Load rate optimization method for improving differential evolution coupling step-by-step screening and rational function

Abstract

The invention discloses an improved differential evolution coupling step-by-step screening and rational function load rate optimization method, which comprises an offline preparation stage and an online optimization stage, the offline preparation stage comprises the following steps: pre-generating a rated capability sorting table of equipment combinations, dividing capability demand ranges of different load rate intervals, establishing an equipment load rate energy efficiency relation model, defining a cost function and a target function, and numbering and sorting all possible equipment operation combinations from small to large according to the total rated capability of the combinations. A combination capability interval corresponding to the load rate is listed for each sorted combination according to a plurality of percentage intervals, and the online optimization stage comprises an equipment combination pre-screening stage and a load rate optimization stage. In the equipment combination pre-screening stage, starting and stopping equipment is dynamically selected according to the ratio of the sum of the capabilities of all the equipment in the current combination to the current total demand of the system. The method solves the technical problems of low optimization efficiency, poor solution quality and the like in the prior art.

Description

Technical Field

[0001] This invention relates to the field of load rate optimization technology for complex engineering systems, and in particular to an improved load rate optimization method using differential evolution coupled stepwise screening and rational functions. Background Technology

[0002] In complex engineering fields such as energy systems, communication networks, and industrial manufacturing, how to rationally allocate the load rate of each component according to dynamically changing total demand has always been a key issue in improving system operating efficiency and stability. As the scale of modern engineering systems continues to expand, traditional optimization methods are gradually revealing insurmountable limitations. Taking a large central air conditioning system as an example, when facing the coordinated control task of dozens of chiller units, conventional mixed-integer programming or heuristic algorithms need to simultaneously handle the joint optimization problem of equipment start-up and shutdown states and load rate allocation. The search space dimension grows exponentially with the number of devices, leading to a sharp increase in computational complexity.

[0003] A deeper challenge stems from the unique mathematical characteristics of the objective function. In typical scenarios such as refrigeration systems and communication base stations, core indicators like total system energy consumption and channel capacity are often expressed as rational functions. For example, total energy consumption can be modeled as the sum of the ratios of the load rate of each device to its energy efficiency function. These functions exhibit numerical sensitivity, with the denominator approaching zero, in low-load regions (e.g., when chillers operate below 20% load and energy efficiency drops sharply). This not only causes computational divergence in traditional gradient descent and particle swarm optimization algorithms but also leads the optimization process into invalid solution regions. The coordinated handling of multiple types of constraints also constitutes a technical challenge. Practical engineering optimization requires simultaneously satisfying equality constraints (e.g., strict matching of total load demand), inequality constraints (e.g., equipment safety operation thresholds), and physical limits (e.g., minimum start-up and shutdown intervals for units). Fixed penalty coefficients cannot adapt to the search requirements at different stages of the optimization process. In the early stages, insufficient penalty may result in a large number of invalid solutions, while in the later stages, excessive penalty may obscure the true target trend. At the same time, existing methods fail to fully consider the priority difference between equality constraints and flexible constraints, resulting in wasted algorithm resources on satisfying secondary constraints and significantly reducing search efficiency.

[0004] Although some existing algorithms, such as genetic algorithms, particle swarm optimization, and differential evolution algorithms, can achieve load rate optimization calculations, they suffer from low optimization efficiency and the final solution being a non-optimal solution or containing invalid solutions due to the aforementioned challenges. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the existing technologies. It provides an improved load factor optimization method using differential evolution coupled stepwise screening and rational functions. This method addresses core issues faced by load factor optimization in complex engineering systems, such as the curse of dimensionality caused by the high-dimensional combinatorial search space, numerical instability due to the denominator approaching zero in rational functions, and the complexity of co-processing multiple types of constraints. These issues lead to low optimization efficiency and poor solution quality in existing technologies when handling highly nonlinear and nonconvex optimization scenarios where the objective function is the sum of multiple rational functions. The technical solution of this invention's improved load factor optimization method using differential evolution coupled stepwise screening and rational functions includes: The optimization is carried out in stages, including an offline preparation stage and an online optimization stage. The offline preparation stage involves pre-generating a rated capacity ranking table of equipment combinations, dividing the capacity demand range into different load rate intervals, establishing an equipment load rate-energy efficiency relationship model, and defining cost functions and objective functions to provide a pre-calculated data foundation and mathematical framework for subsequent stages. This includes the following steps: Combine all possible device operations by group Total capacity Sort by number from smallest to largest. List the load rate for each sorted combination in multiple percentage ranges. The corresponding range of combinatorial capabilities, The online optimization phase includes a device combination pre-screening phase and a load rate optimization phase. The device combination pre-screening stage is based on the current combination. The ratio of the total capacity of all equipment to the current total demand of the system. Dynamically select which devices to start or stop.

[0006] In the load rate optimization stage, the start-stop equipment combination selected in the equipment combination pre-screening stage is used as the system total cost formula. The system total cost formula is used as the objective function to apply the improved differential evolution algorithm for optimization, including population initialization, gradient sensitivity mutation strategy, and numerator and denominator hierarchical mutation strategy. Beneficial effects

[0007] This invention improves the differential evolution coupled step-by-step screening and rational function load rate optimization method. Compared with the prior art, its beneficial effects are as follows: The method achieves a breakthrough through a phased optimization strategy: First, a combined pre-screening mechanism is introduced in the first stage, which greatly reduces the complexity of the objective function; then, in order to address the convergence problem in rational function optimization, the differential evolution algorithm is improved in a targeted manner, including initialization correction, adaptive penalty term, gradient sensitivity mutation strategy, numerator and denominator hierarchical mutation strategy, and stability verification and other core improvements. This phased optimization architecture achieves high optimization efficiency and good solution quality. While ensuring computational accuracy, it significantly improves the solution speed and reduces the risk of getting trapped in local optima. It is effectively applicable to the high-efficiency optimization needs of complex engineering scenarios such as power system planning, communication network planning, refrigeration system planning, and industrial manufacturing planning. It is especially suitable for complex engineering scenarios where the objective function has significant rational function characteristics, such as energy efficiency optimization of refrigeration systems and energy consumption management of communication base stations. Attached Figure Description

[0008] Figure 1 The flowchart shows the overall process of the improved differential evolution coupled stepwise screening and rational function load rate optimization method of this invention. Figure 2 This is a flowchart of sub-stage B2, the load rate optimization stage, of the improved differential evolution coupled step-by-step screening and rational function load rate optimization method of this invention. Detailed Implementation

[0009] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are described clearly and completely. Obviously, the described embodiments are only some embodiments of the present invention, 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.

[0010] This invention improves the load rate optimization method of differential evolution coupled with stepwise screening and rational functions, implementing load rate optimization in a two-stage manner: an offline preparation stage and an online optimization stage. The steps include: I. Offline Preparation Stage Its offline preparation phase provides a pre-calculated data foundation and mathematical framework for subsequent phases by pre-generating a rated capacity ranking table for equipment combinations, dividing the capacity demand range for different load rate intervals, establishing an equipment load rate-energy efficiency relationship model, and defining cost and objective functions. The specific steps include: 1. Combine all possible equipment operation methods into groups. Total capacity Sort by number from smallest to largest. Total capacity. :

[0011] In the formula, Indicates device Rated supply capacity Representative group The sum of capabilities.

[0012] 2. For each sorted combination, list the combined capacity ranges corresponding to load rates of 75% to 90%, 65% to 90%, 55% to 90%, and 45% to 90%. (Equipment) Load rate:

[0013] In the formula, Indicates device Rated supply capacity Representative of the equipment Real-time load.

[0014] 3. Load of a single device and cost To calculate performance :

[0015] In the formula, Representative equipment The cost, Representative equipment The load.

[0016] 4. Fit the relationship between the load rate and performance of a single piece of equipment: .

[0017] 5. Computing equipment Load distribution rate The relationship with load rate

[0018]

[0019] in Indicates the total combined load. Indicates the equipment in the combination load so:

[0020] Replacement device From the relationship between load factor and energy efficiency, we can obtain the relationship between load distribution percentage and energy efficiency: .

[0021] 6. Calculate the first... The cost of the equipment makes : .

[0022] 7. Calculate the total system cost and construct the objective function:

[0023]

[0024] In the formula, the optimization variable is .

[0025] II. Online Optimization Phase The online optimization phase includes a device combination pre-screening phase and a load rate optimization phase: I) Equipment Combination Pre-screening Stage The equipment combination pre-screening stage includes: First, define the resource supply-demand ratio:

[0026]

[0027] In the formula, This represents the current total demand of the system (a dynamic variable that changes over time). Indicates equipment Rated supply capacity Representative group The sum of the capabilities of all the equipment.

[0028] Based on the current combination The ratio of the total capacity of all equipment to the current total demand of the system. Dynamically selectable equipment (or units) to start or stop, specifically including: 1. High-load operating conditions: If RDR consistently exceeds 90% for more than T1 (e.g., 2 hours), prioritize options with larger total capacity and a load factor between 75% and 90%. Resource combination; if no solution is found, expand the search range sequentially to 65%~90%, then 55%~90%; 2. Low load condition: If RDR consistently exceeds 90% for more than T2 (e.g., 2 hours), prioritize options with smaller total capacity and a load factor between 75% and 90%. Combine resources and expand the search range according to the same rules.

[0029] 3. Steady-state operating conditions: Except for high-load and low-load operating conditions, and with RDR fluctuations within ±5%, the current combination is maintained. The final output of the above process, the combination of start-stop devices, will be used as input for the load rate optimization stage, effectively reducing the number of rational functions in the objective function and lowering the complexity of the objective function.

[0030] II) Load Rate Optimization Phase The start-up and shutdown equipment combinations selected during the equipment combination pre-screening stage are used as the basis for the total system cost formula. The improved differential evolution algorithm is applied to optimize the system's total cost formula as the objective function. 1. Population initialization and correction: Several individuals are generated within the feasible region of load allocation rate. When generating the initial population, if the individuals... Right now Satisfies any denominator The calculated value of the denominator is slightly shifted away from zero: .

[0031] 2. Adaptive penalty term: Introducing a dynamic weight penalty term into the objective function to suppress searches near the zero of the denominator:

[0032] in, The minimum denominator value calculated based on the current population individuals in the objective function. Adjustment:

[0033] when When approaching zero, ≈1, near The punishment is the strongest; when As the exponent increases, the exponent term decreases. Lowering the punishment reduces its severity. The equality constraint is:

[0034] Inequality constraints:

[0035] Multiply by the sum of the two terms to cover the violation amount for all constraint types. When the constraint includes both equality and inequality constraints, it can be decomposed into... , respectively equal to:

[0036]

[0037] In the formula This represents the scale parameter under different scenarios, used to normalize constraint violation rates. Represents the iterative algebra, which varies with the iterative algebra ( The incrementing of the normalization constraint strengthens the penalty for the normalization constraint, forcing the population to converge quickly to the feasible region. This represents the average constraint violation amount, based on the average constraint violation amount. Exponential growth is employed, with a focus on suppressing severely out-of-bounds individuals. An adaptive penalty term is calculated for each experimental individual and updated. and .

[0038] 3. Gradient sensitivity variation strategy: Calculate individuals Gradient of each denominator polynomial ; Adjust the variable asynchronous length along the opposite direction of the gradient, away from the zero point of the denominator:

[0039] in, This is the sensitivity coefficient (default 0.1~0.5). The larger the gradient norm, the greater the step size adjustment, accelerating the move away from the denominator zero; conversely, the step size decreases to maintain stability. like Force an escape operation and generate a new individual: in, To escape the step size (e.g., 0.01), move along the gradient direction, which is equivalent to performing gradient ascent, ensuring that you stay away from the zero point of the denominator.

[0040] 4. Stratification variation strategy for numerator and denominator: The numerator and denominator coefficients of rational functions are divided into groups with independent variations, and the numerator group is subjected to a radical parameter. The denominator uses conservative parameters. Furthermore in Calculations are performed based on this:

[0041] Each generation uses probability Stratified variation is triggered if population diversity is below a threshold, such as the average distance between individuals. Then it will be forcibly enabled; In the population The formula for calculating the average Euclidean distance of an individual is:

[0042] Within the same generation, the gradient calculation and step size adjustment for gradient sensitivity variation are performed first, followed by the grouping variation of the numerator and denominator hierarchical variation strategy. The step size adjustment affects all variables, while the grouping parameters of the numerator and denominator hierarchical variation strategy only apply to the numerator and denominator coefficients.

[0043] 5. Crossover and fitness assessment: (1) Crossover: generating experimental individuals; (2) Fitness assessment: Calculate the objective function value of the experimental individuals; (3) Apply penalty: Update the calculated value and Multiply by the corresponding penalty factor, add to the total fitness, and retain the better-fitting individuals for the next generation.

[0044] 6. Stability verification: Iterate through each generation, repeating steps such as adaptive penalty term calculation, gradient sensitivity variation, numerator and denominator hierarchical variation, crossover and fitness evaluation to obtain the optimal solution. Then, the steps of neighborhood sampling and failure compensation optimization are performed. (1) Neighborhood sampling: To increase the robustness of the final optimal solution, the optimal solution Add random perturbation , Generate multiple sampling points and verify whether the sampling points still satisfy the requirements. ; (2) Failure Compensation Optimization: If a certain proportion of sampling points fail, then... The initial value is used, and then a few more generations of optimization are performed in the neighborhood.

[0045] In an embodiment of the load rate optimization method for a data center cooling system's chiller unit in this invention, which utilizes the improved differential evolution coupled step-by-step screening and rational function load rate optimization method, the specific steps of the offline preparation stage and the online optimization stage are as follows: Offline preparation phase: 1. Unit (equipment) type: 4 centrifugal chiller units, abbreviated as A, B, C, and D, with rated supply capacity of In the refrigeration system, the specific equipment The rated cooling capacities are 800RT, 600RT, 400RT, and 400RT, respectively.

[0046] 2. Calculate the total capacity of all equipment in each combination, i.e., the total customized cooling capacity of the combination:

[0047] Then sort the combinations by rated cooling capacity from smallest to largest (unit: RT): 400 (C / D) → 600 (B) → 800 (A / C+D) → 1000 (B+C / B+D) → 1200 (A+C / A+D) → 1400 (A+B / B+C+D) → 1600 (A+C+D) → 1800 (A+B+C / A+B+D) → 2200 (A+B+C+D). / represents or. List the capacity ranges for each combination: 75% to 90%, 65% to 90%, 55% to 90%, and 45% to 90%. For example, the 75% to 90% capacity range for combination (A+C) is: .

[0048] 3. Through the chiller load Divide by its cost (i.e., energy consumption) to obtain performance And the specific performance of the refrigeration system is :

[0049] Refitting the load rate of a single device and its energy efficiency Relational formula: .

[0050] 4. Calculate the load rate of a single device. and load distribution percentage Relationship:

[0051] Substitute again Its energy efficiency From the relation, we obtain a new expression: .

[0052] 5. Calculate the total cost of the refrigeration system. That is, total energy consumption. Construct the objective function and load distribution percentage. To optimize variables: .

[0053] Online optimization phase: 1. During the pre-screening phase of its equipment combination, the pre-screening of unit (equipment) start-up and shutdown is implemented according to the following load rate matching rules: Taking the currently active combination (B+C+D) as an example, the rated cooling capacity... The current cooling capacity required is 1400RT. For 1000RT, calculate equal:

[0054] If it is less than 90%, and continues for another 2 hours, the calculated value of the combination (A+C) is 75% 900RT and 90% 1080RT. The current cooling capacity requirement is between the two, so a new combination (A+C) is matched.

[0055] The online optimization phase in this embodiment also includes the construction of optimization algorithms and optimization processes: 2. Optimize Algorithm Construction For the selected start-stop unit combinations Given (A+C), its optimization objective is:

[0056] In the formula, It is the rated cooling capacity of the unit combination. For the unit The percentage of load distribution, i.e., the optimization variable. A quadratic function in one variable ; The constraints are: st

[0057] Add the constraint violation amount and the adaptive penalty term that suppresses the search near the denominator zero to the objective function:

[0058] Among them performance Specifically in the refrigeration system , Initialize to ,so:

[0059]

[0060] Initialize to 500. Initializing to 1000, we get:

[0061] .

[0062] 3. Optimize processes In this embodiment (1) Population initialization Random generation: Using a uniform distribution to randomly generate... scope The initial population. If That is, close to zero, let Equal to 0.01, regenerate Or put Correction: ; (2) Update dynamic parameters ① Calculate the minimum COP value of the current population. , ② Update , ③、 To normalize the parameters, set the rated total load to 2200, and calculate the average violation amount. and iterative algebra ,For example It equals 0.1. Equals 100, Update ,have to:

[0063]

[0064] .

[0065] 4. Gradient sensitivity variation strategy (1) Gradient calculation: For each individual Calculate the gradient of the COP of each denominator polynomial: ; (2) Step size adjustment, set sensitivity coefficient Equals 0.2: ; (3) Forced escape, set the escape step length It equals 0.05, if ,implement: .

[0066] 5. Stratification and variation strategy for numerator and denominator Molecular group In Using aggressive parameters denominator group In Using conservative parameters Furthermore in Calculations are performed based on this:

[0067] Triggering condition: Set If the population diversity is equal to 0.1, Force the activation of the hierarchical mutation strategy.

[0068] 6. Crossover and fitness assessment (1) Crossover: generating experimental individuals; (2) Fitness assessment: Calculate the objective function value of the experimental individuals. ; (3) Apply penalty: Update the calculated value and Multiply by the corresponding penalty term and add to the total fitness. Individuals with better fitness are retained for the next generation.

[0069] 7. Stability Verification Iterate through each generation, repeating steps such as adaptive penalty term calculation, gradient sensitivity variation, numerator and denominator hierarchical variation, crossover and fitness evaluation to obtain the optimal solution. Then, the following steps are performed: neighborhood sampling and failure compensation optimization. (1) Neighborhood sampling: for the optimal solution Add ±3% random perturbation to generate 100 sampling points, and verify whether the sampling points still satisfy the denominator... ; (2) If a certain proportion of sampling points fail, then Using the initial values, optimize for another 10 generations within the neighborhood. Obtain the optimal load distribution percentage, and further calculate the load rate of each device.

[0070] The remaining methods, steps, and related factors of this embodiment for optimizing the load rate of the chiller units in a certain data center cooling system are similar to the corresponding methods, steps, and related factors of the offline preparation stage and the online optimization stage described above.

[0071] It should be noted that, in this document, the term "comprising" or any other variations thereof is intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0072] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An improved method for load factor optimization by coupling differential evolution with stepwise screening and rational functions, characterized in that: The optimization is carried out in stages, including an offline preparation stage and an online optimization stage. The offline preparation phase involves pre-generating a rated capacity ranking table for equipment combinations, dividing capacity demand ranges into different load rate intervals, establishing an equipment load rate-energy efficiency relationship model, and defining cost and objective functions. This provides a pre-calculated data foundation and mathematical framework for subsequent phases, and includes the following steps: All possible equipment operation combinations are numbered and sorted from smallest to largest according to the total rated capacity of the combination; For each sorted combination, list the combined capacity range corresponding to the load rate according to multiple percentage ranges; The online optimization phase includes a device combination pre-screening phase and a load rate optimization phase. The equipment combination pre-screening stage dynamically selects start-up and shutdown equipment based on the ratio of the total capacity of each piece of equipment in the current combination to the current total demand of the system.

2. The improved differential evolution coupled stepwise screening and rational function load rate optimization method according to claim 1, characterized in that: In the load rate optimization stage, the start-stop equipment combination selected in the equipment combination pre-screening stage is used as the system total cost formula. The system total cost formula is used as the objective function to apply the improved differential evolution algorithm for optimization, including population initialization, gradient sensitivity mutation strategy, and numerator and denominator hierarchical mutation strategy.

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