Multi-modal multi-target micro-grid optimization method based on constraint multi-modal dominance

Abstract

The invention discloses a multi-modal multi-target microgrid optimization method based on constraint multi-modal dominance. The method comprises the following steps: obtaining a plurality of targets of microgrid optimization; a convergence file and a diversity file which have complementary effects are initialized, the convergence file guides search to develop towards the CPF direction, and the diversity file uses a two-stage environment selection process to reserve a plurality of equivalent solutions of different fields; evaluating target values and constraint violations of the convergence archives and the diversity archives; iteration is carried out until the maximum number of function evaluation times is reached; and outputting a final micro-grid optimization scheme. According to the method, feasibility is preferentially considered by adopting a limited multi-modal dominating relation, meanwhile, solutions of different modals are reserved, and the modal recognition radius is dynamically adjusted according to distribution; a two-stage environment selection strategy is adopted, the decision space is widely explored at first, local optimum is reserved, and then high-quality solutions are gradually concerned.

Description

Technical Field

[0001] The present invention belongs to the technical field of microgrid optimization, and in particular relates to a multi-modal and multi-objective microgrid optimization method based on constrained multi-modal domination. Background Art

[0002] Optimization plays a key role in solving a wide range of practical problems across various scientific and engineering disciplines. These problems often involve simultaneously considering multiple conflicting objectives, such as minimizing cost while maximizing performance, or balancing efficiency with robustness. These problems are known as multi-objective optimization problems (MOPs). These problems arise in various fields, including engineering design, resource allocation, transportation, and energy management.

[0003] The conflicting objectives of microgrid optimization may include economic costs and environmental protection requirements, power supply reliability and energy efficiency, etc. Each objective corresponds to specific indicators, such as cost minimization, carbon emission minimization, energy loss minimization, etc. At the same time, optimization methods involve a variety of algorithms, such as genetic algorithms and particle swarm optimization, as well as how to deal with these conflicts, such as using multi-objective optimization algorithms or comprehensive evaluation methods. Therefore, constrained multimodal multi-objective optimization (CMMMO) is a challenging but crucial problem in the field of microgrid optimization, because it requires simultaneously approximating the Pareto optimal frontier, maintaining the diversity of the decision space, and meeting complex constraint requirements. Existing multimodal multi-objective optimization research has largely ignored the impact of constraints, and constrained multi-objective optimization methods often fail to address the multimodal nature of the problem.

[0004] Over the past few decades, a large number of algorithms have been developed to solve multi-objective optimization problems (MOPs), many of which have achieved remarkable success in approximating the Pareto optimal front. However, traditional multi-objective optimization typically focuses on finding a set of Pareto optimal solutions without considering the existence of equivalent solutions in the decision space. This limitation has led to a growing interest in solving multimodal multi-objective optimization problems (MMOPs), where the goal is not only to approximate the Pareto front PF but also to identify diverse equivalent solutions in the decision space. The ability to identify and maintain such diversity is crucial for practical applications because it provides decision makers with the flexibility to choose among equally optimal solutions based on practical considerations such as manufacturability, robustness, or implementation constraints.

[0005] Despite the increasing attention paid to multi-objective optimization (MMOPs), research on constrained MMOPs (CMMOPs) remains limited, despite the ubiquity of constraints in real-world problems. Constraints restrict the feasible region of the decision space and can significantly increase the difficulty of optimization. In most cases, constraints cannot be ignored because solutions that violate the constraints are infeasible and meaningless in practice. However, existing MMOP studies often simplify the problem by assuming an unconstrained scenario, which limits their applicability to real-world problems. Although constrained multi-objective optimization has been extensively studied, these methods often fail to address the challenges unique to the multimodal nature of CMMOPs. As a result, a significant gap exists in the literature, and effectively solving CMMOPs remains an open and challenging research problem.

[0006] The difficulty in solving CMMOPs lies in the need to balance three competing objectives: convergence, diversity, and feasibility. Convergence requires the algorithm to identify solutions that are very close to the true Pareto optimal front, which requires effective exploration and exploitation capabilities. Diversity involves maintaining a wide range of solutions in the decision space, ensuring that equivalent optima in multimodal problems are fully discovered and retained. Feasibility, on the other hand, requires that solutions satisfy all problem constraints, which severely restricts the search space and hinders the algorithm's ability to find the optimal solution. These three objectives often conflict with each other, making it extremely challenging to design an algorithm that effectively balances them. Furthermore, the multimodal nature of the problem further complicates the optimization process, as the algorithm must not only approximate the Pareto optimal front but also identify and retain multiple equivalent solutions in the decision space. This combination of objectives makes CMMOPs one of the most challenging problem classes in multi-objective optimization. Summary of the Invention

[0007] To address these issues, we propose a collaborative evolutionary algorithm based on constrained multimodal dominance (CMD-CoEA) to solve CMMOPs. We employ two coevolving populations: a convergent population that effectively identifies the true PF while maintaining sufficient diversity, and a diverse population that retains multiple optimal solutions across different domains of the decision space.

[0008] To achieve the above objectives, the present application discloses a multi-modal multi-objective microgrid optimization method based on constrained multi-modal dominance, comprising the following steps:

[0009] Obtain multiple objectives for microgrid optimization;

[0010] Initialize convergence profiles with complementary effects and Diversity Archives Wherein, the convergence profile Guide the search towards the constrained Pareto front, the diversity profile A two-stage environment selection process is used to retain multiple equivalent solutions in different domains;

[0011] Evaluating Convergence Profiles and Diversity Archives Target values ​​and constraint violations;

[0012] Iterate until the maximum number of function evaluations is reached; in each iteration, perform the following steps: perform mating selection on parents based on crowding distance; select the best parent from the convergence archive and Diversity Archives Generating offspring; the convergence profile The convergence profile is updated by combining it with the offspring and using an enhanced diversity measure; the diversity profile The update is performed via a two-stage process, first preserving multimodality using restricted multimodal dominance relations, and then refining the selection using a quality control mechanism based on ε-dominance, where ε is the constraint value;

[0013] Output the final microgrid optimization plan.

[0014] Furthermore, the diversity metric not only prioritizes feasibility and convergence, but also maintains the diversity of objective and decision spaces; specifically, all individuals will be ranked according to their objective value and overall constraint violation; if the number of non-dominated solutions exceeds N, where N is the number of solutions, a quadratic selection method based on the diversity of the dual space will be adopted to select the solution, otherwise, the first solution will be retained.

[0015] Furthermore, an adaptive ε constraint relaxation strategy is used to dynamically adjust the ε value during the entire evolution process, and its formula is as follows:

[0016]

[0017] where ε t is the relaxation threshold of the tth generation, ε init is the initial relaxation threshold, T c is the algebra of relaxation termination, α>0 is the shape parameter that controls the rate of descent;

[0018] The initial relaxation threshold ε init Determined dynamically based on the constraint violation distribution in the initial population:

[0019]

[0020] Among them, φ(x i ) represents the overall constraint violation of the solution in the initial population, x i is the i-th solution.

[0021] Furthermore, the quadratic selection method based on dual space diversity for updating the convergence archive includes: when the number of non-dominated solutions |F| is less than or equal to the required archive size N c When N is reached, all non-dominated solutions are directly saved in the convergence archive. Otherwise, the diversity contribution of each solution in the objective space and decision space is calculated, the solution with the lowest diversity contribution is determined, and it is deleted from the archive. This process continues until the archive size is reduced to N c ;

[0022] The diversity metric Δ of the dual space ds It is expressed as follows:

[0023] Δ ds (x) = Δ o (x)+Δ d (x)

[0024]

[0025] Among them, Δ o (x) and Δ d (x) represents the diversity contribution of solution x in the target space and decision space respectively; and Represents the distance between solution x and solution y in the jth target dimension and the kth decision variable dimension respectively; and are the first and second nearest neighbors of solution x in the jth target dimension; and are the first and second nearest neighbors of the solution x in the dimension of the kth decision variable; and are the maximum and minimum values ​​of the j-th objective and k-th decision variable in the current archive, respectively.

[0026] Furthermore, the two-stage environment selection process combines constrained multimodal dominance relations with an ε-dominated quality control mechanism;

[0027] For any two solutions x1 and x2 in the decision space, the restricted multimodal dominance relationship is expressed as follows if and only if one of the following conditions holds:

[0028]

[0029] where φ(x) represents the constraint violation of solution x, d(x1,x2) is the Euclidean distance between two solutions x1,x2 in the normalized decision space, r is the modal identification radius, Indicates that x1 is Pareto dominant in the target space;

[0030] The first condition ensures that feasible solutions are always better than infeasible solutions, thus guiding the search into the feasible region; the second condition ensures that dominance is established among feasible solutions only if they belong to the same mode and one is Pareto better than the other in the objective space; the third condition compares infeasible solutions based on constraint violations, giving priority to solutions with lower violation values.

[0031] Furthermore, the modal identification radius r adopts a dynamic radius adjustment mechanism:

[0032]

[0033] Among them, d i,j is x i and x j The Euclidean distance between them; r represents half of the average distance between all solutions, which gradually decreases as the evolution proceeds.

[0034] Furthermore, the first stage of the two-stage environment selection process uses the CMD relation for multimodality preservation, which identifies non-dominated solutions in all modalities by computing the CMD rank of each solution in the combined population. Select non-dominated solutions with CMD level less than 1 to form the initial filter set if The included solution is smaller than the required archive size N d , then other solutions are selected according to their CMD level until the archive is filled; on the contrary, Δ ds (x) Adopting the decision space diversity metric to iteratively eliminate the solutions with the worst diversity contribution until the archive size constraint is met;

[0035] The second stage applies a quality control mechanism based on ε dominance to ensure the quality of the solutions within each mode. Specifically, it involves first extracting traditionally non-dominated solutions from the ε combined population; these solutions are initially designated as non-dominated solutions, the combined population is then refined into an ε-filtered set before entering the first stage.

[0036] The beneficial effects of this application include:

[0037] A constrained multimodal dominance (CMD) relationship is adopted to prioritize feasibility while retaining solutions from different modalities, and the modal identification radius is dynamically adjusted according to population distribution.

[0038] A two-stage environment selection strategy is adopted, which initially explores the decision space extensively, retains local optima, and then gradually focuses on high-quality solutions via an ε-domination method. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1Flowchart of the processing of this application. DETAILED DESCRIPTION

[0040] The present invention will be further described below with reference to the accompanying drawings, but the present invention is not limited in any way. Any changes or substitutions made based on the teachings of the present invention fall within the scope of protection of the present invention. Before introducing the embodiments of the present application, some terms involved in the present application are explained.

[0041] 1. The constrained multi-objective optimization problem (CMOP) can be expressed as follows:

[0042] minF(x)=(f1(x),…,f m (x))

[0043]

[0044] where x is the decision vector in the decision space Ω and F(x) is the value of x. i The target vector. and separately are the lower and upper bounds. g j (x) and h respectively j (x) is the jth inequality and equality constraint, whose number is q and pq respectively. The constraint violation x for the jth constraint is usually calculated as follows:

[0045]

[0046] The overall constraint violation φ(x) is defined as:

[0047]

[0048] Given a decision variable vector (i.e., solution), it is feasible only if the overall constraint violation is zero. For two feasible solutions, x1 and x2, if f h (x1)≤f h (x2) For And f g (x1) <f g (x2) For When no other feasible solution dominates, the solution is called Pareto optimal. The graph of all Pareto optimal solutions in the objective space forms the Pareto front (PF). To distinguish, the terms constrained PF (CPF) and unconstrained PF (UPF) are often used to represent the PF of constrained and unconstrained multi-objective optimization problems. When solving a CMOP, the goal is to approximate the PF with a set of well-converged and well-distributed feasible solutions.

[0049] CMMOPs present unique challenges that traditional evolutionary algorithms (EAs) struggle to effectively address. These challenges stem from the need to simultaneously balance three competing requirements: constraints, convergence, and preservation of multimodality. Most existing methods focus on addressing one or two of these requirements while neglecting the others. Traditional constraint handling techniques in MOEAs prioritize feasibility but often fail to preserve multimodality in the decision space. Similarly, multimodal optimization algorithms excel at finding multiple equivalent solutions but often lack effective constraint handling mechanisms.

[0050] To solve CMMOP efficiently, we develop the CMD-CoEA algorithm by maintaining two collaborative archives: a convergence archive focused on approximating the constrained Pareto front, and a diversity archive dedicated to preserving multiple equivalent solutions in different domains in the decision space.

[0051]

[0052] The above algorithm introduces the framework of the proposed algorithm. The algorithm maintains two independent archives with complementary functions: the convergence archive We focus on efficiently approximating the true constrained CPF using vanilla MOEA while maintaining diversity in both the objective and decision spaces via an improved crowding distance. We aim to retain multiple equivalent solutions in different domains of the decision space using a two-stage environment selection process using the CMD method.

[0053] Specifically, this application first initializes )and ), and then evaluate their objective values ​​and constraint violations. The main loop continues until MaxEval reaches the maximum number of function evaluations. In each iteration, the following steps are performed: (1) Mating selection is performed on the parents based on the crowding distance. (2) Offspring are generated from the two archives. (3) By combining the convergent archive with the offspring and Update the convergence profile using the enhanced diversity metric. (4) Diversity Profile The update is performed via a two-stage process, first preserving multimodality using restricted multimodal dominance relations, and then refining the selection using an ε-dominance method.

[0054] The synergistic interaction between the two archives is a key feature of this application. The convergence archive guides the search towards the CPF, while the diversity archive preserves multiple equivalent solutions from different domains. This dual-population approach enables this application to effectively balance the competing requirements of constraint satisfaction, convergence, and multimodality preservation.

[0055] The primary purpose of the convergence profile is to effectively approximate the true CPF. Unlike traditional MOEAs, the convergence profile in this application employs an enhanced selection strategy that prioritizes not only feasibility and convergence but also maintains diversity in the objective and decision spaces. Specifically, all individuals are ranked based on their objective value and overall constraint violation. If the number of non-dominated solutions exceeds N, an improved diversity-based second selection method is employed to select a solution. Otherwise, N solutions are retained as the first choice.

[0056] When implementing ε-dominance techniques to handle constraints, ε is typically fixed. However, this static approach often leads to poor performance: small values ​​of ε in the early stages may hinder the algorithm's ability to explore promising areas in the infeasible obstacle, while large values ​​of ε in the later stages may negatively impact convergence to a truly feasible solution. To address this limitation, in one embodiment, the present application proposes an adaptive ε constraint relaxation strategy that dynamically adjusts the value of ε throughout the evolution process, as follows:

[0057]

[0058] where ε t is the relaxation threshold of the tth generation, ε init is the initial relaxation threshold, T c is the number of generations at which relaxation is terminated, and α>0 is the shape parameter that controls the rate of descent. The initial relaxation threshold ε init is determined dynamically based on the distribution of constraint violations in the initial population:

[0059]

[0060] Among them, it represents φ(x i ) The overall constraint violation of the solutions in the initial population. i

[0061] Description of the adaptive ε constraint relaxation strategy: relaxation threshold ε t Starting from a value proportional to the average constraint violation in the initial population and gradually decreasing according to a nonlinear schedule, it reaches zero at t = T c .

[0062] The shape parameter α controls the speed ε at which the value decreases over time. In the implementation of this application, we set α=2 to favor exploration in the early stages while ensuring a smooth transition to strict constraint processing in the later stages. c Set to 0.8T max , where T max is the maximum number of generations that ensures that the algorithm transitions to exact constraint processing in the last 20% of the evolution process.

[0063] Maintaining a diverse set of solutions in both the target space and the decision space is crucial for fully exploring the search space and discovering multiple equivalent solutions. To achieve a balance between convergence and diversity, in one embodiment, the present application proposes a quadratic selection (DS2) method based on dual space diversity to update the convergence archive. Specifically, when the number of non-dominated solutions |F| is less than or equal to the required archive size N c , all non-dominated solutions are directly saved in the convergence archive. Otherwise, this application calculates the diversity contribution of each solution in the objective space and decision space, determines the solution with the lowest diversity contribution, and deletes it from the archive. This process continues until the archive size is reduced to N c .

[0064] Dual space diversity metric Δ ds It can be expressed as follows:

[0065] Δ ds (x) = Δ o (x)+Δ d (x)

[0066]

[0067] Among them, Δ o (x) and Δ d (x) represents the diversity contribution of solution x in the target space and decision space respectively; and Represents the distance between solution x and solution y in the jth target dimension and the kth decision variable dimension respectively; and are the first and second nearest neighbors of solution x in the jth target dimension; and are the first and second nearest neighbors of the solution x in the dimension of the kth decision variable; and are the maximum and minimum values ​​of the j-th objective and k-th decision variable in the current archive, respectively.

[0068] Solutions in crowded areas in the target space (left) or decision space (right) have low diversity contributions and are candidates for elimination. By considering both spaces simultaneously, the proposed method can maintain diversity in both spaces.

[0069] In the target space (left), solutions in crowded regions contribute less diversity than solutions in sparse regions. Similarly, in the decision space (right), solutions that cluster together contribute less diversity. By considering both spaces simultaneously, our approach maintains a balance between target space distribution and decision space exploration.

[0070] The diversity profile in this application is specifically designed to maintain a diverse set of solutions across different modalities in the decision space. Unlike convergence profiles that primarily focus on approximating the CPF, the diversity profile aims to retain multiple equivalent solutions that may map to the same or similar points on the Pareto front PF. To achieve this goal efficiently, in one embodiment, this application employs a two-stage environment selection process that combines a constrained multimodal dominance (CMD) relationship with a quality control mechanism based on ε dominance.

[0071] While local convergence metrics have proven effective in many cases, they struggle to cope with constraint boundary distortions and cannot accurately capture multimodal structures in confined spaces. To address these limitations, we propose a constrained multimodal dominance (CMD) framework that cleverly combines constraint handling with multimodality preservation. The CMD relation employs a three-level comparison strategy that prioritizes feasibility while retaining solutions from different modalities.

[0072] For any two solutions x1 and x2 in the decision space, the constraints are constrained multimodal dominated if and only if one of the following conditions holds:

[0073]

[0074] where φ(x) represents the constraint violation of solution x, d(x1,x2) is the Euclidean distance between two solutions in the normalized decision space, r is the modal identification radius, Indicates that x1 is Pareto dominant in the target space.

[0075] The first condition (C1) ensures that feasible solutions are always superior to infeasible solutions, thus guiding the search into the feasible region. The second condition (C2) establishes dominance among feasible solutions only if they belong to the same mode (i.e., their decision space distance is within the mode identification radius) and one is Pareto superior to the other in the objective space. This allows solutions from different modes to be retained even if they have dominant objective values. The third condition (C3) compares infeasible solutions based on constraint violations, prioritizing solutions with lower violation values.

[0076] A key component of the CMD relationship is the modal identification radius r, which determines whether two solutions belong to the same mode. In order to adapt to different problem environments without the need for problem-specific adjustments, this application adopts a dynamic radius adjustment mechanism:

[0077]

[0078] Among them, d i,j is x i and x jThe Euclidean distance between them. r represents half of the average distance between all solutions, which decreases as the evolution proceeds.

[0079] The updating process of the diversity archive adopts a two-stage environment selection approach, where the first stage focuses on multimodal preservation using the CMD relationship, while the second stage applies an ε-dominance-based quality control mechanism to ensure the quality of solutions within each modality.

[0080]

[0081]

[0082] The first stage focuses on multimodal preservation using CMD relations. It does this by calculating the CMD rank I for each solution in the combined population. CMD To identify non-dominated solutions in all modes (Solutions with a CMD level less than 1 (i.e., non-dominated solutions) are selected to form the initial filter set '.if The included solution is smaller than the required archive size N d , then other solutions are selected according to their CMD level until the archive is filled. ds (x) A decision space diversity metric is used to iteratively eliminate the solutions with the worst diversity contribution until the archive size constraint is met.

[0083] The CMD level (Constrained Multi-Modal Dominance Level) is an existing technology in this field. Its evaluation usually requires combining multi-dimensional indicators such as system goals, constraints, modal switching performance, and task completion effects, such as modal switching success rate, modal conflict rate, constraint violation penalty value, Pareto front coverage, etc., which will not be repeated in this application.

[0084] The second phase starts when the evolution process reaches a mature state (determined by s>0.5, where s is the evolution progress and ranges from 0 to 1), and applies a quality control mechanism based on ε dominance to ensure the quality of the solutions within each mode. This phase first extracts traditionally non-dominated solutions from the ε combined population. These solutions are initially designated as Non-dominated solutions. The combined population is then refined to this ε-filtered set and then enters the first stage.

[0085] The method ensures that solutions from different modes are retained regardless of the objective value, while maintaining a quality threshold to prevent the retention of significantly worse solutions from the same mode. By combining these mechanisms, the algorithm achieves robust performance in both the exploration and exploitation phases, effectively discovering and retaining multiple equivalent optima in the CMMOP.

[0086] The dual-profile co-evolution framework in this application strategically balances convergence and diversity throughout the optimization process. To gain a deeper understanding of the dynamic interaction between the convergence profile and the diversity profile, this application uses a multi-polygon problem with 10 decision variables and 2 objectives as a benchmark and analyzes the solution distribution at different evolution stages.

[0087] Evolution of solution distribution at different stages of the search process: In the early stage (10%), the adaptive ε constraint relaxation strategy of this application sets a relatively large value ε t , allowing solutions with high constraint violations to be retained in the Diversity Archive (DA). This strategic relaxation enables exploration of promising regions across infeasible barriers. Meanwhile, the Convergence Archive (CA) employs a convergence-first approach through its dual space diversity-based selection method, quickly approximating the true Pareto front and transferring this convergence information to guide the Diversity Archive.

[0088] As the search enters the middle stage (40%), the adaptive ε t The value is gradually reduced according to the proposed nonlinear scheme, thereby improving the convergence quality of solutions in the diversity archive. During this critical phase, the CMD relationship begins to effectively preserve local Pareto sets of acceptable quality through its three-level comparison strategy, which prioritizes feasibility while retaining solutions from different modalities. Notably, the convergence archive only identifies two of the four global Pareto sets at this stage, focusing primarily on target space convergence.

[0089] By the late stage (70%), the two-stage environmental selection process in the Diversity Archive has refined the selection of solutions for different ecological niches, maintaining a balance between multimodal preservation and solution quality. The synergy between the two archives has become more apparent, with the Diversity Archive transferring information from multiple Pareto sets to the Convergence Archive.

[0090] In the final stage (100%), this cooperative mechanism finally paid off – the convergence profile successfully identified all four global Pareto sets while maintaining excellent convergence to the true Pareto front. The diversity profile achieved the primary goal of constrained multimodal multi-objective optimization by retaining multiple equivalent solutions across different modalities through CMD-based selection.

[0091] With the optimization εt As our adaptive plan progresses and decreases, the algorithm systematically discards lower-quality solutions. This shift shifts our focus toward refinement, significantly improving convergence and distribution in later stages and ultimately outperforming competing algorithms.

[0092] In summary, our co-evolutionary framework effectively balances the competing requirements of constraint satisfaction, convergence, and multimodal preservation. The convergence archive provides critical guidance for the constrained Pareto front in the early stages, while the diversity archive ensures the discovery and preservation of multiple equivalent Pareto sets through its CMD relationship and two-stage selection process. In the later stages, the two archives collaborate to optimize convergence quality and solution diversity. This balanced approach enables our application to successfully identify all equivalent Pareto sets while maintaining excellent convergence properties, making it particularly effective for constrained multimodal and multi-objective optimization problems such as microgrid optimization.

[0093] This application proposes a cooperative dual-population framework that effectively balances the competing requirements of convergence, diversity, and feasibility, taking a significant step forward in solving the challenging problem of constrained multimodal multi-objective optimization. By effectively balancing convergence, diversity, and feasibility, it provides multiple high-quality implementations for microgrid optimization while satisfying all problem constraints.

[0094] As used herein, the word "preferred" is intended to serve as an example, instance, or illustration. Any aspect or design described herein as "preferred" is not necessarily to be construed as advantageous over other aspects or designs. Rather, the use of the word "preferred" is intended to present concepts in a concrete manner. As used in this application, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or." That is, unless otherwise specified or clear from the context, "X employs A or B" is intended to mean any of the naturally inclusive permutations. That is, if X employs A; X employs B; or X employs both A and B, then "X employs A or B" is satisfied in any of the foregoing examples.

[0095] Moreover, although the present disclosure has been shown and described with respect to one or implementation, those skilled in the art will think of equivalent variations and modifications based on reading and understanding of this specification and the accompanying drawings. The present disclosure includes all such modifications and variations and is limited only by the scope of the appended claims. In particular, with respect to the various functions performed by the above-mentioned components (such as elements, etc.), the terms used to describe such components are intended to correspond to any component (unless otherwise indicated) that performs the specified function of the component (such as it is functionally equivalent), even if structurally different from the disclosed structure that performs the function in the exemplary implementation of the present disclosure shown herein. In addition, although the specific features of the present disclosure have been disclosed with respect to only one of several implementations, such features can be combined with one or other features of other implementations that can be desired and advantageous for a given or specific application. Moreover, insofar as the terms "including", "having", "containing" or their variations are used in specific embodiments or claims, such terms are intended to be included in a manner similar to the term "comprising".

[0096] The functional units in the embodiments of the present invention may be integrated into a single processing module, or each unit may exist physically separately, or multiple or more units may be integrated into a single module. The aforementioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium. The aforementioned storage medium may be a read-only memory, a magnetic disk, or an optical disk, etc. The aforementioned devices or systems may execute the storage method in the corresponding method embodiment.

[0097] In summary, the above embodiment is one implementation method of the present invention, but the implementation method of the present invention is not limited to the described embodiment. Any other changes, modifications, substitutions, combinations, and simplifications that deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A multi-modal and multi-objective microgrid optimization method based on constrained multi-modal dominance, characterized by: It includes the following steps: Obtain multiple objectives for microgrid optimization; Initialize convergence profiles with complementary effects and Diversity Archives Wherein, the convergence profile Guide the search towards the constrained Pareto front, the diversity profile A two-stage environment selection process is used to retain multiple equivalent solutions in different domains; Evaluating Convergence Profiles and Diversity Archives Target values ​​and constraint violations; Iterate until the maximum number of function evaluations is reached; in each iteration, perform the following steps: perform mating selection on parents based on crowding distance; select the best parent from the convergence archive and Diversity Archives Generating offspring; the convergence profile The convergence profile is updated by combining it with the offspring and using an enhanced diversity measure; the diversity profile The update is performed via a two-stage process, first preserving multimodality using restricted multimodal dominance relations, and then refining the selection using a quality control mechanism based on ε-dominance, where ε is the constraint value; Output the final microgrid optimization plan.

2. The multi-modal multi-objective microgrid optimization method based on constrained multi-modal dominance according to claim 1 is characterized in that: The diversity metric not only prioritizes feasibility and convergence but also maintains diversity in the objective and decision spaces; specifically, all individuals are ranked according to their objective values and overall constraint violations; if the number of non-dominated solutions exceeds N, where N is the number of solutions, a quadratic selection method based on dual-space diversity is used to select solutions, otherwise, the first solution is retained.

3. The multi-modal multi-objective microgrid optimization method based on constrained multi-modal dominance according to claim 1, characterized in that: Use an adaptive ε-constraint relaxation strategy to dynamically adjust the ε value throughout the evolutionary process, and its formula is as follows: where ε t is the relaxation threshold of the tth generation, ε init is the initial relaxation threshold, T c is the algebra of relaxation termination, α>0 is the shape parameter that controls the rate of descent; The initial relaxation threshold ε init Determined dynamically based on the distribution of constraint violations in the initial population: Among them, φ(x i ) represents the overall constraint violation of the solution in the initial population, x i is the i-th solution.

4. The multi-modal multi-objective microgrid optimization method based on constrained multi-modal dominance according to claim 1, characterized in that: The quadratic selection method based on dual space diversity updates the convergence archive by: when the number of non-dominated solutions |F| is less than or equal to the required archive size N c When N is reached, all non-dominated solutions are directly saved in the convergence archive. Otherwise, the diversity contribution of each solution in the objective space and decision space is calculated, the solution with the lowest diversity contribution is determined, and it is deleted from the archive. This process continues until the archive size is reduced to N. c ; The diversity metric Δ of the dual space ds It is expressed as follows: D ds (x)=Δ o (x)+D d (x) Among them, Δ o (x) and Δ d (x) represents the diversity contribution of solution x in the target space and decision space respectively; and Represents the distance between solution x and solution y in the jth target dimension and the kth decision variable dimension respectively; and are the first and second nearest neighbors of solution x in the jth target dimension; and are the first and second nearest neighbors of the solution x in the dimension of the kth decision variable; and are the maximum and minimum values ​​of the j-th target and the maximum and minimum values ​​of the k-th decision variable in the current archive respectively.

5. The multi-modal multi-objective microgrid optimization method based on constrained multi-modal dominance according to claim 1, characterized in that: The two-stage environmental selection process combines the restricted multi-modal dominance relationship with the quality control mechanism of ε-domination; For any two solutions x1 and x2 in the decision space, the restricted multimodal dominance relationship is expressed as follows if and only if one of the following conditions holds: x1 < CMD x2 where φ(x) represents the constraint violation of solution x, d(x1, x2) is the Euclidean distance between two solutions x1 and x2 in the normalized decision space, r is the mode recognition radius, and x1 < x2 means x1 Pareto-dominates in the objective space; The first condition ensures that feasible solutions are always better than infeasible solutions, thus guiding the search into the feasible region; The second condition ensures that dominance is established between feasible solutions only when the feasible solutions belong to the same mode and one Pareto-dominates the other in the objective space; the third condition compares infeasible solutions according to the constraint violation and preferentially selects the solution with a lower violation value.

6. The multi-modal multi-objective microgrid optimization method based on constrained multi-modal dominance according to claim 5, characterized in that: The mode recognition radius r adopts a dynamic radius adjustment mechanism: Among them, d i,j is x i and x j The Euclidean distance between them; r represents half of the average distance between all solutions, which gradually decreases as the evolution proceeds.

7. The multi-modal multi-objective microgrid optimization method based on constrained multi-modal dominance according to claim 6, characterized in that: The first stage of the two-stage environment selection process uses the CMD relation for multimodality preservation, which identifies non-dominated solutions across all modalities by computing the CMD rank of each solution in the combined population. Select non-dominated solutions with CMD level less than 1 to form the initial filter set if The included solution is smaller than the required archive size N d , then other solutions are selected according to their CMD level until the archive is filled; on the contrary, Δ ds (x) Adopting the decision space diversity metric to iteratively eliminate the solutions with the worst diversity contribution until the archive size constraint is met; In the second stage, a quality control mechanism based on ε-domination is applied to ensure the quality of solutions within each mode, specifically including: first, extract traditionally non-dominated solutions from the ε-combined population; These solutions were originally specified as non-dominated solutions, the combined population is then refined into an ε-filtered set before entering the first stage.

Images