Multi-objective particle swarm optimization method and system based on multi-strategy improvement

Abstract

The present application relates to the field of power system optimization. Disclosed are a multi-objective particle swarm optimization method and system based on multi-strategy improvement. The method comprises: using a multi-strategy improved multi-objective particle swarm optimization algorithm to solve a multi-objective optimization model of a power supply of a generator state monitoring apparatus; and combining three improved strategies, i.e., adaptive adjustment of an inertia weight, coexistence of a decomposition algorithm and Pareto dominance, and introduction of a mutation factor. The present application overcomes the defects of conventional multi-objective particle swarm algorithms, and achieves a better distribution of a Pareto front, thereby obtaining the best Pareto optimal solution set. The present application solves the problems of conventional multi-objective particle swarm algorithms in solving a multi-objective optimization problem, such as premature convergence to a local non-dominated solution, and sub-optimal distribution of a Pareto front caused by an improper external archive update strategy, thereby improving the operational efficiency and reliability of a power supply system of an apparatus.

Description

A Multi-Strategy Improved Multi-Objective Particle Swarm Optimization Method and System

[0001] This application claims priority to Chinese Patent Application No. 202411532710.9, filed on October 30, 2024, entitled "A Multi-Target Particle Swarm Optimization Method and System Based on Multi-Strategy Improvement", the entire contents of which are incorporated herein by reference. Technical Field

[0002] This application relates to the field of power system optimization technology, and in particular to a multi-objective particle swarm optimization method and system based on multi-strategy improvement. Background Technology

[0003] The generator condition monitoring device is battery powered, making it more flexible and reliable in generator maintenance sites. Currently, lithium-ion batteries are widely used due to their advantages such as high energy density, low self-discharge rate, and long cycle life. In some generator condition monitoring projects, the power supply used by the monitoring instruments is required to provide pulse power. A hybrid energy storage system employing both energy-type and power-type energy storage elements can optimize the overall performance of the generator condition monitoring device's own power supply system.

[0004] Optimizing the power supply of a detection device based on a hybrid energy storage system is a complex nonlinear optimization problem with multiple objectives, constraints, and variables. It is difficult to solve using traditional mathematical methods. For example, the traditional particle swarm optimization method is prone to getting trapped in local optima, and the obtained solution set is diverse or has poor convergence when solving multi-objective optimization problems. Summary of the Invention

[0005] The purpose of this application is to provide a multi-strategy improved multi-objective particle swarm optimization method and system, which can solve the problems of premature convergence to local non-dominated solutions and Pareto front suboptimal distribution caused by improper external archive update strategy in solving multi-objective optimization problems by traditional multi-objective particle swarm optimization algorithm, thereby improving the efficiency and reliability of the device power system.

[0006] To solve the above-mentioned technical problems, this application provides the following technical solution:

[0007] Firstly, this application provides a multi-strategy improved multi-objective particle swarm optimization method, which includes: initializing weight vectors, reference points, and particle velocities and positions; initializing inertial weights using an adaptive nonlinear correction strategy; updating individual optimal solutions using a decomposition strategy; calculating the dynamic density distance of particles; selecting the global optimal solution using a roulette wheel algorithm; introducing a mutation factor to randomly mutate particles, increasing the diversity and randomness of the population; updating external archives; storing the Pareto optimal solution set; eliminating inferior solutions; and selecting solutions closer to the Pareto front through Pareto dominance relations.

[0008] Optionally, the initialization of inertia weights includes: optimizing the inertia weights in the algorithm using an adaptive nonlinear correction strategy for inertia weights; as the number of iterations increases, the use of an exponential function nonlinearly adjusts the inertia weights from a maximum value to a minimum value; and the search performance of the algorithm is enhanced by adjusting the adaptive control parameter alpha.

[0009] Optionally, the decomposition strategy includes: the optimization model of the hybrid energy storage system is a bi-objective optimization, using the Tchebycheff aggregation function for scalarization calculation, and guiding the population evolution by pre-setting a set of uniformly distributed reference weight vectors in the objective space, with each individual in the population corresponding to a reference weight vector. During the initialization operation in the early stage of the algorithm, the decomposition algorithm is incorporated, and the multi-objective problem is scalarized and decomposed into n independent sub-problems using the Tchebycheff decomposition method, with each sub-problem corresponding to a specific weight vector.

[0010] Optionally, the Tchebycheff decomposition method includes: performing scalarization calculations using the Tchebycheff aggregation function;

[0011] The formula is expressed as:

[0012] Among them, g TCH λ represents the aggregate function. i The reference weight vector for the i-th particle is selected using a uniform distribution method, z. * Let R represent the reference point, and let f represent the decision space. i (x) represents each target.

[0013] Optionally, the individual optimal solution includes: evaluating the decision result using the concept of Pareto optimality. Pareto optimality describes a state in which the advantage of a certain objective cannot be further improved without compromising any objective. In a decision space containing other solutions, if a solution is Pareto-dominant, that is, the decision vector of the solution is not dominated by any other vector, then this solution is called a Pareto optimal solution. When solving multi-objective optimization problems, the optimal solution consists of a series of Pareto optimal solutions that cannot dominate each other. The set of solutions is called the Pareto optimal solution set. Correspondingly, the corresponding point of the current solution in the objective function space forms the Pareto front.

[0014] Optionally, the selection of the global optimal solution includes: employing a method combining dynamic dense distance sorting and roulette wheel sorting as the global optimal solution selection strategy. Dynamic dense distance reflects the density between particles, indicating the uniformity of the solution. In the multi-objective optimization model of the hybrid energy storage system, particle x... i The formula for dense distance is:

[0015] Where, x j and x k Indicates the relationship with particle x i The two closest particles, f 1,max f represents the maximum value of the first objective function. 2,max This represents the maximum value of the second objective function;

[0016] The particles in the Pareto optimal solution set are sorted by dense distance. From the top 20% of the solutions, a roulette wheel algorithm is used to select a solution as the global optimal solution, which guides the direction of population evolution.

[0017] Optionally, the update of the external archive includes: due to the existence of the particle swarm, the particle swarm algorithm generates multiple non-dominant solutions in a single execution, and an external archive method is adopted, wherein the archive is intended to store the Pareto optimal solution set, prevent the archive from being over-expanded, increase computational complexity, impose a limit on the maximum storage capacity of the external archive, and ensure normal operation.

[0018] Secondly, this application also provides a system for applying the multi-strategy improved multi-objective particle swarm optimization method described in the first aspect, wherein the multi-strategy improved multi-objective particle swarm optimization system includes: an initialization module, an optimization strategy execution module, a global optimal solution selection module, and an external file management module;

[0019] The initialization module is responsible for initializing the particle's position, velocity, weight vector, and reference point parameters, and implementing an adaptive nonlinear correction strategy to initialize the inertial weights.

[0020] The optimization strategy execution module applies the Tchebycheff decomposition method to scalarize the multi-objective problem, guides population evolution, updates the optimal solution of individuals, calculates the dynamic density distance of particles, and introduces a mutation factor to randomly mutate the particles.

[0021] The global optimal solution selection module sorts the Pareto optimal solution set according to the dynamic dense distance and uses the roulette wheel algorithm to select the global optimal solution from the sorted solutions.

[0022] The external file management module stores and manages the Pareto optimal solution set, filters better solutions through Pareto dominance relations, controls the size of the external file, and avoids over-expansion and computational complexity.

[0023] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the multi-strategy improved multi-objective particle swarm optimization method described in the first aspect.

[0024] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the multi-strategy improved multi-objective particle swarm optimization method described in the first aspect.

[0025] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0026] Considering the various constraints in the operation of hybrid energy storage systems, a multi-objective optimization scheduling problem model is established. To better solve the power supply optimization scheduling problem of hybrid energy storage systems and overcome the problems of traditional multi-objective particle swarm optimization algorithms being prone to getting trapped in local optima and having poor convergence and diversity of Pareto optimal solution sets, a multi-strategy improved particle swarm optimization algorithm is proposed. An adaptive nonlinear adjustment strategy of inertia weights is adopted to balance the algorithm's ability to explore locally and develop globally. The decomposition algorithm and Pareto dominance sorting are integrated to balance the convergence and diversity of the Pareto optimal solution sets obtained by the algorithm. A mutation factor is introduced to improve the randomness and diversity of the population during the algorithm iteration process and avoid getting trapped in local optima. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 is a schematic flowchart of a multi-strategy improved multi-objective particle swarm optimization method provided in an embodiment of this application.

[0029] Figure 2 is a schematic diagram of the Pareto dominance of the dual-objective space of a multi-objective particle swarm optimization method based on multi-strategy improvement provided in an embodiment of this application.

[0030] Figure 3 is a schematic diagram of the coexistence of decomposition and Pareto domination in a multi-objective particle swarm optimization method based on multi-strategy improvement provided in an embodiment of this application.

[0031] Figure 4 is a flowchart of solving a multi-objective optimization model for a hybrid energy storage system based on a multi-strategy improved multi-objective particle swarm optimization method according to an embodiment of this application.

[0032] Figure 5 shows the test load curve of a generator condition monitoring device based on a multi-strategy improved multi-objective particle swarm optimization method according to an embodiment of this application.

[0033] Figure 6 shows the Pareto front of a traditional multi-objective particle swarm optimization algorithm based on a multi-strategy improved multi-objective particle swarm optimization method provided in an embodiment of this application.

[0034] Figure 7 is a schematic diagram of the Pareto front of a multi-strategy improved multi-objective particle swarm optimization algorithm provided in an embodiment of this application.

[0035] Figure 8 is a schematic diagram of the working modules of a multi-objective particle swarm optimization system based on multi-strategy improvement provided in an embodiment of this application. Detailed Implementation

[0036] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without inventive effort should fall within the scope of protection of this application.

[0037] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0038] Secondly, the term "an embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of this application. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that excludes other embodiments.

[0039] This application is described in detail with reference to the schematic diagrams. When detailing the embodiments of this application, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not according to the usual scale. Furthermore, the schematic diagrams are merely examples and should not limit the scope of protection of this application. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0040] Furthermore, it should be noted in the description of this application that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing this application and for simplification, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0041] Unless otherwise expressly specified and limited, the terms "installation," "connection," and "joining" in this application should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; similarly, they can refer to mechanical connections, electrical connections, or direct connections, or indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0042] Example 1, referring to Figures 1-3, is the first embodiment of this application. This embodiment provides a multi-strategy improved multi-objective particle swarm optimization method, including:

[0043] S1: Initialize the weight vector, reference point, particle velocity and position, and initialize the inertial weights using an adaptive nonlinear correction strategy.

[0044] Furthermore, the particle swarm optimization algorithm is widely used in engineering practice and other fields due to its small number of control parameters. However, since the control parameters used are random, there is no clear theoretical basis for optimal parameter setting during the design process, making it difficult to achieve the optimal configuration of the system. To solve this problem, this patent adopts an adaptive nonlinear correction strategy for inertia weight to optimize the inertia weight in the algorithm, as shown in formula (1):

[0045] Among them, Tmax ω represents the total number of iterations. max and ω min These represent the maximum and minimum values ​​of the inertia weight; alpha represents the adaptive control parameter. As the number of iterations increases, the use of an exponential function nonlinearly adjusts the inertia weight from a maximum value of 0.9 to a minimum value of 0.4. This strategy can further enhance the algorithm's search performance by adjusting the adaptive control parameter alpha.

[0046] S2: Update the individual optimal solution using a decomposition strategy, calculate the dynamic density distance of particles, select the global optimal solution using a roulette wheel algorithm, introduce a mutation factor, and randomly mutate the particles to increase the diversity and randomness of the population.

[0047] Furthermore, the optimization problem of the hybrid energy storage system proposed in this patent is a multi-objective optimization problem, involving the simultaneous optimization of multiple objectives. These objectives are contradictory to some extent, making it impossible to evaluate the obtained solutions. However, in multi-objective optimization algorithms, it is necessary to select a solution set to guide the optimization or to eliminate poor solutions, thereby continuously optimizing the solution set generated in each generation. The Pareto optimality concept is generally used to evaluate the decision results.

[0048] Pareto optimality describes a state where, without compromising any objective, it is impossible to further enhance the advantage of a particular objective. In other words, once Pareto optimality is reached, improving one objective will inevitably lead to the deterioration of other objectives. This relationship is called Pareto dominance or Pareto supremacy, a standard commonly used in multi-objective optimization algorithms, and can be described by formula (2):

[0049] In the formula, x and y are the decision vectors in the Pareto optimization algorithm, composed of n-dimensional decision variables; D represents the dimension of the objective. Given two decision variables x and y, for any individual i among D individuals, if x is not better than the objective value f(y) corresponding to y on all objective values ​​f(x), and there exists at least one (the j-th) objective value where y performs better than x, then in this case, y is said to be dominant over x, or y is Pareto-dominant over x. In other words, Pareto optimality describes a state where, without compromising any objective, it is impossible to further improve the advantage of a certain objective. In other words, once Pareto optimality is reached, improving one objective will inevitably lead to the deterioration of other objectives. This relationship is called Pareto dominance or Pareto supremacy, and it is the standard used in multi-objective optimization algorithms.

[0050] In a decision space containing other solutions, if a solution is Pareto-dominant, meaning its decision vector is not dominated by any other vector, then this solution is called a Pareto optimal solution. In solving multi-objective optimization problems, the optimal solution found is often not just one, but a series of Pareto optimal solutions that cannot dominate each other. This set of solutions is called the Pareto optimal solution set. Correspondingly, the points corresponding to these solutions in the objective function space form the Pareto front. The Pareto dominance relationships in the bi-objective space are shown in Figure 2, where solutions 1, 2, and 3 do not have a dominance relationship and are also not dominated by other solutions; these solutions are all Pareto optimal solutions. The solution set of arcs 1, 2, and 3 constitutes the Pareto optimal solution set, and arcs 1, 2, and 3 represent the Pareto front. In addition, solution 2 dominates solutions 4, 5, 7, and 8, where solution 5 is dominated by solution 2 but also dominates solutions 7 and 8, while solutions 4, 5, and 6 do not have a dominance relationship with each other.

[0051] The purpose of solving multi-objective optimization problems is to obtain a set of solutions that are uniformly distributed and as close as possible to the Pareto front, characterized by excellent convergence and diversity. However, traditional multi-objective particle swarm optimization algorithms use the Pareto dominance sorting rule to update the optimal solution, resulting in poor diversity of the obtained solution set. To address this issue, this patent introduces a decomposition algorithm to improve the diversity of the obtained solution set. Since the optimization model of the hybrid energy storage system is a bi-objective optimization, the Tchebycheff aggregation function is used for scalarization calculation, as shown in equations (3) and (4):

[0052] In the formula, g TCH (·) denotes the aggregation function, λ denotes the reference weight vector of particles in the particle swarm optimization algorithm, and z * λ represents the reference point of a particle in the particle swarm optimization algorithm. i The reference weight vector for the i-th particle is selected using a uniform distribution method, z. i * Let R be the reference point for the i-th particle, and let R represent the decision space.

[0053] The decomposition algorithm guides population evolution by pre-defining a set of uniformly distributed reference weight vectors in the target space. Each individual in the population corresponds to a reference weight vector, thus ensuring population diversity. Therefore, the multi-objective optimization problem of a hybrid energy storage system can be decomposed into objective quantum problems with different weights and solved simultaneously. During the initial initialization phase, the decomposition algorithm is incorporated, using the Tchebycheff decomposition method to scalarize the multi-objective problem and further decompose it into several independent subproblems, each corresponding to a specific weight vector. This method ensures that the weight vector for each subproblem is different and matched to a specific individual. By uniformly dividing the solution space into N distinct regions, N scalarized subproblems are obtained.

[0054] Unlike Pareto domination, which selects solutions based on domination relationships, the decomposition strategy transforms the objective into a series of scalar quantum problems with different reference weights. This allows each subproblem to not only update its own solution set but also benefit its neighboring subproblems, thus achieving collaborative updates of the solution set. This mechanism significantly enhances the diversity of the entire solution set.

[0055] This application uses a dual-objective, three-reference-weight-vector approach as an example, as shown in Figure 3. In Figure 3, the target space is divided into three parts by the three reference-weight vectors, where z... * = (minf1, minf2) represents the minimum value of each objective function. The decomposition strategy retains the optimal solution mainly based on the distance between the particle and the weight vector. Particles 1, 2, and 4 are all retained, thus maintaining the diversity of the solution set. If Pareto dominance is added after the decomposition strategy, since particle 3 dominates particle 2, particle 3 is retained and particle 2 is removed, making particles 1, 3, and 4 closer to the Pareto front, thereby improving convergence.

[0056] The decomposition algorithm transforms the multi-objective problem of hybrid energy storage systems into multiple subproblems with different weights. Each subproblem updates itself while generating new solutions, thus improving the diversity of the Pareto optimal solution set. Pareto domination, on the other hand, can quickly select solutions with higher dominance levels by comparing the dominance relationships between solutions, resulting in better convergence. However, it can lead to uneven solution distribution and poor diversity. By using the decomposition algorithm first and then applying Pareto domination, the Pareto front can simultaneously possess good convergence and diversity.

[0057] In multi-objective particle swarm optimization (PSO) algorithms, individual optimal solutions guide particles towards local optima, improving the overall search efficiency and convergence of the population. Global optimal solutions guide the entire population towards global optima, ensuring the algorithm finds approximate solutions in the solution space. This reflects the overall search capability and diversity of the population, effectively preventing the algorithm from getting trapped in local optima and thus improving its global search capability and solution diversity. Therefore, storing and updating individual and global optimal solutions is crucial for the effectiveness of multi-objective PSO algorithms.

[0058] This section employs a decomposition strategy to update individual optimal solutions, guiding the individual optimal particle to reference information from neighboring particles during evolution, thereby increasing the diversity of the solution set. The update strategy is as follows:

[0059] Calculate g of the particle's current position (i.e., the new solution) according to formula (3). TCH (x(i)λ,z * ) and its historical best position (i.e., the old solution) g TCH (pbest|λ,z * ), and compare their sizes, where pbest is the optimal position searched by the i-th particle, also known as the individual optimal solution.

[0060] If g TCH (pbest|λ,z * )>g TCH (x(i)λ,z * If the position of the current particle is updated to the new individual optimal solution, then the position of the particle will be updated to the new individual optimal solution.

[0061] If g TCH (pbest|λ,z * )<g TCH (x(i)λ,z * If ), then the individual optimal solution remains unchanged.

[0062] If g TCH (pbestλ,z * ) = g TCH (x(i)|λ,z * If a solution is randomly selected, then a new optimal solution for that individual is established.

[0063] This section employs a method combining dynamic density distance sorting and roulette wheel algorithm as the global optimal solution selection strategy. Dynamic density distance reflects the close proximity between particles, thus reflecting the uniformity of the solution. Taking the multi-objective optimization model of the hybrid energy storage system in this patent as an example, particle x... i The formula for the dense distance is shown in equation (5):

[0064] In the formula, x j and x k Indicates the relationship with particle x i The two closest particles; f 1,max f represents the maximum value of the first objective function. 2,max This represents the maximum value of the second objective function.

[0065] The particles in the Pareto optimal solution set are sorted by dense distance. From the top 20% of the solutions, a roulette wheel algorithm is used to select a solution as the global optimal solution, thereby guiding the direction of population evolution.

[0066] S3: Update external archives, store Pareto optimal solution set, remove inferior solutions, and filter out solutions that are closer to the Pareto front through Pareto dominance relations.

[0067] Furthermore, due to the existence of particle swarm optimization, the PSO algorithm can generate multiple non-dominant solutions in a single execution. To update and maintain these non-dominant solutions, this patent employs a traditional external archive method, where the archive is designed to store the Pareto optimal solution set. However, the size of the external archive cannot be infinitely large, and to prevent excessive expansion of the archive, thereby increasing computational complexity, it is necessary to impose a limit on the maximum storage capacity of the external archive to ensure its proper functioning.

[0068] The external archive maintenance strategy in this application is based on the degree of constraint violation. During each iteration, once the number of external archives exceeds a preset limit, individuals with higher constraint violation rates are removed, thus guiding the population to concentrate in areas with lower constraint violation rates. This strategy ensures that the algorithm can effectively advance the solution optimization process while satisfying the constraints.

[0069] To prevent multi-objective particle swarm optimization (PSO) from converging to local Pareto fronts, a mutation factor is introduced. This increases the diversity and randomness of the population during iterations, thus preventing premature convergence. This strategy allows PSO to better explore the search space and avoid being confined to local Pareto boundaries when dealing with multi-objective optimization problems in hybrid energy storage systems. The specific implementation method is as follows:

[0070] (1) For the current particle x, based on the current iteration number t and the maximum iteration number T max And the mutation rate m is used to calculate the variation factor p;

[0071] (2) Obtain a random number rand. If rand is less than p, then randomly select a decision variable of the particle to mutate, while the other decision variables remain unchanged; if rand is not less than p, then remain unchanged.

[0072] (3) If a particle needs to mutate, first randomly select the j-th decision variable x(j) of particle x, and then calculate the mutation range d based on the mutation factor; Var max d=p*(Var max -Var min (7)

[0073] Among them, Var max and Var min These are the maximum and minimum values ​​of the specified decision variables, respectively.

[0074] (4) Calculate the upper and lower bounds of the variation based on d, with the upper bound being U. b = x(j) + d, with a lower bound of L b =x(j)-d. And pay attention to out-of-bounds handling, U b =min(U b Var max ), L b =max(L b Var min ).

[0075] (5) Finally, within the range of variation [L] b U b Select a random number from the range [] to obtain a new x(j).

[0076] (6) After a particle mutates, it is necessary to compare whether the mutated particle is better. If the mutated particle is better, the particle is updated; otherwise, it is not updated. Similarly, it is necessary to compare the new particle with the particle's pbest. If the new particle is better than pbest, pbest is updated; otherwise, it is not updated.

[0077] Example 2, referring to Figures 4-7, is an embodiment of this application, providing a multi-strategy improved multi-objective particle swarm optimization method. To verify the beneficial effects of this application, scientific demonstration is carried out through experiments.

[0078] (1) Parameter initialization: Input relevant parameters such as voltage and capacity of the hybrid energy storage system;

[0079] (2) Algorithm initialization: Set the particle population size N, the number of external files, the maximum number of iterations, and the upper and lower limits for particle position and velocity. Initialize the weight vector, reference point, and particle velocity and position consistent with the population size. The particle position information includes the charging and discharging power of the lithium-ion battery and supercapacitor in the hybrid energy storage system;

[0080] (3) Calculate the objective function value for each particle under different current particle position conditions;

[0081] (4) Update the individual particle's optimal solution pbest according to the allocation strategy;

[0082] (5) Calculate the close proximity I(x) of each particle according to formula (5). i The solutions are sorted in descending order, and the global optimal solution gbest is selected from the top 20% of the sorted solutions using the roulette wheel algorithm. The Pareto solution set is then updated.

[0083] (6) Update the inertial weights, as well as the velocities and positions of all particles, and update pbest after random mutation;

[0084] (7) Update external files and determine if the external files have overflowed. If so, delete the inferior solutions. If not, continue.

[0085] (8) Update the iteration count and determine if the maximum iteration count has been reached. If yes, end the loop and output the optimal scheduling scheme and its corresponding objective function values. If no, return to step (5) and continue.

[0086] During the experiment, the test load was sampled once per minute, as shown in Figure 5:

[0087] Compared with the traditional multi-objective particle swarm optimization algorithm, the multi-objective particle swarm optimization method based on multi-strategy improvement proposed in this patent is used to solve the multi-objective optimization model of the power supply of the hybrid energy storage system. The results are closer to the Pareto front in the objective space and more uniformly distributed, that is, the convergence and diversity are better, as shown in Figures 6 and 7.

[0088] It should be noted that the above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit it. Although this application has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of this application without departing from the spirit and scope of the technical solutions of this application, and all such modifications and substitutions should be covered within the scope of the claims of this application.

[0089] Example 3, the third embodiment of this application, differs from the previous two embodiments in that:

[0090] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0091] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0092] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0093] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0094] Example 4, referring to Figure 8, is an embodiment of this application, providing a multi-objective particle swarm optimization system based on multi-strategy improvement. The system includes: an initialization module 1, an optimization strategy execution module 2, a global optimal solution selection module 3, and an external file management module 4.

[0095] Initialization module 1 is responsible for initializing the particle's position, velocity, weight vector, and reference point parameters, and implementing an adaptive nonlinear correction strategy to initialize the inertial weights;

[0096] The optimization strategy execution module 2 applies the Tchebycheff decomposition method to standardize the multi-objective problem and guide population evolution, update the optimal solution of individuals, calculate the dynamic density distance of particles, and introduce a mutation factor to randomly mutate particles;

[0097] The global optimal solution selection module 3 sorts the Pareto optimal solution set according to the dynamic dense distance and uses the roulette wheel algorithm to select the global optimal solution from the sorted solutions;

[0098] External file management module 4 stores and manages the Pareto optimal solution set, filters better solutions through Pareto dominance relations, controls the size of external files, and avoids over-expansion and computational complexity.

[0099] It should be noted that the above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit it. Although this application has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of this application without departing from the spirit and scope of the technical solutions of this application, and all such modifications and substitutions should be covered within the scope of the claims of this application.

Claims

1. A multi-strategy improved multi-objective particle swarm optimization method, characterized in that, The multi-strategy improved multi-objective particle swarm optimization method includes: Initialize the weight vector, reference point, particle velocity, and position, and use an adaptive nonlinear correction strategy to initialize the inertial weights; The individual optimal solution is updated using a decomposition strategy, the dynamic density distance of particles is calculated, the global optimal solution is selected by combining the roulette wheel algorithm, and a mutation factor is introduced to randomly mutate the particles, thereby increasing the diversity and randomness of the population. Update external archives, store Pareto optimal solution sets, remove inferior solutions, and filter out solutions that are closer to the Pareto front through Pareto dominance relations.

2. The multi-strategy improved multi-objective particle swarm optimization method according to claim 1, characterized in that, The initial inertia weight includes: using an adaptive nonlinear correction strategy for inertia weight to optimize the inertia weight in the algorithm. As the number of iterations increases, the use of an exponential function nonlinearly adjusts the inertia weight from the maximum value to the minimum value. The search performance of the algorithm is enhanced by adjusting the adaptive control parameter alpha.

3. The multi-strategy improved multi-objective particle swarm optimization method according to claim 2, characterized in that, The decomposition strategy includes: the optimization model of the hybrid energy storage system is a bi-objective optimization, and the Tchebycheff aggregation function is used for scalarization calculation. A set of uniformly distributed reference weight vectors is pre-defined in the objective space to guide the population evolution. Each individual in the population corresponds to a reference weight vector. During the initialization operation in the early stage of the algorithm, the decomposition algorithm is incorporated. The Tchebycheff decomposition method is used to scalarize the multi-objective problem and decompose it into n independent sub-problems. Each sub-problem corresponds to a specific weight vector.

4. The multi-strategy improved multi-objective particle swarm optimization method according to claim 3, characterized in that, The Tchebycheff decomposition method includes: performing scalarization calculations using the Tchebycheff aggregation function; The formula is expressed as: Among them, g TCH Let λ represent the aggregate function. i The reference weight vector for the i-th particle is selected using a uniform distribution method, z. * Let R represent the reference point, and let f represent the decision space. i (x) represents each target.

5. The multi-strategy improved multi-objective particle swarm optimization method according to claim 4, characterized in that, The individual optimal solution includes: evaluating the decision results using the concept of Pareto optimality. Pareto optimality describes a state where, without compromising any objective, it is impossible to further enhance the advantage of a certain objective. In a decision space containing other solutions, if a solution is Pareto-dominant, meaning that the decision vector of the current solution is not dominated by any other vector, then this solution is called a Pareto optimal solution. When solving multi-objective optimization problems, the optimal solution consists of a series of Pareto optimal solutions that cannot dominate each other. The set of solutions is called the Pareto optimal solution set. Correspondingly, the point corresponding to the current solution in the objective function space forms the Pareto front.

6. The multi-strategy improved multi-objective particle swarm optimization method according to claim 5, characterized in that, The selection of the global optimal solution includes: employing a method combining dynamic dense distance sorting and roulette wheel algorithm as the global optimal solution selection strategy. Dynamic dense distance reflects the density between particles, indicating the uniformity of the solution. In the multi-objective optimization model of the hybrid energy storage system, particle x... i The formula for dense distance is: Where, x j and x k Indicates the relationship with particle x i The two closest particles, f 1,max f represents the maximum value of the first objective function. 2,max This represents the maximum value of the second objective function; The particles in the Pareto optimal solution set are sorted by dense distance. From the top 20% of the solutions, a roulette wheel algorithm is used to select a solution as the global optimal solution, which guides the direction of population evolution.

7. The multi-strategy improved multi-objective particle swarm optimization method according to claim 1, characterized in that, The updated external archive includes: due to the existence of the particle swarm, the particle swarm algorithm generates multiple non-dominant solutions in a single execution. An external archive method is adopted, wherein the archive is intended to store the Pareto optimal solution set, prevent the archive from being over-expanded, increase computational complexity, and impose a limit on the maximum storage capacity of the external archive to ensure normal operation.

8. A system applying the multi-strategy improved multi-objective particle swarm optimization method according to any one of claims 1 to 7, characterized in that, The multi-objective particle swarm optimization system based on multi-strategy improvement includes: an initialization module, an optimization strategy execution module, a global optimal solution selection module, and an external file management module; The initialization module is responsible for initializing the particle's position, velocity, weight vector, and reference point parameters, and implementing an adaptive nonlinear correction strategy to initialize the inertial weights. The optimization strategy execution module applies the Tchebycheff decomposition method to scalarize the multi-objective problem, guides population evolution, updates the optimal solution of individuals, calculates the dynamic density distance of particles, and introduces a mutation factor to randomly mutate the particles. The global optimal solution selection module sorts the Pareto optimal solution set according to the dynamic dense distance and uses the roulette wheel algorithm to select the global optimal solution from the sorted solutions. The external file management module stores and manages the Pareto optimal solution set, filters better solutions through Pareto dominance relations, controls the size of the external file, and avoids over-expansion and computational complexity.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the multi-strategy improved multi-objective particle swarm optimization method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the multi-strategy improved multi-objective particle swarm optimization method according to any one of claims 1 to 7.

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