Multi-objective equilibrium optimization method for railway construction management based on improved MOPSO algorithm

Abstract

The application discloses a railway construction management multi-objective balanced optimization method based on an improved MOPSO algorithm, which comprises the following steps: 1) under the premise of meeting the basic constraint conditions of a railway construction project, four objective function optimization models are constructed, and each objective function optimization model corresponds to an optimization target; 2) according to the four objective function optimization models constructed in the step 1), a multi-objective balanced optimization model is constructed; 3) the multi-objective balanced optimization model constructed in the step 2) is iteratively solved by using an improved multi-objective particle swarm optimization MOPSO algorithm, and an optimal solution set of the project under the balance of four aspects of a construction period, resources, cost and safety is obtained. The method can effectively consider the four optimization targets of the construction period, resources, cost and safety of the railway construction project, can significantly improve the convergence speed, diversity maintenance capability and constraint processing flexibility of the MOPSO algorithm, and provides an efficient, reliable multi-objective comprehensive decision support tool for railway construction management.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent management of railway construction, in particular to a railway construction management multi-objective balanced optimization method based on an improved MOPSO algorithm. BACKGROUND

[0002] Railway construction projects are usually large in scale, with many procedures, and various constraints (contract duration, safety regulations, resource supply, and quality standards, etc.) intertwined, with natural coupling constraints between the four core objectives (duration, safety, resources, and cost). Specifically, measures such as parallel work and day-and-night construction taken to compress the duration often lead to a sharp increase in resource input intensity, directly pushing up the cost of labor, equipment rental, etc. If resource allocation or construction process is excessively reduced to control cost, it will break the quality control threshold and even cause accidents such as scaffold collapse and collision during existing line construction. Ignoring the hidden defects of safety and quality management not only may cause direct losses such as personnel casualties and engineering rework, but also will trigger high repair costs in the later operation and maintenance stage, forming a vicious cycle of "cost - safety - quality". In the current practice of railway construction management, traditional control methods such as the patent with the publication number CN118134438B - a railway construction management multi-objective balanced optimization method and system still mainly use linear weighted summation, resulting in some projects placing resource input and cost control in a secondary position to ensure the duration of contract performance. Some projects compress cost through static budget cutting, lacking dynamic prediction of safety and quality risks. Such methods have two major limitations: first, they fail to fully consider the nonlinear coupling relationship between the four objectives, for example, the impact of resource supply fluctuations on the duration is not a simple linear correlation; second, they lack systematic balanced optimization logic and cannot achieve multi-objective coordination at the global level. SUMMARY

[0003] The purpose of the present application is to address the shortcomings of existing multi-objective evolutionary algorithms in terms of convergence speed, solution set diversity maintenance, complex constraint processing, and safety and quality quantification, and to propose a railway construction management multi-objective balanced optimization method based on an improved MOPSO algorithm, which can effectively improve the convergence efficiency and uniform distribution ability of the algorithm in a complex constraint environment, and provide a fast and reliable multi-objective comprehensive decision support tool for railway construction management.

[0004] To achieve the above purpose, the present application provides the following technical solutions.

[0005] The present application first proposes a railway construction management multi-objective balanced optimization method based on an improved MOPSO algorithm, including the following steps:

[0006] 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.

[0007] 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 ;

[0008] Step S2: Based on the four objective function optimization models constructed in Step S1, construct a multi-objective equilibrium optimization model;

[0009] 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.

[0010] Specifically, the process of constructing the four objective function optimization models in step S1 is as follows:

[0011] 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:

[0012] ;

[0013] In the above formula, The set of all feasible paths; This is the kth feasible path; For process The duration;

[0014] 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;

[0015] 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:

[0016] ;

[0017] In the above formula, , , Each represents a process. the equipment, manpower, and material consumption, , , is a resource weight coefficient; N is the total number of processes included in the project;

[0018] The constraint condition of the resource consumption minimum objective function includes the upper limit of equipment, manpower, and material supply;

[0019] Step S13, the total cost of the project includes three parts of direct cost, indirect cost, and time-related incentive function, and the total cost minimum objective function of the project is constructed The expression is:

[0020] ;

[0021] In the above formula, is the direct cost of the process ; is the indirect cost of the process , r is the indirect cost rate per unit duration, is the incentive and punishment function related to the planned duration deviation, , , respectively, the delay penalty coefficient and the advance reward coefficient, is the total duration of the project, is the planned duration;

[0022] The cost constraint of the total cost minimum objective function of the project is: , is the maximum budget limit of the total cost of the project;

[0023] Step S14, based on the minimum reasonable and feasible ALARP principle and the system reliability theory, the safety investment of the process and the accident probability are fitted with an exponential relationship to obtain the fitting function :

[0024] ;

[0025] In the above formula, is the initial accident probability without safety investment; is the accident risk reduction efficiency coefficient corresponding to the safety investment , ; is the base number of natural exponential;

[0026] The expression of the safety level maximum objective function is:

[0027] ;

[0028] In the above formula, For process Expected losses in the event of an accident.

[0029] Specifically, step S2 involves constructing a multi-objective equilibrium optimization model. Represented as:

[0030] ;

[0031] In the above formula, This represents the set of feasible solutions that satisfy all constraints.

[0032] 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.

[0033] Specifically, the improved multi-objective particle swarm optimization (MOPSO) algorithm in step S3 is calculated as follows:

[0034] Step S31: Initialize the population;

[0035] 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 first The initial position vector of each particle Within their respective constraints, the initial population is generated by random integer encoding, and the velocity vector is randomly initialized according to the variable scale. And calculate the first The target vector of each particle total violation degree is calculated if the constraint is violated and the objective value is revised according to the adaptive constraint penalty strategy;

[0036] Step S32, set the total violation degree and the adaptive constraint penalty strategy;

[0037] total violation degree is expressed as:

[0038] ;

[0039] In the above formula, is the over-limit amount of the mth constraint, is the normalized weight;

[0040] Adaptive constraint penalty strategy: set the penalty threshold , the penalty coefficient of the particle is:

[0041] ;

[0042] In the above formula, represents 6 percentage points;

[0043] Revised multi-objective equilibrium optimization model is: ;

[0044] Step S33, hierarchical dynamic adjustment of inertia weight;

[0045] In order to achieve smooth transition between iteration progress and population diversity, a Logistic-mixed type expression is used:

[0046] ;

[0047] In the above formula, is the inertia weight adjusted by population diversity; is the current iteration number, is the population diversity index of the mth generation, that is, the average of the Euclidean distance between two particles; is the initial diversity index; exp represents the exponential operation with base e; is the adjustment parameter, , , , ;

[0048] Step S34, external archive maintenance;

[0049] A fixed-capacity external archive Archive is maintained, and the current population non-dominated solution is stored in Archive every iteration, and if​ 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.

[0050] Step S35: Execute speed and location update;

[0051] Step S36: Feasibility repair and penalty in parallel;

[0052] 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.

[0053] Step S37: Iteration termination determination and output;

[0054] 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.

[0055] 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:

[0056] ;

[0057] ;

[0058] In the above formula, For the first The particle in the first t The velocity vector at +1 iteration; For the first The particle in the first t The velocity vector at the next iteration; For individual learning factors; As a social learning factor; , is a random number in the interval [0, 1]; is the position vector of the i-th particle at the j-th iteration; is the position vector of the i-th particle at the j-th iteration; t is the position vector of the i-th particle at the j-th iteration; is the position vector of the i-th particle at the j-th iteration; is the position vector of the i-th particle at the j-th iteration; t is the position vector of the i-th particle at the j-th iteration; is the individual optimal position; is the representative solution selected from the external archive;

[0059] After each iteration, the optimal solution set is updated by non-dominated sorting and screening with the external archive; when the number of iterations reaches the maximum number of iterations or the change in the output result of the Archive is less than the preset threshold value within 10 consecutive iterations, the iteration is terminated and the non-dominated solution set after multi-objective optimization is output ; each solution is a trade-off optimal solution under four optimization target dimensions of duration, resource, cost and safety, so as to select a specific construction scheme according to the actual requirements of the project.

[0060] Secondly, on the basis of the above technical scheme, the application further provides a railway construction management multi-objective balanced optimization system based on the improved MOPSO algorithm, comprising a model construction module, a multi-objective integration module, an optimization solving module and a user interaction module.

[0061] The model construction module is used to read construction network data, resource consumption data, cost data and safety data, and construct four objective function optimization models with the shortest project duration, the least resource consumption, the lowest total project cost and the highest safety level as optimization targets, respectively.

[0062] The multi-objective integration module is used to combine the four objective function optimization models and the constraint conditions into a unified multi-objective balanced optimization model.

[0063] The optimization solving module is used to realize the improved MOPSO algorithm, including a hierarchical dynamic inertia weight adjustment strategy, an adaptive constraint penalty strategy, an external archive + crowding distance + PCCS hybrid maintenance strategy and an elite reservation strategy, and iteratively solves the multi-objective balanced optimization model.

[0064] The user interaction module is used to display the iteration solution result as a graphical interface, and supports online browsing, comparison, parameter tuning and scheme decision-making of the user.

[0065] Thereafter, the application further provides a railway construction management multi-objective balanced optimization device based on the improved MOPSO algorithm, comprising: at least one processor and a memory in communication with the processor, instructions stored in the memory being executed by the processor to implement the railway construction management multi-objective balanced optimization method based on the improved MOPSO algorithm proposed in the above technical solution.

[0066] Finally, the application also provides a computer readable storage medium having a computer program stored thereon, the computer program being used to implement the railway construction management multi-objective balanced optimization method based on the improved MOPSO algorithm proposed in the above technical solution.

[0067] Compared with the prior art, the application has the following beneficial effects:

[0068] The application can significantly improve the convergence speed, diversity maintenance capability and constraint processing flexibility of the algorithm while effectively balancing the four optimization objectives of the railway construction project, i.e., the construction period, resources, cost and safety, thereby providing an efficient and reliable multi-objective comprehensive decision support tool for railway construction management. BRIEF DESCRIPTION OF DRAWINGS

[0069] In order to more intuitively understand the technical implementation scheme of the application, the following briefly describes the drawings involved in the embodiments of the application. These drawings are used to assist in describing the embodiments and are not a limitation of the application. Those skilled in the art can make derivative designs based on the drawings without creative labor.

[0070] Figure 1 is a logic flow chart of the railway construction management multi-objective balanced optimization method based on the improved MOPSO algorithm of the application;

[0071] Figure 2 is a functional structure schematic diagram of the railway construction management multi-objective balanced optimization system based on the improved MOPSO algorithm of the application;

[0072] Figure 3 is a running flow chart of the railway construction management multi-objective balanced optimization device based on the improved MOPSO algorithm of the application;

[0073] Figure 4 is a process flow chart of the railway construction network in the embodiment of the application;

[0074] Figure 5 is a safety benefit function curve schematic diagram constructed based on the ALARP principle in the embodiment of the application;

[0075] Figure 6is an example of two-dimensional visualization of non-dominated solutions in the target space in the embodiment of the present application;

[0076] Figure 7 is a comparison chart of Spread curves of frontiers under different methods in the embodiment of the present application;

[0077] Figure 8 is a comparison chart of Hypervolume curves of hyper-volumes under different methods in the embodiment of the present application. DETAILED DESCRIPTION

[0078] In order to facilitate those skilled in the art to understand and implement the present application, the steps of the method of the present application are described in detail below, and it should be understood that these embodiments are only used to illustrate the present application and not to limit the scope of the present application. In addition, it should be understood that those skilled in the art can make various modifications or modifications to the present application after reading the content taught by the present application, and these equivalent forms also fall within the scope defined by the claims attached to the present application.

[0079] Embodiment 1

[0080] As shown in Figure 1 , the present embodiment discloses a railway construction management multi-objective balanced optimization method based on an improved MOPSO algorithm, comprising the following steps:

[0081] Step S1, under the premise of meeting the basic constraint conditions of the railway construction project, four objective function optimization models are constructed, and each objective function optimization model corresponds to an optimization objective;

[0082] The four objective function optimization models are respectively a project duration shortest objective function , a resource consumption least objective function , a project total cost lowest objective function , and a safety level highest objective function ;

[0083] Step S2, according to the four objective function optimization models constructed in step S1, a multi-objective balanced optimization model is constructed;

[0084] Step S3, the multi-objective balanced optimization model constructed in step S2 is iteratively solved by using an improved multi-objective particle swarm optimization MOPSO algorithm, and an optimal solution set of the project under the balance of duration, resource, cost and safety is obtained.

[0085] Specifically, the process of constructing four objective function optimization models in step S1 is as follows:

[0086] Step S11, based on the critical path method, the project process is constructed as a network diagram, and the longest time of the path is defined as the total duration, then the project duration shortest objective function The expression of the project duration minimum objective function is:

[0087]

[0088] In the above formula, is the set of all feasible paths; is the kth feasible path; is the duration of the process

[0089] The constraint condition of the project duration minimum objective function is the duration of the process is located in the closed interval of the minimum duration limit of each process and the maximum duration of each process ;

[0090] As shown in Figure 4 , an example of a process flow diagram of a railway construction network is given, which shows the main process content of the railway construction process. It should be noted that Figure 4 the process flow shown in the above is only given to facilitate the understanding of the meaning of "process " in the embodiment by the person skilled in the art, and the "process " in the method of the present application only contains these processes. In the actual railway construction process, the construction decision maker can further add or delete related processes according to the needs of railway construction.

[0091] Step S12, based on the consumption of three types of resources of equipment, manpower and materials, the expression of the resource consumption minimum objective function is:

[0092]

[0093] In the above formula, , , respectively represent the equipment, manpower and material consumption of the process , , , is the resource weight coefficient; N is the total number of processes included in the project;

[0094] The constraint condition of the resource consumption minimum objective function includes the upper limit of the supply of equipment, manpower and materials;

[0095] The total cost of the project includes direct cost, indirect cost and time-related incentive function, and the expression of the total cost minimum objective function is:

[0096] ​​​​ ;

[0097] In the above formula, is the direct cost of the process ; is the indirect cost of the process , r is the indirect cost rate of the unit duration, is the incentive and punishment function related to the planned duration deviation, , , respectively are the delay penalty coefficient, the advance reward coefficient, is the total project duration, is the planned duration;

[0098] The cost constraint of the project total cost minimum objective function is: , is the maximum budget limit of the total project cost;

[0099] Step S14, as shown in Figure 5 , based on the minimum reasonable and feasible ALARP principle and the system reliability theory, the safety investment of the process and the accident probability are fitted with exponential relationship to obtain the fitting function :

[0100] ;

[0101] In the above formula, is the initial accident probability without safety investment; is the accident risk reduction efficiency coefficient corresponding to the safety investment ; ; is the base of natural exponential; in this embodiment ;

[0102] Then the expression of the safety level highest objective function is:

[0103] ;

[0104] In the above formula, is the expected loss of the process accident.

[0105] Specifically, the multi-objective equilibrium optimization model constructed in step S2 is represented as:

[0106] ; ​

[0107] In the above formula, This represents the set of feasible solutions that satisfy all constraints.

[0108] 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.

[0109] Specifically, the improved multi-objective particle swarm optimization (MOPSO) algorithm in step S3 is calculated as follows:

[0110] Step S31: Initialize the population;

[0111] 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 first The initial position vector of each particle Within their respective constraints, the initial population is generated by random integer encoding, and the velocity vector is randomly initialized according to the variable scale. And calculate the first The target vector of 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;

[0112] Step S32: Set the total violation rate and adaptive constraint penalty strategy;

[0113] Total violation Represented as:

[0114] ;

[0115] In the above formula, For the first The excess of a constraint, For normalized weights;

[0116] Adaptive constraint penalty strategy: setting a penalty threshold For particles The penalty coefficients are:

[0117] ;

[0118] In the above formula, This represents 6 percentage points;

[0119] Modified multi-objective equilibrium optimization model for: ;

[0120] Step S33: Layered dynamic adjustment of inertia weight;

[0121] To achieve a smooth transition between iteration progress and population diversity, a logistic-mixed expression is used:

[0122] ;

[0123] In the above formula, Adaptive adjustment of inertia weights to accommodate population diversity; This represents the current iteration number. For the first The population diversity index is 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, , , ;

[0124] Step S34: External archive maintenance;

[0125] 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;

[0126] Step S35: Execute speed and location update;

[0127] Step S36, feasibility repair in parallel with penalty;

[0128] Immediately after position update, total violation degree is evaluated If Penalty is calculated according to and repair is attempted: first local fine-tuning, reducing resources of certain process or delaying non-critical process, if repair is not possible, replace with similar feasible solution in Archive or back to the historical optimal position of the particle, thereby improving feasible solution ratio and stabilizing search process;

[0129] Step S37, iteration termination determination and output;

[0130] Repeat step S35-step S36 until the maximum number of iterations or the change in output results of Archive in the last 10 iterations is less than the preset threshold, then stop iteration; output all non-dominated solutions in Archive as the optimal solution set; according to the actual needs of the project, the user selects a specific construction scheme from the optimal solution set.

[0131] Further, the speed and position update of step S35, in the iteration solving process, after the initialization of the population, the particles update the speed and position according to the following formula:

[0132] ;

[0133] ;

[0134] In the above formula, is the velocity vector of the th particle in the t th iteration; is the velocity vector of the th particle in the t th iteration; is the individual learning factor; is the social learning factor; , are random numbers in the interval [0, 1]; is the position vector of the th particle in the t th iteration; is the position vector of the th particle in the t th iteration; is the individual optimal position; is the representative solution selected from the external archive;

[0135] After each iteration, the optimal solution set is updated by non-dominated sorting and external archive screening; when the number of iterations reaches the maximum number of iterations or the output result of the Archive changes less than the preset threshold within 10 consecutive iterations, the iteration is terminated and the non-dominated solution set after multi-objective optimization is output ; each solution balances the optimal under the four optimization target dimensions of duration, resources, cost, and safety, so that users can select specific construction schemes according to actual project needs.

[0136] A railway construction example is given below to compare the method of the present application with the traditional linear weighting method, NSGA-II method, and MOPSO method under the same construction data to demonstrate the progressiveness of the method of the present application compared with existing methods.

[0137] I. Project parameters and constraints

[0138] Planned duration: 120 days

[0139] Equipment usage: 10 excavators, 5 automobile cranes

[0140] Manpower usage: 200 people

[0141] Main material monthly usage: 2000 tons of sand and stone per month, 500 tons of cement per month

[0142] Maximum budget limit: 4.5 x 10 8 million yuan

[0143] Safety investment interval: total amount 5~10 x 10 6 million yuan

[0144] Safety baseline and fitting: take typical .

[0145] II. Process splitting and duration interval

[0146] Table 1, process splitting and duration interval table

[0147] ;

[0148] III. Representative recommended scheme based on improved MOPSO algorithm

[0149] 1) Determine the process duration (unit: days), refer to Table 1:

[0150] A=3, B=18, C=20, D=30, E=18, F=22, G=6, H=20, I=18, J=10

[0151] 2) Critical Path: A→C→E→F→G→H→I→J;

[0152] 3) Project Duration: =3+20+18+22+6+20+18+10=117 days < 120 days;

[0153] 4) Process Schedule (d for day):

[0154] A: D1-D3 (3d, temporary facilities);

[0155] B: D4-D21 (18d, subgrade excavation);

[0156] C: D4-D23 (20d, bridge foundation);

[0157] D: D4-D33 (30d, tunneling);

[0158] E: D24-D41 (18d, pier construction);

[0159] F: D42-D63 (22d, beam prefabrication);

[0160] G: D64-D69 (6d, deck system);

[0161] H: D70-D89 (20d, track installation);

[0162] I: D90-D107 (18d, electromechanical / signal);

[0163] J: D108-D117 (10d, static acceptance and joint debugging);

[0164] 5) Resources and Personnel:

[0165] D4-D21 (B, C, D are in parallel peak period):

[0166] Excavator: B=5, C=3, D=2 ⇒ Total = 10 (= upper limit);

[0167] Crane: C=2, D=0, B=0 ⇒ Total = 2 (≤ 5);

[0168] Personnel: B=70, C=60, D=60 ⇒ Total = 190 (≤ 200);

[0169] The rest of the period is transferred by process segment by segment, ensuring that any period does not exceed the upper limit.

[0170] 6) Main materials are rolled monthly:

[0171] Sand and gravel: allocated to B / C / E / F / G, balanced according to production capacity, not more than 2000t per month;

[0172] Cement: assigned to C / E / F / G, no more than 500t per month;

[0173] Set =1; =0.6; =0.3; calculated =2.73×10 5 (weighted units);

[0174] 7) Cost

[0175] Direct cost (unit: million yuan):

[0176] B=3800, C=5200, D=6900, E=4200, F=5800, G=900, H=3600, I=4200, J=600, A=300, =36300 million yuan;

[0177] Indirect cost (unit: million yuan):

[0178] r= 45 million yuan / day, =117 days; =5262 million yuan;

[0179] Incentive and punishment (unit: million yuan):

[0180] Contract 120 days, 3 days in advance, =40 million yuan / day, reward 120 million yuan;

[0181] Total cost: =41445 million yuan = 4.1445×10 8 million < maximum budget limit 4.5×10 8 million yuan;

[0182] 8) Safety investment and risk expenditure

[0183] Take total safety investment 800 million yuan, distribution (unit: million yuan): B=80, C=120, D=220, E=70, F=120, G=20, H=80, I=70, J=10, A=10;

[0184] 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;

[0185] Expected loss: (unit: ten thousand yuan): B=500, C=800, D=1500, E=600, F=700, G=200, H=800, I=600, J=150;

[0186] Safety level: =1030 ten thousand yuan, which is about 50% lower than the risk expenditure in the case of "minimum investment" (3% of the total safety investment), falling into the "tolerable and continuously improved" interval of ALARP;

[0187] IV. Comparison with existing methods

[0188] Under the above data set, the improved MOPSO algorithm proposed in the present application and the traditional linear weighting method, NSGA-II method and MOPSO method were statistically evaluated for 50 independent runs (the evaluation function and the constraint condition were the same), and the index comparison results are shown in Table 2 as follows, wherein, as shown in Figure 7 and Figure 8 , the Spread of the frontiers of different methods and the Hypervolume convergence curve comparison chart are shown respectively.

[0189] Table 2, comparison results of the present application method and the traditional method under the same data set

[0190] ;

[0191] As can be seen from Table 2, the improved MOPSO algorithm of the present application has faster convergence speed and reaches a higher Hypervolume value compared with the traditional method, and the proportion of feasible solutions in the convergence result is higher, and the generated solution is closer to the theoretical optimal frontier; as shown in Figure 7 , the solution points of the linear weighting algorithm are scattered and it is difficult to form an effective frontier, and although the NSGA-II algorithm and the traditional MOPSO algorithm can produce non-dominated solutions, the distribution is uneven and some areas lack representativeness; in comparison, the solution generated by the improved MOPSO algorithm of the present application is closer to the theoretical optimal frontier, and performs better in the trade-off between duration and cost, and the solution set is evenly distributed and covers comprehensively, indicating that the method of the present application has stronger adaptability and convergence ability in multi-objective optimization; as shown in Figure 8 , the linear weighting algorithm has almost no convergence characteristics, and although the NSGA-II algorithm and the traditional MOPSO algorithm have improved at the beginning, they are prone to oscillation or premature convergence; while the improved MOPSO algorithm of the present application can quickly reach a higher Hypervolume value after a small number of iterations, and maintain stable convergence in the subsequent, which embodies the better convergence speed and global search ability, and provides more reliable solution set support for the multi-objective balanced optimization of railway construction.

[0192] In summary, the method of the present application can effectively avoid weight mutation by using Logistic-mixed inertia weight, and can make the feasible region "correct" faster by parallel mechanism of feasibility repair and penalty, and can significantly improve the coverage and diversity of the front by the combination of congestion degree and PCCS under fixed archive capacity, so as to provide more reliable solution set support for railway construction multi-objective balanced optimization.

[0193] Embodiment 2

[0194] This embodiment is to realize the multi-objective balanced optimization method as described in Embodiment 1, and as shown in the figure, a multi-objective balanced optimization system for railway construction management based on improved MOPSO algorithm is disclosed, which comprises a model construction module, a multi-objective integration module, an optimization solving module and a user interaction module. Figure 2

[0195] The model construction module is used to read construction network data, resource consumption data, cost data and safety data, and construct four objective function optimization models with the shortest project duration, the least resource consumption, the lowest total project cost and the highest safety level as the optimization objectives respectively; specifically including:

[0196] The duration target is based on the critical path method;

[0197] The resource target is calculated according to the consumption of equipment, manpower and materials;

[0198] The cost target considers direct cost, indirect cost and advance / delay incentive;

[0199] The safety target is converted into a safety benefit function through ALARP and reliability theory;

[0200] The multi-objective integration module is used to combine the four objective function optimization models and the constraint conditions into a unified multi-objective balanced optimization model, forming a unified four-dimensional objective vector and a feasible solution constraint set; supporting:

[0201] Target joint;

[0202] Constraint summary;

[0203] Feasible region analysis;

[0204] The optimization solving module is used to realize the improved MOPSO algorithm, including hierarchical dynamic inertia weight adjustment strategy, adaptive constraint penalty strategy, external archive + congestion degree distance + PCCS mixed maintenance strategy and elite reservation strategy, to iteratively solve the multi-objective balanced optimization model; specifically including:

[0205] Dynamic weight adjustment;

[0206] Penalty coefficient calculation;​

[0207] Archive screening and management;

[0208] Elite reservation and individual update mechanism, etc.

[0209] The user interaction module is used to display the front solution set of the iterative solution result in a graphical interface, and support online browsing (single solution query), comparison (multi-solution scheme comparison and analysis), parameter optimization (weight adjustment, constraint parameter modification) and scheme decision-making of the user.

[0210] Embodiment 3

[0211] The embodiment discloses a railway construction management multi-objective equilibrium optimization equipment based on an improved MOPSO algorithm, which is equipped with a multi-objective equilibrium optimization system as in Embodiment 2, as shown in the figure, comprising: at least one processor and a memory and an input / output device in communication therewith, instructions stored in the memory being executed by the processor, the input / output device being used for inputting construction parameters, constraint conditions, user preference settings and outputting optimized construction schemes, realizing the multi-objective equilibrium optimization method as recorded in Embodiment 1. Figure 3

[0212] Embodiment 4

[0213] The embodiment discloses a computer readable storage medium, and a computer program is stored on the computer readable storage medium, and the computer program is executed by a processor to realize the multi-objective equilibrium optimization method as recorded in Embodiment 1.

[0214] The above is only a preferred embodiment of the present application, and does not limit other forms of the present application. Any person skilled in the art can use the disclosed technical content to make changes or modifications to equivalent embodiments. However, any simple modification, equivalent change and modification made according to the technical essence of the present application without departing from the technical solution content of the present application still falls within the protection scope of the present application.​

Claims

1. A railway construction management multi-objective balanced optimization method based on an improved MOPSO algorithm, characterized in that, The method comprises the following steps: Step S1, under the premise of meeting the basic constraint conditions of the railway construction project, four objective function optimization models are constructed, each of which corresponds to an optimization objective; The four objective function optimization models are respectively a shortest project duration objective function , a least resource consumption objective function , a lowest total project cost objective function and a highest safety level objective function ; Step S2, according to the four objective function optimization model constructed in step S1, a multi-objective equilibrium optimization model is constructed, and the multi-objective equilibrium optimization model constructed is is represented as: ； In the above formula, denotes the set of feasible solutions that satisfy all the constraints; The constraint conditions of the multi-objective balanced optimization model comprise: minimum and maximum duration limits of the process; upper limits of equipment, manpower and material supply; total project cost budget; safety investment interval; Step S3, the multi-objective balanced optimization model constructed in step S2 is iteratively solved by using the improved multi-objective particle swarm optimization MOPSO algorithm to obtain an optimal solution set of the project under the balance of duration, resource, cost and safety; The improved multi-objective particle swarm optimization MOPSO algorithm has the following calculation process: Step S31, initializing 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 first The initial position vector of each particle Within their respective constraints, the initial population is generated by random integer encoding, and the velocity vector is randomly initialized according to the variable scale. And calculate the first The target vector of 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, setting total violation degree and adaptive constraint penalty strategy; total violation degree is represented as: ； In the above formula, is the first constraint over-limit, is the normalized weight; Adaptive constraint penalty strategy: set a penalty threshold , the penalty coefficient of the particle has: ； In the above formulae, represents 6 percentage points; Revised multi-objective equilibrium optimization model To: ; Step S33, hierarchical dynamic adjustment of inertia weight; In order to achieve smooth transition between iteration progress and population diversity, a Logistic-mixed type expression is adopted: ； In the above formula, is the population diversity adaptive adjustment inertia weight; is the current iteration number, is the initial diversity index of the first generation population, i.e., the Euclidean distance between two particles; is the diversity index of the first generation population, i.e., the Euclidean distance between two particles; is the initial diversity index; exp represents the exponential operation with base e; is the adjustment parameter, , , ; Step S34, external archive maintenance; Maintain a fixed-capacity external archive Archive, and store the current population non-dominated solutions into Archive at each iteration, if First, calculate the crowding distance of each non-dominated solution, and remove the crowded solutions from small to large according to the crowding distance to preliminarily reduce; if still over limit, then map the remaining solutions to the Parallel Coordinate Cell System (PCCS), PCCS divides each dimension of the objective space into several cells, and the non-dominated solutions in the same cell and with the distance of objective vectors less than the threshold are considered to be highly similar, and after clustering according to the similarity, further screen out the redundancy in each cell, and preferentially retain the cell boundaries and representative end-point solutions to maintain the uniform coverage of the non-dominated solutions in the entire objective space. Step S35, executing speed and position updating; 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 judgment and output; Repeat step S35-S36 until the maximum number of iterations is reached Or the change of the output result of the Archive in the last 10 iterations is less than the preset threshold value, then stop the iteration; output all non-dominated solutions in the Archive as the optimal solution set; and the user can select a specific construction scheme from the optimal solution set according to the actual requirements of the project.

2. The railway construction management multi-objective balanced optimization method 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, project process is constructed into a network diagram based on the critical path method, and the longest time of the path is defined as the total duration, so the shortest target function of the project duration The expression is: ； In the above formula, is a set of all feasible paths; is the kth feasible path; is the duration of the process . The constraint condition of the shortest target function of the project duration is the duration of the process The minimum duration limit of each process The maximum duration of each process The closed interval of the minimum duration limit of each process and the maximum duration of each process Step S12, based on the equipment, human and material resources consumption, the resource consumption of the minimum objective function is constructed The expression is: ； In the above formula, , , respectively represent the equipment, manpower, and material usage of the process , , , is the resource weight coefficient; N is the total number of processes included in the project; The constraint conditions of the resource consumption minimum objective function comprise upper limits of equipment, manpower and material supply; Step S13, the total cost of the project includes direct cost, indirect cost and time-related incentive function three parts, the total cost of the project is constructed the lowest objective function The expression is: ； In the above formula, is the direct cost of the process; is the indirect cost of the process, is the indirect cost rate per unit of duration, r is the incentive-penalty function related to the deviation of the planned duration, , , , are the delay penalty coefficient and the advance reward coefficient, respectively, is the total duration of the project, is the planned duration;​ The cost constraint of the total project cost minimum objective function is: , is the maximum budget limit of the total project cost; Step S14, based on the lowest reasonable and feasible ALARP principle and system reliability theory, the safety investment of the process and the accident probability are calculated The exponential relationship is fitted to obtain the fitting function : ； In the above formula, is the initial accident probability without safety investment; is the accident risk reduction efficiency coefficient corresponding to safety investment ; ; is the base number of natural exponent; The security level highest objective function The expression is: ； In the above formula, To process Expected loss from an accident.

3. The railway construction management multi-objective equilibrium optimization method based on the improved MOPSO algorithm according to claim 2, characterized in that, The executing speed and position updating in step S35, after initializing the population in the iterative solving process, the particle updates the speed and position according to the following formula: ； ； In the above formulae, is the velocity vector of the i-th particle at the j-th iteration; is the velocity vector of the i-th particle at the j-th iteration; t is the velocity vector of the i-th particle at the j-th iteration; is the velocity vector of the i-th particle at the j-th iteration; is the velocity vector of the i-th particle at the j-th iteration; t is the velocity vector of the i-th particle at the j-th iteration; is the individual learning factor; is the social learning factor; , is a random number in the interval [0, 1]; is the position vector of the i-th particle at the j-th iteration; is the position vector of the i-th particle at the j-th iteration; t is the position vector of the i-th particle at the j-th iteration; is the position vector of the i-th particle at the j-th iteration; is the position vector of the i-th particle at the j-th iteration; t is the position vector of the i-th particle at the j-th iteration; is the individual optimal position; is the representative solution selected from the external archive; After each iteration, the optimal solution set is updated by non-dominated sorting and external archive screening; when the number of iterations reaches the maximum number of iterations or the change of the output result of Archive in the last 10 iterations is less than the preset threshold, the iteration is terminated and the non-dominated solution set after multi-objective optimization is output ; each solution balances the optimal solution under the four optimization target dimensions of time, resources, cost and safety, so that users can choose specific construction schemes according to actual project needs.

4. A railway construction management multi-objective balanced optimization system based on an improved MOPSO algorithm, characterized in that, The system comprises a model construction module, a multi-objective integration module, an optimization solving module and a user interaction module; The model construction module is used for reading construction network data, resource consumption data, cost data and safety data, and constructing four objective function optimization models with the shortest project duration, the least resource consumption, the lowest total project cost and the highest safety level as optimization objectives, respectively; The four objective function optimization models are respectively a shortest project duration objective function , a least resource consumption objective function , a lowest total project cost objective function , and a highest safety level objective function ; The multi-objective integration module is used for combining the four objective function optimization models and the constraint conditions into a unified multi-objective balanced optimization model; The multi-objective balancing optimization model is represented as: ； In the above formula, denotes the set of feasible solutions that satisfy all the constraints; The constraint conditions of the multi-objective balanced optimization model comprise: minimum and maximum duration limits of the process; upper limits of equipment, manpower and material supply; total project cost budget; safety investment interval; The optimization solving module is used for implementing the improved MOPSO algorithm, including hierarchical dynamic inertia weight adjustment strategy, adaptive constraint penalty strategy, external archive + crowding distance + PCCS hybrid maintenance strategy and elite reservation strategy, and iteratively solving the multi-objective balanced optimization model; The calculation process of the improved MOPSO algorithm is as follows: Step S31, initializing 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 first The initial position vector of each particle Within their respective constraints, the initial population is generated by random integer encoding, and the velocity vector is randomly initialized according to the variable scale. And calculate the first The target vector of 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, setting total violation degree and adaptive constraint penalty strategy; total violation degree is represented as: ； In the above formula, is the first constraint of the over-limit amount, is the normalized weight; Adaptive constraint penalty strategy: set a penalty threshold , the penalty coefficient of the particle has: ； In the above formulae, represents 6 percentage points; Revised multi-objective equilibrium optimization model To: ; Step S33, hierarchical dynamic adjustment of inertia weight; In order to achieve smooth transition between iteration progress and population diversity, a Logistic-mixed type expression is adopted: ； In the above formula, Adaptive adjustment of inertia weight for population diversity; is the current iteration number, is the initial diversity index; exp represents the exponential operation with base e; is the diversity index of the current generation, i.e., the average Euclidean distance between two particles; is the initial diversity index; exp represents the exponential operation with base e; is the adjustment parameter, , , ; Step S34, external archive maintenance; Maintain a fixed-capacity external archive Archive, and store the current population non-dominated solutions into Archive at each iteration, if First, calculate the crowding distance of each non-dominated solution, and remove the crowded solutions from small to large according to the crowding degree to preliminarily reduce; if still over limit, then map the remaining solutions to the parallel coordinate cell system (PCCS), PCCS divides each dimension of the target space into several cells, and the non-dominated solutions in the same cell and with the distance of target vectors less than the threshold value are considered to be highly similar, and after clustering according to the similarity, further screen out the redundancy in each cell, and preferentially retain the cell boundaries and representative end-point solutions to maintain the uniform coverage of non-dominated solutions in the entire target space. Step S35, executing speed and position updating; 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 judgment and output; Repeat steps S35-S36 until a maximum number of iterations is reached or the change in the output result of the Archive is less than a preset threshold value in 10 consecutive iterations, the iteration is stopped; all non-dominated solutions in the Archive are output as an optimal solution set; and a user selects a specific construction scheme from the optimal solution set according to actual project requirements; The user interaction module is used to display the front solution set in a graphical interface before iteration solution, and supports user online browsing, comparison, parameter optimization and scheme decision.

5. A railway construction management multi-objective balanced optimization device based on an improved MOPSO algorithm, characterized in that, The application relates to a method for realizing multi-objective equilibrium optimization of railway construction management based on an improved MOPSO algorithm. The computer readable storage medium stores a computer program, and the computer program is used to realize the method for realizing multi-objective equilibrium optimization of railway construction management based on the improved MOPSO algorithm.

6. A computer-readable storage medium, characterized in that, ​

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