

[0027] Impurity constraint equation at the environmental emission point:

[0028]

[0029] in, It is the maximum impurity concentration of wastewater discharged into the environment, in ppm.

[0030] The logical constraint equations of water flow between each unit are:

[0031]

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

[0033] First, the upper and lower bounds of the outlet impurity concentration are set, and the population size of the genetic algorithm optimization process is specified. A set of outlet impurity concentrations is randomly generated within the population range as the parent chromosomes, and the parent chromosomes are input into the constraint model. The constraint model adopts a mixed integer linear programming model MILP, and the MILP includes equations (2)-(4), equations (8)-(10) and equations (11)-(14). Then, the constraint model is optimized and solved to obtain the annual total cost, and the solved annual total cost is returned to the genetic algorithm.

[0034] The parent chromosome is subjected to crossover mutation to obtain the daughter chromosome. The random combination of the impurity concentrations at the outlets of different water use units in the parent chromosome is called crossover. During the crossover process, the disturbance is generated based on the outlet impurity concentration corresponding to the parent chromosome, and the solution near the parent chromosome is obtained, which is called mutation.

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

[0036] The objective function of the MILP model is to minimize the total annual cost (TAC2):

[0037]

[0038] The impurity concentration balance constraint equation at the inlet of the water unit is:

[0039]

[0040] The mass balance equation of the impurity removal process of the water unit is:

[0041]

[0042] Constraint equation for impurity concentration at environmental discharge:

[0043]

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

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

[0046] (1) The present 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 sub-model at 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 global optimal solutions and design plans with lower annual total costs, thereby ensuring design quality.

[0048] (3) The present invention can solve the minimum annual total cost under given parameter conditions by establishing a constraint model, and then find the optimal outlet impurity concentration under global conditions through a genetic algorithm and solve the corresponding flow between each water unit to obtain the global optimal industrial water network design plan; compared with the random algorithm and the pinch point analysis method, the application of the present invention does not need to preset parameters based on experience before solving, which reduces the requirements for operators and can meet the design requirements of uncommon industrial water networks; compared with the deterministic algorithm, the genetic algorithm framework proposed by the present invention is an intelligent evolution 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 the impurity concentration at the outlet of the water unit. Compared with the traditional genetic algorithm, the proposed penalty-free genetic algorithm does not need to set a penalty term, and is easier to search for the global optimal solution and design plan, avoiding the problem of solution combination explosion and excessive solution time in the solution process, and improving the optimization solution efficiency of the industrial water network design. The present invention can optimize and solve large-scale industrial water networks that are usually difficult to optimize and design, and obtain their minimum annual costs and the corresponding outlet impurity concentrations and water flow rates of water use units, thereby completing the optimal value solution and optimal solution design for the industrial water network, thereby improving the overall design efficiency and economy. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0050] Figure 2 It is an optimization design method for industrial water networks based on a genetic algorithm framework.

[0051] Figure 3 It 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 is the annual total cost change of the genetic algorithm solution process. DETAILED DESCRIPTION

[0054] The present invention is described in further detail below.

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

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

[0057] S2: A general superstructure is used to establish a mathematical model for the optimal design of industrial water networks. This mathematical model is a mixed integer nonlinear programming model MINLP, including formulas (1)-(10).

[0058] The objective function of MINLP is to minimize the total annual cost TAC1:

[0059]

[0060] Where, fw represents the fresh water consumption, in t / h; fw u 、fwd、fuu u,v ,fuu u,u They represent the flow rate of fresh water to the water-using unit, the flow rate of fresh water to the environmental discharge point, the flow rate between water-using units, and the water flow rate from the water-using unit to the environmental discharge point, all in t / h; zfw u 、zfwd、zfuu u,v 、zfuu u,u They respectively represent the binary integer variables for judging whether the flow from fresh water to the water-using unit exists, the binary integer variables for judging whether the flow from fresh water to the environmental discharge point exists, the binary integer variables for judging whether the flow between water-using units exists, and the binary integer variables for judging whether the water flow from the water-using unit to the environmental discharge point exists; and represent the annual operating time and fresh water unit price, in units of h and $ / t, respectively; is the equipment investment depreciation factor, unitless; US represents the set of water use units; is the fixed installation cost per unit length of pipeline, in $ / m; is the purchase cost of pipeline per unit length, in $ / m; is the distance from fresh water to the water-using unit, is the distance from the fresh water to the environmental discharge point, is the distance between water-using units, It is the distance from the water use unit to the environmental discharge point, in meters.

[0061] Fresh water flow balance constraint equation:

[0062]

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

[0064]

[0065] Among them, fu u It represents the water flow rate entering the water use unit u, in t / h;

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

[0067]

[0068] The impurity concentration balance constraint equation at the inlet of the water unit is:

[0069]

[0070] Among them, cout v Represents the impurity concentration variable at the outlet of the water unit, It indicates the maximum impurity concentration at the inlet of the water unit, and the unit is ppm.

[0071] The mass balance equation of the impurity removal process of the water unit is:

[0072]

[0073] in, Indicates the impurity load of the water use unit in kg / h.

[0074] Impurity constraint equation at the environmental emission point:

[0075]

[0076] in, It is the maximum impurity concentration of wastewater discharged into the environment, in ppm.

[0077] The logical constraint equations of water flow between each unit are:

[0078]

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

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

[0081] The parent chromosome is subjected to crossover mutation to obtain the daughter chromosome. The random combination of the impurity concentrations at the outlets of different water use units in the parent chromosome is called crossover. During the crossover process, the disturbance is generated based on the outlet impurity concentration corresponding to the parent chromosome, and the solution near the parent chromosome is obtained, which is called mutation.

[0082] Then input the offspring chromosome into the constraint model to obtain the annual total cost, select the chromosome with fitness greater than the preset value as the parent to perform crossover mutation again to obtain the offspring chromosome, and then input the offspring chromosome into the constraint model, and repeat this process until the minimum annual total cost under the current conditions is obtained. The genetic algorithm framework is as follows Figure 3 shown.

[0083] The objective function of the MILP model is to minimize the total annual cost (TAC2):

[0084]

[0085] The impurity concentration balance constraint equation at the inlet of the water unit is:

[0086]

[0087] The mass balance equation of the impurity removal process of the water unit is:

[0088]

[0089] Constraint equation for impurity concentration at environmental discharge:

[0090]

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

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

[0093] S1: Extract relevant data of water use unit and pipeline equipment investment cost, including fresh water unit price, annual operation time, equipment investment depreciation factor, impurity content of water use unit, upper limit of impurity concentration at water use unit inlet, upper limit of impurity concentration at water use unit outlet, upper limit of concentration of environmental wastewater discharge, etc. The water use unit data of test case 1 and case 2 are shown in Table 1. The upper limit of impurity concentration of external wastewater discharge is 800.0ppm. The parameters of equipment investment are: Fwc=1$ / t; and Both are 100m.

[0094] Table 1 Input data of the test case

[0095]

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

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

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

[0099] The developed genetic algorithm is used to optimize the case and obtain the industrial water network design scheme with the minimum annual total 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. Compared with the optimization result of the local solver (DICOPT) (TAC = 1,820,016.0 $ / yr), the optimization result of case 1 reduced TAC by 5.88%; compared with the optimization result of the global solver (BARON) (TAC = 1,712,940.0 $ / yr), the genetic algorithm was able to obtain the same TAC (1,712,940.0 $ / yr), but the optimization time was reduced by 36.06%; compared with the optimization result of the local solver (DICOPT) (TAC = 2,154,823.0 $ / yr), the optimization result of case 2 reduced TAC by 11.54%; compared with the optimization result of the global solver (BARON) (TAC = 1,906,080.0 $ / yr), the genetic algorithm was able to obtain the same TAC (1,906,080.0 $ / yr), but the optimization time was reduced by 36.06%.

[0100] Table 2 Optimization results of test cases

[0101]

[0102] from Figure 5 It can be seen that the genetic algorithm can quickly find a solution close to the optimal value when solving the problem of minimizing the total annual cost, and rarely falls into the local optimal value during the solution process; in addition, the genetic algorithm can also adjust the population size according to the number of decision variables of the solution target, 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 rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A method for optimizing the design of industrial water networks based on a genetic algorithm framework, comprising the following steps: S1: Extract relevant data on water use units and pipeline equipment investment costs, including fresh water unit price, annual operation 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 environmental wastewater discharge; S2: A mathematical model for the optimal design of industrial water networks is established using a general superstructure. This mathematical model is a mixed integer nonlinear programming model MINLP, including formulas (1)-(10); The objective function of MINLP is to minimize the total annual cost TAC1: Where, fw represents the fresh water consumption, in t / h; fw u 、fwd、fuu u,v ,fuu u,u They represent the flow rate of fresh water to the water-using unit, the flow rate of fresh water to the environmental discharge point, the flow rate between water-using units, and the water flow rate from the water-using unit to the environmental discharge point, all in t / h; zfw u 、zfwd、zfuu u,v 、zfuu u,u They respectively represent the binary integer variables for judging whether the flow from fresh water to the water-using unit exists, the binary integer variables for judging whether the flow from fresh water to the environmental discharge point exists, the binary integer variables for judging whether the flow between water-using units exists, and the binary integer variables for judging whether the water flow from the water-using unit to the environmental discharge point exists; and represent the annual operating time and fresh water unit price, in units of h and $ / t, respectively; is the equipment investment depreciation factor, unitless; US represents the set of water use units; is the fixed installation cost per unit length of pipeline, in $ / m; is the purchase cost of pipeline per unit length, in $ / m; is the distance from fresh water to the water-using unit, is the distance from the fresh water to the environmental discharge point, is the distance between water-using units, is the distance from the water-using unit to the environmental discharge point, in meters; Fresh water flow balance constraint equation: Flow balance constraint equation at the inlet of the water unit: Among them, fu u It represents the water flow rate entering the water use unit u, in t / h; Flow balance constraint equation at the outlet of the water unit: The impurity concentration balance constraint equation at the inlet of the water unit is: Among them, cout v Represents the impurity concentration variable at the outlet of the water unit, Indicates the maximum impurity concentration at the inlet of the water unit, the unit is ppm; The mass balance equation of the impurity removal process of the water unit is: in, Indicates the impurity load of the water-using unit in kg / h; Impurity constraint equation at the environmental emission point: in, The maximum impurity concentration of wastewater discharged into the environment, in ppm; The logical constraint equations of water flow between each unit are: S3: The outlet impurity concentration As the chromosome in the genetic algorithm optimization process, the annual total cost obtained is used as the basis for judging the individual fitness. The smaller the annual total cost, the higher the individual fitness. The upper and lower bounds of the outlet impurity concentration are set, and the population size of the genetic algorithm optimization process is specified. A set of outlet impurity concentrations is first randomly generated within the population range as the parent chromosome, and the parent chromosome is input into the constraint model. The constraint model adopts a mixed integer linear programming model MILP, and the MILP includes equations (2)-(4), equations (8)-(10) and equations (11)-(14); the constraint model is then optimized and solved to obtain the annual total cost, and the solved annual total cost is returned to the genetic algorithm; The parent chromosome is subjected to crossover mutation to obtain the daughter chromosome. The random combination of the impurity concentrations at the outlets of different water-using units in the parent chromosome is called crossover. In the crossover process, the disturbance is generated based on the impurity concentration at the outlet corresponding to the parent chromosome, and the solution near the parent chromosome is called mutation. Then input the offspring chromosome into the constraint model to obtain the annual total cost, select the chromosome with fitness greater than the preset value as the parent to perform crossover mutation again to obtain the offspring chromosome, and then input the offspring chromosome into the constraint model, and repeat this process until the minimum annual total cost under the current conditions is obtained; The objective function of the MILP model is to minimize the total annual cost (TAC2): The impurity concentration balance constraint equation at the inlet of the water unit is: The mass balance equation of the impurity removal process of the water unit is: Constraint equation for impurity concentration at environmental discharge: S4: Record the outlet impurity concentration corresponding to the minimum annual total cost The water flow rate of each unit and the solution time are calculated to obtain the global optimal network design solution.

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