A multi-objective optimization method for optimization design of radiative cooling materials and structures

Abstract

This invention relates to the field of radiation cooling material structure design, and discloses a multi-objective optimization method for the optimized design of radiation cooling materials and structures. The method involves constructing a multi-objective optimization model for the radiation cooling materials and structures; initializing a set of weight vectors, a population of candidate solutions, and an ideal point; performing objective evaluation and aggregation evaluation on the candidate solutions; establishing and updating the dynamic matching relationship between the weight vectors and candidate solutions through a dynamic association modeling mechanism based on the aggregation evaluation results, ensuring that each weight vector is associated with only one candidate solution that best matches its search direction during the same iteration; adaptively updating the set of weight vectors based on the distribution state of the candidate solutions; defining and evaluating the congestion entropy of candidate solutions; triggering a control mechanism to process the candidate solution population based on the threshold judgment results; executing the above steps until a preset termination condition is met, and outputting the optimization results of the radiation cooling materials and structures.

Description

Technical Field

[0001] This invention relates to the field of radiation cooling material structure design, and more specifically to a multi-objective optimization method for the optimization design of radiation cooling materials and structures. Background Technology

[0002] Radiation cooling technology, as a passive cooling method that can achieve cooling without external energy input, is widely used in energy-saving buildings, energy systems and thermal management. Based on special radiation cooling materials or structures, it radiates heat energy into outer space within the atmospheric transparent window band, while suppressing the absorption of solar radiation, thereby achieving a cooling effect below the ambient temperature.

[0003] In existing technologies, the design of radiation-cooled materials and structures is often abstracted into a multi-objective optimization problem. Current techniques primarily employ performance-driven or empirical parameter-based approaches. However, due to the unique characteristics of radiation-cooled materials and structures, the actual optimization process requires consideration of multiple conflicting performance indicators, such as infrared radiation capability, solar reflectivity, environmental adaptability, and manufacturing cost. These problems are characterized by significant conflicts between objectives, high coupling of design variables, and complex target space structures. Existing radiation-cooling modeling and optimization methods are not well-suited to balancing these performance indicators. On one hand, the solution set tends to cluster in local regions during optimization, resulting in insufficient coverage of the performance space. On the other hand, distribution control strategies introduced to maintain solution set diversity often weaken the algorithm's convergence efficiency, making it difficult to obtain stable and reliable optimization results under limited computational resources. Performance-driven or empirical parameter-based objective optimization methods employ static weights and fixed search directions. When the target space morphology changes with variables during radiation-cooling optimization, conventional methods become unsuitable. Therefore, there is an urgent need for an optimization method that can adapt to the design objective optimization requirements of radiation-cooled materials and structures, balancing convergence, diversity, and adaptability. Summary of the Invention

[0004] Purpose of the invention: To address the problems mentioned in the background art, this invention discloses a multi-objective optimization method for the optimal design of radiation cooling materials and structures. Based on a multi-objective optimization algorithm, a dynamic correlation modeling mechanism and weight adaptive update are coupled to construct a crowding entropy control mechanism, enabling radiation cooling materials and structures to achieve an effective trade-off among multiple performance objectives such as infrared radiation performance, solar radiation suppression capability, environmental adaptability, and structural design feasibility, thereby obtaining a radiation cooling design scheme with optimal comprehensive performance.

[0005] Technical solution:

[0006] This invention discloses a multi-objective optimization method for the optimized design of radiation cooling materials and structures, the method comprising the following steps:

[0007] S1: Construct a multi-objective optimization model for radiation cooling materials and structures;

[0008] S2: Initialize the weight vector set, candidate solution population and ideal point, and perform target evaluation and aggregation evaluation on the candidate solutions;

[0009] S3: Based on the aggregated evaluation results, a dynamic matching relationship between the weight vector and the candidate solution is established and updated through a dynamic association modeling mechanism, so that each weight vector is associated with only one candidate solution that best matches its search direction in the same iteration process;

[0010] S4: Adaptively update the weight vector set based on the distribution state of candidate solutions;

[0011] S5: Define and evaluate the crowding entropy of candidate solutions, and trigger the control mechanism to process the candidate solution population based on the threshold judgment result;

[0012] S6: Execute the above steps until the preset termination condition is met, and output the optimization results of the radiation cooling material and structure.

[0013] Furthermore, the objective function of the multi-objective optimization model described in S1 is used to characterize the optimization requirements of the radiative cooling system in different performance dimensions, including but not limited to conflicting objective functions such as the average emissivity of the atmospheric window f1(x), the solar spectral absorptivity f2(x), and the overall cost f3(x). The multi-objective optimization problem is expressed as:

[0014]

[0015] Where x represents the radiation cooling design parameter vector, and the design parameters include, but are not limited to, the type of radiation cooling material, the material type in the multilayer membrane structure, the geometric thickness parameters of each membrane layer, and the structural arrangement.

[0016] Furthermore, the design parameters satisfy the constraints of structural manufacturability and application environment:

[0017]

[0018] The objective function includes, but is not limited to: maximizing the infrared radiation capability within the atmospheric transparency window band, minimizing the solar absorptivity within the visible and near-infrared bands, improving the stability of radiative cooling performance, and reducing the complexity or cost of structural design.

[0019] In the atmospheric transparency window band [λ] a min , λ a max Within [the atmosphere], the average emissivity of the atmospheric window is defined as:

[0020]

[0021] Where ε(λ, x) represents the spectral emissivity of the radiation-cooled structure at wavelength λ;

[0022] In the solar spectrum band [λ] s min , λ s max Within [the solar spectrum], the absorptivity is defined as:

[0023]

[0024] Where α(λ, x) is the spectral absorbance, I sol (λ) represents the standard solar spectral irradiance.

[0025] The comprehensive cost per unit area is defined as:

[0026]

[0027] Where, d l Let c be the thickness of the l-th layer. l mat C represents the cost per unit thickness of the corresponding material. fab (L) represents the manufacturing cost related to the number of film layers and process complexity. After modeling is completed, the candidate solution population, weight vector set, and ideal point are initialized.

[0028] Furthermore, S2 introduces a set of weight vectors, decomposes the multi-objective optimization problem based on these weight vectors, and uses a weighted Chebyshev method to aggregate and evaluate candidate solutions.

[0029]

[0030] Where w is the set of all subproblems, K is the number of weight vectors, and z ∗ Let f be an ideal point vector. i (x)−z i ∗ | represents the difference between the solution x and the ideal value in the i-th objective. The multi-objective optimization problem is decomposed based on the set of weight vectors, and the original multi-objective problem is transformed into multiple sub-problems. The search is carried out in parallel under the guidance of different weight vectors.

[0031] Furthermore, S3 establishes and updates the dynamic matching relationship between the weight vector and the candidate solutions through a dynamic association modeling mechanism, specifically as follows:

[0032] Define candidate solution x j With weight vector w k Match degree:

[0033]

[0034] By applying a uniqueness constraint, we find a direction among all directions w that minimizes the matching degree ϕ, ensuring that each candidate solution is associated with only one weight vector in a single iteration. The association rule is expressed as:

[0035]

[0036] To avoid the same candidate solution being repeatedly associated with multiple weight vectors, when multiple weight vectors correspond to the same candidate solution, the final association relationship is determined according to the principle of minimum matching degree.

[0037] Furthermore, the weight vector update described in S4, based on the dynamic association mechanism, updates the weight vector according to the distribution of candidate solutions in the target space, defining the distribution density function of candidate solutions in the target space:

[0038]

[0039] Where, N j Indicates candidate solution x j The neighborhood set; if there are density anomaly regions or the association between weight vectors and quantum problems fails in the target space, the adaptive update of the weight vector is triggered. By adjusting the direction or density of the weight vector, the search direction can be dynamically adjusted with the changes in the target space structure, thereby enhancing the adaptability to complex target space structures.

[0040] Furthermore, S5 quantifies and evaluates the local density distribution of candidate solutions in the target space, defining candidate solutions x. j The crowding entropy in the target space is:

[0041]

[0042] Where, p j,i It represents the normalized neighborhood density ratio of the candidate solution in the i-th objective dimension. The smaller the crowding entropy value, the more crowded the region where the candidate solution is located; the larger the crowding entropy value, the more uniform the distribution of the candidate solution.

[0043] Furthermore, when the crowding entropy assessment result is lower than a preset threshold, a control mechanism is triggered. By reconstructing the candidate solution population, while ensuring the convergence performance of the solution set, candidate solutions from relatively sparsely distributed regions in the target space are introduced to restore the uniform coverage of the solution set in the target space and avoid excessive clustering of the solution set. The preset threshold is based on adjustment parameters. set up:

[0044]

[0045] Among them, CE th The crowding entropy threshold, The parameters are adjusted to control the trigger sensitivity of the diverse regulatory mechanisms;

[0046] The control mechanism is as follows:

[0047]

[0048] Among them, P sparse This represents the set of candidate solutions introduced from the sparse region of the target space.

[0049] Furthermore, the specific steps of S6 are as follows:

[0050] The optimization process terminates when one of the following conditions is met:

[0051]

[0052] Among them, t max Let ϵ be the maximum number of iterations and ε be the convergence threshold. Repeat the above steps until a preset termination condition is met. When the termination condition is met, the Pareto optimal solution set is output as follows:

[0053]

[0054] Output a set of Pareto optimal solutions that effectively balance multiple performance objectives such as infrared radiation performance, solar absorption suppression capability, and stability, as the optimization design result of radiation cooling materials and structures.

[0055] Beneficial effects:

[0056] 1. This invention introduces a dynamic correlation modeling mechanism to dynamically adjust the correspondence between the weight vector and the candidate solution based on the performance of the candidate solution in different search directions. This avoids the same candidate solution being reused in multiple search directions, alleviates the problem of local clustering of the solution set in the target space during multi-objective optimization, and improves the uniformity of the distribution of the solution set in multiple different performance target dimensions that characterize radiative cooling performance.

[0057] 2. Based on the distribution of candidate solutions in the target space, this invention adaptively updates and adjusts the weights of the search direction, enabling the optimization process to dynamically match the trade-offs between different performance objectives as the shape of the target space changes. This improves the adaptability of multi-objective optimization methods in non-convex, multi-peak, or irregular target spaces, and avoids the decrease in optimization efficiency caused by a fixed search direction.

[0058] 3. This invention introduces a diversity assessment and control mechanism based on crowding entropy to quantitatively assess the local density distribution of candidate solutions in the target space and reconstruct or update the solution set when its diversity is insufficient. Without disrupting the convergence trend of the optimization process, it effectively maintains the coverage of the solution set in the target space, achieving a balance between convergence performance and solution set diversity.

[0059] 4. This invention achieves an effective trade-off among multiple conflicting performance objectives, such as enhanced infrared radiation, suppressed solar absorption, performance stability, and structural feasibility, outputting a Pareto solution set with optimal overall performance. This provides diverse and highly selectable optimization schemes for the design of radiation cooling materials and structures. The proposed multi-objective optimization method is not dependent on a specific radiation cooling material system or structural form, can adapt to different material combinations and structural parameter settings, and is easily integrated with existing radiation cooling design processes and computational platforms, demonstrating good engineering applicability and promotional value. Attached Figure Description

[0060] Figure 1 This is a flowchart of the overall method of the present invention;

[0061] Figure 2 This is a schematic diagram of the multi-objective evolutionary optimization algorithm (IMOA-CE) that integrates dynamic correlation and crowding entropy in this invention.

[0062] Figure 3 This is a comparison chart of the IGD evolution curves of the IMOA-CE algorithm in this invention embodiment;

[0063] Figure 4 This is a comparison chart showing the effects of the IMOA-CE algorithm and the traditional MOEA / D algorithm in optimizing radiation cooling materials and structures according to embodiments of the present invention. Detailed Implementation

[0064] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0065] like Figure 1-2 As shown, this invention discloses a multi-objective optimization method for the optimized design of radiation cooling materials and structures. The method steps are as follows:

[0066] S1: To address the design requirements of radiation cooling materials and structures, the radiation cooling optimization problem is modeled as a multi-objective optimization problem. Based on a multi-objective optimization algorithm, a multi-objective evolutionary optimization algorithm (IMOA-CE) integrating dynamic correlation and crowding entropy is constructed. The multi-objective optimization problem includes at least two conflicting optimization objectives to characterize the optimization requirements of the radiation cooling system in different performance dimensions. The optimization objectives include conflicting objective functions such as the average emissivity of the atmospheric window, the absorptivity of the solar spectrum, and the overall cost. The corresponding optimization variables include, but are not limited to, the type of radiation cooling material, the selection of materials for each layer in the multilayer membrane structure, the membrane thickness parameters, and the arrangement of the multilayer structure.

[0067] S2: After completing the modeling of the multi-objective optimization problem, initialize the candidate solution population, weight vector set, and ideal point for decomposing and solving the multi-objective optimization problem. The multi-objective optimization problem is decomposed using the weight vector set, transforming the original multi-objective optimization problem into multiple sub-problems. Based on the evaluation results of the candidate solution population under different weight vectors, an initial multi-directional parallel search is conducted.

[0068] S3: During the optimization iteration process, a dynamic association modeling mechanism is introduced based on the performance of candidate solutions under different weight vectors. This mechanism dynamically establishes and updates the matching relationship between weight vectors and candidate solutions. Through this dynamic association mechanism, each weight vector is preferentially associated with the candidate solution that best matches its search direction, avoiding the same candidate solution being repeatedly associated by multiple weight vectors. This improves the utilization efficiency of search resources and characterizes the dynamic association characteristics between different optimization objectives as the search process progresses.

[0069] Specifically, after completing the multi-objective problem decomposition in step S2, each weight vector corresponds to a sub-problem, and the fit of candidate solutions in the search direction is evaluated using an aggregation function. To achieve effective matching between weight vectors and candidate solutions, the aggregation evaluation value of candidate solutions in each weight vector direction is first calculated using an aggregation function based on weighted Chebyshev distance. For each weight vector, the candidate solution with the smallest aggregation evaluation value is found in the current candidate solution set as its candidate association object. When multiple weight vectors simultaneously select the same candidate solution, priority is determined based on the size of the aggregation evaluation value, and the candidate solution is assigned to the weight vector with the smallest evaluation value. For weight vectors that are not successfully associated, the candidate solution with the smallest evaluation value is re-selected from the remaining candidate solutions for association.

[0070] S4: After completing the dynamic association in step S3, evaluate the distribution of the current candidate solutions in the target space to determine whether an adaptive update of the weight vector set is needed. When uneven distribution or insufficient coverage of candidate solutions in the target space is detected, adjust the direction or density of the weight vectors to dynamically match the search direction with changes in the target space structure, thereby improving the adaptability of the multi-objective optimization method to complex and non-uniform target space structures.

[0071] Specifically, the solution set is considered not to meet the distribution equilibrium condition when any of the following conditions occur: candidate solutions exhibit significant clustering in local regions of the target space; candidate solutions have insufficient coverage areas in the target space; or some subproblems corresponding to the weight vector set have not been associated with valid candidate solutions for a long period. When any of the above conditions are met, it indicates a certain degree of directional mismatch between the current weight vector distribution and the Pareto front shape, requiring adaptive adjustment of the weight vector set to improve the search direction distribution in the target space. Therefore, proceed to step S5 to update the weight vector direction or density.

[0072] S5: During the optimization process, a diversity evaluation mechanism based on congestion entropy is introduced to quantitatively measure the local density distribution of candidate solutions in the target space. Congestion entropy is used to characterize the degree of distribution balance of candidate solutions in the target space. When candidate solutions are excessively clustered in local regions, their corresponding congestion entropy value decreases; when candidate solutions are evenly distributed in the target space, their corresponding congestion entropy value is higher.

[0073] S6: When the evaluation result based on crowding entropy indicates that the diversity of the candidate solution population is lower than a preset threshold, a control mechanism is triggered. The crowding entropy threshold is adaptively determined based on the overall distribution state of the current candidate solution population. Specifically, the average crowding entropy of the current population is first calculated to reflect the uniformity of the overall population distribution. This is then multiplied by an adjustment parameter. To set the preset threshold value for regulation. The diversity regulation mechanism adjusts the distribution of the solution set by screening, replacing or reconstructing the candidate solution population. Under the premise of ensuring the convergence performance of candidate solutions, it introduces candidate solutions from relatively sparse regions in the target space to restore the uniform coverage of the solution set in the target space and avoid solution set degradation or local clustering during the optimization process.

[0074] S7: Repeat the above steps until the preset termination condition is met. When the termination condition is met, output a set of Pareto optimal solutions that achieve an effective trade-off among multiple performance objectives, as the optimization design result of the radiation cooling material and structure.

[0075] Specifically, S1 models the optimization problem of radiation cooling materials and structures as a multi-objective optimization problem. Its objective function characterizes the optimization requirements of the radiation cooling system across different performance dimensions. These include, but are not limited to, conflicting objective functions such as the average emissivity of the atmospheric window f1(x), the absorptivity of the solar spectrum f2(x), and the overall cost f3(x). The multi-objective optimization problem is expressed as:

[0076]

[0077] Where x represents the radiation cooling design parameter vector, and the design parameters include, but are not limited to, the type of radiation cooling material, the selection of materials for each layer in the multilayer membrane structure, the geometric thickness parameters of each membrane layer, and the structural arrangement.

[0078]

[0079] The design parameters must meet the constraints of structural manufacturability and application environment:

[0080]

[0081] Objective functions include, but are not limited to: maximizing infrared radiation capability within the atmospheric transparency window band, minimizing solar absorptivity within the visible and near-infrared bands, improving the stability of radiative cooling performance, and reducing structural design complexity or cost.

[0082] In the atmospheric transparency window band [λ] a min , λ a max Within [the atmosphere], the average emissivity of the atmospheric window is defined as:

[0083]

[0084] Where ε(λ, x) represents the spectral emissivity of the radiation-cooled structure at wavelength λ.

[0085] In the solar spectrum band [λ] s min , λ s max Within [the solar spectrum], the absorptivity is defined as:

[0086]

[0087] Where α(λ, x) is the spectral absorbance, I sol (λ) represents the standard solar spectral irradiance.

[0088] The comprehensive cost per unit area is defined as:

[0089]

[0090] Where, d l Let c be the thickness of the l-th layer. l mat C represents the cost per unit thickness of the corresponding material. fab (L) represents the manufacturing cost related to the number of film layers and process complexity. After modeling is completed, the candidate solution population, weight vector set, and ideal point are initialized.

[0091] Specifically, in step S2, a set of weight vectors is introduced:

[0092]

[0093] Where W is the set of all subproblems, K is the number of weight vectors, and the w-th subproblem is the weight vector of the set of subproblems. k The weight vectors for each subproblem. Each weight vector satisfies:

[0094]

[0095] The multi-objective optimization problem is decomposed based on weight vectors, and candidate solutions are aggregated and evaluated using a weighted Chebyshev method.

[0096]

[0097] Among them, z ∗ Let f be an ideal point vector. i (x)−z i ∗ | represents how far solution x deviates from the ideal value for the i-th objective; the greater the deviation, the worse the performance in that objective dimension. The multi-objective optimization problem is decomposed based on a set of weight vectors, transforming the original multi-objective problem into multiple sub-problems, and the search is carried out in parallel under the guidance of different weight vectors.

[0098] Specifically, in step S3, a dynamic correlation and matching relationship between the weight vector and the candidate solution is established based on the aggregated evaluation results of the candidate solution under each weight vector.

[0099] Define candidate solution x j With weight vector w k The matching degree is:

[0100]

[0101] By applying a uniqueness constraint, we find a direction among all directions W that minimizes the matching degree ϕ, ensuring that each candidate solution is associated with only one weight vector in a single iteration. The association rule is expressed as:

[0102]

[0103] To avoid the same candidate solution being repeatedly associated with multiple weight vectors, when multiple weight vectors correspond to the same candidate solution, the final association relationship is determined according to the principle of minimum matching degree. This improves the efficiency of search resource utilization and characterizes the dynamic association characteristics between different performance objectives as the search process progresses.

[0104] Specifically, in step S4, based on the dynamic association mechanism, it is determined whether the weight vector needs to be updated according to the distribution of candidate solutions in the target space.

[0105] Define the distribution density function of the candidate solution in the objective space as follows:

[0106]

[0107] Where, N j Indicates candidate solution x j The neighborhood set.

[0108] When anomaly regions or insufficiently covered regions are detected in the target space, an adaptive update of the weight vector is triggered. By adjusting the direction or density of the weight vector, the search direction can be dynamically adjusted according to changes in the target space structure, thereby improving the adaptability of the optimization method to complex target space structures.

[0109] Specifically, in step S5, a diversity evaluation mechanism based on crowding entropy is introduced to quantitatively evaluate the local density distribution of candidate solutions in the target space.

[0110] Define candidate solution x j The crowding entropy in the target space is:

[0111]

[0112] Where, p j,i This represents the normalized neighborhood density ratio of candidate solutions in the i-th objective dimension. The smaller the crowding entropy value, the more crowded the region where the candidate solution is located; the larger the crowding entropy value, the more uniform the distribution of candidate solutions.

[0113] Then, based on the proportionality coefficient Set a diversity threshold:

[0114]

[0115] Among them, CE th The crowding entropy threshold, This is a parameter used to adjust the trigger sensitivity of the diverse control mechanism. In a specific embodiment, the proportionality coefficient... The value can be set according to the problem size or target dimension, for example, 0.2 to 0.4. In this embodiment, a value of 0.2 is preferred. .

[0116] When the average crowding entropy of the candidate solution population satisfies:

[0117]

[0118] Specifically, in step S6, when the crowding entropy evaluation result is lower than the preset threshold, it indicates that the current candidate solution has local clustering or insufficient coverage in the target space, triggering the control mechanism. By screening, replacing or reconstructing the candidate solution population, candidate solutions from relatively sparsely distributed regions in the target space are introduced under the premise of ensuring the convergence performance of the solution set, so as to restore the uniform coverage of the solution set in the target space and avoid excessive clustering of the solution set.

[0119] The control mechanism works through replacing candidate solutions in crowded regions, preserving candidate solutions in sparse regions, generating new candidate solutions in sparse regions, and reconstructing the candidate solution population.

[0120] Calculate the crowding entropy value of all candidate solutions according to step S5, and sort the candidate solutions according to the crowding entropy from smallest to largest. Candidate solutions with smaller crowding entropy values ​​indicate that the solution set density in their respective regions is higher.

[0121] When a crowded region is detected, select several candidate solutions with the minimum crowding entropy from the crowded region and delete or replace them to reduce the solution set density of the region.

[0122] To further improve coverage in the target space, after identifying sparse regions, a new candidate solution set P is generated using the following method. sparse In the target space, several candidate solutions with the largest crowding entropy values ​​are selected as representative solutions for the sparse region, and new candidate solutions are generated based on these representative solutions. New candidate solutions can be generated using crossover operators, mutation operators, or differential evolution operators. The set of generated new candidate solutions is denoted as:

[0123] P sparse ={x1 new x2 new ,...,x k new}

[0124] in, represents the generated candidate solution, and k represents the number of newly generated candidate solutions.

[0125] The newly generated candidate solution set The solution set is merged with the current candidate solution population, and then filtered based on non-dominance relations and crowding entropy evaluation to form a new candidate solution population. When the number of candidate solutions exceeds the population size, the candidate solution with the smallest crowding entropy value is deleted first, thereby maintaining a uniform distribution of the solution set in the target space.

[0126]

[0127] Among them, P sparse This represents the set of candidate solutions introduced from the sparse region of the target space.

[0128] By using the above-mentioned control methods, the uniform coverage of the solution set in the target space can be restored while maintaining the convergence performance of candidate solutions, avoiding solution set degradation or local clustering during the optimization process, thereby improving the stability and search efficiency of multi-objective optimization algorithms under complex Pareto front conditions.

[0129] Specifically, in step S7, the optimization process terminates when one of the following conditions is met:

[0130]

[0131] Among them, t max Let ε be the maximum number of iterations, and ϵ be the convergence threshold. Repeat the above steps until a preset termination condition is met. When the termination condition is met, the Pareto optimal solution set is output as follows:

[0132]

[0133] Output a set of Pareto optimal solutions that effectively balance multiple performance objectives such as infrared radiation performance, solar absorption suppression capability, and stability, as the optimization design result of radiation cooling materials and structures.

[0134] Finally, to verify the superiority and effectiveness of the multi-objective evolutionary optimization method (IMOA-CE) integrating dynamic correlation and crowding entropy described in this invention in the optimization problem of radiation-cooled materials and structures, comparative experiments were conducted on the IGD results of five algorithms—MOEA / D-UR, MOEA / D-URAW, MOEA / D-VOV, PeEA, and TS-NSGA-II—on a WFG test suite instance. By comparing the performance of the five methods in terms of convergence performance, solution set distribution uniformity, and stability, the ability of this invention to achieve convergence and diversity-based synergistic optimization under complex objective space conditions was evaluated. Secondly, comparative experiments were conducted with the MOEA / D algorithm in the optimization problem of radiation-cooled materials and structures, where MOEA / D employs a fixed-weight vector decomposition and neighborhood update mechanism for multi-objective optimization.

[0135] To ensure fairness in the comparison, IMOA-CE and the comparison algorithm use the same basic settings. Population size: N=150, maximum number of iterations T. max =300, Number of weight vectors K=N, Neighborhood size B=20, Mutation probability η m =30, mutation index P m=1 / D, where D is the number of decision probabilities, and the number of independent runs is 30.

[0136] like Figure 3 As shown, IMOA-CE exhibits a relatively stable convergence trend across all test problems, quickly reaching a low IGD level in the early stages and maintaining good optimization accuracy in the later stages. Experimental results demonstrate that IMOA-CE performs robustly across WFG4–WFG9 tests, consistently achieving superior convergence results. Therefore, it can be concluded that the IMOA-CE strategy is effective for solving the WFG series of multi-objective optimization problems.

[0137] Table 1 shows the IGD results of IMOA-CE and five other algorithms (MOEA / D-UR, MOEA / D-URAW, MOEA / D-VOV, PeEA, and TS-NSGA-II) on nine test cases. The table reveals that IMOA-CE achieves higher PF approximation results on most test problems, specifically WFG2, WFG4–WFG7, and WFG9. Furthermore, in a few instances such as WFG3 and WFG8, the proposed algorithm yields better results, demonstrating that different algorithms retain their advantages under specific problem structures. In terms of average ranking, IMOA-CE has the lowest average ranking of 1.5786 among all algorithms, further validating its overall performance advantage on this set of test problems.

[0138] Table 1

[0139]

[0140] like Figure 4 As shown, in the process of optimizing the design of radiation-cooled materials and structures, the method of this invention can achieve a rapid decrease in the comprehensive radiation-cooling optimization index in the early stage of optimization, indicating that it can more efficiently search for material and structural combinations with excellent radiation-cooling performance. In the later stage of iteration, the optimization process of the method of this invention tends to be stable and converges to a better performance level with small overall fluctuations. In contrast, the convergence speed of the traditional multi-objective optimization algorithm MOEA / D is slower. The above results show that the method of this invention has higher optimization efficiency and better stability in the engineering application scenario of optimizing the design of radiation-cooled materials and structures.

[0141] The foregoing description of the embodiments enables those skilled in the art to make or use the present invention. Various modifications to the embodiments will be readily apparent to those skilled in the art. The general principles of the invention may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention should not be limited to the embodiments shown herein, but should cover the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-objective optimization method for the optimized design of radiation cooling materials and structures, characterized in that, The method includes the following steps: S1: Construct a multi-objective optimization model for radiation cooling materials and structures; S2: Initialize the weight vector set, candidate solution population and ideal point, and perform target evaluation and aggregation evaluation on the candidate solutions; S3: Based on the aggregated evaluation results, a dynamic matching relationship between the weight vector and the candidate solution is established and updated through a dynamic association modeling mechanism, so that each weight vector is associated with only one candidate solution that best matches its search direction in the same iteration process; S4: Adaptively update the weight vector set based on the distribution state of candidate solutions; S5: Define and evaluate the crowding entropy of candidate solutions, and trigger the control mechanism to process the candidate solution population based on the threshold judgment result; S6: Execute the above steps until the preset termination condition is met, and output the optimization results of the radiation cooling material and structure.

2. The multi-objective optimization method for the optimized design of radiation cooling materials and structures according to claim 1, characterized in that, The objective function of the multi-objective optimization model described in S1 is used to characterize the optimization requirements of the radiative cooling system in different performance dimensions, including but not limited to conflicting objective functions such as the average emissivity of the atmospheric window f1(x), the absorptivity of the solar spectrum f2(x), and the overall cost f3(x). The multi-objective optimization problem is expressed as: ； Where x represents the radiation cooling design parameter vector, and the design parameters include, but are not limited to, the type of radiation cooling material, the material type in the multilayer membrane structure, the geometric thickness parameters of each membrane layer, and the structural arrangement.

3. The multi-objective optimization method for the optimized design of radiation cooling materials and structures according to claim 2, characterized in that, The design parameters satisfy the constraints of structural manufacturability and application environment: ； The objective function includes, but is not limited to: maximizing the infrared radiation capability within the atmospheric transparency window band, minimizing the solar absorptivity within the visible and near-infrared bands, improving the stability of radiative cooling performance, and reducing the complexity or cost of structural design. In the atmospheric transparency window band [λ] a min , λ a max Within [the atmosphere], the average emissivity of the atmospheric window is defined as: ； Where ε(λ, x) represents the spectral emissivity of the radiation-cooled structure at wavelength λ; In the solar spectrum band [λ] s min , λ s max Within [the solar spectrum], the absorptivity is defined as: ； Where α(λ, x) is the spectral absorbance, I sol (λ) represents the standard solar spectral irradiance. The comprehensive cost per unit area is defined as: ； Where, d l Let c be the thickness of the l-th layer. l mat For the corresponding material unit thickness cost, C fab (L) represents the manufacturing cost related to the number of film layers and process complexity. After modeling is completed, the candidate solution population, weight vector set, and ideal point are initialized.

4. The multi-objective optimization method for the optimized design of radiation cooling materials and structures according to claim 1, characterized in that, S2 introduces a set of weight vectors, decomposes the multi-objective optimization problem based on these weight vectors, and uses a weighted Chebyshev method to aggregate and evaluate candidate solutions. ； Where w is the set of all subproblems, K is the number of weight vectors, and z ∗ Let f be an ideal point vector. i (x)−z i ∗ | represents the difference between the solution x and the ideal value in the i-th objective. The multi-objective optimization problem is decomposed based on the set of weight vectors, and the original multi-objective problem is transformed into multiple sub-problems. The search is carried out in parallel under the guidance of different weight vectors.

5. The multi-objective optimization method for the optimized design of radiation cooling materials and structures according to claim 1, characterized in that, S3 establishes and updates the dynamic matching relationship between the weight vector and the candidate solution through a dynamic association modeling mechanism, specifically: Define candidate solution x j With weight vector w k Match degree: ； By applying a uniqueness constraint, we find a direction among all directions w that minimizes the matching degree ϕ, ensuring that each candidate solution is associated with only one weight vector in a single iteration. The association rule is expressed as: ； To avoid the same candidate solution being repeatedly associated with multiple weight vectors, when multiple weight vectors correspond to the same candidate solution, the final association relationship is determined according to the principle of minimum matching degree.

6. The multi-objective optimization method for the optimized design of radiation cooling materials and structures according to claim 5, characterized in that, The weight vector update described in S4, based on the dynamic association mechanism, updates the weight vector according to the distribution of candidate solutions in the target space, defining the distribution density function of candidate solutions in the target space: ； Where, N j Indicates candidate solution x j The neighborhood set; if there are density anomaly regions or the association between weight vectors and quantum problems fails in the target space, the adaptive update of the weight vector is triggered. By adjusting the direction or density of the weight vector, the search direction can be dynamically adjusted with the changes in the target space structure, thereby enhancing the adaptability to complex target space structures.

7. The multi-objective optimization method for the optimized design of radiation cooling materials and structures according to claim 1, characterized in that, S5 quantifies and evaluates the local density distribution of candidate solutions in the target space, defining candidate solutions x. j The crowding entropy in the target space is: ； Where, p j,i It represents the normalized neighborhood density ratio of the candidate solution in the i-th objective dimension. The smaller the crowding entropy value, the more crowded the region where the candidate solution is located; the larger the crowding entropy value, the more uniform the distribution of the candidate solution.

8. The multi-objective optimization method for the optimized design of radiation cooling materials and structures according to claim 7, characterized in that, When the crowding entropy assessment result is lower than a preset threshold, a control mechanism is triggered. By reconstructing the candidate solution population, candidate solutions from relatively sparsely distributed regions in the target space are introduced while ensuring the convergence performance of the solution set. This restores the uniform coverage of the solution set in the target space and avoids excessive clustering of solutions. The preset threshold is based on adjustment parameters. set up: ； Among them, CE th The crowding entropy threshold, The parameters are adjusted to control the trigger sensitivity of the diverse regulatory mechanisms; The control mechanism is as follows: ； Among them, P sparse This represents the set of candidate solutions introduced from the sparse region of the target space.

9. The multi-objective optimization method for the optimized design of radiation cooling materials and structures according to claim 1, characterized in that, The specific steps for S6 are as follows: The optimization process terminates when one of the following conditions is met: ； Among them, t max Let ϵ be the maximum number of iterations and ε be the convergence threshold. Repeat the above steps until a preset termination condition is met. When the termination condition is met, the Pareto optimal solution set is output as follows: ； Output a set of Pareto optimal solutions that effectively balance multiple performance objectives such as infrared radiation performance, solar absorption suppression capability, and stability, as the optimization design result of radiation cooling materials and structures.

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