BIM-based method for sudden spatial interference diagnosis and rescheduling

Abstract

The present invention discloses a method for diagnosing and rescheduling sudden spatial interference based on BIM, which generates a three-dimensional construction model using BIM technology, excludes unacceptable spatial interference, and generates a BIM model combining progress, cost, and resources; identifies and diagnoses spatial interference problems through manual reporting, alarm devices configured by construction equipment, and environmental equipment detection during the construction process, and extracts and processes problem information in a BIM information integration management platform; establishes three scheduling strategies to deal with the problem: a heuristic repair strategy, a mode reselection strategy, and a complete rescheduling strategy, and decision makers make choices based on actual conditions and the application of scheduling strategies, and update data in the BIM information integration management platform to form a new construction schedule and cost. Use BIM technology to control construction before construction, select specific solutions for actual problems to make decisions, ensure smooth construction, and improve construction site operation efficiency.

Description

Technical Field

[0001] The present invention relates to a sudden space interference diagnosis and dispatching technology, and in particular to a sudden space interference diagnosis and re-dispatching method based on BIM. Background Art

[0002] With the rapid economic development and continuous advancement of engineering construction technology, since the 1980s, domestic and foreign projects have begun to show the characteristics of large-scale and complex. The number of equipment and personnel involved in the construction process has increased significantly, and the management requirements and difficulty of the construction site have continued to increase. Therefore, in the actual implementation process, they often face many unpredictable uncertain events.

[0003] Among these uncertain events, there is a type of sudden spatial interference events, which are often caused or aggravated by activity postponements, changes in resource space requirements, or deviations in managers' estimates of the degree of interference. It is crucial to adjust the remaining project scheduling plans in real time and adaptively to reduce the plan changes caused by spatial interference, thereby ensuring the progress and cost of the project.

[0004] At present, in the actual construction process, most people have basically introduced BIM technology to control the entire process of the project. The parameterization and visualization of BIM technology can realize the storage and processing of multi-party information data and realize a three-dimensional perception of the project. Through BIM technology, obvious collision problems and spatial interference problems can be identified before construction. During the construction process, the data information is summarized and processed on the platform through the obtained problem information. Decision makers analyze the problems and choose strategies. The corresponding construction schedule changes and cost information and other related changes are quickly generated through embedded methods, thereby ensuring the smooth progress of construction.

[0005] In view of the above characteristics, the engineering industry urgently needs to combine BIM technology to develop solutions to deal with sudden spatial interference problems, ensure the high quality and smooth progress of engineering construction, and improve the ability of managers to deal with sudden problems. Summary of the invention

[0006] Purpose of the invention: The purpose of the present invention is to solve the deficiencies in the prior art and to provide a BIM-based method for diagnosing and rescheduling sudden spatial interference.

[0007] Technical solution: A BIM-based sudden spatial interference diagnosis and rescheduling method of the present invention comprises the following steps:

[0008] S1. Obtain the progress, space, personnel, resources and cost information related to the sudden spatial interference problem in the construction project;

[0009] (A) Associate the initial progress plan, cost and other information of the project with the three-dimensional entity elements, and generate the construction space 3D information and progress, resource, cost management information on the BIM information integration management platform before construction begins;

[0010] (B) During the construction project, relevant information on sudden spatial interference problems is obtained through personnel reporting, equipment alarms, and on-site inspections, and uploaded to the BIM information integration management platform to obtain relevant progress, space, personnel, resources, and cost information involved in the sudden spatial interference problem;

[0011] S2. Based on the information obtained in step S1 about the sudden spatial interference problem that needs to be solved, a general engineering reactive scheduling optimization model considering spatial interference is established, wherein the goal of the engineering reactive scheduling optimization model is to minimize the project reactive scheduling cost;

[0012] S3. Based on the engineering reactive scheduling optimization model in step S2, three different reactive scheduling strategies are used to solve the sudden spatial interference problem according to the actual situation, as follows:

[0013] S301, according to different degrees of constraints on the project activity sequence and rush mode, three scheduling strategies are selected and established, namely, heuristic repair strategy, mode reselection strategy and complete rescheduling strategy;

[0014] S302, pre-processing, i.e., before reactive scheduling, the enumeration method is used to calculate the feasible construction mode for each activity, and the construction mode with the lowest cost under the agreed construction days is selected. The resulting set is directly called in the subsequent cost calculation;

[0015] S303. After preprocessing is completed, different solution methods are selected for the three scheduling strategies:

[0016] S303a, using a heuristic scheduling method to solve the heuristic repair strategy, that is, keeping the list order unchanged, and re-arranging the construction mode of the unstarted activities (including interfering activities);

[0017] S303b, using the taboo simulated annealing method TSA to solve the mode reselection strategy. This solution is different from S303b in that it considers the balance between progress and cost;

[0018] S303c. A two-stage hybrid method combined with a taboo search annealing method is used to solve the complete rescheduling strategy. This strategy reselects the mode and schedules the unstarted activities, that is, the sequence of activities, the activity execution time, and the construction mode are all re-decided to achieve the optimal rescheduling cost.

[0019] Furthermore, the construction content of the engineering reaction scheduling optimization model generally considering spatial interference in step S2 is as follows:

[0020] S201, the objective function is shown in formula (1):

[0021]

[0022] f T is the reactive scheduling cost of the project; i represents the project activity, N = {0, 1, ..., n, n + 1} represents the project set, 0 and n + 1 are the virtual start and end activities respectively; w i is the unit delay cost of activity i; s i is the start time of activity i; s i ′ is the start time of activity i in the original project plan; α i Add the unit cost of construction personnel to activity i; p i is the actual number of construction workers in activity i; is the number of people required for the normal construction mode of activity i; d i is the actual duration of activity i; β i is the unit overtime cost of activity i; h i is the number of overtime days for activity i;

[0023] S202, the constraints are as shown in equations (2) to (17):

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039] q ik 2 s i ≥0 (32)

[0040] in:

[0041] Formula (2) represents the project activity process constraint. The start time of an activity should not be earlier than the end time of its immediate predecessor activity.

[0042] Equations (3) and (4) represent avoiding the occurrence of unacceptable spatial conflicts;

[0043] Formula (5) indicates that the workload to be completed in the rush construction mode is the same as that in the normal construction mode;

[0044] Formula (6) represents the calculation of construction efficiency under the overcrowding mode;

[0045] Formula (7) and Formula (8) express the relationship between the number of construction workers and whether there is overcrowding. If the number of construction workers exceeds the normal number of construction workers, the activity is overcrowded. Otherwise, the number of construction workers is the number of people in the normal construction mode.

[0046] Formula (9) represents the percentage of the total elastic space of activity i that is occupied by other activities during the activity duration;

[0047] Formula (10) represents the calculation of quality factor q i , expressed as a function related to congestion factor, overcrowding and overtime;

[0048] Formula (11) and Formula (12) respectively calculate the impact of overstaffing and overtime on activity quality;

[0049] Formula (13) indicates that the quality factor of the restricted activity shall not be lower than the lower quality limit Q i ;

[0050] Formula (14) to (17) represent the value range of the defined decision variables, where the number of construction workers shall not exceed the maximum number of construction workers for the activity, and the overtime hours shall not be longer than the prescribed overtime hours;

[0051] in, The duration required for the normal construction mode of activity i; The amount of flexibility required to perform activity i; e ij is the sensitivity of the elastic space of activity i to being occupied by the elastic space of activity j; Q i is the acceptable lower limit of activity i quality, Q i ∈[0,1]; aij ∈{0,1} is the process relationship between activities;

[0052] If activity i is the immediate predecessor of activity j, then a ij =1; otherwise a ij =0; H is the normal working hours of a single person per day, usually H = 8h; H 0 The fixed overtime hours per person per day, usually H 0 =4h; B ij is the spatial interference matrix;

[0053] If there is no spatial interference ASI between activities i and j, then B ij =0;

[0054] If there is spatial interference ASI between activity i and activity j, B ij =1;

[0055] If there is unacceptable spatial interference USI between activity i and activity j, B ij =2;γ i is the influence parameter of overcrowding on the construction efficiency of activity i; M is an arbitrarily large positive number; is the sensitivity of the quality of activity i to overcrowding construction; is the sensitivity of the quality of activity i to overtime; The maximum number of construction workers for activity i; is the sensitivity of the quality of activity i to spatial congestion; y ij ∈{0,1} means that activity j starts to execute after activity i is completed, y ij =1; otherwise, y ij =0; C i ∈{0,1} is when activity i is overloaded, C i =1; otherwise, C i =0; is the set of activities being run on time slice t; is the time set during which activity i is working; is the congestion factor completed for activity i; Quality loss caused by overcrowding in activity i; The quality loss caused by overtime work for activity i; q i ∈[0,1] is the quality factor of activity i completed.

[0056] Furthermore, the detailed process of step S302 is as follows:

[0057] S302a, set one day of rush work, the number of construction workers is the normal number of construction workers, and calculate the required extra overtime time h:

[0058]

[0059] d i is the actual duration of activity i, is the duration required for the normal construction mode of activity i, is the number of people required for the normal construction mode of activity i, C i When activity i is overloaded, C i =1, otherwise, C i =0,W i is the construction efficiency of activity i, H is the normal working time of a single person per day, usually H = 8h, H 0 The fixed overtime hours per person per day, usually H 0 =4h;

[0060] S302b, determine whether the overtime hours meet the Constraints. If the constraints are not met, reduce the construction time or increase the number of construction workers. If they are met, proceed to the next step.

[0061] S302c, calculate the current activity quality:

[0062]

[0063] is the sensitivity of the quality of activity i to overcrowding, is the congestion factor completed by activity i, The quality loss caused by overcrowding in activity i, Quality loss caused by overtime work for activity i;

[0064] S302d, determine whether the current construction quality meets q i ≥Q i If the constraint is not met, increase the number of construction workers. If it is met, proceed to the next step.

[0065] S302e, calculate the current rush work cost, and save the construction period, number of construction workers, overtime time and cost in this mode in a list, add a construction worker or reduce the construction time to repeat the above operation until the construction period is 0.

[0066] Furthermore, the specific process of solving the heuristic repair strategy using the heuristic scheduling method in step S303a is as follows:

[0067] S303a-1. According to the start time of activity i and the start time of the interfering activity, determine the sequence numbers of the executed activities and the unexecuted activities, and remove them respectively according to the order of the pre-planned activity list to form two new activity lists L. done and L todo , and concatenate the two into a complete new activity list Lnew =[L done ,L todo ];

[0068] S303a-2, starting from the interfering activity, obtain the maximum rush time t through preprocessing max , and compare it with the delayed time L delay In contrast, if t max ≥L delay , then L delay The rush time for the intervening activity, the corresponding cost is the total cost of the scheduling plan, the original schedule is not changed, if it is not satisfied, proceed to the next step;

[0069] S303a-3, if t max <L delay , then postpone it to the next key activity, return to S303a-1 operation, repeat until all delayed progress is caught up or the project is completed, complete the schedule planning, and the delay cost of each delayed activity plus the corresponding cost of all catch-up activities is the total scheduling cost.

[0070] Furthermore, the specific process of the step S303b using the taboo simulated annealing method TSA to solve the mode reselection strategy is as follows:

[0071] S303b-1. According to the start time of the activity and the start time of the interfering activity, determine the sequence numbers of the executed activity and the unexecuted activity, and remove them respectively according to the order of the pre-planned activity list to construct two new activity lists L. done and L todo , for L todo The activities in the adopt the taboo simulated annealing search method;

[0072] S303b-2, construct an initial solution based on a greedy method, and obtain an initial solution solution S, wherein the solution represented by the solution is represented by a code consisting of a string of integers, and the position of the number corresponds to the activity at that position in the known activity sequence;

[0073] S303b-3. Apply the domain operator of addition and subtraction to each digital code in the solution S to generate the neighborhood N(S) of TAS. The maximum number of iterations generated is S. MAX ;

[0074] S303b-4, search the neighborhood to obtain a new solution S'. If the cost of the new solution is less than the current solution, update the current solution to the new solution and update the current target value to the optimal target value. Otherwise, continue the iteration without updating the solution.

[0075] S303b-5, until the maximum number of iterations is reached, the method is terminated, the optimal solution and its target value are output, and the scheduling plan with the lowest cost is obtained;

[0076] When constructing the initial solution based on the greedy method in step S303b-2, first select the rush work activities and their modes from low to high according to the rush work cost in the construction mode set obtained in the S302 preprocessing (active tasks have different rush work modes, such as adding some people to rush work, letting the current people work overtime, or a combination of the above two categories), and then recalculate the maximum rush work days for each activity in the schedule for the selected mode. If the calculated plan still causes delays in the schedule, reselect the calculation until no new activities are delayed, output the schedule under this mode, and obtain the initial solution.

[0077] Furthermore, the specific process of solving the complete rescheduling strategy by using a two-stage hybrid method combined with a taboo search annealing method is as follows:

[0078] S303c-1. For the interference activities and the subsequent activities, the possible construction sequences that avoid unacceptable spatial interference (USI) are listed by enumeration method, and the project network set consisting of the new process and the original process is obtained;

[0079] S303c-2. For each new network structure in the project network set obtained in S303c-1, the three objectives of duration, cost and resource balance are balanced, and the NSGA-II method is used to solve the scheduling problem with variable duration under the influence of acceptable spatial interference ASI, and the non-inferior solution set of each new network structure is calculated;

[0080] S303c-3, summarizing all non-inferior solutions and selecting a non-dominated solution set from them;

[0081] S303c-5. Each solution in the non-dominated solution set is represented by a code consisting of a string of integers, and the neighborhood operators of addition and subtraction are applied to the codes to generate the neighborhood N(S) of TAS. The maximum number of iterations generated is S. MAX ;

[0082] S303c-6, search the neighborhood to obtain a new solution. If the cost of the new solution is less than the current solution, update the current solution to the new solution and update the current target value to the optimal target value. Otherwise, continue the iteration without updating the solution.

[0083] S303c-7, until the maximum number of iterations is reached, the method is terminated, the optimal solution and its target value are output, and the optimal construction mode and scheduling cost under multiple objectives are obtained.

[0084] Furthermore, the specific process of the enumeration method in step S303c-1 is as follows:

[0085] (a) Based on the sudden spatial interference situation, experts make judgments based on the new information and update the spatial interference matrix {B ij};

[0086] (b) According to the spatial interference activity information in the spatial interference matrix, the process relationship is added by enumeration method and checked whether it conflicts with the process relationship of the original project network (i.e., a loop is generated). If the no-loop condition is met, the corresponding process relationship is added to the current network, otherwise, the process relationship is discarded;

[0087] (c) Repeat the above step (b) to generate a set of all possible network structures. Each network structure avoids serious spatial interference by manually adding process relationships.

[0088] Furthermore, the specific process of solving the problem using the NSGA-II method in step S303c-2 is as follows:

[0089] (a) Encode each network structure in the obtained structure set

[0090] In addition to the virtual start and end activities, the project consists of n activities; the design code consists of 2n elements, denoted as DML = (Δ 1 ,…,Δ n ,m 1 ,…m n ); any Δ in the first n elements i Represents the relative delay time of activity i, that is, relative to the earliest possible start time of activity i, and then delayed by Δ i unit time; the next n are the mode selections for the corresponding activities, m∈M i ;

[0091] (b) Set the maximum number of iterations Maxgen, randomly generate the initial population, i.e., n types of construction schedules corresponding to each network structure, recorded as set P', perform crossover and mutation operations on the initial population, and obtain the offspring population;

[0092] (c) Merge the parent population and the child population, and use the fast non-dominated sorting operator, the crowding distance sorting operator, and the elite selection strategy operator on the merged population to select suitable individuals as the parent population of the next generation;

[0093] (d) Continue the traditional crossover and mutation operations to generate a new offspring population, then merge the parent and offspring populations, and repeat the above operations until the number of cycles reaches the maximum number of iterations to obtain the final solution;

[0094] (e) Decode the obtained solution. Starting from time 0, the execution activities in each time period are gradually determined according to the project development time. At the same time, the resource usage is calculated. If the resource limit is exceeded, the solution is determined to be an infeasible solution, and the decoding is stopped. The solution is not included in the non-dominated solution set. If it does not exceed the limit, proceed to the next step.

[0095] (f) Continue to calculate the spatial interference degree of each execution activity, calculate the work efficiency, the cumulative workload completed at the end of the period, and the remaining workload, and determine whether each execution activity is completed until all activities are completed, and then output the non-dominated set of the engineering schedule.

[0096] Furthermore, the fast non-dominated sorting operator in step (c) performs the following steps:

[0097] (c1) Each solution in the population has two properties: the number of dominant solutions p and the number of solution individuals n that dominate individual p in the population. p , compare the first solution p in the population with all other members in the set P' one by one. If p dominates a member q in P', for example, the cost, resource balance and duration corresponding to solution p are better than solution q, then solution p dominates solution q, and solution q is removed from P';

[0098] (c2) If solution p is not dominated by any member of P', then p becomes a first-level non-dominated solution, and the individuals in the set are given the same number 1, forming a first-level dominated solution;

[0099] (c3) Eliminate the first-layer dominant solution from the population and repeat the above operation to form the second-layer dominant solution;

[0100] (c4) and so on, until all populations are stratified and multi-layer non-dominated solutions are obtained.

[0101] Furthermore, the crowding distance sorting operator in step (c) performs the following steps:

[0102] (c1) For individuals in the same dominant layer, the individuals at the two ends of the unified non-dominated layer are better than those with the largest or smallest objective function value, so the distance is set to a very large positive number;

[0103] (c2) For the solution in the middle, its crowding distance is L i According to the formula

[0104]

[0105] Calculate, where, assuming there are O targets, Respectively represent the function values ​​of two adjacent volume targets o, Respectively represent the maximum and minimum values ​​of the target o;

[0106] (c3) After the calculation, individuals with larger crowding distances are preferably selected in subsequent operations.

[0107] Furthermore, the steps of executing the elite strategy selection operator in step (c) are:

[0108] (c1) For the merged population, first initialize the parent population to an empty set;

[0109] (c2) Select individuals in the dominant layer in descending order according to the dominant sequence number, and determine whether the total number of parent individuals selected after adding the individuals in the non-dominated layer exceeds the population size. If not, add all individuals in the non-dominated layer to the parent population and select the next dominant individual. If it exceeds, proceed to the next step.

[0110] (c3) If the population size is exceeded, individuals are selected in descending order according to the crowding distance of individuals in the dominant layer;

[0111] (c4) The operator stops until the number of parent populations reaches the set population size.

[0112] Beneficial effect: The construction BIM technology of the present invention controls the construction process in real time, summarizes and processes the progress information, personnel information and cost information related to the construction, and through multi-faceted detection of the site, records and uploads the records in the face of sudden spatial interference problems, and further considers measures such as increasing the number of construction personnel and increasing the construction time to deal with the disturbance of the plan by spatial interference, thereby optimizing the construction schedule, solving the spatial interference problem, improving the operating efficiency of the construction site, and ensuring the smooth progress of the construction.

[0113] Compared with the prior art, the present invention has the following advantages:

[0114] (1) Based on BIM technology, the present invention records, updates and summarizes information such as personnel, equipment, progress and cost in the construction process in real time, comprehensively detects and feedbacks information in real time, records sudden spatial interference problems, and provides three reactive scheduling strategies for decision makers to choose from. It can realize timely repair of temporary uncertain disturbances and ensure the progress of construction.

[0115] (2) The present invention comprehensively considers the personnel, progress, cost and other aspects required to solve the spatial interference problem, and comprehensively considers the impact of increasing personnel on activity efficiency, as well as the impact of ASI and rush work strategies on activity quality. Three methods are proposed for three strategies, including taboo and two-stage methods, to efficiently generate engineering scheduling plans, progress plans and cost updates to minimize scheduling costs during response. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] Figure 1 It is a schematic diagram of the overall process of the present invention;

[0117] Figure 2 It is a schematic diagram of the pretreatment process in the present invention;

[0118] Figure 3 It is a schematic diagram of the process flow of the taboo simulated annealing method;

[0119] Figure 4 It is a schematic diagram of the NSGA-II method flow chart;

[0120] Figure 5 A system structure diagram of an embodiment of the present invention;

[0121] Figure 6 A schematic diagram of engineering related information in one embodiment of the present invention;

[0122] Figure 6 (a) is a schematic diagram of basic information of an activity in an embodiment, Figure 6 (b) is a schematic diagram of a 3-D model of a building in the embodiment, Figure 6 (c) is a schematic diagram of a project network in an embodiment, Figure 6 (d) is a schematic diagram of the space for activities in the embodiment. DETAILED DESCRIPTION

[0123] The technical solution of the present invention is described in detail below, but the protection scope of the present invention is not limited to the embodiments.

[0124] like Figure 5 As shown, the BIM-based sudden spatial interference diagnosis and rescheduling method of the present invention includes a BIM information integration management platform, environmental detection equipment, and a construction facility alarm device, wherein data processing is realized by an embedded method of the BIM information integration management platform;

[0125] Before construction, BIM Revit builds a 3D visualization model of the project site. Using the parametric characteristics of the BIM model, collision checks and spatial conflict detection are performed on the sub-projects and structures of the project construction. Problems are recorded to generate an information database, and corrections are made to achieve model optimization, generate schedules and spatial layout information;

[0126] There are three ways to identify problems during construction. The first is manual reporting, where on-site construction personnel directly identify problems and record and upload problem information. The second is through the equipment alarm system. If problems such as insufficient working space or path blockage occur during equipment operation, the equipment stops running and alarms, thereby obtaining location-related information on the information platform. The third is the on-site environmental detection device, which performs real-time visual detection of the construction process, issues early warnings for sudden spatial interference problems, and reports real-time data.

[0127] Identify the problem based on the acquired information data, check whether there is the same problem in the problem information database to find a solution, if not found, calculate the results of different scheduling strategies through the embedded method, the decision maker will choose according to the actual situation, and update the calculated construction mode and schedule plan to the decision maker for reactive scheduling

[0128] like Figures 1 to 4 As shown, the BIM-based sudden spatial interference diagnosis and rescheduling method of the present invention comprises the following steps:

[0129] S1. Obtain the progress, space, personnel, resources and cost information related to the sudden spatial interference problem in the construction project;

[0130] S2. Based on the information obtained in step S1 about the sudden spatial interference problem that needs to be solved, a general engineering reactive scheduling optimization model considering spatial interference is established, wherein the goal of the engineering reactive scheduling optimization model is to minimize the project reactive scheduling cost;

[0131] S201, the objective function is shown in formula (1):

[0132]

[0133] f T is the reactive scheduling cost of the project; i represents the project activity, N = {0, 1, ..., n, n + 1} represents the project set, 0 and n + 1 are the virtual start and end activities respectively; w i is the unit delay cost of activity i; s i is the start time of activity i; s i ′ is the start time of activity i in the original project plan; α i Add the unit cost of construction personnel to activity i; p i is the actual number of construction workers in activity i; is the number of people required for the normal construction mode of activity i; d i is the actual duration of activity i; β i is the unit overtime cost of activity i; h i is the number of overtime days for activity i;

[0134] S202, the constraints are as shown in equations (2) to (17):

[0135]

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150] q ik 2 s i ≥0 (48)

[0151] in:

[0152] Formula (2) represents the project activity process constraint. The start time of an activity should not be earlier than the end time of its immediate predecessor activity.

[0153] Equations (3) and (4) represent avoiding the occurrence of unacceptable spatial conflicts;

[0154] Formula (5) indicates that the workload to be completed in the rush construction mode is the same as that in the normal construction mode;

[0155] Formula (6) represents the calculation of construction efficiency under the overcrowding mode;

[0156] Formula (7) and Formula (8) express the relationship between the number of construction workers and whether there is overcrowding. If the number of construction workers exceeds the normal number of construction workers, the activity is overcrowded. Otherwise, the number of construction workers is the number of people in the normal construction mode.

[0157] Formula (9) represents the percentage of the total elastic space of activity i that is occupied by other activities during the activity duration;

[0158] Formula (10) represents the calculation of quality factor q i , expressed as a function related to congestion factor, overcrowding and overtime;

[0159] Formula (11) and Formula (12) respectively calculate the impact of overstaffing and overtime on activity quality;

[0160] Formula (13) indicates that the quality factor of the restricted activity shall not be lower than the lower quality limit Q i ;

[0161] Formula (14) to (17) represent the value range of the defined decision variables, where the number of construction workers shall not exceed the maximum number of construction workers for the activity, and the overtime hours shall not be longer than the prescribed overtime hours;

[0162] in, The duration required for the normal construction mode of activity i; The amount of flexibility required to perform activity i; e ij is the sensitivity of the elastic space of activity i to being occupied by the elastic space of activity j; Q i is the acceptable lower limit of activity i quality, Q i ∈[0,1]; a ij ∈{0,1} is the process relationship between activities;

[0163] If activity i is the immediate predecessor of activity j, then a ij =1; otherwise a ij =0; H is the normal working hours of a single person per day, usually H = 8h; H 0 The fixed overtime hours per person per day, usually H 0 =4h; B ij is the spatial interference matrix;

[0164] If there is no spatial interference ASI between activities i and j, then B ij =0;

[0165] If there is spatial interference ASI between activity i and activity j, B ij =1;

[0166] If there is unacceptable spatial interference USI between activity i and activity j, B ij =2;γ i is the influence parameter of overcrowding on the construction efficiency of activity i; M is an arbitrarily large positive number; is the sensitivity of the quality of activity i to overcrowding construction; is the sensitivity of the quality of activity i to overtime; The maximum number of construction workers for activity i; is the sensitivity of the quality of activity i to spatial congestion; y ij ∈{0,1} means that activity j starts to execute after activity i is completed, y ij =1; otherwise, y ij =0; C i∈{0,1} is when activity i is overloaded, C i =1; otherwise, C i =0; is the set of activities being run on time slice t; is the time set during which activity i is working; is the congestion factor completed for activity i; Quality loss caused by overcrowding in activity i; The quality loss caused by overtime work for activity i; q i ∈[0,1] is the quality factor of activity i completed;

[0167] S3. Based on the engineering reactive scheduling optimization model in step S2, three different reactive scheduling strategies are used to solve the sudden spatial interference problem according to the actual situation, as follows:

[0168] S301, according to different degrees of constraints on the project activity sequence and rush mode, three scheduling strategies are established, namely, heuristic repair strategy, mode reselection strategy and complete rescheduling strategy;

[0169] S302, pre-processing, i.e., before reactive scheduling, the enumeration method is used to calculate the feasible construction mode for each activity, and the construction mode with the lowest cost under the agreed construction days is selected. The resulting set is directly called in the subsequent cost calculation;

[0170] S302a, set one day of rush work, the number of construction workers is the normal number of construction workers, and calculate the required extra overtime time h:

[0171]

[0172] d i is the actual duration of activity i, is the duration required for the normal construction mode of activity i, is the number of people required for the normal construction mode of activity i, C i When activity i is overloaded, C i =1, otherwise, C i =0,W i is the construction efficiency of activity i, H is the normal working time of a single person per day, usually H = 8h, H 0 The fixed overtime hours per person per day, usually H 0 =4h;

[0173] S302b, determine whether the overtime hours meet the Constraints. If the constraints are not met, reduce the construction time or increase the number of construction workers. If they are met, proceed to the next step.

[0174] S302c, calculate the current activity quality:

[0175]

[0176] is the sensitivity of the quality of activity i to overcrowding, is the congestion factor completed by activity i, The quality loss caused by overcrowding in activity i, Quality loss caused by overtime work for activity i;

[0177] S302d, determine whether the current construction quality meets q i ≥Q i If the constraint is not met, increase the number of construction workers. If it is met, proceed to the next step.

[0178] S302e, calculating the current rush work cost, and saving the construction period, number of construction workers, overtime time and cost in this mode in a list, adding a construction worker or reducing the construction time to repeat the above operation until the construction period is 0;

[0179] S303. After preprocessing is completed, different solution methods are selected for the three scheduling strategies:

[0180] S303a, using a heuristic scheduling method to solve the heuristic repair strategy, that is, keeping the list order unchanged, re-arranging the construction mode of the unstarted activities, where the unstarted activities include the interference activities;

[0181] S303a-1. According to the start time of activity i and the start time of the interfering activity, determine the sequence numbers of the executed activities and the unexecuted activities, and remove them respectively according to the order of the pre-planned activity list to form two new activity lists L. done and L todo , and concatenate the two into a complete new activity list L new =[L done ,L todo ];

[0182] S303a-2, starting from the interfering activity, obtain the maximum rush time t through preprocessing max , and compare it with the delayed time L delay In contrast, if t max ≥L delay , then L delay The rush time for the intervening activity, the corresponding cost is the total cost of the scheduling plan, the original schedule is not changed, if it is not satisfied, proceed to the next step;

[0183] S303a-3, if t max <L delay, then postpone to the next key activity, return to S303a-1, repeat until all delayed progress is completed or the project is completed, complete the schedule preparation, and the delay cost of each delayed activity plus the corresponding cost of all rushed activities is the total scheduling cost;

[0184] S303b, using the taboo simulated annealing method TSA to solve the mode reselection strategy. This solution is different from S303b in that it considers the balance between progress and cost;

[0185] S303b-1. According to the start time of the activity and the start time of the interfering activity, determine the sequence numbers of the executed activity and the unexecuted activity, and remove them respectively according to the order of the pre-planned activity list to construct two new activity lists L. done and L todo , for L todo The activities in the adopt the taboo simulated annealing search method;

[0186] S303b-2, construct an initial solution based on a greedy method, and obtain an initial solution solution S, wherein the solution represented by the solution is represented by a code consisting of a string of integers, and the position of the number corresponds to the activity at that position in the known activity sequence;

[0187] S303b-3. Apply the domain operator of addition and subtraction to each digital code in the solution S to generate the neighborhood N(S) of TAS. The maximum number of iterations generated is S. MAX ;

[0188] S303b-4, search the neighborhood to obtain a new solution S'. If the cost of the new solution is less than the current solution, update the current solution to the new solution and update the current target value to the optimal target value. Otherwise, continue the iteration without updating the solution.

[0189] S303b-5, until the maximum number of iterations is reached, the method is terminated, the optimal solution and its target value are output, and the scheduling plan with the lowest cost is obtained;

[0190] When constructing the initial solution based on the greedy method in step S303b-2, first select the rush work activities and their modes from the construction mode set obtained in the preprocessing of S302 according to the rush work cost from low to high, and then recalculate the maximum rush work days for each activity in the schedule for the selected mode. If the calculated solution still causes the schedule to be delayed, reselect the calculation until no new activities are delayed, output the schedule under this mode, and obtain the initial solution;

[0191] S303c, a two-stage hybrid method combined with a taboo search annealing method is used to solve the complete rescheduling strategy. This strategy reselects the mode and schedules the unstarted activities, that is, the sequence of activities, the activity execution time and the construction mode are all re-decided to achieve the optimal rescheduling cost;

[0192] S303c-1. For the interference activities and the subsequent activities, the possible construction sequences that avoid unacceptable spatial interference (USI) are listed by enumeration method, and the project network set consisting of the new process and the original process is obtained;

[0193] S303c-2. For each new network structure in the project network set obtained in S303c-1, the three objectives of duration, cost and resource balance are balanced, and the NSGA-II method is used to solve the scheduling problem with variable duration under the influence of acceptable spatial interference ASI, and the non-inferior solution set of each new network structure is calculated;

[0194] S303c-3, summarizing all non-inferior solutions and selecting a non-dominated solution set from them;

[0195] S303c-5. Each solution in the non-dominated solution set is represented by a code consisting of a string of integers, and the neighborhood operators of addition and subtraction are applied to the codes to generate the neighborhood N(S) of TAS. The maximum number of iterations generated is S. MAX ;

[0196] S303c-6, search the neighborhood to obtain a new solution. If the cost of the new solution is less than the current solution, update the current solution to the new solution and update the current target value to the optimal target value. Otherwise, continue the iteration without updating the solution.

[0197] S303c-7, until the maximum number of iterations is reached, the method is terminated, the optimal solution and its target value are output, and the optimal construction mode and scheduling cost under multiple objectives are obtained.

[0198] In the present invention, the heuristic repair strategy is applicable to activities with extremely strict schedule requirements and difficult activity resource scheduling; the mode reselection strategy is applicable to projects with sensitive project costs and difficult activity resource scheduling; and the complete rescheduling strategy is applicable to projects with sensitive project costs and simple activity resource scheduling.

[0199] Example:

[0200] according to Figure 5 and Figure 1As shown in the figure, the BIM sudden space interference diagnosis and dispatching system includes environmental detection equipment, BIM information integration management platform and construction facility alarm device. The embedded methods of space detection module, progress management module, cost management module, etc. linked to the BIM information management platform realize data processing. Specifically, it can be divided into the preventive design stage before construction, the stage of identifying interference problems during construction, and the stage of adaptive adjustment of management plans such as progress and cost after the event.

[0201] The implementation process of this invention is illustrated by taking the San Francisco International Airport terminal expansion project as an engineering example. In the pre-construction design stage, a three-dimensional model is established through BIM Revit, Civil 3D and other software, and unacceptable spatial interference of the project is eliminated through collision checks and space detection, and basic information of activities required to complete the project is generated, such as Figure 6 By linking the 3D model with other information such as progress and cost in the BIM information integration management platform, each activity has two execution modes, and the activity information of the generated case is shown in Table 1.

[0202] Table 1 Case activity information

[0203]

[0204]

[0205] During the construction process, it was discovered through personnel reporting that there was interference in the resource work space within Activity 2 and Activity 5. This situation occurred when managers underestimated the activity work space and improper resource allocation caused resource congestion, resulting in loss of work efficiency and delays. The delay situation is shown in Table 2.

[0206] Table 2 Delay situation of calculation example

[0207]

[0208] After identifying the interfering activities, we start to compare and select strategies. We determine the maximum number of construction workers for each activity based on the construction efficiency, and find a certain number of construction workers p. Before this number, the construction efficiency will increase with each additional construction worker. After this number, the construction efficiency will decrease with each additional construction worker. Then p is the maximum number of construction workers for this activity. Based on formula (13), the parameter γ that affects the efficiency of overstaffing is i and normal construction staff If it is known, the maximum number of construction personnel for each activity can be expressed as If the obtained p i is a decimal, then when p i If the decimal part is ≤5, it will be rounded down, otherwise it will be rounded up. Table 3 shows the γ i= 0.5 when each activity has a different execution mode.

[0209] Table 3 Activity execution mode

[0210]

[0211]

[0212] Referring to the conclusion of Jeunet and Orm (2020), the impact factor of overtime on quality Set as overcrowding impact factor The other fixed parameters and method parameters are shown in Table 4.

[0213] Table 4 Method parameters

[0214]

[0215] The overstaffing cost of each activity unit is set by random number generation, with a range of [100,300]. The unit overtime cost is 1.5 times the overstaffing cost. The delay cost of each activity is a randomly generated parameter, and two parameter generation rules are set. The range of rule 1 is [600,1000], and the range of rule 2 is [0,1600]. The results are shown in Table 5.

[0216] Table 5 Unit dispatch cost

[0217]

[0218] The results obtained according to the above parameter settings are shown in Table 6. Strategy 1 represents the heuristic repair strategy, strategy 2 represents the mode reselection strategy, and strategy 3 represents the complete rescheduling strategy. Among them, the results where the execution time of each activity is different from the original schedule are displayed in bold, and the optimal results of the reactive scheduling of each case are displayed in underline.

[0219] Table 6 Optimal solutions of three strategies

[0220]

[0221]

[0222]

[0223] From the above results, we can see that when the delay cost is high, taking reactive scheduling for sudden spatial interference can effectively reduce the scheduling cost. The earlier the spatial interference occurs, the larger the optimization space of reactive scheduling. The comparative experiment of the three strategies shows that strategy 1 has a simple calculation method and higher calculation efficiency, but strategies 2 and 3 have larger search spaces and are easy to obtain solutions with lower scheduling costs; strategy 2 is suitable for situations where the delay cost difference between activities is not large; although strategy 3 is complex in calculation, it is more advantageous when the delay cost difference between activities is large.

Claims

1. A method for sudden spatial interference diagnosis and rescheduling based on BIM, characterized by: The following steps are involved: S1. Obtain the progress, space, personnel, resources and cost information related to the sudden spatial interference problem in the construction project; S2. Based on the information obtained in step S1 about the sudden spatial interference problem that needs to be solved, a general engineering reactive scheduling optimization model considering spatial interference is established, wherein the goal of the engineering reactive scheduling optimization model is to minimize the project reactive scheduling cost; S3. Based on the engineering reactive scheduling optimization model in step S2, three different reactive scheduling strategies are used to solve the sudden spatial interference problem according to the actual situation, as follows: S301, according to different degrees of constraints on the project activity sequence and rush mode, three scheduling strategies are selected and established, namely, heuristic repair strategy, mode reselection strategy and complete rescheduling strategy; S302, pre-processing, i.e., before reactive scheduling, the enumeration method is used to calculate the feasible construction mode for each activity, and the construction mode with the lowest cost under the agreed construction days is selected. The resulting set is directly called in the subsequent cost calculation; S303. After preprocessing is completed, different solution methods are selected for the three scheduling strategies: S303a, using a heuristic scheduling method to solve the heuristic repair strategy, that is, keeping the list order unchanged, re-arranging the construction mode of the unstarted activities, where the unstarted activities include the interference activities; S303b, using taboo simulated annealing method TSA to solve the mode reselection strategy; S303c, a two-stage hybrid method combined with a taboo search annealing method is used to solve the complete rescheduling strategy. This strategy reselects the mode and schedules the unstarted activities, that is, the sequence of activities, the activity execution time and the construction mode are all re-decided to achieve the optimal rescheduling cost; The construction content of the engineering reaction scheduling optimization model generally considering spatial interference in step S2 is as follows: S201, the objective function is shown in formula (1): f T is the reactive scheduling cost of the project; i represents the project activity, N = {0, 1, ..., n, n + 1} represents the project set, 0 and n + 1 are the virtual start and end activities respectively; w i is the unit delay cost of activity i; s i is the start time of activity i; s i ′ is the start time of activity i in the original project plan; α i Add the unit cost of construction personnel to activity i; p i is the actual number of construction workers in activity i; The number of people required for the normal construction mode of activity i; d i is the actual duration of activity i; β i is the unit overtime cost of activity i; h i is the number of overtime days for activity i; S202, the constraints are as shown in equations (2) to (17): s i ≥0 (17) in: Formula (2) represents the project activity process constraint. The start time of an activity should not be earlier than the end time of its immediate predecessor activity. Equations (3) and (4) represent avoiding the occurrence of unacceptable spatial conflicts; Formula (5) indicates that the workload to be completed in the rush construction mode is the same as that in the normal construction mode; Formula (6) represents the calculation of construction efficiency under the overcrowding mode; Formula (7) and Formula (8) express the relationship between the number of construction workers and whether there is overcrowding. If the number of construction workers exceeds the normal number of construction workers, the activity is overcrowded. Otherwise, the number of construction workers is the number of people in the normal construction mode. Formula (9) represents the percentage of the total elastic space of activity i that is occupied by other activities during the activity duration; Formula (10) represents the calculation of quality factor q i , expressed as a function related to congestion factor, overcrowding and overtime; Formula (11) and Formula (12) respectively calculate the impact of overstaffing and overtime on activity quality; Formula (13) indicates that the quality factor of the restricted activity shall not be lower than the lower quality limit Q i ; Formula (14) to (17) represent the value range of the defined decision variables, where the number of construction workers shall not exceed the maximum number of construction workers for the activity, and the overtime hours shall not be longer than the prescribed overtime hours; in, The duration required for the normal construction mode of activity i; The amount of flexibility required to perform activity i; e ij is the sensitivity of the elastic space of activity i to being occupied by the elastic space of activity j; Q i is the acceptable lower limit of activity i quality, Q i ∈[0,1]; a ij ∈{0,1} is the process relationship between activities; If activity i is the immediate predecessor of activity j, then a ij =1; otherwise a ij =0; H is the normal working hours of a single person per day; H0 is the fixed overtime hours of a single person per day; B ij is the spatial interference matrix; If there is no spatial interference ASI between activities i and j, then B ij =0; If there is spatial interference ASI between activity i and activity j, B ij =1; If there is unacceptable spatial interference USI between activity i and activity j, B ij =2;γ i is the impact parameter of overcrowding on the construction efficiency of activity i; M is an arbitrarily large positive number; is the sensitivity of the quality of activity i to overcrowding construction; is the sensitivity of the quality of activity i to overtime; The maximum number of construction workers for activity i; is the sensitivity of the quality of activity i to spatial congestion; y ij ∈{0,1} means that activity j starts to execute after activity i is completed, y ij =1; otherwise, y ij =0; C i ∈{0,1} is when activity i is overloaded, C i =1; otherwise, C i =0; is the set of activities being run on time slice t; is the time set during which activity i is working; is the congestion factor completed for activity i; Quality loss caused by overcrowding in activity i; The quality loss caused by overtime work for activity i; q i ∈[0,1] is the quality factor of activity i completed; The detailed process of step S302 is as follows: S302a, set one day of rush work, the number of construction workers is the normal number of construction workers, and calculate the required extra overtime time h: d i is the actual duration of activity i, is the duration required for the normal construction mode of activity i, is the number of people required for the normal construction mode of activity i, C i When activity i is overloaded, C i =1, otherwise, C i =0,W i is the construction efficiency of activity i, H is the normal working hours of a person per day, and H0 is the fixed overtime hours of a person per day; S302b, determine whether the overtime hours meet the Constraints. If the constraints are not met, reduce the construction time or increase the number of construction workers. If they are met, proceed to the next step. S302c, calculate the current activity quality: is the sensitivity of the quality of activity i to overcrowding, is the congestion factor completed by activity i, The quality loss caused by overcrowding in activity i, Quality loss caused by overtime work for activity i; S302d, determine whether the current construction quality meets q i ≥Q i If the constraint is not met, increase the number of construction workers. If it is met, proceed to the next step. S302e, calculating the current rush work cost, and saving the construction period, number of construction workers, overtime time and cost in this mode in a list, adding a construction worker or reducing the construction time to repeat the above operation until the construction period is 0; The specific process of solving the heuristic repair strategy using the heuristic scheduling method in step S303a is as follows: S303a-1. According to the start time of activity i and the start time of the interfering activity, determine the sequence numbers of the executed activities and the unexecuted activities, and remove them respectively according to the order of the pre-planned activity list to form two new activity lists L. done and L todo , and concatenate the two into a complete new activity list L new =[L done ,L todo ]; S303a-2, starting from the interfering activity, obtain the maximum rush time t through preprocessing max , and compare it with the delayed time L delay In contrast, if t max ≥L delay , then L delay The rush time for the intervening activity, the corresponding cost is the total cost of the scheduling plan, the original schedule is not changed, if it is not satisfied, proceed to the next step; S303a-3, if t max <L delay , then postpone to the next key activity, return to S303a-1, repeat until all delayed progress is completed or the project is completed, complete the schedule preparation, and the delay cost of each delayed activity plus the corresponding cost of all rushed activities is the total scheduling cost; The specific process of step S303b using the taboo simulated annealing method TSA to solve the mode reselection strategy is as follows: S303b-1. According to the start time of the activity and the start time of the interfering activity, determine the sequence numbers of the executed activity and the unexecuted activity, and remove them respectively according to the order of the pre-planned activity list to construct two new activity lists L. done and L todo , for L todo The activities in the adopt the taboo simulated annealing search method; S303b-2, construct an initial solution based on a greedy method, and obtain an initial solution solution S, wherein the solution represented by the solution is represented by a code consisting of a string of integers, and the position of the number corresponds to the activity at that position in the known activity sequence; S303b-3. Apply the domain operator of addition and subtraction to each digital code in the solution S to generate the neighborhood N(S) of TAS. The maximum number of iterations generated is S. MAX ; S303b-4, search the neighborhood to obtain a new solution S'. If the cost of the new solution is less than the current solution, update the current solution to the new solution and update the current target value to the optimal target value. Otherwise, continue the iteration without updating the solution. S303b-5, until the maximum number of iterations is reached, the method is terminated, the optimal solution and its target value are output, and the scheduling plan with the lowest cost is obtained; When constructing the initial solution based on the greedy method in step S303b-2, first select the rush work activities and their modes from the construction mode set obtained in the preprocessing of S302 according to the rush work cost from low to high, and then recalculate the maximum rush work days for each activity in the schedule for the selected mode. If the calculated solution still causes the schedule to be delayed, reselect the calculation until no new activities are delayed, output the schedule under this mode, and obtain the initial solution; The specific process of solving the complete rescheduling strategy by using a two-stage hybrid method combined with a tabu search annealing method is as follows: S303c-1. For the interference activities and the subsequent activities, the possible construction sequences that avoid unacceptable spatial interference (USI) are listed by enumeration method, and the project network set consisting of the new process and the original process is obtained; S303c-2. For each new network structure in the project network set obtained in S303c-1, the three objectives of duration, cost and resource balance are balanced, and the NSGA-II method is used to solve the scheduling problem with variable duration under the influence of acceptable spatial interference ASI, and the non-inferior solution set of each new network structure is calculated; S303c-3, summarizing all non-inferior solutions and selecting a non-dominated solution set from them; S303c-5. Each solution in the non-dominated solution set is represented by a code consisting of a string of integers, and the neighborhood operators of addition and subtraction are applied to the codes to generate the neighborhood N(S) of TAS. The maximum number of iterations generated is S. MAX ; S303c-6, search the neighborhood to obtain a new solution. If the cost of the new solution is less than the current solution, update the current solution to the new solution and update the current target value to the optimal target value. Otherwise, continue the iteration without updating the solution. S303c-7, until the maximum number of iterations is reached, the method is terminated, the optimal solution and its target value are output, and the optimal construction mode and scheduling cost under multiple objectives are obtained.

2. The BIM-based sudden spatial interference diagnosis and rescheduling method according to claim 1, characterized in that: The specific process of the enumeration method in step S303c-1 is as follows: (a) Based on the sudden spatial interference situation, make judgments based on the new information and update the spatial interference matrix {B ij}； (b) According to the spatial interference activity information in the spatial interference matrix, the process relationship is added by enumeration method and checked whether it conflicts with the process relationship of the original project network. If the no-loop condition is met, the corresponding process relationship is added to the current network, otherwise, the process relationship is discarded; (c) Repeat the above step (b) to generate a set of all possible network structures. Each network structure avoids serious spatial interference by manually adding process relationships.

3. The method for sudden spatial interference diagnosis and rescheduling based on BIM according to claim 1, characterized in that: The specific process of solving the problem using the NSGA-II method in step S303c-2 is as follows: (a) Encode each network structure in the obtained structure set In addition to the virtual start and end activities, the project consists of n activities; the design code consists of 2n elements, denoted as DML = (Δ1,…,Δ n ,m1,…m n ); any Δ in the first n elements i Represents the relative delay time of activity i, that is, relative to the earliest possible start time of activity i, and then delayed by Δ i It starts after n units of time; the next n are the mode selections for the corresponding activities; (b) Set the maximum number of iterations Maxgen, randomly generate the initial population, i.e., n types of construction schedules corresponding to each network structure, recorded as set P', perform crossover and mutation operations on the initial population, and obtain the offspring population; (c) Merge the parent population and the child population, and use the fast non-dominated sorting operator, the crowding distance sorting operator, and the elite selection strategy operator on the merged population to select suitable individuals as the parent population of the next generation; (d) Continue the traditional crossover and mutation operations to generate a new offspring population, then merge the parent and offspring populations, and repeat the above operations until the number of cycles reaches the maximum number of iterations to obtain the final solution; (e) Decode the obtained solution. Starting from time 0, the execution activities in each time period are gradually determined according to the project development time. At the same time, the resource usage is calculated. If the resource limit is exceeded, the solution is determined to be an infeasible solution, and the decoding is stopped. The solution is not included in the non-dominated solution set. If it does not exceed the limit, proceed to the next step. (f) Continue to calculate the spatial interference degree of each execution activity, calculate the work efficiency, the cumulative workload completed at the end of the period, and the remaining workload, and determine whether each execution activity is completed until all activities are completed, and then output the non-dominated set of the engineering schedule.

4. The BIM-based sudden spatial interference diagnosis and rescheduling method according to claim 3 is characterized in that: The fast non-dominated sorting operator in step (c) performs the following steps: (c1) Each solution in the population has two properties: the number of dominant solutions p and the number of solution individuals n that dominate individual p in the population. p , compare the first solution p in the population with all other members in the set P' one by one. If p dominates a member q in P', and the cost, resource balance and duration corresponding to solution p are better than solution q, it means that solution p dominates solution q, and solution q is removed from P'; (c2) If solution p is not dominated by any member of P', then p becomes a first-level non-dominated solution, and the individuals in the set are given the same number 1, forming a first-level dominated solution; (c3) Eliminate the first-layer dominant solution from the population and repeat the above operation to form the second-layer dominant solution; (c4) and so on, until all populations are stratified and multi-layer non-dominated solutions are obtained.

5. The BIM-based sudden spatial interference diagnosis and rescheduling method according to claim 3 is characterized by: The steps of executing the crowding distance sorting operator in step (c) are: (c1) For individuals in the same dominant layer, the individuals at the two ends of the unified non-dominated layer are better than those with the largest or smallest objective function value, so the distance is set to a very large positive number; (c2) For the solution in the middle, its crowding distance is L i According to the formula Calculate, where, assuming there are O targets, Respectively represent the function values ​​of two adjacent volume targets o, Respectively represent the maximum and minimum values ​​of the target o; (c3) After the calculation, individuals with larger crowding distance are given priority in subsequent operations.

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