Nuclear production system design optimization MILP method considering economic life and module type selection

Abstract

The invention discloses a mixed integer linear programming method for optimization design of a nuclear production system considering economic life and module type selection, and relates to the technical field of economic bearable optimization design of the nuclear production system. The method comprises the following steps: 1, determining life cycle cost composition based on nuclear production system characteristics; 2, defining parameter representation of system operation task requirements and module design alternative scheme data; step 3, establishing a nuclear production system design optimization MILP model considering economic life and module type selection; and 4, solving the model through a branch and bound algorithm, outputting an economic life optimal value and a corresponding module type selection combination, and realizing collaborative optimization design of life decision and module configuration. According to the method, a full-cycle economical efficiency quantification tool can be provided for the nuclear production system in the design stage, the life cycle cost per hour is fully reduced, the service life and module architecture of the system are scientifically decided, and the economic affordability of the system is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of economic affordability design optimization of nuclear production systems, and in particular to a MILP method for design optimization of nuclear production systems that takes both economic life and module selection into consideration. Background Art

[0002] Existing affordability technologies for nuclear production systems typically only optimize costs within a specific lifecycle phase for a given system architecture, for example by optimizing maintenance strategies and adjusting spare parts inventories to reduce maintenance costs. However, the design life of nuclear production systems is often pre-set to a high margin. From a full lifecycle economic perspective, such conservative designs may be economically uneconomical. Furthermore, there is a tight coupling between system design life and module selection. Long-life designs require the use of highly redundant, high-cost modules, such as corrosion-resistant materials and multi-redundant control modules, while short-life designs can employ more economical module solutions. Furthermore, coupling can exist between the design options for different system modules, making customized, economically optimal configurations tailored to the design life a significant challenge in nuclear production system design. Summary of the Invention

[0003] To address the above problems, the present invention proposes a mixed integer linear programming (MILP) method for nuclear production system design optimization that takes into account both economic life and module selection. Aiming at the specific characteristics of the nuclear production system, the method analyzes the cost structure of the system's entire life cycle based on engineering structure decomposition and comprehensive cost analysis, and constructs an "economic life-module selection" collaborative optimization model. During the design phase, the economic life that minimizes the system's hourly life cycle cost is determined, and the corresponding optimal module configuration combination is screened at the same time.

[0004] A MILP method for nuclear production system design optimization that takes into account both economic life and module selection includes the following steps:

[0005] Step 1: Analysis of the cost structure of the system throughout its life cycle;

[0006] Specifically, the nuclear production system is decomposed into a "system-module" architecture based on the engineering structure decomposition method. The specific characteristics of the system at each life cycle stage are analyzed to achieve cost synthesis. The system's full life cycle costs mainly include: system development costs, system batch production costs, system operating costs, system maintenance and support costs, and system decommissioning and disposal costs.

[0007] Among them, the system development cost is the ratio of the sum of the development costs of all modules constituting the system to the system production batch; the system batch production cost is the sum of the batch production costs of all modules constituting the system; as a long-term continuous production system, the operating cost of the nuclear production system can be regarded as a constant on an hourly scale; the maintenance and support cost required by the nuclear production system within the system design life is the sum of the fault repair costs and end-of-life replacement costs required by all modules in the system within the system design life; the decommissioning disposal cost required by the nuclear production system within the system design life includes two parts: the periodic product disposal cost required by the system within the design life and the system decommissioning cost at the end of its life.

[0008] Step 2: Define the parameter representation of system operation task requirements and module design alternatives data;

[0009] Specifically, let the set of module types constituting the system be N, i be the serial number of the module type and i=1,2,…,|N|, and the set of design solutions for the i-th model be S i , j is the serial number of the design scheme of module i and j=1,2,…,|S i |, the set of design solutions j1 and j2 that are mutually related between two different modules i1 and i2 is U, and the set of design solutions j1 and j2 that are mutually exclusive between two different modules i1 and i2 is V, where i1∈N, i2∈N, i1≠i2, j1∈S i1 , j1∈S i2 , the production batch of the system is B, according to the characteristics of the production system, assuming that the hourly usage fee during its service life is a fixed constant k, the workload operation ratio of the system and the i-th module is θ i , the number of modules of type i installed in the system is A i The unit development cost of the i-th module under the j-th design scheme is dc ij The single-machine batch production cost of the i-th module under the j-th design scheme is pc ij The mean time between failures of the i-th module under the j-th design scheme is mf ij , the physical life of the i-th type module under the j-th design scheme is pl ij , the fault repair cost of the i-th module under the j-th design scheme is rc ij The end-of-life replacement cost of the i-th module under the j-th design solution is ec ij , whether the i-th type module can be repaired to rw under the j-th design scheme ij , whether the i-th module can be replaced by ew under the j-th design scheme ij The fixed disposal period for nuclear waste generated by the system is pd, the single disposal cost is fd, the decommissioning cost of the entire system is FE, and the planning lower limit of the system design life is L min, the planning upper limit of the system design life is L max , M is a large number such as 9999, and S is a small number such as 0.0001.

[0010] Step 3: Establish a MILP model for nuclear production system design optimization that takes into account both economic life and module selection. This model uses the system design life and module selection scheme as decision variables, minimizes the hourly life cycle cost, and coordinates the coupling relationship between the system engineering architecture, module design scheme, and maintenance support constraints.

[0011] Specifically, based on engineering structure decomposition, the nuclear production system is decomposed from top to bottom into a "system-module" engineering architecture. The work requirements of the system within its design life are allocated to each component module through the operation ratio. Each module incurs module development costs, module batch production costs, module usage costs, module maintenance and support costs, and module decommissioning and disposal costs during its life cycle. The costs of each module are integrated from the bottom up to obtain the full life cycle cost of the entire system. The system design life and the selection combination of the system's component modules are used as decision variables to determine the system life design value and the corresponding module configuration combination that minimizes the system's hourly full cycle cost.

[0012] Step 3.1: Define the decision variables for the collaborative optimization of “economic life-module selection” for nuclear production systems;

[0013] L: design service life of the nuclear production system;

[0014] HLCC: The hourly life cycle cost of a nuclear production system when its design life is L;

[0015] DC: Development cost of the nuclear production system to meet life cycle requirements up to L;

[0016] PC: The batch production cost required for the nuclear production system to meet the life work to L;

[0017] OC: The cost of using the nuclear production system to meet the life cycle requirements up to L;

[0018] MS: Maintenance and support costs required for the nuclear production system to meet its life cycle up to L;

[0019] RD: decommissioning costs required for nuclear production systems to meet their lifespan up to L;

[0020] wl i : The workload requirement assigned to the component module i of the nuclear production system when the system design life is L;

[0021] nr i : The expected number of fault repairs required for the component module i of the nuclear production system when the system design life is L;

[0022] mri : The cost of repairing the failure of the component module i of the nuclear production system when the system design life is L;

[0023] ne i : non-negative integer variable, the end-of-life replacement cost of component module i of the nuclear production system when the system design life is L;

[0024] me i : The cost of repairing the failure of the component module i of the nuclear production system when the system design life is L;

[0025] nd: non-negative integer variable, the number of periodic disposals of products required by the nuclear production system when its design life is L;

[0026] x ij : 0 or 1 variable, which is 1 if and only if module i selects design option j, otherwise it is 0;

[0027] Step 3.2: Establish the objective function of “economic life-module selection” optimization;

[0028]

[0029] Among them, HLCC is the established objective function, L is the design life decision variable of the system, LCC is the full life cycle cost of the nuclear production system, DC is the development cost of the nuclear production system, PC is the batch production cost of the nuclear production system, OC is the operating cost required for the nuclear production system to meet the life cycle work up to L, MS is the maintenance and support cost required for the nuclear production system to meet the life cycle work up to L, and RD is the decommissioning disposal cost required for the nuclear production system to meet the life cycle work up to L;

[0030] Step 3.3: Establish system development cost calculation constraints;

[0031]

[0032] Among them, x ij is the design selection decision variable for module i;

[0033] Step 3.4: Establish system development cost calculation constraints;

[0034]

[0035] Step 3.5: Establish system usage fee calculation constraints;

[0036] OC=L·k(4)

[0037] Step 3.6: Establish module workload calculation constraints;

[0038]

[0039] Among them, wl i The workload requirement assigned to the component module i of the nuclear production system when the system design life is L;

[0040] Step 3.7: Establish system maintenance guarantee cost calculation constraints;

[0041]

[0042] Among them, mr i is the fault repair cost required for the component module i of the nuclear production system when the system design life is L, me i is the end-of-life replacement cost of component module i of the nuclear production system when the system design life is L;

[0043] Step 3.8: Establish module fault repair cost calculation constraints;

[0044]

[0045]

[0046]

[0047] Among them, nr i is the expected number of fault repairs required for the component module i of the nuclear production system when the system design life is L;

[0048] Step 3.9: Establish the calculation constraints of module life replacement cost;

[0049]

[0050]

[0051]

[0052] Among them, ne i is the number of replacements required for the component module i of the nuclear production system when the system design life is L;

[0053] Step 3.10: Establish system decommissioning and disposal cost calculation constraints;

[0054]

[0055]

[0056] RD=nd·fd+FE (15)

[0057] Where nd is the number of periodic disposals of products required for the nuclear production system when its design life is L;

[0058] Step 3.11: Module selection scheme and coupling relationship constraints;

[0059]

[0060]

[0061]

[0062] Step 3.12: Variable value constraints;

[0063] L∈[L min ,L max ] (19)

[0064] HLCC,LCC,OC,MS,RR≥0 (20)

[0065]

[0066]

[0067]

[0068] Step 4: Linear modeling of the objective function based on arctangent interval segmentation;

[0069] Specifically: According to the planning lower limit value L of the design life of the nuclear production system min With the upper limit value L max , estimate the range of system life cycle cost [LCC min ,LCC max ], constructing the numerical solution interval of the objective function LCC / L. Based on the monotonic convergence property of the inverse tangent function, the angle partitioning operator θ = arctan(LCC / L) is introduced to divide the numerical solution interval of the objective function into multiple seamless discrete subintervals with a maximum absolute error of δ. The boundary LCC / L value of each interval is used to approximate the true value of the objective function.

[0070] Step 4.1: Introduce additional decision parameters and variables;

[0071] SA a : 0 or 1 variable, 1 if and only if the angle argtan(LCC / L) is in the subinterval a of (45°, 90°], otherwise 0;

[0072] SB b : 0 or 1 variable, 1 if and only if the angle argtan(LCC / L) is in the subinterval b of (0°, 45°], 0 otherwise;

[0073] NA: variable SA a The number of parameters;

[0074] NB: variable SB b The number of parameters;

[0075] LCC max : The maximum estimated value of the life cycle cost of the nuclear production system within the entire life design plan;

[0076] LCC min : The minimum estimated life cycle cost of a nuclear production system within the entire life cycle design plan;

[0077] δ: Maximum acceptable error percentage value of the linearization of the objective function;

[0078] Step 4.2: Use the arctangent interval partitioning method to linearize and approximate the fractional objective function;

[0079]

[0080] Step 4.3: Determine the constraints of the segmentation interval where the objective function is located;

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] Step 4.4: Additional parameter and variable value constraints;

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093] Step 5: Solve the MILP model for nuclear production system design optimization that takes into account both economic life and module selection, and obtain the optimal solution for the "economic life-module selection" synergy that minimizes the hourly life cycle cost of the nuclear production system in long-term operation.

[0094] Compared with the prior art, the present invention has the following beneficial effects:

[0095] The present invention can forward estimate the full life cycle cost of a nuclear production system under any design life and module selection configuration based on the engineering structure decomposition and cost synthesis method, and can obtain the "economic life-module selection" collaborative optimization solution with the lowest hourly full life cycle cost of the nuclear production system in long-term operation in the form of a solvable MILP model as the basis for the system's "life-architecture" design. This can fully get rid of the economic uneconomical problems caused by the current long-life design paradigm, the large number of design alternatives for system component modules, and the difficulty in making decisions due to coupling relationships between design schemes of different modules, fully reduce system costs, optimize system life and selection architecture, and improve the economic affordability of the system. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 This is a flow chart of the MILP method for design optimization of a nuclear production system taking into account both economic life and module selection, as described in the present invention. Figure 2 It is a schematic diagram of the objective function value range arctangent value interval segmentation linearization method adopted by the present invention. Figure 3 This is a schematic diagram comparing the hourly life cycle costs of different modules in the nuclear production system under different design lifespans. DETAILED DESCRIPTION

[0096] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0097] A MILP method for nuclear production system design optimization that takes into account both economic life and module selection, such as Figure 1 As shown, it includes the following steps:

[0098] Step 1: Analysis of the cost structure of the system throughout its life cycle;

[0099] Specifically, the nuclear production system is decomposed into a "system-module" architecture based on the engineering structure decomposition method. The specific characteristics of the system at each life cycle stage are analyzed to achieve cost synthesis. The system's full life cycle costs mainly include: system development costs, system batch production costs, system operating costs, system maintenance and support costs, and system decommissioning and disposal costs.

[0100] Among them, the system development cost is the ratio of the sum of the development costs of all modules constituting the system to the system production batch; the system batch production cost is the sum of the batch production costs of all modules constituting the system; as a long-term continuous production system, the operating cost of the nuclear production system can be regarded as a constant on an hourly scale; the maintenance and support cost required by the nuclear production system within the system design life is the sum of the fault repair costs and end-of-life replacement costs required by all modules in the system within the system design life; the decommissioning disposal cost required by the nuclear production system within the system design life includes two parts: the periodic product disposal cost required by the system within the design life and the system decommissioning cost at the end of its life.

[0101] Step 2: Define the parameter representation of system operation task requirements and module design alternatives data;

[0102] Specifically, let the set of module types constituting the system be N, i be the serial number of the module type and i=1,2,…,|N|, and the set of design solutions for the i-th model be S i , j is the serial number of the design scheme of module i and j=1,2,…,|S i |, the set of design solutions j1 and j2 that are mutually related between two different modules i1 and i2 is U, and the set of design solutions j1 and j2 that are mutually exclusive between two different modules i1 and i2 is V, where i1∈N, i2∈N, i1≠i2, j1∈S i1 , j1∈S i2 , the production batch of the system is B, according to the characteristics of the production system, assuming that the hourly usage fee during its service life is a fixed constant k, the workload operation ratio of the system and the i-th module is θ i , the number of modules of type i installed in the system is A i The unit development cost of the i-th module under the j-th design scheme is dc ij The single-machine batch production cost of the i-th module under the j-th design scheme is pc ij The mean time between failures of the i-th module under the j-th design scheme is mf ij , the physical life of the i-th type module under the j-th design scheme is pl ij , the fault repair cost of the i-th module under the j-th design scheme is rc ij The end-of-life replacement cost of the i-th module under the j-th design solution is ec ij , whether the i-th type module can be repaired to rw under the j-th design scheme ij , whether the i-th module can be replaced by ew under the j-th design scheme ij The fixed disposal period for nuclear waste generated by the system is pd, the single disposal cost is fd, the decommissioning cost of the entire system is FE, and the planning lower limit of the system design life is L min, the planning upper limit of the system design life is L max , M is a large number such as 9999, S is a small number such as 0.0001, NA is the variable SA a NB is the number parameter of the variable SB b The number of parameters, LCC max LCC is the maximum estimated value of the system's life cycle cost. min is the minimum estimated value of the system's life cycle cost, and δ is the maximum acceptable error percentage of the linearization of the objective function.

[0103] Step 3: Establish a MILP model for nuclear production system design optimization that takes into account both economic life and module selection. This model uses the system design life and module selection scheme as decision variables, minimizes the hourly life cycle cost, and coordinates the coupling relationship between the system engineering architecture, module design scheme, and maintenance support constraints.

[0104] Specifically, based on engineering structure decomposition, the nuclear production system is decomposed from top to bottom into a "system-module" engineering architecture. The work requirements of the system within its design life are allocated to each component module through the operation ratio. Each module incurs module development costs, module batch production costs, module usage costs, module maintenance and support costs, and module decommissioning and disposal costs during its life cycle. The costs of each module are integrated from the bottom up to obtain the full life cycle cost of the entire system. The system design life and the selection combination of the system's component modules are used as decision variables to determine the system life design value and the corresponding module configuration combination that minimizes the system's hourly full cycle cost.

[0105] Step 3.1: Define the decision variables for the collaborative optimization of “economic life-module selection” for nuclear production systems;

[0106] L: design service life of the nuclear production system;

[0107] HLCC: The hourly life cycle cost of a nuclear production system when its design life is L;

[0108] DC: Development cost of the nuclear production system to meet life cycle requirements up to L;

[0109] PC: The batch production cost required for the nuclear production system to meet the life work to L;

[0110] OC: The cost of using the nuclear production system to meet the life cycle requirements up to L;

[0111] MS: Maintenance and support costs required for the nuclear production system to meet its life cycle up to L;

[0112] RD: decommissioning costs required for nuclear production systems to meet their lifespan up to L;

[0113] wl i: The workload requirement assigned to the component module i of the nuclear production system when the system design life is L;

[0114] nr i : The expected number of fault repairs required for the component module i of the nuclear production system when the system design life is L;

[0115] mr i : The cost of repairing the failure of the component module i of the nuclear production system when the system design life is L;

[0116] ne i : non-negative integer variable, the end-of-life replacement cost of component module i of the nuclear production system when the system design life is L;

[0117] me i : The cost of repairing the failure of the component module i of the nuclear production system when the system design life is L;

[0118] nd: non-negative integer variable, the number of periodic disposals of products required by the nuclear production system when its design life is L;

[0119] x ij : 0 or 1 variable, which is 1 if and only if module i selects design option j, otherwise it is 0;

[0120] SA a : 0 or 1 variable, 1 if and only if the angle argtan(LCC / L) is in the subinterval a of (45°, 90°], otherwise 0;

[0121] SB b : 0 or 1 variable, 1 if and only if the angle argtan(LCC / L) is in the subinterval b of (0°, 45°], 0 otherwise;

[0122] Step 3.2: Establish the objective function of “economic life-module selection” optimization, and use the range interval segmentation method to linearize the fractional objective function. The schematic diagram of the linear approximation method is as follows: Figure 2 As shown;

[0123]

[0124] Among them, HLCC is the established objective function, L is the design life decision variable of the system, LCC is the full life cycle cost of the nuclear production system, SA a and SB b Positioning decision variables for the intervals of arctangent value partitioning of the objective function value;

[0125] Step 3.3: Constraints on the values of relevant parameters of the objective function linearization;

[0126]

[0127]

[0128]

[0129]

[0130] Step 3.4: Determine the constraints of the segmentation interval where the objective function is located;

[0131] LCC=DC+PC+OC+MS+RD (41)

[0132]

[0133]

[0134]

[0135]

[0136]

[0137] Among them, DC is the research and development cost of the nuclear production system, PC is the batch production cost of the nuclear production system, OC is the operating cost required for the nuclear production system to meet the life cycle of L, MS is the maintenance and support cost required for the nuclear production system to meet the life cycle of L, and RD is the decommissioning and disposal cost required for the nuclear production system to meet the life cycle of L;

[0138] Step 3.5: Establish system development cost calculation constraints;

[0139]

[0140] Among them, x ij is the design selection decision variable for module i

[0141] Step 3.6: Establish system development cost calculation constraints;

[0142]

[0143] Step 3.7: Establish system usage fee calculation constraints;

[0144] OC=L·k (49)

[0145] Step 3.8: Establish module workload calculation constraints;

[0146]

[0147] Among them, wl iThe workload requirement assigned to the component module i of the nuclear production system when the system design life is L;

[0148] Step 3.9: Establish system maintenance guarantee cost calculation constraints;

[0149]

[0150] Among them, mr i is the fault repair cost required for the component module i of the nuclear production system when the system design life is L, me i is the end-of-life replacement cost of component module i of the nuclear production system when the system design life is L;

[0151] Step 3.10: Establish module fault repair cost calculation constraints;

[0152]

[0153]

[0154]

[0155] Among them, nr i is the expected number of fault repairs required for the component module i of the nuclear production system when the system design life is L;

[0156] Step 3.11: Establish the calculation constraints of module life replacement cost;

[0157]

[0158]

[0159]

[0160] Among them, ne i is the number of replacements required for the component module i of the nuclear production system when the system design life is L;

[0161] Step 3.12: Establish system decommissioning and disposal cost calculation constraints;

[0162]

[0163]

[0164] RD=nd·fd+FE (60)

[0165] Where nd is the number of periodic disposals of products required for the nuclear production system when its design life is L;

[0166] Step 3.13: Selection constraints and solution coupling constraints;

[0167]

[0168]

[0169]

[0170] Step 3.14: Variable value constraints;

[0171] L∈[L min ,L max ] (64)

[0172] HLCC,LCC,OC,MS,RR≥0 (65)

[0173]

[0174]

[0175]

[0176]

[0177]

[0178] Step 4: Solve the MILP model for nuclear production system design optimization that takes into account both economic life and module selection, and obtain the optimal solution for the "economic life-module selection" synergy that minimizes the hourly life cycle cost of the nuclear production system in long-term operation.

[0179] This implementation uses the branch-and-bound algorithm embedded in the commercial MILP solver CPLEX 12.9.0 on the GNU / Linux 4.15.0-142-generic x86_64 operating system to solve the model, with the gap parameter set to 10. -5 , the gap calculation formula is as follows:

[0180]

[0181] In order to demonstrate the superiority of the "economic life-module selection" collaborative optimization design proposed in this paper, two models were established in this implementation. The MILP model constructed by this invention is named Economic Life Collaborative Design Model 1, referred to as Model 1, and the system life is designed as the planning upper limit value and the optimal configuration of the module under this life is used as a control and is named Maximum Planned Life Design Model 2, referred to as Model 2.

[0182] The solution method of Model 2 is as follows: input the MILP model constructed by the present invention and named it Economic Life Collaborative Design Model 1, use the fix operation provided by the commercial MILP solver CPLEX to fix the value of the variable L to the system life design upper limit value L max , at this time, Model 1 is transformed into Model 2, and CPLEX can be used directly to solve the model.

[0183] Two MILP models are tested and verified for 9 test cases. Assume that the system consists of |N| modules, 6≤|N|≤18, and each module i has |S i | alternative design schemes, 6≤|S i |≤12, i∈N, the maximum acceptable error percentage of the objective function linearization is 0.1%;

[0184] To facilitate the representation of model results, this embodiment introduces several symbols to represent the results of each model: the optimal value of hourly life cycle cost obtained by the model is represented by HLCC, the optimal value of design life obtained by the model is represented by DL, and the optimal value of life cycle cost obtained by the model is represented by LCC;

[0185] To facilitate quantification of model differences, this embodiment introduces the following indicators to quantify the differences in the results of each model: The hourly full life cycle cost difference is expressed as D HLCC The design life difference is expressed as D DL The difference in the total life cycle cost is expressed as D LCC The calculation formula is as follows:

[0186]

[0187]

[0188]

[0189] The experimental results are shown in Table 1. Both models can find the optimal solution on all instances. In instances other than 2 and 6, Model 1 can ensure that when the absolute error between the objective function value and the actual objective function value is less than 0.1%, more than 10% of the full life cycle cost value is saved. The economic life value is significantly less than the planned upper limit of the system life design. The average design life difference reaches 14.17%, and the hourly full life cycle cost value of 5 instances is reduced by more than 10%. Combining the three difference quantitative index values, the overall performance of Model 1 is better than that of Model 2;

[0190] Table 1 Comparison of results of the two models

[0191] In the actual design of nuclear production systems, designers sometimes need to analyze the changing trend of the objective function, i.e., the hourly full life cycle cost, with the design life. In this case, the system design life value can be traversed with equal steps within the design life planning interval and fixed. The fix operation provided by the commercial MILP solver CPLEX is used to solve the economic life collaborative design model 1 constructed in this invention, and the detailed changing trend of the objective function with the design life is obtained, as shown in the following example: Figure 3 As shown;

[0192] From the above results, it can be seen that the economic life collaborative design model is superior to the maximum planned life design model in terms of hourly full life cycle costs and total life cycle costs. Therefore, for nuclear production systems, blindly adopting a long design paradigm and extending the system's service life without considering the consumption of hourly full life cycle costs is economically unreliable. At the same time, the configuration of system components should be customized according to different design life values to achieve "economic life-module selection" collaborative optimization. From the perspective of minimizing hourly costs, the economic life of the system identified by the present invention can provide a reliable measurement basis for the service life design of nuclear production systems, and can be used to optimize the selection strategy for design life matching modules, effectively improving the economic affordability of nuclear production systems.

Claims

1. A MILP method for nuclear production system design optimization that takes into account both economic life and module selection, comprising the following steps: (1) Analysis of the system's full life cycle cost structure: Based on the engineering structure decomposition method, the nuclear production system is decomposed into a "system-module" architecture. The specific characteristics of the system at each life cycle stage are analyzed to achieve cost synthesis. The system's full life cycle stage costs mainly include: System development costs, system batch production costs, system operating costs, system maintenance and support costs, and system decommissioning and disposal costs; (2) Define the parameter representation of the system operation task requirements and module design alternative scheme data; set the module type set that constitutes the system as N, i is the serial number of the module type and i = 1, 2, ..., |N|, and the design scheme set of the i-th model is S i , j is the serial number of the design scheme of module i and j=1,2,…,|S i |, the set of design solutions j1 and j2 that are mutually related between two different modules i1 and i2 is U, and the set of design solutions j1 and j2 that are mutually exclusive between two different modules i1 and i2 is V, where i1∈N, i2∈N, i1≠i2, j1∈S i1 , j1∈S i2 , the production batch of the system is B, according to the characteristics of the production system, assuming that the hourly usage fee during its service life is a fixed constant k, the workload operation ratio of the system and the i-th module is θ i , the number of modules of type i installed in the system is A i The unit development cost of the i-th module under the j-th design scheme is dc ij The single-machine batch production cost of the i-th module under the j-th design scheme is pc ij The mean time between failures of the i-th module under the j-th design scheme is mf ij , the physical life of the i-th type module under the j-th design scheme is pl ij , the fault repair cost of the i-th module under the j-th design scheme is rc ij The end-of-life replacement cost of the i-th module under the j-th design solution is ec ij , whether the i-th type module can be repaired to rw under the j-th design scheme ij , whether the i-th module can be replaced by ew under the j-th design scheme ij The fixed disposal period for nuclear waste generated by the system is pd, the single disposal cost is fd, the decommissioning cost of the entire system is FE, and the planning lower limit of the system design life is L min , the planning upper limit of the system design life is L max , M is a large number such as 9999, S is a small number such as 0.0001, NA is the variable SA a NB is the number parameter of the variable SB b The number of parameters, LCC max LCC is the maximum estimated value of the system's life cycle cost. min is the minimum estimated value of the system's life cycle cost, and δ is the maximum acceptable error percentage of the linearization of the objective function. (3) Establish a MILP model for nuclear production system design optimization that takes into account both economic life and module selection; (3.1) Define the decision variables for the collaborative optimization of "economic life-module selection" for nuclear production systems; Let variable L represent the design service life of the nuclear production system; let variable HLCC represent the hourly life cycle cost of the nuclear production system when the design service life is L; Set the variable DC to represent the development cost required for the nuclear production system to meet the life cycle requirements up to L; Set the variable PC to represent the batch production cost required for the nuclear production system to meet the life cycle work to L; The variable OC is set to represent the cost of using the nuclear production system to meet the life cycle requirements up to L; The variable MS is set to represent the maintenance cost required for the nuclear production system to meet its life cycle requirements up to L. Set the variable RD to represent the decommissioning cost required for the nuclear production system to meet its service life L; set the variable wl i represents the workload requirement assigned to the component module i of the nuclear production system when the system design life is L; Set the variable nr i represents the expected number of fault repairs required for component module i of the nuclear production system when the system design life is L; Set the variable mr i represents the fault repair cost required for the component module i of the nuclear production system when the system design life is L; Set the variable ne i represents a non-negative integer variable, the end-of-life replacement cost of component module i of the nuclear production system when the system design life is L; Set the variable me i represents the fault repair cost required for the component module i of the nuclear production system when the system design life is L; Set the variable nd to represent a non-negative integer variable, the number of periodic disposals of the product required by the nuclear production system when the design life is L; set the variable x ij represents a 0 or 1 variable, which is 1 if and only if module i selects design option j, otherwise it is 0; Set variable SA a Represents a 0 or 1 variable, which is 1 if and only if the angle argtan(LCC / L) is within the subinterval a of (45°, 90°], otherwise it is 0; set the variable SB b represents a 0 or 1 variable, which is 1 if and only if the angle argtan(LCC / L) is within the subinterval b of (0°, 45°], and 0 otherwise; (3.2) The objective function of "economic life-module selection" optimization is established, and the range interval partitioning method is used to linearize and approximate the fractional objective function: (3.3) Constraints on the values of the parameters related to the linearization of the objective function: (3.4) Deterministic constraints on the segmentation interval of the objective function: LCC=DC+PC+OC+MS+RD (3.5) Establish system development cost calculation constraints: (3.6) Establish system development cost calculation constraints: (3.7) Establish system usage fee calculation constraints: OC=L·k (3.8) Establish module workload calculation constraints: (3.9) Establish system maintenance and support cost calculation constraints: (3.10) Establish module fault repair cost calculation constraints: (3.11) Establish the calculation constraints for module end-of-life replacement costs: (3.12) Establish constraints for calculating system decommissioning costs: RD=nd·fd+FE (3.13) Selection constraints and scheme coupling constraints: (3.14) Variable value constraints: L∈[L min ,L max ] HLCC,LCC,OC,MS,RR≥0 (4) The MILP model for nuclear production system design optimization that takes into account both economic life and module selection is solved by the branch and bound algorithm, and the optimal solution of the "economic life-module selection" synergistic effect is obtained, which minimizes the hourly life cycle cost of the nuclear production system in long-term operation.

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