Railway construction management multi-objective equalization optimization method based on improved MOPSO algorithm

Abstract

The invention discloses a railway construction management multi-objective equilibrium optimization method based on an improved MOPSO algorithm, and the method comprises the steps: 1) constructing four objective function optimization models on the premise of meeting the basic constraint conditions of a railway construction project, and enabling each objective function optimization model to correspond to an optimization objective; 2) according to the four objective function optimization models constructed in the step 1), constructing a multi-objective equilibrium optimization model; and 3) performing iterative solution on the multi-objective equilibrium optimization model constructed in the step 2) by using an improved multi-objective particle swarm optimization MOPSO algorithm to obtain an optimal solution set of the project under equilibrium in four aspects of construction period, resource, cost and safety. According to the method, the convergence speed, the diversity maintenance capability and the constraint processing flexibility of the MOPSO algorithm can be remarkably improved while the four optimization objectives of the construction period, the resources, the cost and the safety of the railway construction project are effectively considered, and an efficient and reliable multi-objective comprehensive decision support tool is provided for railway construction management.

Description

Technical Field

[0001] This invention relates to the field of intelligent management technology for railway construction, specifically a multi-objective equilibrium optimization method for railway construction management based on an improved MOPSO algorithm. Background Technology

[0002] Railway construction projects are typically large-scale and involve numerous procedures. Various constraints (contractual deadlines, safety regulations, resource supply, and quality standards, etc.) are intertwined, and there is a natural coupling and constraint relationship between the four core objectives (schedule, safety, resources, and cost). Specifically, measures such as parallel operations and day and night construction adopted to shorten the schedule often lead to a surge in resource input intensity, directly driving up costs such as labor and equipment leasing. On the other hand, excessive reduction in resource allocation or simplification of construction processes to control costs may exceed quality control thresholds and even cause safety accidents such as scaffolding collapses and collisions with existing lines. Furthermore, neglecting the implicit management defects of safety and quality may not only cause direct losses such as casualties and project rework, but also trigger high repair costs in the later operation and maintenance phase, forming a vicious cycle of "cost-safety-quality". In current railway construction management practices, traditional control methods, such as the patent with publication number CN118134438B—a multi-objective equilibrium optimization method and system for railway construction management—still primarily rely on linear weighted summation. This leads some projects to prioritize resource input and cost control over ensuring project completion, while others compress costs through static budgeting, lacking dynamic prediction of safety and quality risks. These methods have two major limitations: first, they fail to fully consider the non-linear coupling relationships among the four objectives, for example, the impact of resource supply fluctuations on the project schedule is not a simple linear correlation; second, they lack a systematic equilibrium optimization logic, failing to achieve global multi-objective coordination. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of existing multi-objective evolutionary algorithms in terms of convergence speed, solution set diversity maintenance, complex constraint handling, and safety quality quantification. It proposes a multi-objective equilibrium optimization method for railway construction management based on an improved MOPSO algorithm, which can effectively improve the convergence efficiency and frontier uniformity distribution capability of the algorithm under complex constraint environments, and provide a fast and reliable multi-objective integrated decision support tool for railway construction management.

[0004] To achieve the above objectives, the present invention provides the following technical solutions.

[0005] This invention first proposes a multi-objective equilibrium optimization method for railway construction management based on an improved MOPSO algorithm, comprising the following steps: Step S1: Under the premise of meeting the basic constraints of the railway construction project, construct four objective function optimization models, each of which corresponds to an optimization objective. The four objective function optimization models are respectively the objective functions for minimizing project duration. Minimize resource consumption objective function Minimize total project cost objective function and the objective function with the highest safety level ; Step S2: Based on the four objective function optimization models constructed in Step S1, construct a multi-objective equilibrium optimization model; Step S3: Iteratively solve the multi-objective equilibrium optimization model constructed in step S2 using the improved multi-objective particle swarm optimization (MOPSO) algorithm to obtain the optimal solution set under the equilibrium of project schedule, resources, cost, and safety.

[0006] Specifically, the process of constructing the four objective function optimization models in step S1 is as follows: Step S11: Based on the critical path method, construct a network diagram of the project's processes, define the longest path duration as the total project duration, and then determine the objective function for minimizing the project duration. The expression is: ; In the above formula, The set of all feasible paths; This is the kth feasible path; For process The duration; The constraint condition of the objective function for minimizing the project duration is the process. Duration Minimum time limit for each process and the maximum construction period for each process Within the closed interval; Step S12: Based on the consumption of three types of resources—equipment, manpower, and materials—construct the objective function for minimizing resource consumption. The expression is: ; In the above formula, , , Each represents a process. The amount of equipment, manpower, and materials used. , , This refers to the resource weighting coefficient. N This represents the total number of processes included in the project. The constraints of the objective function that minimizes resource consumption include the upper limits of equipment, manpower, and material supply; Step S13: The total project cost includes three parts: direct cost, indirect cost, and time-related incentive function. The objective function for minimizing the total project cost is constructed. The expression is: ; In the above formula, For process The direct costs; For process Indirect costs, r The indirect cost rate per unit construction period. For the incentive penalty function related to the deviation from the planned schedule, , , These are the delay penalty coefficient and the early reward coefficient, respectively. The total project duration, For the planned construction period; The cost constraint of the objective function for minimizing the total cost of the project is: , This is the maximum budget limit for the total project cost; Step S14: Based on the Least Reasonable Feasibility (ALARP) principle and system reliability theory, the process is... Security investment With accident probability By fitting with an exponential relationship, the fitted function is obtained. : ; In the above formula, The initial accident probability without any safety measures in place; To make corresponding security investments The efficiency coefficient for reducing accident risk. ; The base of the natural index; The objective function with the highest safety level The expression is: ; In the above formula, For process Expected losses in the event of an accident.

[0007] Specifically, step S2 involves constructing a multi-objective equilibrium optimization model. Represented as: ; In the above formula, This represents the set of feasible solutions that satisfy all constraints. The constraints of the multi-objective equilibrium optimization model include: minimum and maximum time limits for each process; upper limits for equipment, manpower, and material supply; total project cost budget; and safety investment range.

[0008] Specifically, the improved multi-objective particle swarm optimization (MOPSO) algorithm in step S3 is calculated as follows: Step S31: Initialize the population; Set population size Maximum number of iterations Archive capacity Individual learning factors Social learning factors Lower bound of inertia weight Inertia weight upper limit Initial penalty coefficient Punishment growth factor By process Duration Process Equipment, manpower, and material usage , , Process direct costs Process Indirect costs and safety investment in each process As decision variables, they constitute the initial position vector of each particle. Within their respective constraints, the initial population is generated using random integer encoding; the velocity vector is randomly initialized according to the variable scale. And calculate the target vector for each particle. If a constraint is violated, the total violation degree is calculated. And adjust the target value according to the adaptive constraint penalty strategy; Step S32: Set the total violation rate and adaptive constraint penalty strategy; Total violation Represented as: ; In the above formula, For the first The excess of a constraint, For normalized weights; Adaptive constraint penalty strategy: setting a penalty threshold For particles The penalty coefficients are: ; In the above formula, This represents 6 percentage points; Modified multi-objective equilibrium optimization model for: ; Step S33: Layered dynamic adjustment of inertia weight; To achieve a smooth transition between iteration progress and population diversity, a logistic-mixed expression is used: ; In the above formula, Adaptive adjustment of inertia weights to accommodate population diversity; This represents the current iteration number. For the first A measure of population diversity, specifically the mean Euclidean distance between two particles. exp represents the initial diversity index; exp indicates the exponential operation with base e. To adjust the parameters, , , ; Step S34: External archive maintenance; Maintain a fixed-capacity external archive, `Archive`. In each iteration, store the current non-dominated solutions of the population into `Archive`. First, the crowding distance of each non-dominated solution is calculated, and dense solutions are eliminated in ascending order of crowding to initially reduce the number of solutions. If the number of solutions still exceeds the limit, the remaining solutions are mapped to a parallel coordinate unit system (PCCS). PCCS divides each dimension of the target space into several units. Non-dominated solutions in the same unit and whose target vector distance is less than the threshold are considered highly similar. After clustering by similarity, redundancy is further eliminated in each unit. Unit boundary and representative endpoint solutions are retained first to maintain uniform coverage of non-dominated solutions throughout the target space. Step S35: Execute speed and location update; Step S36: Feasibility repair and penalty in parallel; Immediately assess the total violation rate after the location is updated. ,like Then according to Calculate penalties and attempt to fix: First, make local fine-tuning by reducing resources for a certain process or postponing non-critical processes. If it cannot be fixed, replace it with a similar feasible solution in Archive or roll back to the historical best position of the particle, thereby improving the feasible solution ratio and stabilizing the search process. Step S37: Iteration termination determination and output; Repeat steps S35-S36 until the maximum number of iterations is reached. If the change in the output of Archive is less than a preset threshold within 10 consecutive iterations, the iteration stops; all non-dominated solutions in Archive are output as the optimal solution set; users can select specific construction schemes from the optimal solution set according to the actual needs of the project.

[0009] Furthermore, in step S35, the velocity and position update is performed. During the iterative solution process, after initializing the population, the particles update their velocity and position according to the following formula: ; ; In the above formula, For the first i The particle in the first t The velocity vector at +1 iteration; For the first i The particle in the first t The velocity vector at the next iteration; For individual learning factors; As a social learning factor; , A random number within the interval [0,1]; For the first i The particle in the first t The position vector at the next iteration; For the first i The particle in the first t The position vector at +1 iterations; The optimal position for the individual; A representative solution selected from the external archive; After each iteration, the optimal solution set is updated by non-dominated sorting and external archive filtering; when the number of iterations reaches the maximum number of iterations... If the change in Archive's output within 10 consecutive iterations is less than a preset threshold, the iteration terminates and the non-dominated solution set after multi-objective optimization is output. Each solution The optimal balance is achieved across four optimization dimensions: schedule, resources, cost, and safety, allowing users to select specific construction plans based on their actual project needs.

[0010] Secondly, based on the above technical solutions, this invention also provides a multi-objective equilibrium optimization system for railway construction management based on an improved MOPSO algorithm, including a model building module, a multi-objective integration module, an optimization solution module, and a user interaction module; The model building module is used to read construction network data, resource consumption data, cost data, and safety data, and to build four objective function optimization models with the optimization objectives of shortest project duration, least resource consumption, lowest total project cost, and highest safety level. The multi-objective integration module is used to merge the four objective function optimization models and constraints into a unified multi-objective equilibrium optimization model. The optimization solution module is used to implement the improved MOPSO algorithm, including a hierarchical dynamic inertia weight adjustment strategy, an adaptive constraint penalty strategy, an external archive + congestion distance + PCCS hybrid maintenance strategy, and an elite retention strategy, to iteratively solve the multi-objective equilibrium optimization model; The user interaction module is used to display the iterative solution results in a graphical interface, and supports users to browse, compare, optimize parameters, and make scheme decisions online.

[0011] Subsequently, the present invention further provides a multi-objective equilibrium optimization device for railway construction management based on an improved MOPSO algorithm, comprising: at least one processor and a memory communicating with it, wherein the instructions stored in the memory are executed by the processor to realize the multi-objective equilibrium optimization method for railway construction management based on the improved MOPSO algorithm proposed in the above technical solution.

[0012] Finally, the present invention also provides a computer-readable storage medium storing a computer program for implementing the multi-objective equilibrium optimization method for railway construction management based on the improved MOPSO algorithm proposed in the above technical solution. Compared with the prior art, the present invention has the following beneficial effects: This invention introduces strategies such as hierarchical dynamic inertia weights, adaptive constraint penalties, external archiving + congestion degree + PCCS hybrid maintenance, and elite retention. While effectively balancing the four optimization objectives of railway construction projects—schedule, resources, cost, and safety—it can significantly improve the algorithm's convergence speed, diversity maintenance capabilities, and constraint handling flexibility, providing a highly efficient and reliable multi-objective comprehensive decision support tool for railway construction management. Attached Figure Description

[0013] To provide a more intuitive understanding of the technical implementation of this invention, the accompanying drawings involved in the embodiments of this invention are briefly described below. These drawings are used to assist in illustrating the implementation methods and are not intended to limit the invention. Those skilled in the art can make derivative designs based on the drawings without creative effort.

[0014] Figure 1 This is a flowchart illustrating the multi-objective equilibrium optimization method for railway construction management based on the improved MOPSO algorithm of this invention. Figure 2 This is a functional structure diagram of the multi-objective equilibrium optimization system for railway construction management based on the improved MOPSO algorithm of this invention; Figure 3 This is a flowchart of the operation of the multi-objective equilibrium optimization equipment for railway construction management based on the improved MOPSO algorithm of this invention. Figure 4 This is a flowchart of the railway construction network in an embodiment of the present invention; Figure 5 This is a schematic diagram of the security benefit function curve constructed based on the ALARP principle in an embodiment of the present invention; Figure 6 This is a two-dimensional visualization example of the non-dominated solution in the target space in an embodiment of the present invention; Figure 7 This is a comparison chart of the spread curves of front uniformity under different methods in the embodiments of the present invention; Figure 8 This is a comparison chart of hypervolume convergence curves under different methods in the embodiments of the present invention. Detailed Implementation

[0015] To facilitate understanding and implementation of the present invention by those skilled in the art, the various steps of the method proposed in this invention are described in detail below. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various modifications or alterations to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0016] Example 1 like Figure 1 As shown in the figure, this embodiment discloses a multi-objective equilibrium optimization method for railway construction management based on an improved MOPSO algorithm, including the following steps: Step S1: Under the premise of meeting the basic constraints of the railway construction project, construct four objective function optimization models, each of which corresponds to an optimization objective. The four objective function optimization models are respectively the objective functions for minimizing project duration. Minimize resource consumption objective function Minimize total project cost objective function and the objective function with the highest safety level ; Step S2: Based on the four objective function optimization models constructed in Step S1, construct a multi-objective equilibrium optimization model; Step S3: Iteratively solve the multi-objective equilibrium optimization model constructed in step S2 using the improved multi-objective particle swarm optimization (MOPSO) algorithm to obtain the optimal solution set under the equilibrium of project schedule, resources, cost, and safety.

[0017] Specifically, the process of constructing the four objective function optimization models in step S1 is as follows: Step S11: Based on the critical path method, construct a network diagram of the project's processes, define the longest path duration as the total project duration, and then determine the objective function for minimizing the project duration. The expression is: ; In the above formula, The set of all feasible paths; This is the kth feasible path; For process The duration; The constraint condition of the objective function for minimizing the project duration is the process. Duration Minimum time limit for each process and the maximum construction period for each process Within the closed interval; like Figure 4 As shown, an example of a process flow diagram for a railway construction network is provided, illustrating the main processes involved in railway construction. It should be noted that... Figure 4 The process flow shown is only for the convenience of those skilled in the art to understand the "process" in this embodiment. The meaning of "" is given, and not "process" in the method of this invention. "These are just the basic procedures. In actual railway construction, decision-makers may add or remove related procedures as needed."

[0018] Step S12: Based on the consumption of three types of resources—equipment, manpower, and materials—construct the objective function for minimizing resource consumption. The expression is: ; In the above formula, , , Each represents a process. The amount of equipment, manpower, and materials used. , , This refers to the resource weighting coefficient. N This represents the total number of processes included in the project. The constraints of the objective function that minimizes resource consumption include the upper limits of equipment, manpower, and material supply; The total project cost comprises three parts: direct costs, indirect costs, and time-related incentive functions. The objective function for minimizing the total project cost is constructed as follows: The expression is: ; In the above formula, For process The direct costs; For process Indirect costs, r The indirect cost rate per unit construction period. For the incentive penalty function related to the deviation from the planned schedule, , , These are the delay penalty coefficient and the early reward coefficient, respectively. The total project duration, For the planned construction period; The cost constraint of the objective function for minimizing the total cost of the project is: , This is the maximum budget limit for the total project cost; Step S14, as follows Figure 5 As shown, based on the Least Reasonable Feasibility (ALARP) principle and system reliability theory, the process is analyzed. Security investment With accident probability By fitting with an exponential relationship, the fitted function is obtained. : ; In the above formula, The initial accident probability without any safety measures in place; To make corresponding security investments The efficiency coefficient for reducing accident risk. ; The base of the natural index; in this embodiment ; The objective function with the highest safety level The expression is: ; In the above formula, For process Expected losses in the event of an accident.

[0019] Specifically, step S2 involves constructing a multi-objective equilibrium optimization model. Represented as: ; In the above formula, This represents the set of feasible solutions that satisfy all constraints. The constraints of the multi-objective equilibrium optimization model include: minimum and maximum time limits for each process; upper limits for equipment, manpower, and material supply; total project cost budget; and safety investment range.

[0020] Specifically, the improved multi-objective particle swarm optimization (MOPSO) algorithm in step S3 is calculated as follows: Step S31: Initialize the population; Set population size Maximum number of iterations Archive capacity Individual learning factors Social learning factors Lower bound of inertia weight Inertia weight upper limit Initial penalty coefficient Punishment growth factor By process Duration Process Equipment, manpower, and material usage , , Process direct costs Process Indirect costs and safety investment in each process As decision variables, they constitute the initial position vector of each particle. Within their respective constraints, the initial population is generated using random integer encoding; the velocity vector is randomly initialized according to the variable scale. And calculate the target vector for each particle. If a constraint is violated, the total violation degree is calculated. And adjust the target value according to the adaptive constraint penalty strategy; Step S32: Set the total violation rate and adaptive constraint penalty strategy; Total violation Represented as: ; In the above formula, For the first The excess of a constraint, For normalized weights; Adaptive constraint penalty strategy: setting a penalty threshold For particles The penalty coefficients are: ; In the above formula, This represents 6 percentage points; Modified multi-objective equilibrium optimization model for: ; Step S33: Layered dynamic adjustment of inertia weight; To achieve a smooth transition between iteration progress and population diversity, a logistic-mixed expression is used: ; In the above formula, Adaptive adjustment of inertia weights to accommodate population diversity; This represents the current iteration number. For the first A measure of population diversity, specifically the mean Euclidean distance between two particles. exp represents the initial diversity index; exp indicates the exponential operation with base e. To adjust the parameters, , , ; Step S34: External archive maintenance; Maintain a fixed-capacity external archive, `Archive`. In each iteration, store the current non-dominated solutions of the population into `Archive`. First, the crowding distance of each solution is calculated, and dense solutions are eliminated in ascending order of crowding to initially reduce the number of solutions. If the number of solutions still exceeds the limit, the remaining solutions are mapped to a parallel coordinate unit system (PCCS). PCCS divides each dimension of the target space into several units. Solutions in the same unit with a target vector distance less than a threshold are considered highly similar. After clustering by similarity, redundancy is further eliminated within each unit, prioritizing the retention of solutions at unit boundaries and representative endpoints. Figure 6 As shown, this is done to maintain a uniform coverage of non-dominated solutions throughout the target space; Step S35: Execute speed and location update; Step S36: Feasibility repair and penalty in parallel; Immediately assess the total violation rate after the location is updated. ,like Then according to Calculate penalties and attempt to fix: First, make local fine-tuning by reducing resources for a certain process or postponing non-critical processes. If it cannot be fixed, replace it with a similar feasible solution in Archive or roll back to the historical best position of the particle, thereby improving the feasible solution ratio and stabilizing the search process. Step S37: Iteration termination determination and output; Repeat steps S35-S36 until the maximum number of iterations is reached. If the change in the output of Archive is less than a preset threshold within 10 consecutive iterations, the iteration stops; all non-dominated solutions in Archive are output as the optimal solution set; users can select specific construction schemes from the optimal solution set according to the actual needs of the project.

[0021] Furthermore, in step S35, the velocity and position update is performed. During the iterative solution process, after initializing the population, the particles update their velocity and position according to the following formula: ; ; In the above formula, For the first i The particle in the first t The velocity vector at +1 iteration; For the first i The particle in the first t The velocity vector at the next iteration; For individual learning factors; As a social learning factor; , A random number within the interval [0,1]; For the first i The particle in the first t The position vector at the next iteration; For the first i The particle in the first t The position vector at +1 iterations; The optimal position for the individual; A representative solution selected from the external archive; After each iteration, the optimal solution set is updated by non-dominated sorting and external archive filtering; when the number of iterations reaches the maximum number of iterations... If the change in Archive's output within 10 consecutive iterations is less than a preset threshold, the iteration terminates and the non-dominated solution set after multi-objective optimization is output. Each solution All of them represent the optimal balance among four optimization objectives: construction period, resources, cost, and safety, allowing users to choose specific construction solutions based on the actual needs of their projects.

[0022] The following is a railway construction example, comparing the method of the present invention with the traditional linear weighted method, NSGA-II method, and MOPSO method under the same construction data, to demonstrate the advancement of the present invention method compared with existing methods.

[0023] I. Project Parameters and Constraints; Planned construction period: 120 days; Equipment usage: 10 excavators and 5 truck cranes; Manpower required: 200 people; Monthly consumption of main materials: 2000t / month of sand and gravel, 500t / month of cement; Maximum budget limit: 4.5 × 10 8 Yuan; Safety investment range: Total amount 5~10×10 6 Yuan; Safety baseline and fitting: taking typical examples .

[0024] II. Process Breakdown and Duration Range; Table 1. Process Breakdown and Duration Range Table ; III. Representative Recommendation Schemes Based on the Improved MOPSO Algorithm 1) The determined duration (unit: days), see Table 1: A=3, B=18, C=20, D=30, E=18, F=22, G=6, H=20, I=18, J=10; 2) Critical path: A→C→E→F→G→H→I→J; 3) Project duration: =3+20+18+22+6+20+18+10=117 days < 120 days; 4) Process scheduling (d represents the number of days): A: D1–D3 (3d, temporary facilities); B: D4–D21 (18d, roadbed excavation); C: D4–D23 (20d, bridge foundation); D: D4–D33 (30d, tunnel excavation); E: D24–D41 (18d, pier construction). F: D42–D63 (22d, precast beams); G: D64–D69 (6d, bridge deck system); H: D70–D89 (20d, track mounting); I: D90–D107 (18d, electromechanical / signal); J: D108–D117 (10d, static acceptance and commissioning); 5) Resources and personnel: D4–D21 (peak period when B, C, and D occur simultaneously): Excavator: B=5, C=3, D=2 ⇒ Total=10 (=upper limit); Crane: C=2, D=0, B=0 ⇒ Total = 2 (≤5); Personnel: B=70, C=60, D=60 ⇒ Total=190 (≤200); During the remaining time periods, the transfer is carried out segment by segment according to the work process to ensure that the upper limit is not exceeded at any time.

[0025] 6) Major materials are processed on a monthly rolling basis: Sand and gravel: allocated to B / C / E / F / G, based on production capacity, not exceeding 2000t per month; Cement: allocated to C / E / F / G, not exceeding 500t per month; set up =1; =0.6; =0.3; calculated to =2.73×10 5 (Weighted unit); 7) Cost Direct costs (unit: 10,000 yuan): B=3800, C=5200, D=6900, E=4200, F=5800, G=900, H=3600, I=4200, J=600,A=300, =363 million yuan; Indirect costs (unit: 10,000 yuan): r= 450,000 yuan / day =117 days; =52.62 million yuan; Incentives and penalties (unit: 10,000 yuan): The contract is for 120 days, with a 3-day advance notice period. =400,000 yuan / day, with a reward of 1.2 million yuan; Total cost: =414.45 million yuan=4.1445×10 8 Yuan < Maximum budget limit 4.5 × 10 8 Yuan; 8) Safety investment and risk expenditure The total safety investment is 8 million yuan, allocated as follows (unit: 10,000 yuan): B=80, C=120, D=220, E=70, F=120, G=20, H=80, I=70, J=10, A=10; Accident probability: Take (Unit: %): B=1.0, C=1.2, D=1.5, E=1.0, F=1.0, G=0.8, H=1.2, I=1.0, J=0.6; =3.0×10-7 / Yuan; Expected loss: (Unit: 10,000 yuan): B=500, C=800, D=1500, E=600, F=700, G=200, H=800, I=600, J=150; Safety level: =10.3 million yuan, which is more than 50% lower than the "minimum investment" (3% of total safety investment) scenario, falling within ALARP's "tolerable and continuously improving" range; IV. Comparison with existing methods Under the aforementioned dataset, the improved MOPSO algorithm proposed in this invention was independently run 50 times against the traditional linear weighted method, NSGA-II method, and MOPSO method (with the same evaluation function and constraints). The comparison results are shown in Table 2 below. Where, as... Figure 7 and Figure 8 The figures shown are comparisons of the frontier uniformity spread and hypervolume convergence curves for different methods.

[0026] Table 2. Comparison results of the method of this invention and the traditional method on the same dataset. ; As shown in Table 2, the improved MOPSO algorithm of this invention converges faster and achieves a higher hypervolume value compared to the traditional method. The proportion of feasible solutions in the convergence results is higher, and the generated solutions are closer to the theoretical optimal frontier. Figure 7 As shown, the solution points of the linear weighted algorithm are scattered and difficult to form an effective front. Although the NSGA-II algorithm and the traditional MOPSO algorithm can produce non-dominated solutions, their distribution is uneven and some regions lack representativeness. In contrast, the improved MOPSO algorithm of this invention generates solutions that are closer to the theoretical optimal front, performs better in the trade-off between time and cost, and has a balanced and comprehensive solution set, indicating that the method of this invention has stronger adaptability and convergence ability in multi-objective optimization. Figure 8 As shown, the linear weighted algorithm has almost no convergence characteristics. Although the NSGA-II algorithm and the traditional MOPSO algorithm have some improvement in the early stage, they are prone to oscillation or premature convergence. However, the improved MOPSO algorithm of this invention can quickly reach a high hypervolume value after a few iterations and maintain stable convergence in the subsequent stages, demonstrating better convergence speed and global search capability, and providing more reliable solution set support for multi-objective equilibrium optimization of railway construction.

[0027] In summary, the method of this invention adopts Logistic-hybrid inertial weights to enable the model to explore widely in the early stage and converge stably in the later stage, which can effectively avoid weight mutation. At the same time, the parallel mechanism of feasibility repair and penalty makes the feasible region "return to normal" faster. The combination of congestion degree and PCCS retains the endpoints and representative solutions under a fixed archive capacity, which can significantly improve frontier coverage and diversity, and provide more reliable solution set support for multi-objective equilibrium optimization of railway construction.

[0028] Example 2 This embodiment is to implement the multi-objective equilibrium optimization method described in Embodiment 1, such as... Figure 2 As shown, a multi-objective equilibrium optimization system for railway construction management based on an improved MOPSO algorithm is disclosed, including a model building module, a multi-objective integration module, an optimization solution module, and a user interaction module; The model building module is used to read construction network data, resource consumption data, cost data, and safety data, and to construct four objective function optimization models with the optimization objectives of shortest project duration, least resource consumption, lowest total project cost, and highest safety level; specifically including: The project schedule target is based on the critical path method; Resource targets are calculated based on three categories of consumption: equipment, manpower, and materials. Cost targets take into account direct costs, indirect costs, and incentives for early / delayed progress. The security objective is transformed into a security benefit function using ALARP and reliability theory; The multi-objective integration module is used to merge the four objective function optimization models and constraints into a unified multi-objective equilibrium optimization model, forming a unified four-dimensional objective vector and feasible solution constraint set; supports: Target unification; Constraint summary; Feasibility domain resolution; The optimization solution module is used to implement the improved MOPSO algorithm, including a hierarchical dynamic inertia weight adjustment strategy, an adaptive constraint penalty strategy, an external archive + congestion distance + PCCS hybrid maintenance strategy, and an elite retention strategy, to iteratively solve the multi-objective equilibrium optimization model; specifically including: Dynamic weight adjustment; Penalty coefficient calculation; Archive filtering and management; Elite retention and individual renewal mechanisms, etc.; The user interaction module is used to display the frontier solution set of the iterative solution results in a graphical interface, and supports users to browse (single solution query), compare (multiple solution scheme comparison and analysis), optimize parameters (weight adjustment, constraint parameter modification) and make scheme decisions online.

[0029] Example 3 This embodiment discloses a multi-objective equilibrium optimization device for railway construction management based on an improved MOPSO algorithm. This device is equipped with the multi-objective equilibrium optimization system shown in Embodiment 2. Figure 3 As shown, it includes: at least one processor and a memory communicating with it, as well as an input / output device. The instructions stored in the memory are executed by the processor, and the input / output device is used to input construction parameters, constraints, user preference settings, and output an optimized construction plan, thereby realizing the multi-objective equilibrium optimization method described in Example 1.

[0030] Example 4 This embodiment discloses a computer-readable storage medium storing a computer program that, when executed by a processor, implements the multi-objective equilibrium optimization method as described in Embodiment 1.

[0031] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A multi-objective equilibrium optimization method for railway construction management based on an improved MOPSO algorithm, characterized in that, The following steps are involved: Step S1: Under the premise of meeting the basic constraints of the railway construction project, construct four objective function optimization models, each of which corresponds to an optimization objective. The four objective function optimization models are respectively the objective functions for minimizing project duration. Minimize resource consumption objective function Minimize total project cost objective function and the objective function with the highest safety level ; Step S2: Based on the four objective function optimization models constructed in Step S1, construct a multi-objective equilibrium optimization model; Step S3: Iteratively solve the multi-objective equilibrium optimization model constructed in step S2 using the improved multi-objective particle swarm optimization (MOPSO) algorithm to obtain the optimal solution set under the equilibrium of project schedule, resources, cost, and safety.

2. The multi-objective equilibrium optimization method for railway construction management based on the improved MOPSO algorithm according to claim 1, characterized in that, The process of constructing the four objective function optimization models in step S1 is as follows: Step S11: Based on the critical path method, construct a network diagram of the project's processes, define the longest path duration as the total project duration, and then determine the objective function for minimizing the project duration. The expression is: ； In the above formula, The set of all feasible paths; This is the kth feasible path; For process The duration; The constraint condition of the objective function for minimizing the project duration is the process. Duration Minimum time limit for each process and the maximum construction period for each process Within the closed interval; Step S12: Based on the consumption of three types of resources—equipment, manpower, and materials—construct the objective function for minimizing resource consumption. The expression is: ； In the above formula, , , Each represents a process. The amount of equipment, manpower, and materials used. , , This refers to the resource weighting coefficient. N This represents the total number of processes included in the project. The constraints of the objective function that minimizes resource consumption include the upper limits of equipment, manpower, and material supply; Step S13: The total project cost includes three parts: direct cost, indirect cost, and time-related incentive function. The objective function for minimizing the total project cost is constructed. The expression is: ； In the above formula, For process The direct costs; For process Indirect costs, r The indirect cost rate per unit construction period. For the incentive penalty function related to the deviation from the planned schedule, , , These are the delay penalty coefficient and the early reward coefficient, respectively. The total project duration, For the planned construction period; The cost constraint of the objective function for minimizing the total cost of the project is: , This is the maximum budget limit for the total project cost; Step S14: Based on the Least Reasonable Feasibility (ALARP) principle and system reliability theory, the process is... Security investment With accident probability By fitting with an exponential relationship, the fitted function is obtained. : ； In the above formula, The initial accident probability without any safety measures in place; To make corresponding security investments The efficiency coefficient for reducing accident risk. ; The base of the natural index; The objective function with the highest safety level The expression is: ； In the above formula, For process Expected losses in the event of an accident.

3. The multi-objective equilibrium optimization method for railway construction management based on the improved MOPSO algorithm according to claim 2, characterized in that, The construction of the multi-objective equilibrium optimization model mentioned in step S2 is as follows: Represented as: ； In the above formula, This represents the set of feasible solutions that satisfy all constraints. The constraints of the multi-objective equilibrium optimization model include: minimum and maximum time limits for each process; upper limits for equipment, manpower, and material supply; total project cost budget; and safety investment range.

4. The multi-objective equilibrium optimization method for railway construction management based on the improved MOPSO algorithm according to claim 3, characterized in that, The improved multi-objective particle swarm optimization (MOPSO) algorithm in step S3 is calculated as follows: Step S31: Initialize the population; Set population size Maximum number of iterations Archive capacity Individual learning factors Social learning factors Lower bound of inertia weight Inertia weight upper limit Initial penalty coefficient Punishment growth factor By process Duration Process Equipment, manpower, and material usage , , Process direct costs Process Indirect costs and safety investment in each process As decision variables, they constitute the initial position vector of each particle. Within their respective constraints, the initial population is generated by random integer encoding. The velocity vector is randomly initialized according to the variable scale. And calculate the target vector for each particle. If a constraint is violated, the total violation degree is calculated. And adjust the target value according to the adaptive constraint penalty strategy; Step S32: Set the total violation rate and adaptive constraint penalty strategy; Total violation Represented as: ； In the above formula, For the first The excess of a constraint, For normalized weights; Adaptive constraint penalty strategy: setting a penalty threshold For particles The penalty coefficients are: ； In the above formula, This represents 6 percentage points; Modified multi-objective equilibrium optimization model for: ; Step S33: Layered dynamic adjustment of inertia weight; To achieve a smooth transition between iteration progress and population diversity, a logistic-mixed expression is used: ； In the above formula, Adaptive adjustment of inertia weights to accommodate population diversity; This represents the current iteration number. For the first A measure of population diversity, specifically the mean Euclidean distance between two particles. exp represents the initial diversity index; exp indicates the exponential operation with base e. To adjust the parameters, , , ; Step S34: External archive maintenance; Maintain a fixed-capacity external archive, `Archive`. In each iteration, store the current non-dominated solutions of the population into `Archive`. First, the crowding distance of each non-dominated solution is calculated, and dense solutions are eliminated in ascending order of crowding to initially reduce the number of solutions. If the number of solutions still exceeds the limit, the remaining solutions are mapped to a parallel coordinate unit system (PCCS). PCCS divides each dimension of the target space into several units. Non-dominated solutions in the same unit and whose target vector distance is less than the threshold are considered highly similar. After clustering by similarity, redundancy is further eliminated in each unit. Unit boundary and representative endpoint solutions are retained first to maintain uniform coverage of non-dominated solutions throughout the target space. Step S35: Execute speed and location update; Step S36: Feasibility repair and penalty in parallel; Immediately assess the total violation rate after the location is updated. ,like Then according to Calculate penalties and attempt to fix: First, make local fine-tuning by reducing resources for a certain process or postponing non-critical processes. If it cannot be fixed, replace it with a similar feasible solution in Archive or roll back to the historical best position of the particle, thereby improving the feasible solution ratio and stabilizing the search process. Step S37: Iteration termination determination and output; Repeat steps S35-S36 until the maximum number of iterations is reached. If the change in the output of Archive is less than a preset threshold within 10 consecutive iterations, the iteration stops; all non-dominated solutions in Archive are output as the optimal solution set; users can select specific construction schemes from the optimal solution set according to the actual needs of the project.

5. The multi-objective equilibrium optimization method for railway construction management based on the improved MOPSO algorithm according to claim 4, characterized in that, Step S35 describes the performance update of velocity and position. During the iterative solution process, after initializing the population, the particles update their velocity and position according to the following formula: ； ； In the above formula, For the first i The particle in the first t The velocity vector at +1 iteration; For the first i The particle in the first t The velocity vector at the next iteration; For individual learning factors; As a social learning factor; , A random number within the interval [0,1]; For the first i The particle in the first t The position vector at the next iteration; For the first i The particle in the first t The position vector at +1 iterations; The optimal position for the individual; A representative solution selected from the external archive; After each iteration, the optimal solution set is updated by non-dominated sorting and external archive filtering; when the number of iterations reaches the maximum number of iterations... If the change in Archive's output within 10 consecutive iterations is less than a preset threshold, the iteration terminates and the non-dominated solution set after multi-objective optimization is output. Each solution All of them represent the optimal balance among four optimization objectives: construction period, resources, cost, and safety, allowing users to choose specific construction solutions based on the actual needs of their projects.

6. A multi-objective equilibrium optimization system for railway construction management based on an improved MOPSO algorithm, characterized in that, It includes a model building module, a multi-objective integration module, an optimization solution module, and a user interaction module; The model building module is used to read construction network data, resource consumption data, cost data, and safety data, and to build four objective function optimization models with the optimization objectives of shortest project duration, least resource consumption, lowest total project cost, and highest safety level. The multi-objective integration module is used to merge the four objective function optimization models and constraints into a unified multi-objective equilibrium optimization model. The optimization solution module is used to implement the improved MOPSO algorithm, including a hierarchical dynamic inertia weight adjustment strategy, an adaptive constraint penalty strategy, an external archive + congestion distance + PCCS hybrid maintenance strategy, and an elite retention strategy, to iteratively solve the multi-objective equilibrium optimization model; The user interaction module is used to display the iterative solution results in a graphical interface, and supports users to browse, compare, optimize parameters, and make scheme decisions online.

7. A multi-objective equilibrium optimization device for railway construction management based on an improved MOPSO algorithm, characterized in that, include: At least one processor and a memory communicating therewith, wherein instructions stored in the memory are executed by the processor to implement the multi-objective equilibrium optimization method for railway construction management based on the improved MOPSO algorithm as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program for implementing the multi-objective equilibrium optimization method for railway construction management based on the improved MOPSO algorithm as described in any one of claims 1-5.

Images