A constraint multi-objective optimization collaborative design method with diversity enhancement

Abstract

The application discloses a constraint multi-objective optimization collaborative design method with diversity enhancement, relates to the technical field of industrial design, and comprises the following steps: for a complex constraint multi-objective optimization problem in an industrial design target, a plurality of functionally complementary collaborative evolution tasks are constructed; based on the collaborative evolution tasks, in a search process, unconstrained frontier information, relaxed constraint frontier information, infeasible region diversity information and feasible boundary competition information are simultaneously utilized to perform constraint multi-objective optimization collaborative design on the industrial design target. The application improves the approximation capability of a constraint Pareto frontier, the quality of feasible solution distribution and the practical applicability in engineering constraint optimization problems.

Description

Technical Field

[0001] This invention relates to the field of industrial design technology, and more specifically, to a multi-objective optimization collaborative design method with enhanced diversity constraints. Background Technology

[0002] Constrained multi-objective optimization problems are widely found in many industrial fields such as engineering optimization, mechanical structure design, energy scheduling, path planning, and intelligent manufacturing. These problems require finding trade-offs among multiple conflicting optimization objectives while satisfying a series of complex constraints such as size, performance, safety, and energy consumption. Moreover, the feasible region in real-world engineering often exhibits complex characteristics such as irregularity, narrowness, fracture, and non-convexity. The Pareto front of real constraints is often close to the boundary of the feasible region or even surrounded by infeasible regions, which makes the algorithm need to take into account global exploration, constraint satisfaction, and maintenance of solution set diversity. The difficulty of solving these problems is much higher than that of unconstrained multi-objective optimization, making it a key and challenging technical problem in the industry. Currently, existing constrained multi-objective evolutionary algorithms are mainly divided into five categories: First, methods based on constraint dominance rules, which select individuals based on the principle of prioritizing feasible solutions, achieving simplicity and fast convergence of feasible solutions. However, in the early stages of evolution, high-value infeasible solutions at the constraint boundaries are easily discarded, resulting in local convergence and insufficient global search capability. Second, methods based on penalty functions, which transform constrained problems into unconstrained problems through penalty terms, have wide applicability. However, the penalty factor depends on manual experience setting, which is prone to problems such as loss of search information or convergence stagnation. Third, methods based on ε-constraint dynamic relaxation, which broadens the early search range through phased tightening and loosening of constraints. However, the threshold control strategy has poor universality and is prone to premature shrinkage of the search range or waste of iteration resources. Fourth, multi-population co-evolutionary methods, which rely on population division of labor to achieve feasibility. The first approach involves collaborative search with infeasible solutions, but lacks diversity enhancement and dynamic resource control mechanisms, making it difficult to obtain a complete and uniform Pareto front in complex feasible regions. The second approach, the closest to the present invention, uses a multi-task assisted evolutionary method to broaden the search dimension and mine unconstrained and relaxed constraint front information by decomposing multiple auxiliary tasks. However, it has significant technical shortcomings. On the one hand, it adopts a fixed resource allocation mode, making it impossible to dynamically allocate computing power according to the algorithm's iteration lifecycle, resulting in low resource utilization. On the other hand, it focuses on convergence optimization and lacks diversity enhancement mechanisms, easily leading to uneven front distribution and incomplete coverage. Furthermore, when facing narrow, fragmented, or infeasible regions, the single task search dimension makes it difficult to overcome complex constraint barriers, easily leading to local convergence and omission of optimal solutions. Taking the optimization of a multi-plate clutch brake as an example, it needs to balance the conflicting goals of lightweight design and rapid braking under multiple stringent engineering constraints. The design variables have strong nonlinear coupling, making it difficult for existing algorithms to output high-quality compromise solutions that are compliant with constraints and have uniform distribution. Summary of the Invention

[0003] To address the aforementioned problems, the present invention aims to provide a constrained multi-objective optimization collaborative design method with enhanced diversity. This method addresses the shortcomings of existing constrained multi-objective optimization algorithms, such as weak adaptability to complex constraints, low accuracy in front-end approximation, poor solution set diversity, and waste of computational resources, thereby meeting the needs of high-precision and high-complexity engineering optimization.

[0004] To achieve the above technical objectives, this application provides a constrained multi-objective optimization collaborative design method with enhanced diversity, comprising the following steps: To address the complex, multi-objective optimization problem with constraints in industrial design goals, we construct multiple complementary co-evolutionary tasks. Based on the co-evolution task, this study utilizes unconstrained frontier information, relaxed constraint frontier information, infeasible region diversity information, and feasible boundary competition information simultaneously during the search process to perform constrained multi-objective optimization collaborative design of industrial design objectives.

[0005] Preferably, when constructing multiple co-evolutionary tasks with complementary functions, the unconstrained front exploration task UPF, the relaxed constraint front exploration task SPF, the diversity enhancement task DVS, and the constrained Pareto front preservation task CPF are constructed as co-evolutionary tasks.

[0006] Preferably, in co-evolutionary tasks, the most advanced part of the target is explored through UPF tasks without considering any constraints; Explore the region between identified UPFs and current possible CPFs using SPF missions; The DVS task finds the region formed by the interconnection of all current optimal feasible solutions in the offspring, where the region can radiate to the infeasible region, so that the total constraint violation value of the individuals retained in the entire uniform target space is minimized. The CPF task utilizes the dominance relationship between objective values ​​and constraint violation values ​​to select feasible solutions.

[0007] Preferably, when performing the search, the environment selection for the UPF and SPF tasks is completed using a frontier mutual traction search strategy.

[0008] Preferably, when performing a search, a diversity enhancement strategy based on the dominance region partitioning is used to complete the environment selection for the DVS task.

[0009] Preferably, during the search, a convergence-driven feasible boundary expansion strategy is used to complete the environment selection for the CPF task.

[0010] Preferably, during the search, the search is performed using differential evolution operators and genetic algorithm operators to generate candidate offspring, thereby enriching the source of candidate solutions.

[0011] Preferably, during the search, the global search capability in the continuous decision variable space is enhanced by the differential evolution operator, and the population recombination and local perturbation capability is maintained by the genetic algorithm operator.

[0012] Preferably, when performing constrained multi-objective optimization collaborative design, a lifecycle-based resource allocation strategy is introduced to enhance resource allocation for different tasks in different design cycles.

[0013] Preferably, when performing resource allocation, more resources are allocated to UPF and SPF tasks in the early stage of design; the role of DVS tasks is enhanced in the middle stage of design; and more resources are allocated to CPF tasks in the later stage of design.

[0014] Based on the same inventive concept, this invention also discloses a constrained multi-objective optimization collaborative design system with enhanced diversity, comprising: The building blocks are used to construct multiple complementary co-evolutionary tasks for complex constrained multi-objective optimization problems in industrial design goals. The collaborative design module is used to perform constrained multi-objective optimization collaborative design of industrial design goals based on co-evolution tasks, simultaneously utilizing unconstrained frontier information, relaxed constraint frontier information, infeasible region diversity information, and feasible boundary competition information during the search process.

[0015] The present invention discloses the following technical effects: The SRCMOEA proposed in this invention explores unconstrained fronts and relaxed constraint fronts through UPF and SPF tasks, respectively, enabling the population to gradually approach the real constrained Pareto front from a larger search range, thereby improving the frontier search capability under complex constraint environments.

[0016] This invention promotes the co-evolution of four types of tasks—UPF, SPF, DVS, and CPF—and introduces a lifecycle resource allocation strategy, enabling different tasks to play a major role at different evolutionary stages, thereby improving the utilization rate of search resources.

[0017] The proposed DVS diversity enhancement task can utilize efficient infeasible solutions in the same dominant layer region to fill the distribution gaps in the current constrained Pareto front; the CPF task is responsible for retaining competing solutions that satisfy the constraints and have good convergence. Compared with existing methods, this invention can better balance constraint feasibility, front convergence, and solution set diversity, and is suitable for multi-objective optimization problems with narrow feasible regions, fractures, or complex constraint boundaries. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of the method described in this invention.

[0020] Figure 2 This is the IGDp convergence graph of SRCMOEA described in this invention and nine comparison algorithms.

[0021] Figure 3 This is the HV convergence graph of SRCMOEA described in this invention and 9 comparison algorithms.

[0022] Figure 4 This refers to the lifecycle parameter setting described in this invention.

[0023] Figure 5 This is a feasible compromise solution for the SRCMOEA output in the design target space of the multi-plate clutch brake described in this invention.

[0024] Figure 6 This is a comparison between the SRCMOEA output and the random sampling results described in this invention.

[0025] Figure 7 This is the quality-braking time trade-off curve of the candidate solution described in this invention.

[0026] Figure 8 This is a comparison of the feasibility of SRCMOEA described in this invention with random sampling. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0028] like Figure 1As shown, this invention provides a constrained multi-objective optimization collaborative design method with enhanced diversity (SRCMOEA). This method constructs unconstrained frontier exploration tasks, relaxed constraint frontier exploration tasks, diversity enhancement tasks, and constrained Pareto frontier preservation tasks, enabling different tasks to perform functions such as frontier exploration, boundary traction, diversity supplementation, and preservation of feasible high-quality solutions during the search process. Simultaneously, this invention introduces a lifecycle-based resource allocation strategy, dynamically adjusting computational resources according to the roles of different tasks at different stages of evolution. This allows for expanding the search scope in the early stages, strengthening constraint boundary exploration in the middle stages, and focusing on preserving high-quality feasible solutions in the later stages, thereby improving overall search efficiency.

[0029] In one embodiment, the technical solution of the present invention generally includes four types of co-evolutionary tasks and a lifecycle resource allocation strategy. The four types of tasks are unconstrained front exploration task (UPF), relaxed constraint front exploration task (SPF), diversity enhancement task (DVS), and constrained Pareto front preservation task (CPF).

[0030] In one embodiment, the present invention proposes three environment selection strategies: 1. Using a frontier mutual traction search strategy to complete the environment selection for UPF and SPF tasks; 2. Using a diversity enhancement strategy based on dominance region partitioning to complete the environment selection for DVS tasks; 3. Using a convergence-driven feasible boundary expansion strategy to complete the environment selection for CPF tasks. Specifically, the UPF task is responsible for exploring the frontier of the objective without considering any constraints, unaffected by complex constraints, to quickly reach the UPF region in the early stages and skip meaningless intermediate searches; the SPF task is responsible for exploring the region between the identified UPF and the current possible CPF, providing a solution set that effectively transmits the advantages accumulated by UPF to CPF exploration; the DVS task does not focus on the convergence of individuals, but rather on finding the region formed by the interconnection of all current optimal feasible solutions in the offspring. This region should radiate to infeasible regions, minimizing the total constraint violation value of individuals retained in the entire uniform objective space; the CPF task utilizes the dominance relationship between objective value and constraint violation value to select feasible solutions.

[0031] For example, during the evolutionary process, an initial population is first randomly generated, and the objective function value, constraint violation degree, and feasibility state of each individual are calculated. Subsequently, according to the objectives of different tasks, the population information is allocated to four tasks: UPF, SPF, DVS, and CPF. Each task operates under a unified evolutionary framework but uses different environment selection rules, enabling it to perform functions such as frontier exploration, boundary traction, diversity supplementation, and feasible solution preservation, respectively. Through this task division, the search bias caused by a single constraint processing rule can be avoided, allowing both infeasible and feasible solutions to play a role at appropriate stages.

[0032] In one embodiment, based on the four task categories, this invention further introduces a lifecycle-based resource allocation strategy. This strategy posits that the strength of different tasks during the evolutionary process is not constant. In the early stages of evolution, due to the need to expand the search range, more resources can be allocated to UPF and SPF tasks; in the middle stages, due to the need to strengthen exploration near constraint boundaries and supplement diversity, the role of DVS tasks is enhanced; in the later stages of evolution, due to the need to concentrate on preserving high-quality feasible solutions and stabilizing output results, CPF tasks occupy a more important position.

[0033] For example, the present invention can dynamically adjust the computing resources of each task according to the search needs at different stages through a lifecycle resource allocation strategy, thereby improving the overall resource utilization efficiency.

[0034] In one embodiment, the present invention also employs an enhanced evolutionary operator to generate candidate offspring.

[0035] For example, by combining differential evolution operators and genetic algorithm operators for searching, differential evolution operators are suitable for enhancing global search capabilities in continuous decision variable spaces, while genetic algorithm operators are suitable for maintaining population recombination and local perturbation capabilities. The offspring generated by the two types of operators are sent to different task populations to participate in environmental selection, which can obtain richer candidate solution sources in different search regions.

[0036] In summary, this invention does not simply employ a single constraint processing rule, nor does it simply add an auxiliary population. Instead, it achieves an organic combination of unconstrained frontier exploration, relaxed constraint frontier guidance, diversity supplementation, and constrained Pareto frontier preservation through the co-evolution of four types of tasks: UPF, SPF, DVS, and CPF.

[0037] First, this invention designs a four-task co-evolutionary framework, which is a collaborative optimization framework consisting of an unconstrained front exploration task (UPF), a relaxed constraint front exploration task (SPF), a diversity enhancement task (DVS), and a constrained Pareto front preservation task (CPF). UPF expands the search range of the objective space, SPF guides the population from the relaxed constraint region towards the true feasible boundary, DVS enhances the distribution diversity near the front, and CPF preserves competitive candidate solutions that ultimately satisfy the constraints. The four tasks have clear divisions of labor and work together through information collaboration to serve the original constrained multi-objective optimization problem.

[0038] Second, this invention designs a lifecycle-based resource allocation strategy. This strategy dynamically adjusts the computational resources for four types of tasks—UPF, SPF, DVS, and CPF—according to different stages of the evolutionary process, allowing each task to play a major role in its most effective phase. In the early stages of evolution, UPF and SPF are emphasized to expand the search range and discover potential frontier regions; in the middle stages, DVS is enhanced to supplement the diversity near the Pareto front; and in the later stages, CPF is strengthened to retain high-quality feasible solutions and stabilize output results. This lifecycle-based resource allocation strategy avoids search redundancy and computational resource waste caused by fixed resource allocation.

[0039] Third, this invention designs a frontier mutual-guided search mechanism using UPF and SPF. UPF explores the unconstrained Pareto front under weakened constraint influence, providing direction for objective optimization; SPF explores candidate solutions close to the feasible boundary under relaxed constraints, guiding the population from infeasible regions to the truly constrained Pareto front. The synergistic effect of these two mechanisms avoids premature confinement to the current feasible region and prevents the unconstrained search from completely deviating from the true feasible domain.

[0040] Fourth, this invention designs a diversity enhancement strategy based on dominance region partitioning. This invention proposes a diversity enhancement task (DVS), which identifies candidate solutions that have supplementary value to the current constrained Pareto front distribution through dominance region partitioning, search within the same dominance layer, and utilization of infeasible solutions. This strategy does not simply retain all infeasible solutions, but rather selects candidate solutions that can expand the front coverage, fill distribution gaps, or connect broken regions. For individuals highly similar to existing feasible solutions, their retention priority is reduced, thereby reducing duplicate solutions and improving the final solution set distribution.

[0041] Fifth, this invention designs a convergence-driven feasible boundary expansion strategy. This strategy primarily retains feasible solutions that satisfy the constraints, while allowing infeasible solutions with low constraint violation, good objective function performance, and located near the feasible boundary to participate in the competition at a certain stage. This approach can utilize the search value of infeasible solutions near the boundary to drive the population to move towards a better feasible region, avoiding the premature discarding of potentially high-quality solutions by traditional feasibility-first rules.

[0042] Example 1: The proposed SRCMOEA was validated through comparative experiments, ablation experiments, and parameter sensitivity analysis. Experimental results show that SRCMOEA can approximate the constrained Pareto front well in complex constrained multi-objective optimization problems and maintain good solution set diversity.

[0043] First, to verify the overall performance of SRCMOEA, it was compared with existing constrained multi-objective evolutionary algorithms. The comparison algorithms included NSGA-II, PPS, CMOEAMS, C3M, CCMO, DPCPRA, APSEA, DVCEA, and DEST. The experiments used MW, LIRCMOP, DASCMOP, and LSCM as test problems, and IGDp and HV as evaluation metrics. IGDp measures the distance between the obtained solution set and the true constrained Pareto front; a smaller value indicates better convergence. HV measures the coverage of the solution set in the objective space; a larger value indicates better overall performance. The symbols "+", "-", and "=" indicate that the algorithm shows significantly better, significantly worse, or similar performance to SRCMOEA. If the algorithm fails to find a feasible solution in 30 independent runs, its IGDp and HV results are recorded as NaN. All results in the tables are presented as metrics (means), with the best result in each row highlighted in gray.

[0044] Table 1 shows the performance overview of all algorithms on 49 test problems based on IGDp and HV, which strongly demonstrates that the overall performance of SRCMOEA is significantly better than the compared algorithms.

[0045] Table 1 Summary of comparison results for the four test kits To provide a more intuitive understanding of the convergence of the algorithm of this invention, the following graph shows the changes in the IGDp and HV evaluation metrics of some test functions with the number of evaluations, as shown below. Figure 2 , Figure 3 As shown.

[0046] The results show that SRCMOEA converges the fastest, achieving an excellent result almost at 30% of the evaluation attempts. This is attributed to the UPF and SPF tasks in SRCMOEA's frontier exploration, demonstrating the effectiveness of the algorithm in these tasks. Overall, SRCMOEA also achieves better performance metrics compared to other algorithms. Especially in some extreme test environments, this algorithm is more efficient, escaping local optima and finding the complete Power Factor (PF).

[0047] The proposed SRCMOEA consists of four tasks. After removing the necessary CPF and UPF tasks, and using a controlled variable method, the SPF and DVS tasks are further removed, resulting in two sub-versions, which are then compared with the complete SRCMOEA. To verify the effectiveness of the proposed strategy, ablation experiments were conducted on the algorithm. Comparative experiments were performed on the LIRCMOP, DASCMOP, MW, and LSCM test suites, and a summary table is provided below.

[0048] Table 2 Ablation Analysis of Task Modules The table shows the comparison results of the sub-version and normal version of the algorithm with missing SPF and DVS tasks, respectively.

[0049] Ablation experiments show that SRCMOEA performs better on most test problems. For the SPF task, it may not provide additional advantages for some test problems that do not have strong exploration requirements. For the DVS task, almost all test problems have diversity requirements, so diversity enhancement strategies significantly improve the performance of SRCMOEA.

[0050] Sensitivity analysis was conducted to verify the optimal values ​​for each task lifecycle parameter. Comparative experiments were performed on the LIRCMOP, DASCMOP, MW, and LSCM test suites, and a summary table is provided.

[0051] Sensitivity analysis of parameters in Table 3 The table shows the comparison results of each parameter sub-version with the default preset version.

[0052] The results in Table 3 show that setting the lifespan of CPF to 70%t, DVS to 70%t, and UPF and SPF to 25%t all yielded better results than the preset parameter versions. Therefore, the final parameters adopted in this invention are UPF and SPF at 25%t, DVS at 70%t, and CPF at 70%t. Figure 4 As shown.

[0053] In summary, the experimental results demonstrate that the SRCMOEA proposed in this invention can effectively handle complex constrained multi-objective optimization problems, exhibiting good overall performance in terms of frontier approximation, diversity preservation, and engineering feasibility. Furthermore, ablation experiments and parameter sensitivity analysis further illustrate the practical effectiveness of the multi-task collaborative mechanism, DVS diversity enhancement strategy, and lifecycle resource allocation strategy in this invention.

[0054] Example 2: This example uses the design and modeling of a multi-plate clutch brake as an example. In mechanical transmission and vehicle braking systems, multi-plate clutch brakes need to provide stable and controllable braking torque within a limited space. Their design quality directly affects the overall response speed, thermal load, and safety margin. The inner and outer friction radii, friction pad thickness, axial clamping force, and number of friction surfaces collectively determine the friction contact area, average sliding speed, contact pressure, and braking torque. Excessively reducing the structural dimensions can lower the system mass, but the contact pressure, pressure-velocity product, and braking torque constraints are more easily compromised. Simply pursuing shorter braking time usually requires increasing the clamping force or the number of friction surfaces, leading to increased structural mass, axial envelope length, and wear risk. Due to the nonlinear coupling between variables, traditional methods relying on experience to adjust parameters item by item are insufficient to simultaneously consider feasibility and objective trade-offs. A multi-objective evolutionary algorithm is needed to search for a set of alternative design schemes within a complex feasible domain. Therefore, this problem is essentially a multi-objective optimization design problem that balances lightweight design, rapid braking, and engineering safety constraints.

[0055] This invention addresses the design of a multi-plate clutch brake. This problem comprises 5 design variables, 2 optimization objectives, and 8 engineering constraints. While relatively small in scale, it exhibits comprehensive constraint characteristics, clearly demonstrating mechanisms such as constraint violation guidance, utilization of infeasible solutions, and maintenance of constraint Pareto front diversity. Therefore, this invention uses it as a real-world engineering test problem in the SRCMOEA validity specification.

[0056] Based on the above objective function and constraints, a constrained multi-objective optimization problem can be constructed. In the optimization of a multi-plate clutch brake, it is necessary to simultaneously minimize the brake mass and braking time, while satisfying engineering constraints such as minimum radial friction width, maximum axial envelope length, contact pressure, pressure-velocity product, sliding speed, braking time, and braking torque. This problem exhibits significant trade-offs in the objective space and a phenomenon where feasible and infeasible regions are interleaved in the decision space, making it suitable for verifying the search capabilities of constrained multi-objective evolutionary algorithms.

[0057] 1. Based on the existing multi-task co-evolutionary framework, we analyze the characteristics of different constraints through SRCMOEA, and allocate exploration resources for each task through a life cycle-based resource allocation strategy, thereby enhancing the utilization rate of exploration resources in the population.

[0058] 2. This invention utilizes the relationship between Pareto dominance and constraints. By treating constraint violation as an additional dominance ordering rule, it changes the dominance restrictions on some infeasible solutions and guides the explored unconstrained frontier solutions layer by layer towards constrained solutions, thereby quickly locking down the region where the constrained Pareto front is located during the problem-solving process.

[0059] 3. This invention proposes a diversity exploration enhancement strategy to supplement the diversity of the current CPF. This strategy explores regions of the same dominance layer to find infeasible solutions that contribute to diversity, and achieves horizontal exploration of fractured infeasible regions by eliminating some similar feasible solutions.

[0060] Table 4 As shown in Table 4, the above are the specific data of 40 candidate designs for multi-plate clutch brakes, including mass and braking time.

[0061] Table 5 As shown in Table 5, the above are the values ​​of each design variable in the 40 candidate brake schemes, corresponding to the internal friction radius, external friction radius, friction pad thickness, axial clamping force, and effective number of friction surfaces, respectively. Parameter descriptions are shown in Table 6.

[0062] Table 6 This implementation provides a design method for a multi-plate clutch brake based on SRCMOEA, including inputs and outputs. The inputs include population size N, objective function, engineering constraint function, maximum number of evaluations, range of brake design variables, and brake operating parameters. The output includes the quality of each candidate brake scheme. Braking time Constraint violation degree (CV), feasibility status, and internal friction radius (R) i External friction radius R o The parameters include the friction pad thickness h, axial clamping force F, and effective number of friction surfaces z. Specifically, the steps include: Input: Population size N, objective function (brake mass) Braking time Engineering constraint functions to Maximum number of reviews; Step 1: Randomly generate an initial population of candidate brake schemes; Step 2: Calculate the physical properties and engineering constraints of each candidate brake design; Step 3: Construct four types of collaborative tasks: UPF, SPF, DVS, and CPF; Step 4: Allocate computing resources based on the task lifecycle status; Step 5: Generate new candidate brake schemes using differential evolution operators and genetic algorithm operators; Step 6: Use the frontier mutual traction search strategy to complete the environment selection for the UPF and SPF tasks; Step 7: Use a diversity enhancement strategy based on the distance of the brake design variables to complete the environment selection for the DVS task; Step 8: Use a convergence-driven feasible boundary expansion strategy to complete the environment selection for the CPF task; Step 9: Environment selection is complete, resulting in a candidate solution library for multi-plate clutch brakes that meets engineering constraints; Output: R i R o h, F, z , CV and feasibility status.

[0063] The candidate brake scheme in step 1 is represented as x = (R i ,R o ,h,F,z), where R i R represents the radius of internal friction. o Let represent the external friction radius, h represent the friction plate thickness, F represent the axial clamping force, and z represent the effective number of friction surfaces. The candidate scheme population can be represented as: In the formula, N represents the number of candidate brake schemes. Let i represent the i-th candidate brake scheme.

[0064] The core objective functions in step 2 include brake mass and braking time. Brake mass can be expressed as: In the formula, ρ represents the density of the friction plate material. A smaller value indicates a lighter brake structure. Braking time can be expressed as: In the formula, I z M represents the equivalent moment of inertia, ω represents the angular velocity at the start of braking, and M represents the angular velocity at the start of braking. h Indicates braking torque, Represents the residual resistance torque. The smaller the value, the faster the braking response.

[0065] To calculate the brake's mass, braking time, and constraint state, it is necessary to first calculate the contact area, average friction radius, angular velocity, contact pressure, average sliding speed, and braking torque of the candidate solutions, as follows: In the formula, A represents the frictional contact area, and R... s The average friction radius is represented by n, and the shaft speed is represented by P. rz V represents the contact pressure. sr denoted by , where μ represents the average sliding speed and μ represents the coefficient of friction.

[0066] In addition, the engineering constraints of the multi-plate clutch brake must be met, and all constraints are written as follows: The form is ≤0. The formula for calculating the degree of constraint violation is as follows: In the formula, CV(x) = 0 indicates that the candidate solution satisfies all engineering constraints, and CV(x) > 0 indicates that there is a constraint violation. The specific constraint functions are as follows: In the formula, ΔR represents the minimum radial friction width, δ represents the friction plate gap, and L max Indicates the maximum axial envelope length. Indicates the allowable contact pressure. This represents the maximum average sliding speed. Indicates the maximum permissible braking time. represents the required load torque, and s represents the torque safety factor.

[0067] In step 3, the SRCMOEA collaborative task model includes four types of tasks: UPF, SPF, DVS, and CPF. UPF is used to explore the unconstrained mass-braking time front without considering constraints; SPF is used to explore relaxed constraint boundaries, so that the unconstrained front gradually approaches the feasible boundary; DVS is used to supplement candidate schemes with large differences in structural parameters; and CPF is used to retain brake schemes that ultimately meet engineering constraints and have a good mass-time trade-off.

[0068] In step 4, the lifecycle status calculation formula for each task is as follows: in, This represents the feasibility rate of candidate brake schemes in task j. Indicates the average constraint violation rate. This represents the improvement in the trade-off front between quality and braking time, where α, β, and γ represent weights, and ε represents a constant to prevent the denominator from being zero. The amount of resources obtained by each task is: In the formula, η represents the number of candidate solutions assigned to task j, and η represents the resource allocation sensitivity coefficient.

[0069] In step 7, to avoid overly similar output schemes, the structural differences between candidate schemes are evaluated using the brake design variable distance: in, and This represents two candidate brake designs. and Let represent the upper and lower bounds of the i-th design variable, respectively. If the d values ​​of the two feasible solutions are too small and , If the solutions are close to each other, the retention priority of the more crowded solutions is reduced; if the infeasible solution has a small CV and a large d value, it can be used as a supplementary sample of diversity near the fractured feasible region.

[0070] The SRCMOEA multi-plate clutch brake design model consists of an input layer, a variable encoding layer, a physical evaluation layer, a four-task collaborative search layer, and an output layer. For example... Figure 1 As shown, the input layer receives brake operating parameters and variable ranges; the variable encoding layer generates candidate schemes x; and the physical evaluation layer calculates... , The four-task collaborative search layer performs the co-evolution of UPF, SPF, DVS and CPF; the output layer generates a library of brake compromise solutions that meet engineering constraints.

[0071] The brake physical evaluation formula, Pareto dominance relation, differential evolution operator, genetic algorithm operator and non-dominated sorting used in this embodiment are existing technologies that can be adopted. The difference is that the present invention embeds the above-mentioned existing technologies into the design process of multi-plate clutch brakes, and establishes a four-task collaborative resource framework around geometric constraints, pressure and speed constraints and braking dynamics constraints, thereby forming a complete technical solution that can directly output brake structural parameters and performance indicators.

[0072] Experimental results show that the experiment was conducted using MATLAB R2023b software under Windows 10, with a maximum of 10,000 evaluation iterations. The results were displayed using SRCMOEA, yielding 40 candidate solutions, all of which satisfied all constraints. The minimum mass was 0.253905, and the shortest braking time was 0.002784. Figure 5 As shown, several reasonable and efficient multi-plate clutch brake design schemes can be obtained.

[0073] To further illustrate the search results, such as Figure 6 , Figure 7 , Figure 8 As shown, this invention adds a compromise curve for candidate solutions and a feasibility comparison chart. The compromise curve is used to illustrate the conflicting relationship between quality degradation and braking time variation, while the feasibility comparison chart is used to demonstrate that SRCMOEA can generate design solutions that meet engineering constraints more stably than random search.

[0074] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0075] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0076] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A constrained multi-objective optimization collaborative design method with enhanced diversity, characterized in that, Includes the following steps: To address the complex, multi-objective optimization problem with constraints in industrial design goals, we construct multiple complementary co-evolutionary tasks. Based on the aforementioned co-evolution task, during the search process, unconstrained frontier information, relaxed constraint frontier information, infeasible region diversity information, and feasible boundary competition information are simultaneously utilized to perform constrained multi-objective optimization co-design of the industrial design objective.

2. The multi-objective optimization collaborative design method with enhanced diversity according to claim 1, characterized in that: When constructing multiple complementary co-evolutionary tasks, the unconstrained front exploration task UPF, the relaxed constraint front exploration task SPF, the diversity enhancement task DVS, and the constrained Pareto front preservation task CPF are constructed as the co-evolutionary tasks.

3. The multi-objective optimization collaborative design method with enhanced diversity according to claim 2, characterized in that: In co-evolutionary tasks, the UPF task is used to explore the forefront of the target without considering any constraints; Explore the region between the identified UPFs and the currently possible CPFs using SPF missions; The DVS task finds the region formed by the interconnection of all current optimal feasible solutions in the offspring, where the region can radiate to the infeasible region, so that the total constraint violation value of the individuals retained in the entire uniform target space is minimized. The CPF task utilizes the dominance relationship between objective values ​​and constraint violation values ​​to select feasible solutions.

4. The constrained multi-objective optimization collaborative design method with enhanced diversity as described in claim 1, characterized in that: When performing the search, the frontier mutual traction search strategy is used to complete the environment selection for the UPF and SPF tasks.

5. The multi-objective optimization collaborative design method with enhanced diversity according to claim 1, characterized in that: When performing the search, a diversity enhancement strategy based on the dominance region partitioning is used to complete the environment selection for the DVS task.

6. The multi-objective optimization collaborative design method with enhanced diversity according to claim 1, characterized in that: During the search, a convergence-driven feasible boundary expansion strategy is used to complete the environment selection for the CPF task.

7. The constrained multi-objective optimization collaborative design method with enhanced diversity according to claim 1, characterized in that: During the search, differential evolution operators and genetic algorithm operators are used to generate candidate offspring to enrich the source of candidate solutions.

8. The constrained multi-objective optimization collaborative design method with enhanced diversity according to claim 7, characterized in that: During the search, the differential evolution operator enhances the global search capability in the continuous decision variable space, and the genetic algorithm operator maintains the population recombination and local perturbation capabilities.

9. The constrained multi-objective optimization collaborative design method with enhanced diversity according to claim 1, characterized in that: When performing constrained multi-objective optimization collaborative design, a lifecycle-based resource allocation strategy is introduced to enhance resource allocation for different tasks in different design cycles.

10. The constrained multi-objective optimization collaborative design method with enhanced diversity according to claim 9, characterized in that: When allocating resources, in the early stages of design, more resources are allocated to UPF and SPF tasks; in the middle stages of design, the role of DVS tasks is enhanced; and in the later stages of design, more resources are allocated to CPF tasks.

Images