Quantum annealing based multi-objective structural optimization design method for highway simple beam bridges

Abstract

This invention relates to the technical field of bridge engineering, and discloses a multi-objective structural optimization design method for simply supported beam highway bridges based on quantum annealing. Based on pre-defined limits for span, load, deflection, and stress according to specifications, discrete optimization variables are determined; a cross-sectional mechanical model is established, constructing a multi-objective optimization problem with the goal of minimizing cost; a quadratic penalty function is introduced to handle out-of-bounds parameters, transforming it into a QUBO model adapted for quantum computing; quantum annealing is used for global optimization, outputting the optimal cross-sectional parameters, which are then verified by finite element analysis. This invention overcomes the bottleneck of traditional algorithms being prone to local optima. Relying on the quantum tunneling effect, it saves 10%~20% of building materials compared to traditional empirical design while ensuring compliance. Convergence efficiency is improved by over 95%, and the design cycle is reduced from several days to the tens of minutes level. The "quantum initial selection + finite element verification" model fits the existing design process and is easily extended to continuous beams, seismic analysis, and construction optimization, possessing significant engineering value and patent extension potential.

Description

Technical Field

[0001] This invention relates to the technical field of bridge engineering, and in particular to a multi-objective structural optimization design method for simply supported beam highway bridges based on quantum annealing. Background Technology

[0002] Simply supported beam bridges are among the most widely used bridge types in municipal and highway engineering. The conventional design process involves designers initially selecting cross-sectional dimensions based on experience, then conducting multiple trial calculations using finite element software such as Midas / Civil and Bridge Doctor, manually adjusting parameters, and repeatedly verifying strength, deflection, and stability indicators to finally determine the design scheme. The manual trial calculation process requires numerous adjustments, wasting significant manpower. Sometimes, directly using existing bridge structural design drawings leads to wasteful economic practices. Promoting more refined bridge engineering design has become a crucial issue that urgently needs to be addressed for high-quality urban construction and sustainable development.

[0003] Traditional algorithms are prone to getting stuck in local optima when faced with multi-variable and strongly constrained bridge structure optimization problems, and cannot achieve a global optimal match between stress, lightweighting, and cost. The number of design variable combinations is huge, the workload of manual iterative calculation is large, the design cycle is long, it relies on the experience of designers, and the level of standardization and intelligence is low. Traditional optimization algorithms are difficult to couple multiple objective constraints such as deflection, stress, and cost at the same time, and often can only satisfy safety or cost control in a single way, resulting in poor comprehensive matching. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the existing technology and to provide a multi-objective structural optimization design method for simply supported beam bridges in highways based on quantum annealing.

[0005] The objective of this invention is achieved through the following technical solution: a multi-objective structural optimization design method for simply supported beam highway bridges based on quantum annealing, characterized by the following steps:

[0006] S1. Preset the bridge span, design load, and material mechanical parameters. Based on the "Design Specifications for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts", set the allowable limits for deflection and bending stress, and use the allowable limits for deflection and bending stress as constraints for the optimization problem. Determine the optimization variables and their maximum, minimum, and discrete step sizes to form a complete set of discrete parameters.

[0007] S2. Establish the geometric model of the beam section and derive the formula for calculating the moment of inertia of the section; use the classical mechanics formula for simply supported beams to calculate the maximum bending moment, maximum deflection, and maximum bending stress at mid-span; use the total volume of the component to represent the material usage, construct a relative cost model, and establish a one-to-one mapping relationship between the optimization variables of step S1 and the maximum deflection, maximum bending stress, and relative cost at mid-span; thus, a multi-objective, multi-constraint optimization problem is formed with cost minimization as the optimization objective and the constraints of step S1 as the conditions.

[0008] S3. For the maximum mid-span deflection in step S2 exceeding the allowable deflection limit in step S1 and the maximum bending stress in step S2 exceeding the allowable bending stress limit in step S1, an optimization variable combination is formed. The constraints of the optimization variable combination are transformed into a penalty function, and a high penalty value is applied to the optimization variable combination. Cost weight, deflection constraint penalty weight, and stress constraint penalty weight are set to transform the multi-objective multi-constraint optimization problem in step S2 into a single-objective QUBO binary quadratic unconstrained optimization model, which is adapted to the quantum annealing solution architecture.

[0009] S4. The quantum annealing solution architecture is used to perform global iterative optimization on the single-objective QUBO binary quadratic unconstrained optimization model. It traverses all discrete parameter combinations and outputs the globally optimal section parameter combination that simultaneously satisfies stiffness and strength specifications and has the lowest cost.

[0010] S5. Import the global optimal section parameter combination from step S4 into the bridge finite element analysis software, rebuild the finite element model, perform static analysis, deflection check and strength check, and after verifying that it fully complies with the current bridge code requirements, solidify it as the formal bridge design scheme.

[0011] Preferably, the bridge section parameters optimized in step S1 are the beam height, web thickness, flange thickness, and top and bottom plate thickness.

[0012] Preferably, the overall objective function of the single-objective QUBO binary quadratic unconstrained optimization model in step S3 is... for:

[0013] ,

[0014] in, As a weighting factor for construction costs, For relative cost, For deflection constraint penalty term, This is a stress constraint penalty term.

[0015] Preferably, the overall objective function of the single-objective QUBO binary quadratic unconstrained optimization model in step S3 is... for:

[0016] ,

[0017] in, As a weighting factor for construction costs, For relative cost, For deflection constraint penalty term, This is a stress constraint penalty term. This is a penalty term for displacement constraints.

[0018] Preferably, the quadratic function of the deflection constraint penalty term is:

[0019] ,

[0020] in, For the deflection constraint penalty weight, This is the allowable limit for deflection. This represents the maximum deflection at mid-span.

[0021] Preferably, the quadratic function of the stress constraint penalty term is:

[0022]

[0023] Where [σ] is the allowable limit of bending stress, and σ is the maximum bending stress. This represents the stress constraint penalty weight.

[0024] Preferably, the linear function of the displacement constraint penalty term is:

[0025] ,

[0026] in, For displacement constraint penalty weights, Additional displacement calculation values, For additional displacement constraint limits.

[0027] Preferably, the quantum annealing solution architecture in step S4 includes two types: the first is to use a simulated annealing simulator locally to perform classical simulation calculations; the second is to connect to the D-Wave quantum annealing cloud platform or a domestic quantum computing cloud platform to call real quantum bit hardware for solving.

[0028] Preferably, the bridge finite element analysis software in step S5 is Midas / Civil or Bridge Doctor.

[0029] Preferably, the calculation formula for the moment of inertia of the cross section in step S2 includes the calculation formula for the moment of inertia of the rectangular cross section and the calculation formula for the moment of inertia of the T-shaped cross section.

[0030] Preferably, the formula for calculating the moment of inertia of the rectangular section is as follows:

[0031]

[0032] in: Let b be the moment of inertia of the rectangular section, b be the width of the rectangular section, and h be the height of the rectangular section.

[0033] Preferably, the formula for calculating the moment of inertia of the T-section is as follows:

[0034]

[0035] in, Let T be the total moment of inertia at section T. Let be the moment of inertia of the flange about the global neutral axis. Moment of inertia of the web about the overall neutral axis.

[0036] Preferably, the formula for calculating the moment of inertia of the flange about the overall neutral axis is as follows:

[0037] ,

[0038] in, The width of the upper wing edge. For the flange thickness, This is the distance from the centroid of the overall cross-section to the top surface.

[0039] Preferably, the formula for calculating the moment of inertia of the web about the overall neutral axis is as follows:

[0040] ,

[0041] in, The web height, For web thickness, This is the distance from the centroid of the overall cross-section to the top surface.

[0042] Preferably, the formula for calculating the distance from the centroid of the overall cross-section to the top surface is as follows:

[0043] .

[0044] Preferably, the formula for calculating the maximum bending stress of the cross-section in step S2 is:

[0045] ,

[0046] in, The maximum bending stress of the cross section, The maximum bending moment at mid-span, The distance from the farthest fiber in the cross-section to the neutral axis. Let be the moment of inertia of the cross section.

[0047] Preferably, the formula for calculating the maximum bending moment at mid-span is:

[0048] ,

[0049] Among them, the Let L be the uniformly distributed load intensity, and L be the span of the simply supported beam.

[0050] Preferably, the formula for calculating the maximum deflection at mid-span is:

[0051] ,

[0052] Among them, the For uniformly distributed load intensity, For a simply supported beam with span L, For elastic modulus, Let be the moment of inertia of the cross section.

[0053] The present invention has the following advantages and beneficial effects compared with the prior art:

[0054] 1. This invention applies quantum annealing to multi-objective structural optimization of simply supported beam bridges in highways. It is not a simple replacement or conventional application of traditional algorithms, but rather a substantial technological breakthrough addressing the high-dimensional discreteness, strong constraints, and multi-objective characteristics of bridge engineering. Compared to traditional optimization methods such as genetic algorithms, particle swarm optimization, and gradient methods, quantum annealing, relying on the quantum tunneling effect and global parallel traversal characteristics, can completely escape the local optimum trap, ensuring the attainment of the global optimum solution.

[0055] 2. By utilizing the parallel traversal characteristics of quantum annealing, the limitations of local optima in classical algorithms are overcome. At the same time, multiple objectives such as strength, deflection, and cost are taken into account, which can save 10% to 20% of building materials compared with traditional experience design.

[0056] 3. In terms of convergence speed, traditional manual calculations and conventional optimization algorithms require 3 to 5 days of repeated iterations and verifications, while this invention can complete the optimization of parameters across the entire domain in just 3 to 10 minutes, significantly improving convergence efficiency and reducing labor costs and design cycle.

[0057] 4. Directly input the highway bridge regulation limits into the optimization model for automatic compliance screening, reducing the need for repeated manual verification and iteration in the later stages;

[0058] 5. It does not replace existing bridge design software. It adopts the "quantum optimization preliminary selection + finite element calculation verification" mode, which is fully compatible with the existing engineering design process and is very easy to implement and promote.

[0059] 6. It can be extended from simply supported beam bridges to continuous beam bridges, box girder bridges, and truss bridges. It can also be expanded to include multi-dimensional quantum optimization of earthquake resistance, wind resistance, and construction procedures, and has a series of patent extension spaces. Attached Figure Description

[0060] Figure 1 This is a flowchart illustrating the multi-objective structural optimization design method for simply supported beam highway bridges based on quantum annealing, as proposed in this invention. Detailed Implementation

[0061] The invention's objective will be further described in detail below with reference to the accompanying drawings and specific embodiments. The embodiments cannot be described in detail here, but the implementation of the invention is not limited to the following embodiments.

[0062] Example

[0063] like Figure 1 As shown, a multi-objective structural optimization design method for simply supported highway beam bridges based on quantum annealing is presented in this embodiment, which selects a simply supported T-shaped highway bridge with a span of 20m. The method includes the following steps:

[0064] S1. Preset the bridge span, design load, and material mechanics parameters. Based on the "Design Specifications for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts," set allowable deflection and bending stress limits, using these limits as constraints for the optimization problem. Determine the optimization variables and their maximum, minimum, and discrete step sizes to form a complete set of discrete parameters. Optimization variables include bridge section parameters such as beam height, web thickness, flange thickness, and top and bottom plate thickness. The step size is dynamically discrete; different component sizes and quality requirements (e.g., prestressed components, reinforced concrete components, steel structure components, etc.) have different requirements. For example: beam height: step size = 50mm; flange thickness: step size = 10mm; web thickness: step size = 20mm.

[0065] Parameter settings: span L=20m, design load is 10kN / m, material mechanical parameters (i.e. steel yield strength) is 345MPa, allowable deflection limit is L / 500, and allowable bending stress limit is 0.6 times the steel yield strength; optimization variable range: beam height is 1.2~2.5m, web thickness is 0.15~0.35m, flange thickness is 0.12~0.30m, set equal discrete step size: beam height is 50mm, web thickness is 20mm, and flange thickness is 10mm.

[0066] S2. Establish the geometric model of the beam section and derive the calculation formula for the moment of inertia of the section; use the classical mechanics formula for simply supported beams to calculate the maximum bending moment, maximum deflection, and maximum bending stress at mid-span; use the total volume of the component to represent the material usage, construct a relative cost model, and establish a one-to-one mapping relationship between the optimization variables of step S1 and the maximum deflection, maximum bending stress, and relative cost at mid-span; thus, a multi-objective and multi-constraint optimization problem is formed with cost minimization as the optimization objective and the constraints of step S1 as the constraints.

[0067] 1. Input discrete optimization variables: Given a set of defined cross-sectional parameters {H, tw, tf}, this set of variables is the mapping input independent variable. The variable values ​​are strictly limited to the maximum, minimum and discrete step lengths set in step S1. Each set of parameters has only one unique geometric cross-sectional shape, where H is the beam height, tw is the web thickness and tf is the flange thickness.

[0068] 2. Unique solution for cross-sectional geometric parameters: Based on {H,tw,tf}, substitute them into the calculation formula for the moment of inertia of the cross section or the calculation formula for the moment of inertia of the T-section, and calculate the moment of inertia of the rectangular section, the moment of inertia of the centroidal axis, the moment of inertia of the web about the overall neutral axis, and the moment of inertia of the flange about the overall neutral axis step by step; only one set of cross-sectional geometric characteristic values ​​can be calculated for the same set of variables, and the geometric result is unique.

[0069] (1) The calculation formulas for the moment of inertia of a cross section include the calculation formulas for the moment of inertia of a rectangular cross section and the calculation formulas for the moment of inertia of a T-shaped cross section.

[0070] (a) Moment of inertia of rectangular cross section The calculation formula is:

[0071]

[0072] in: Let b be the moment of inertia of the rectangular section, b be the width of the rectangular section, and h be the height of the rectangular section.

[0073] If the centroidal axis is not at the center, it is necessary to shift the axis. The moment of inertia is obtained by calculating step by step using the axis-shifting formula. The axis shifting formula is:

[0074] ,

[0075] in, Let be the moment of inertia of the centroidal axis, A be the area of ​​the rectangular cross section, and d be the interaxial distance.

[0076] (b) The formula for calculating the moment of inertia of the T-section is:

[0077]

[0078] in, Let T be the total moment of inertia at section T. Let be the moment of inertia of the flange about the global neutral axis. Moment of inertia of the web about the overall neutral axis.

[0079] (c) The formula for calculating the moment of inertia of the flange about the overall neutral axis is:

[0080] ,

[0081] in, The width of the upper wing edge. For the flange thickness, This is the distance from the centroid of the overall cross-section to the top surface.

[0082] (d) The formula for calculating the moment of inertia of the web about the overall neutral axis is:

[0083] ,

[0084] in, The web height, For web thickness, This is the distance from the centroid of the overall cross-section to the top surface.

[0085] (e) The formula for calculating the distance from the centroid of the overall cross-section to the top surface is:

[0086] .

[0087] 3. The moment of inertia of the cross section (i.e., moment of inertia of rectangular cross section) or axis shifting moment of inertia or T-section moment of inertia ), simply supported beam span Uniformly distributed load intensity and elastic modulus Substituting these values ​​into the classical mechanics formulas for simply supported beams, we obtain the maximum bending stress.

[0088] (1) The formula for calculating the maximum bending stress is:

[0089] ,

[0090] in, The maximum bending stress of the cross section, The maximum bending moment at mid-span, The distance from the farthest fiber in the cross-section to the neutral axis. Let be the moment of inertia of the cross section.

[0091] (2) Maximum bending moment at mid-span The calculation formula is:

[0092] ,

[0093] Among them, the Let L be the uniformly distributed load intensity, and L be the span of the simply supported beam.

[0094] (3) Maximum deflection at mid-span The calculation formula is:

[0095] ,

[0096] Among them, the For uniformly distributed load intensity, For simply supported beam span, For elastic modulus, Let be the moment of inertia of the cross section.

[0097] Maximum bending moment at mid-span when the input cross-sectional geometric parameters are fixed Maximum deflection at mid-span The calculation results for the maximum bending stress are unique, achieving a one-to-one correspondence between the independent variables and mechanical indicators.

[0098] 4. One-to-one quantification of relative costs

[0099] The volume of the main beam section material is calculated using {H,tw,tf}, and the volume is used as the relative cost quantification index C; the same set of section dimensions corresponds to a unique component volume, thus obtaining a unique relative cost value.

[0100] S3. Compare the maximum mid-span deflection calculated in step S2 with the allowable deflection limit in step S1, and compare the maximum bending stress in step S2 with the allowable bending stress limit set in step S1. For values ​​where the maximum mid-span deflection exceeds the allowable deflection limit and the maximum bending stress exceeds the allowable bending stress limit, form an optimization variable combination (considering displacement constraint penalties, adding additional displacement calculation values ​​exceeding extra displacement constraint limits as one of the optimization variable combinations). Transform the constraints of the optimization variable combination into a penalty function, applying a high penalty value to the optimization variable combination to preemptively eliminate geometrically unreasonable and invalid variable combinations exceeding specification limits. Set cost weights, deflection constraint penalty weights, displacement constraint penalty weights, and stress constraint penalty weights, set according to bridge design requirements. The weight design can avoid the penalty function being too loose or too strict. Transform the multi-objective, multi-constraint optimization problem of step S2 into a single-objective QUBO binary quadratic unconstrained optimization model, adapted to the quantum annealing solution architecture.

[0101] The overall objective function of the single-objective QUBO binary quadratic unconstrained optimization model is:

[0102] or

[0103] ,

[0104] Where F represents the overall objective. As a weighting factor for construction costs, For relative cost, For deflection constraint penalty term, This is a stress constraint penalty term. This is an optional term, representing a displacement constraint penalty.

[0105] 1. The quadratic function of the deflection constraint penalty term is:

[0106] ,

[0107] in, For the deflection constraint penalty weight, This is the allowable limit for deflection. This represents the maximum deflection at mid-span. Physical meaning: The greater the maximum deflection at mid-span exceeds the limit, the more the deflection constraint penalty term increases rapidly in a quadratic order; strong constraint deflection does not exceed the limit.

[0108] 2. The quadratic function of the stress constraint penalty term is:

[0109] ,

[0110] Where [σ] is the allowable limit of bending stress, and σ is the maximum bending stress. This represents the stress constraint penalty weight. Physical meaning: When the maximum bending stress exceeds the allowable limit, the stress constraint penalty term is amplified twice, forcing the optimization model to avoid exceeding the limit section.

[0111] 3. The linear function of the displacement constraint penalty term is:

[0112] ,

[0113] in, For displacement constraint penalty weights, the following applies to exceeding limits: the displacement constraint penalty item takes effect only when the calculated added displacement value exceeds the additional displacement constraint limit; the penalty value for the compliant interval is 0. Additional displacement calculation values, This refers to the additional displacement constraint limit. Physical meaning: Exceeding the limit of the calculated additional displacement is penalized by a displacement constraint term, a gentle constraint used for secondary displacement control indicators.

[0114] Specific examples are as follows:

[0115] Cost weighting =10; The relative cost of this cross-section member is C=280 (dimensionless cost index converted from material volume). Deflection penalty weight. =1000, allowable deflection limit =40mm, maximum deflection at mid-span =50mm, stress penalty weight =1000, allowable limit of bending stress =345MPa, maximum bending stress =380MPa, displacement constraint penalty weight =500, additional displacement calculation value [u]=10mm, additional displacement constraint limit value u=12mm.

[0116] (1) Penalty for exceeding deflection limit =1000×(50−40) 2 =100000;

[0117] (2) Stress constraint penalty item =1000×(380−345) 2 =1225000;

[0118] (3) Displacement constraint penalty term Pμ=500×(12−10)=1000;

[0119] (4) Total target value F = 2800 + 100000 + 1225000 + 1000 = 1328800.

[0120] S4. A quantum annealing solution framework is used to perform global iterative optimization on a single-objective QUBO binary quadratic unconstrained optimization model. It iterates through all discrete parameter combinations and outputs the globally optimal cross-sectional parameter combination that simultaneously satisfies stiffness and strength specifications while minimizing cost. The globally optimal cross-sectional parameter combination includes the optimal beam height, optimal web thickness, and optimal flange thickness. A simulated annealing simulator is used to iterate through all discrete parameter combinations, outputting the globally optimal cross-sectional parameters: optimal beam height of 1.65m, optimal web thickness of 0.20m, and optimal flange thickness of 0.16m.

[0121] There are two types of quantum annealing solution architectures. The first type uses a local simulated annealing simulator to perform classical simulation calculations. The second type connects to the D-Wave quantum annealing cloud platform or a domestic quantum computing cloud platform to call real quantum bit hardware for solving.

[0122] S5. Import the globally optimal section parameter combination from step S4 into bridge finite element analysis software, such as Midas / Civil or Bridge Doctor. Rebuild the finite element model, perform static analysis, deflection verification, and strength verification. After verifying that it fully complies with current bridge code requirements, solidify it as the formal bridge design scheme. In this embodiment, the calculated optimal scheme has a single beam concrete volume of 82.7 m³ and a total steel reinforcement weight of 1.72 t.

[0123] Comparative Example

[0124] The industry standard manual calculation for the standard cross-section is: beam height: 2.0m, web thickness: 0.28m, flange thickness: 0.24m. After cross-section volume calculation, the concrete volume of a single main beam is 100.2m³, and the total weight of the main beam reinforcement is 2.06t. This fully meets the deflection and stress limits of JTG 3362-2018, but the cross-section dimensions are conservative and the material redundancy is large.

[0125] The comparison data between the method of this embodiment and the traditional algorithm is as follows:

[0126] (1) Optimization results of quantum annealing in this embodiment

[0127] The local simulation annealing solution took 6 minutes. The global optimal cross-section had a concrete volume of 82.7 m³ and a total steel weight of 1.72 t, resulting in a 17.0% saving in main materials and meeting all deflection and stress limit requirements of the specifications.

[0128] (2) Optimization results of genetic algorithm

[0129] The standard genetic algorithm was used for iterative optimization, with 500 generations and a population size of 80. After multiple manual trials, the convergence time was approximately 4.2 hours. The algorithm converged to a local optimum cross-section with a beam height of 1.80m, a web thickness of 0.24m, and a flange thickness of 0.20m. The calculated concrete volume of a single main beam was 91.6m³, and the total weight of the reinforcing steel was 1.91t.

[0130] (3) Summary of the difference between the two quantitative methods

[0131] Computation time: The genetic algorithm took 4.2 hours, while quantum annealing took 6 minutes, resulting in a 97.6% improvement in computational efficiency.

[0132] Material saving rate: The material saving rate of genetic algorithm is 8.5%, and the material saving rate of quantum annealing is 17.0%.

[0133] The multi-objective structural optimization design method for simply supported beam highway bridges based on quantum annealing in this embodiment has the following advantages:

[0134] 1. This invention applies quantum annealing to multi-objective structural optimization of simply supported beam bridges in highways. It is not a simple replacement or conventional application of traditional algorithms, but rather a substantial technological breakthrough addressing the high-dimensional discreteness, strong constraints, and multi-objective characteristics of bridge engineering. Compared to traditional optimization methods such as genetic algorithms, particle swarm optimization, and gradient methods, quantum annealing, relying on the quantum tunneling effect and global parallel traversal characteristics, can completely escape the local optimum trap, ensuring the attainment of the global optimum solution.

[0135] 2. By utilizing the parallel traversal characteristics of quantum annealing, the limitations of local optima in classical algorithms are overcome, while simultaneously considering multiple objectives such as strength, deflection, and cost, resulting in material savings of 10% to 20% compared to traditional empirical design.

[0136] 3. In terms of convergence speed, traditional manual calculations and conventional optimization algorithms require 3 to 5 days of iterative verification, while this invention can complete the optimization of parameters across the entire domain in just 3 to 10 minutes, improving convergence efficiency by more than 95% and reducing labor costs and design cycle.

[0137] 4. Directly input the highway bridge regulation limits into the optimization model for automatic compliance screening, reducing the need for repeated manual verification and iteration in the later stages;

[0138] 5. It does not replace existing bridge design software. It adopts the "quantum optimization preliminary selection + finite element calculation verification" mode, which is fully compatible with the existing engineering design process and is very easy to implement and promote.

[0139] 6. It can be extended from simply supported beam bridges to continuous beam bridges, box girder bridges, and truss bridges. It can also be expanded to include multi-dimensional quantum optimization of earthquake resistance, wind resistance, and construction procedures, and has a series of patent extension spaces.

[0140] The above-described specific embodiments are preferred embodiments of the present invention and are not intended to limit the present invention. Any other changes or equivalent substitutions made without departing from the technical solution of the present invention are included within the protection scope of the present invention.

Claims

1. A multi-objective structural optimization design method for simply supported beam highway bridges based on quantum annealing, characterized by: Includes the following steps: S1. Preset the bridge span, design load and material mechanical parameters, and set the allowable deflection limit and bending stress limit according to the "Design Specification for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts". Use the allowable deflection limit and bending stress limit as the constraint conditions of the optimization problem. Determine the optimization variables, their maximum and minimum values, and the discrete step size to form a complete set of discrete parameters; S2. Establish the geometric model of the beam section and derive the formula for calculating the moment of inertia of the section; The maximum bending moment, maximum deflection, and maximum bending stress at mid-span are calculated using classical mechanics formulas for simply supported beams. The material usage is represented by the total volume of the component. A relative cost model is constructed, and a one-to-one mapping relationship is established between the optimization variables of step S1 and the maximum deflection, maximum bending stress, and relative cost at mid-span. This constitutes a multi-objective and multi-constraint optimization problem with cost minimization as the optimization objective and the constraints of step S1 as the conditions. S3. For the maximum mid-span deflection in step S2 exceeding the allowable deflection limit in step S1 and the maximum bending stress in step S2 exceeding the allowable bending stress limit in step S1, an optimization variable combination is formed. The constraints of the optimization variable combination are transformed into a penalty function, and a high penalty value is applied to the optimization variable combination. Cost weight, deflection constraint penalty weight, and stress constraint penalty weight are set to transform the multi-objective multi-constraint optimization problem in step S2 into a single-objective QUBO binary quadratic unconstrained optimization model, which is adapted to the quantum annealing solution architecture. S4. The quantum annealing solution architecture is used to perform global iterative optimization on the single-objective QUBO binary quadratic unconstrained optimization model. It traverses all discrete parameter combinations and outputs the globally optimal section parameter combination that simultaneously satisfies stiffness and strength specifications and has the lowest cost. S5. Import the global optimal section parameter combination from step S4 into the bridge finite element analysis software, rebuild the finite element model, perform static analysis, deflection check and strength check, and after verifying that it fully complies with the current bridge code requirements, solidify it as the formal bridge design scheme.

2. The multi-objective structural optimization design method for simply supported beam highway bridges based on quantum annealing as described in claim 1, characterized in that: The optimization variables in step S1 include bridge section parameters such as beam height, web thickness, flange thickness, and top and bottom plate thickness.

3. The multi-objective structural optimization design method for simply supported beam highway bridges based on quantum annealing according to claim 1, characterized in that: The overall objective function of the single-objective QUBO binary quadratic unconstrained optimization model in step S3 for: ， in, As a weighting factor for construction costs, For relative cost, For deflection constraint penalty term, This is a stress constraint penalty term.

4. The multi-objective structural optimization design method for simply supported beam highway bridges based on quantum annealing according to claim 1, characterized in that: The overall objective function of the single-objective QUBO binary quadratic unconstrained optimization model in step S3 for: ， in, As a weighting factor for construction costs, For relative cost, For deflection constraint penalty term, This is a stress constraint penalty term. This is a penalty term for displacement constraints.

5. The multi-objective structural optimization design method for simply supported beam highway bridges based on quantum annealing according to claim 3 or 4, characterized in that: The quadratic function of the deflection constraint penalty term is: ， in, For the deflection constraint penalty weight, This is the allowable limit for deflection. This represents the maximum deflection at mid-span.

6. The multi-objective structural optimization design method for simply supported beam highway bridges based on quantum annealing according to claim 3 or 4, characterized in that: The quadratic function of the stress constraint penalty term is: Where [σ] is the allowable limit of bending stress, and σ is the maximum bending stress. This represents the stress constraint penalty weight.

7. The multi-objective structural optimization design method for simply supported beam highway bridges based on quantum annealing according to claim 4, characterized in that: The linear function of the displacement constraint penalty term is: ， in, For displacement constraint penalty weights, Additional displacement calculation values, For additional displacement constraint limits.

8. The multi-objective structural optimization design method for simply supported beam highway bridges based on quantum annealing according to claim 1, characterized in that: The quantum annealing solution architecture in step S4 includes two types. The first type is to use a simulated annealing simulator locally to perform classical simulation calculations. The second type is to connect to the D-Wave quantum annealing cloud platform or a domestic quantum computing cloud platform to call real quantum bit hardware for solving.

9. The multi-objective structural optimization design method for simply supported beam highway bridges based on quantum annealing according to claim 1, characterized in that: The bridge finite element analysis software mentioned in step S5 is Midas / Civil or Bridge Doctor.

10. The multi-objective structural optimization design method for simply supported beam highway bridges based on quantum annealing according to claim 1, characterized in that: The calculation formulas for the moment of inertia of the cross section in step S2 include the calculation formulas for the moment of inertia of the rectangular cross section and the calculation formulas for the moment of inertia of the T-shaped cross section.

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