Vector evaluation gradient multi-objective optimization algorithm for data center cooling system decision

Abstract

The invention discloses a vector evaluation gradient multi-objective optimization algorithm for data center cooling system decision making. The overall thought comprises the steps that multi-source sensor data related to a cooling system is obtained according to data center machine room operation logic; performing corresponding preprocessing on data acquired by the sensor to obtain an overall sample; designing a vector evaluation gradient multi-objective optimization algorithm oriented to a data center cooling system decision; the optimization algorithm comprises the definition of a multi-objective optimization problem, uniformly distributed initial populations, population division based on vector evaluation and gradient updating. The optimal decision of the air supply amount and the air supply temperature of the cooling equipment in the cooling system is mainly obtained through an optimization algorithm, and optimal decision parameters are sent to the cooling equipment so as to achieve optimal control over the cooling equipment of the data center. The algorithm provided by the invention ensures that the decision strategy of the cooling equipment can be reasonably and quickly given, so that the appropriate temperature of the machine room and the energy conservation of the cooling equipment are simultaneously realized to meet the requirement of efficient operation of the data center. The energy consumption of the data center can be reduced, and the method is of great significance in promoting green and sustainable development of the data center.

Description

Technical Field

[0001] This invention relates to the fields of artificial intelligence technology and energy consumption optimization, specifically to a vector evaluation gradient multi-objective optimization algorithm for decision-making in data center cooling systems. Background Technology

[0002] With the development of the digital economy, the scale and number of data centers have surged, leading to a continuous increase in their energy consumption. Cooling equipment in cooling systems accounts for 30%-50% of energy consumption, becoming the main energy-consuming component. Traditional extensive cooling control strategies result in significant energy waste. How to achieve efficient energy saving in cooling equipment while ensuring a stable data center environment is a key challenge for the sustainable development of data centers. In real-time decision-making for data center cooling equipment, algorithm computation efficiency is crucial. On the one hand, the data center operating environment is dynamically changing, with frequent fluctuations in factors such as server load, requiring algorithms to respond quickly and adjust operating parameters in real time. On the other hand, the decision-making problem involves multiple parameters and objectives, such as air supply temperature and air volume. Traditional single-objective algorithms are insufficient to meet these requirements, while multi-objective optimization algorithms often suffer from computational complexity and slow convergence. If the algorithm's decision-making time is too long, it will lead to decision lag, not only failing to achieve energy savings but also potentially causing localized overheating in the data center, threatening server stability, and causing economic losses and business interruptions.

[0003] Currently, various multi-objective optimization algorithms exist. Multi-objective differential evolution algorithms achieve optimization through differential mutation, crossover, and selection operations, but their convergence speed and global search capability significantly decrease in high-dimensional spaces. Multi-objective firefly algorithms optimize based on the bioluminescence attraction characteristics of fireflies, with inter-individual information interaction depending on distance and brightness. In high-dimensional and complex cooling equipment decision-making problems, information transmission efficiency is low, and they are prone to getting trapped in local optima. Multi-objective jellyfish search algorithms simulate the swimming and foraging behavior of jellyfish for optimization, requiring numerous individual iterations and complex fitness calculations when dealing with large-scale data center cooling equipment decision-making problems. Multi-objective artificial hummingbird optimization algorithms simulate the foraging process of hummingbirds, requiring frequent updates to position and search strategies during optimization, resulting in high computational overhead. Multi-objective exponential distribution optimization algorithms search based on exponential distribution probability models, with cumbersome probability distribution adjustments and calculations. Based on the above analysis, existing multi-objective optimization algorithms all suffer from insufficient computational efficiency in real-time decision-making for data center cooling equipment, failing to quickly and accurately balance multiple objectives such as suitable room temperature and energy-saving cooling equipment. Therefore, there is an urgent need for a multi-objective optimization algorithm that can overcome the bottleneck of computational efficiency and achieve fast and accurate decision-making to meet the needs of efficient operation of data center cooling equipment systems. Summary of the Invention

[0004] 1. The technical problem to be solved:

[0005] To address the aforementioned technical problems, this invention provides a vector evaluation gradient multi-objective optimization algorithm for data center cooling system decision-making.

[0006] 2. Technical Solution:

[0007] A vector evaluation gradient multi-objective optimization algorithm for decision-making in data center cooling systems, characterized by the following steps:

[0008] Step 1: Obtain historical data affecting data center cooling equipment; after preprocessing the historical data, obtain an overall sample; the relevant data for the data center includes cabinet power consumption, return air temperature, air volume, air supply temperature, total power of internal fans, total power of external fans, total power of compressors, and total power of air conditioners;

[0009] Step 2: Design a vector evaluation gradient multi-objective optimization algorithm for data center cooling system decision-making. This algorithm includes defining the multi-objective optimization problem, a uniformly distributed initial population, population partitioning based on vector evaluation, and gradient updates. The multi-objective optimization problem definition involves constructing objective functions for temperature suitability and energy saving of cooling equipment, as well as constraints on decision parameters. The uniformly distributed initial population uses Sobol sequences to generate more evenly distributed sample points in space, providing a better search starting point for subsequent optimization processes. The population partitioning and gradient updates based on vector evaluation involve performing non-dominated sorting and crowding distance calculations to divide the population into subpopulations, each focusing on optimizing one objective and performing gradient updates.

[0010] Step 3: The optimal decision strategy obtained by the optimization algorithm is sent to the cooling equipment to achieve dynamic optimization and control of the cooling equipment's operating status.

[0011] Further, in step one, relevant data is obtained based on the operating logic between the IT equipment and cooling system in the data center, and preprocessing operations such as cleaning and normalization are performed on the raw data to remove outliers and noise interference, ultimately forming a sample dataset.

[0012] Furthermore, the multi-objective optimization problem defined in step two provides a clear objective and feasible solution space for the subsequent optimization algorithm by accurately constructing the objective functions for suitable temperature and energy saving of cooling equipment, and setting constraints on decision parameters. This enables the algorithm to achieve efficient and energy-saving operation of the cooling system while meeting the actual needs of the data center. Specifically, it includes the following steps:

[0013] S21: Based on the data center's operational logic, the decision parameters include air volume V and air temperature T. sThese parameters directly affect the performance and energy consumption of the cooling system. Taking the decision parameters x = [x1, x2] as the optimization object, F(x) is a multi-objective function constructed from the decision parameters. Considering the actual situation of the computer room, corresponding constraints are established to ensure that the decision parameters take values ​​within the feasible range Ω, thereby guaranteeing the stable operation of the cooling system. The specific formula is as follows:

[0014]

[0015] Where x1 represents V and x2 represents T s f1(x) represents the objective function for achieving a suitable temperature, and f2(x) represents the objective function for energy saving of the cooling equipment. This represents the minimum constraint value for each decision parameter. This represents the maximum constraint value for each decision parameter;

[0016] S22: Through theoretical analysis, a mathematical model is established between cooling capacity and heat dissipation to accurately describe their relationship, and the cooling capacity Q of the cooling equipment at different times t is calculated. C,t and the heat dissipation Q of IT equipment IT,t The objective function f1 is established, and the specific formula is as follows:

[0017]

[0018] Q C =C P ρV(T r -T s (3)

[0019]

[0020] Where ω is a coefficient, C P Let T be the heat capacity of air, ρ be the density of air, and T be the temperature. r T represents the return air temperature. safe For safe temperature;

[0021] S23: The energy consumption of the cooling equipment is determined by the total power P of the internal fan. fan Total power of external fan P efan and the total power P of the compressor com To achieve the energy-saving goals of the data center, a target function f2 needs to be established that comprehensively considers the total power of the internal fans, the total power of the external fans, and the total power of the compressor. The optimization objective of this target function is to minimize the total energy consumption of the cooling system while meeting the cooling needs of the computer room. The specific formula is as follows:

[0022]

[0023] P com =g(T)s (6)

[0024]

[0025] Among them, P ifan For rated input power, V ifan Where is the rated air volume, and g is a nonlinear function of the total compressor power and the air supply temperature;

[0026] Furthermore, the uniformly distributed initial population mentioned in step two is generated using Sobol sequences to create more uniform sample points in space. Sobol sequences are deterministic sequences with low dissimilarity, their core strength being their ability to distribute sample points uniformly in a multidimensional space with extremely high efficiency. Generated through carefully designed mathematical formulas, Sobol sequences ensure uniform coverage of samples within the search space even with a limited number of samples, avoiding sample clustering or sparse regions. Specifically, the steps include:

[0027] S24: Traditional methods of randomly generating the initial population can easily lead to uneven distribution of individuals in the search space. When optimizing the airflow and temperature of data center cooling equipment, the initial population generated by the Sobol sequence can quickly cover parameter combinations under different operating conditions, avoiding the omission of some important areas due to random sampling. The specific formula is as follows:

[0028]

[0029] Among them, s ij ∈[0,1] represents the j-th dimension component of the i-th sample in the Sobol sequence;

[0030] Furthermore, in step two, the population partitioning and gradient update design for vector evaluation involves, in each iteration, first performing non-dominated sorting and crowding distance calculation on the current population, then dividing it into sub-populations, performing gradient updates on each sub-population according to the corresponding objective, and finally merging the sub-populations and performing a selection operation to gradually optimize the individuals in the population, enabling them to achieve better performance while satisfying the two objectives of suitable data center temperature and energy-saving cooling equipment. Specifically, this includes the following steps:

[0031] S25: First, perform a non-dominated ranking on the current population, dividing the individuals in the population into different non-dominated fronts. For individual x... p ,x q Satisfy all objective functions j=1,2,f j (x p )≤f j (x q There exists at least one objective function k such that f k (x p )<f k(x q If x p Dominate x q Then, crowding distance is calculated to measure the distribution of individuals in the target space, maintaining population diversity. The specific formula is as follows:

[0032]

[0033] Among them, CD j For crowded distance, f i max ,f i min For all individuals in the non-dominated frontier, these are the maximum and minimum values ​​of the objective function;

[0034] S26: Introduce a population partitioning method to evaluate the gradient direction using vectors. Divide the population into M subpopulations based on the number of objectives. Each subpopulation focuses on optimizing a single objective. A round-robin index allocation is used to avoid interference between multiple objective functions, allowing each objective function to be optimized more effectively. The optimal individual x in the subpopulation is selected based on the current objective function value. * The specific formula is as follows:

[0035] subpop j ={x k |k≡j mod M,j=0,1} (10)

[0036] Among them, subpop j For the offspring population;

[0037] S27: By optimizing individual x * Perform small positive and negative perturbations, calculate the values ​​of the objective function before and after the perturbations, and then calculate the gradient ▽f based on the central difference. j (x * These gradients are used for gradient descent to update individual characteristics, thereby optimizing the objective function. Then, the best individuals from the subpopulation are selected and merged to form a new population P. * At the same time, ensure that the updated decision parameters satisfy the boundary constraints, as shown in the following formula:

[0038]

[0039] x new =x * -α▽f j (x * (12)

[0040]

[0041] Where ò=1e-6 is the perturbation step size, e iLet x be a unit vector, α be the learning rate, and x be a unit vector. new For the updated individual, x i,new The updated decision parameters are within the feasible region.

[0042] 3. Beneficial effects:

[0043] The vector evaluation gradient multi-objective optimization algorithm for data center cooling system decision-making disclosed in this paper has significant beneficial effects. This optimization algorithm comprehensively considers multiple objectives, employs a population-based optimization strategy, and fully utilizes gradient information. It not only possesses excellent global search capabilities but also effectively maintains population diversity. In the initialization phase, an initial population is generated using a Sobol sequence to ensure uniform distribution of individuals in the solution space, improving the quality of the initial population. During the iteration process, non-dominated sorting and crowding distance calculation continuously maintain population diversity, enabling the algorithm to explore a broader solution space and significantly increasing the probability of obtaining the global optimum. Simultaneously, the algorithm divides the population into multiple subpopulations, each focusing on independently optimizing a single objective. Through gradient updates, it accurately approximates the optimal solution, effectively improving computational efficiency. This algorithm successfully finds a better combination of airflow and air temperature, enabling the cooling system to reduce energy consumption while fully meeting the requirements of the data center environment. Practical application has proven that this algorithm can significantly reduce the energy consumption of the cooling system, enhance the stability of the data center environment, and provide a practical and effective solution for the efficient operation and energy-saving goals of data centers. Attached Figure Description

[0044] Figure 1 This is the overall flowchart of this method;

[0045] Figure 2 A comparison diagram of the Pareto fronts of this invention and other optimization algorithms is provided to verify its validity.

[0046] Figure 3 A comparison chart showing the computation time of this invention and other optimization algorithms is provided to verify its effectiveness. Detailed Implementation

[0047] The present invention will now be described in detail with reference to the accompanying drawings.

[0048] As attached Figure 1 As shown, a vector evaluation gradient multi-objective optimization algorithm for data center cooling system decision-making is characterized by the following steps:

[0049] Step 1: Obtain historical data affecting data center cooling equipment; after preprocessing the historical data, obtain an overall sample; the relevant data for the data center includes cabinet power consumption, return air temperature, air volume, air supply temperature, total power of internal fans, total power of external fans, total power of compressors, and total power of air conditioners;

[0050] Step 2: Design a vector evaluation gradient multi-objective optimization algorithm for data center cooling system decision-making. This algorithm includes defining the multi-objective optimization problem, a uniformly distributed initial population, population partitioning based on vector evaluation, and gradient updates. The multi-objective optimization problem definition involves constructing objective functions for temperature suitability and energy saving of cooling equipment, as well as constraints on decision parameters. The uniformly distributed initial population uses Sobol sequences to generate more evenly distributed sample points in space, providing a better search starting point for subsequent optimization processes. The population partitioning and gradient updates based on vector evaluation involve performing non-dominated sorting and crowding distance calculations to divide the population into subpopulations, each focusing on optimizing one objective and performing gradient updates.

[0051] Step 3: The optimal decision strategy obtained by the optimization algorithm is sent to the cooling equipment to achieve dynamic optimization and control of the cooling equipment's operating status.

[0052] Further, in step one, relevant data is obtained based on the operating logic between the IT equipment and cooling system in the data center, and preprocessing operations such as cleaning and normalization are performed on the raw data to remove outliers and noise interference, ultimately forming a sample dataset.

[0053] Furthermore, the multi-objective optimization problem defined in step two provides a clear objective and feasible solution space for the subsequent optimization algorithm by accurately constructing the objective functions for suitable temperature and energy saving of cooling equipment, and setting constraints on decision parameters. This enables the algorithm to achieve efficient and energy-saving operation of the cooling system while meeting the actual needs of the data center. Specifically, it includes the following steps:

[0054] S21: Based on the data center's operational logic, the decision parameters include air volume V and air temperature T. s These parameters directly affect the performance and energy consumption of the cooling system. Taking the decision parameters x = [x1, x2] as the optimization object, F(x) is a multi-objective function constructed from the decision parameters. Considering the actual situation of the computer room, corresponding constraints are established to ensure that the decision parameters take values ​​within the feasible range Ω, thereby guaranteeing the stable operation of the cooling system. The specific formula is as follows:

[0055]

[0056] Where x1 represents V and x2 represents T s f1(x) represents the objective function for achieving a suitable temperature, and f2(x) represents the objective function for energy saving of the cooling equipment. This represents the minimum constraint value for each decision parameter. This represents the maximum constraint value for each decision parameter;

[0057] S22: Through theoretical analysis, a mathematical model is established between cooling capacity and heat dissipation to accurately describe their relationship, and the cooling capacity Q of the cooling equipment at different times t is calculated. C,t and the heat dissipation Q of IT equipment IT,t The objective function f1 is established, and the specific formula is as follows:

[0058]

[0059] Q C =C P ρV(T r -T s (3)

[0060]

[0061] Where ω is a coefficient, C P Let T be the heat capacity of air, ρ be the density of air, and T be the temperature. r T represents the return air temperature. safe For safe temperature;

[0062] S23: The energy consumption of the cooling equipment is determined by the total power P of the internal fan. fan Total power of external fan P efan and the total power P of the compressor com To achieve the energy-saving goals of the data center, a target function f2 needs to be established that comprehensively considers the total power of the internal fans, the total power of the external fans, and the total power of the compressor. The optimization objective of this target function is to minimize the total energy consumption of the cooling system while meeting the cooling needs of the computer room. The specific formula is as follows:

[0063]

[0064] P com =g(T) s (6)

[0065]

[0066] Among them, P ifan For rated input power, V ifan Where is the rated air volume, and g is a nonlinear function of the total compressor power and the air supply temperature;

[0067] Furthermore, the uniformly distributed initial population mentioned in step two is generated using Sobol sequences to create more uniform sample points in space. Sobol sequences are deterministic sequences with low dissimilarity, their core strength being their ability to distribute sample points uniformly in a multidimensional space with extremely high efficiency. Generated through carefully designed mathematical formulas, Sobol sequences ensure uniform coverage of samples within the search space even with a limited number of samples, avoiding sample clustering or sparse regions. Specifically, the steps include:

[0068] S24: Traditional methods of randomly generating the initial population can easily lead to uneven distribution of individuals in the search space. When optimizing the airflow and temperature of data center cooling equipment, the initial population generated by the Sobol sequence can quickly cover parameter combinations under different operating conditions, avoiding the omission of some important areas due to random sampling. The specific formula is as follows:

[0069]

[0070] Among them, s ij ∈[0,1] represents the j-th dimension component of the i-th sample in the Sobol sequence;

[0071] Furthermore, in step two, the population partitioning and gradient update design for vector evaluation involves, in each iteration, first performing non-dominated sorting and crowding distance calculation on the current population, then dividing it into sub-populations, performing gradient updates on each sub-population according to the corresponding objective, and finally merging the sub-populations and performing a selection operation to gradually optimize the individuals in the population, enabling them to achieve better performance while satisfying the two objectives of suitable data center temperature and energy-saving cooling equipment. Specifically, this includes the following steps:

[0072] S25: First, perform a non-dominated ranking on the current population, dividing the individuals in the population into different non-dominated fronts. For individual x... p ,x q Satisfy all objective functions j=1,2,f j (x p )≤f j (x q There exists at least one objective function k such that f k (x p )<f k (x q If x p Dominate x q Then, crowding distance is calculated to measure the distribution of individuals in the target space, maintaining population diversity. The specific formula is as follows:

[0073]

[0074] Among them, CD jFor crowded distance, f i max ,f i min For all individuals in the non-dominated frontier, these are the maximum and minimum values ​​of the objective function;

[0075] S26: Introduce a population partitioning method to evaluate the gradient direction using vectors. Divide the population into M subpopulations based on the number of objectives. Each subpopulation focuses on optimizing a single objective. A round-robin index allocation is used to avoid interference between multiple objective functions, allowing each objective function to be optimized more effectively. The optimal individual x in the subpopulation is selected based on the current objective function value. * The specific formula is as follows:

[0076] subpop j ={x k |k≡j mod M,j=0,1} (10)

[0077] Among them, subpop j For the offspring population;

[0078] S27: By optimizing individual x * Perform small positive and negative perturbations, calculate the values ​​of the objective function before and after the perturbations, and then calculate the gradient ▽f based on the central difference. j (x * These gradients are used for gradient descent to update individual characteristics, thereby optimizing the objective function. Then, the best individuals from the subpopulation are selected and merged to form a new population P. * At the same time, ensure that the updated decision parameters satisfy the boundary constraints, as shown in the following formula:

[0079]

[0080] x new =x * -α▽f j (x * (12)

[0081]

[0082] Where ò=1e-6 is the perturbation step size, e i Let x be a unit vector, α be the learning rate, and x be a unit vector. new For the updated individual, x i,new The updated decision parameters are within the feasible region.

[0083] Verification example:

[0084] This verification example uses a dataset of cooling equipment in a data center to optimize the decision parameters of the cooling equipment using a vector evaluation gradient multi-objective optimization algorithm for data center cooling system decision-making proposed in this application. Figure 2 Figure 3 shows a comparison of Pareto fronts and computation times for different optimization algorithms on this dataset. By comparing the computation times of different optimization algorithms with different initial population sizes, the advantages of this invention in computational efficiency compared to other optimization algorithms can be more intuitively demonstrated.

Claims

1. A vector evaluation gradient multi-objective optimization algorithm for decision-making in data center cooling systems, characterized in that, Includes the following steps: Step 1: Obtain historical data affecting data center cooling equipment; after preprocessing the historical data, obtain an overall sample; the relevant data for the data center includes cabinet power consumption, return air temperature, air volume, air supply temperature, total power of internal fans, total power of external fans, total power of compressors, and total power of air conditioners; Step 2: Design a vector evaluation gradient multi-objective optimization algorithm for data center cooling system decision-making. This algorithm includes defining the multi-objective optimization problem, a uniformly distributed initial population, population partitioning based on vector evaluation, and gradient updates. The multi-objective optimization problem definition involves constructing objective functions for temperature suitability and energy saving of cooling equipment, as well as constraints on decision parameters. The uniformly distributed initial population is generated using Sobol sequences to create more evenly distributed sample points in space. The vector evaluation population partitioning and gradient updates involve performing non-dominated sorting and crowding distance calculations to divide the population into sub-populations, each focusing on optimizing one objective and performing gradient updates. Step 3: The optimal decision strategy obtained by the optimization algorithm is sent to the cooling equipment for optimized control.

2. The vector evaluation gradient multi-objective optimization algorithm for data center cooling system decision-making according to claim 1, characterized in that, In step one, relevant data is obtained based on the operating logic between the IT equipment and cooling system in the data center. The relevant data is preprocessed, including: removing historical abnormal data, filling in missing values, and data normalization.

3. The vector evaluation gradient multi-objective optimization algorithm for data center cooling system decision-making according to claim 2, characterized in that, In step two, the multi-objective optimization problem is defined by accurately constructing the objective functions for achieving suitable temperature and energy saving of cooling equipment, as well as setting constraints on decision parameters. This provides a clear objective and a feasible solution space for the subsequent optimization algorithm, enabling the algorithm to achieve efficient and energy-saving operation of the cooling system while meeting the actual needs of the data center. Specifically, it includes the following steps: S21: Based on the data center's operational logic, the decision parameters include air volume V and air temperature T. s These parameters directly affect the performance and energy consumption of the cooling system. Taking the decision parameters x = [x1, x2] as the optimization object, F(x) is a multi-objective function constructed from the decision parameters. Considering the actual situation of the computer room, corresponding constraints are established to ensure that the decision parameters take values ​​within the feasible range Ω, thus guaranteeing the stable operation of the cooling system. Specifically, as follows: Where x1 represents V and x2 represents T s f1(x) represents the objective function for achieving a suitable temperature, and f2(x) represents the objective function for energy saving of the cooling equipment. This represents the minimum constraint value for each decision parameter. This represents the maximum constraint value for each decision parameter; S22: Through theoretical analysis, a mathematical model is established between cooling capacity and heat dissipation to accurately describe their relationship, and the cooling capacity Q of the cooling equipment at different times t is calculated. C,t and the heat dissipation Q of IT equipment IT,t The objective function f1 is established as follows: Q C =C P ρV(T r -T s ) (3) Where ω is a coefficient, C P Let T be the heat capacity of air, ρ be the density of air, and T be the temperature. r T represents the return air temperature. safe For safe temperature; S23: The energy consumption of the cooling equipment is determined by the total power P of the internal fan. fan Total power of external fan P efan and the total power P of the compressor com To achieve the energy-saving goals of the data center, a comprehensive objective function f2 needs to be established, taking into account the total power of the internal fans, the total power of the external fans, and the total power of the compressor. The optimization objective of this objective function is to minimize the total energy consumption of the cooling equipment system while meeting the cooling needs of the computer room, as detailed below: P com =g(T s ) (6) Among them, P ifan For rated input power, V ifan denoted as the rated air volume, and g is a nonlinear function of the compressor's total power and air supply temperature.

4. The vector evaluation gradient multi-objective optimization algorithm for data center cooling system decision-making according to claim 3, characterized in that, In step two, the uniformly distributed initial population is generated using Sobol sequences to create more evenly distributed sample points in space. Sobol sequences are deterministic sequences with low dissimilarity, their core strength being their ability to distribute sample points evenly in a multidimensional space with extremely high efficiency. Generated through carefully designed mathematical formulas, Sobol sequences ensure uniform coverage of samples within the search space with a limited number of samples, avoiding sample clustering or sparse regions. Specifically, the steps include: S24: Traditional methods of randomly generating the initial population can easily lead to uneven distribution of individuals in the search space. When optimizing the airflow and temperature of data center cooling equipment, the initial population generated by the Sobol sequence can quickly cover parameter combinations under different operating conditions, avoiding the omission of some important areas due to random sampling, as detailed below: Among them, s ij ∈[0,1] represents the j-th dimension component of the i-th sample in the Sobol sequence.

5. The vector evaluation gradient multi-objective optimization algorithm for data center cooling system decision-making according to claim 4, characterized in that, In step two, the population partitioning and gradient update design for vector evaluation involves, in each iteration, first performing non-dominated sorting and crowding distance calculation on the current population, then dividing it into sub-populations, performing gradient updates on each sub-population according to the corresponding objective, and finally merging the sub-populations and performing a selection operation to gradually optimize the individuals in the population, enabling them to achieve better performance while meeting the two objectives of suitable data center temperature and energy-saving cooling equipment. Specifically, this includes the following steps: S25: First, perform a non-dominated ranking on the current population, dividing the individuals in the population into different non-dominated fronts. For individual x... p ,x q Satisfy all objective functions j=1,2,f j (x p )≤f j (x q There exists at least one objective function k such that f k (x p )<f k (x q If x p Dominate x q Then, crowding distance is calculated to measure the distribution of individuals in the target space, maintaining population diversity, as follows: Among them, CD j For crowded distance, f i max ,f i min For all individuals in the non-dominated frontier, these are the maximum and minimum values ​​of the objective function; S26: Introduce a population partitioning method to evaluate the gradient direction using vectors. Divide the population into M subpopulations based on the number of objectives. Each subpopulation focuses on optimizing a single objective. A round-robin index allocation is used to avoid interference between multiple objective functions, allowing each objective function to be optimized more effectively. The optimal individual x in the subpopulation is selected based on the current objective function value. * , as follows: subpop j ={x k ∣k≡j mod M,j=0,1} (10) Among them, subpop j For the offspring population; S27: By optimizing individual x * Perform small positive and negative perturbations, calculate the objective function before and after the perturbations, and then calculate the gradient based on the central difference. These gradients are used in gradient descent to update individual characteristics, thereby optimizing the objective function. Then, the best individuals from the subpopulation are selected and merged to form a new population P. * At the same time, ensure that the updated decision parameters satisfy the boundary constraints, as follows: Where ò=1e-6 is the perturbation step size, e i Let x be a unit vector, α be the learning rate, and x be a unit vector. new For the updated individual, x i,new The updated decision parameters are within the feasible region.

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