Repeated construction project cost optimization method

Abstract

The invention discloses a repetitive construction project cost optimization method, and particularly relates to the field of project construction. Comprising the following steps: S1, parameter setting: initializing the starting time of a time window and the number of algorithm iterations; s2, generating an initial construction plan; s3, if the starting time of the time window is larger than the difference between the construction period of the initial construction plan and the length of the time window, the starting time of the time window is set to be 0; s4, generating a corresponding relaxation problem by adopting a rolling time domain method; s5, solving the relaxation problem in the step S4 by using a constraint programming method; s6, updating the number of iterations, and updating the starting time of the time window; and S7, repeating the steps S3-S6 until an iteration condition is met, and outputting an optimal solution in an iteration process. By the adoption of the technical scheme, the problem that an existing construction plan compilation method with cost as an optimization target cannot be suitable for different construction scenes is solved, and meanwhile, when medium and large-scale cases are solved, an approximate optimal solution can be obtained within reasonable time.

Description

Technical Field

[0001] The invention relates to the field of engineering construction, and in particular to a method for optimizing costs of repetitive construction projects. Background Art

[0002] The basic goal of construction project management is to ensure the quality of the project, use the least cost, and complete the project as soon as possible within the specified construction period. In the context of the current slowdown in global economic recovery, how to effectively reduce project costs has become the focus of all project participants. The construction plan preparation problem with cost as the optimization target aims to obtain a construction plan with the lowest project cost within a given construction period. At present, various studies on the optimization of repetitive construction project costs mainly focus on: (1) optimizing the interruption costs or idle costs caused by construction interruptions in allowed activities; (2) exploring the impact of different factors or different construction strategies on project costs in real construction scenarios (for example: different factors such as multi-mode and multi-work group; or different construction strategies such as soft logic and rush work); (3) taking cost as one of the optimization targets to achieve multi-objective optimization. In terms of algorithm design, meta-heuristic algorithms represented by genetic algorithms are still the most commonly used optimization algorithms in existing studies.

[0003] In the process of construction planning, the selection and allocation of resources are crucial to reducing project costs and shortening construction periods. In reality, construction projects are usually delivered by contractors after they complete the construction. In pursuit of profit, contractors may undertake multiple projects at the same time, which requires them to reasonably allocate construction resources to ensure that the project is completed on schedule while minimizing costs. Specifically, for any project, the contractor needs to determine the number of work groups to be used for each activity and the amount of resources used by each work group based on the existing resources.

[0004] At present, the existing construction plan preparation with cost as the optimization goal has the following problems:

[0005] 1. The impact of work group resource allocation is generally ignored during the construction plan preparation process: In the construction plan preparation and optimization process for repetitive construction projects, it is usually assumed that the work group resource allocation (construction mode) of the activity is known; or when the work group can choose multiple construction modes, all work groups of the same activity must adopt the same construction mode. In real scenarios, contractors need to use their own construction resources to determine the number of work groups for the activity, as well as the resource allocation of each work group, that is, the construction mode.

[0006] 2. Failure to deeply explore the impact of different construction strategies of work groups on project costs when multiple construction factors coexist: In the process of construction plan preparation, construction is usually carried out according to a fixed construction sequence, that is, a fixed logic, ignoring the fact that work groups can adopt soft logic construction strategies for some types of construction projects (for example, multi-building residential construction projects). Some studies that allow work groups to adopt soft logic construction strategies are usually only aimed at implementing the preparation of construction plans for repetitive construction projects under a single work group or a single mode scenario. When multiple real factors coexist, how various factors or different construction strategies affect project costs, including the various costs that constitute project costs (direct costs, indirect costs), still needs to be discussed in depth.

[0007] 3. Failure to explore the application of different modeling methods or modeling ideas in the process of construction plan preparation: The integer programming method is mainly used to characterize the problem. In terms of modeling ideas, the characterization of the construction process of the work group is still expressed in the form of a matrix, and the impact of different modeling ideas on obtaining the optimal construction plan has not been explored.

[0008] 4. Metaheuristic algorithms have the advantage of solution speed, but their solution quality cannot guarantee optimality, and may even show significant differences in different scenarios.

[0009] 5. Integer programming or constraint programming methods (relying only on solvers such as gurobi and cplex) can theoretically obtain optimal solutions, but their computational efficiency is low. When faced with complex and large-scale case optimization, they may not even be able to obtain feasible solutions within a reasonable time.

[0010] Based on the above problems, it is urgent to develop an optimization method for repetitive construction projects oriented towards cost optimization. Summary of the invention

[0011] The present invention aims to provide a method for optimizing the cost of repetitive construction projects, which solves the problem that the existing construction plan preparation method with cost as the optimization target cannot be applied to different construction scenarios.

[0012] In order to achieve the above object, the technical solution of the present invention is as follows: A method for optimizing repetitive construction project costs, comprising the following steps:

[0013] S1, parameter setting: initialization time window start time, algorithm iteration times;

[0014] S2, generating an initial construction plan;

[0015] S3. If the start time st of the time window is greater than the difference between the duration of the initial construction plan and the length of the time window, the start time of the time window is set to 0;

[0016] S4, using the rolling horizon method to generate the corresponding relaxation problem;

[0017] S5, solving the relaxation problem of step S4 using constraint programming method;

[0018] S6. Update the number of iterations and the start time of the time window;

[0019] S7. Repeat steps S3-S6 until the iteration condition is met, stop the iteration and output the optimal solution in the iteration process.

[0020] Furthermore, the initial construction plan generation method of step S2 is as follows:

[0021] S2.1. Determine the number of work groups used for each activity and the construction mode used by each work group;

[0022] S2.2, use the forward serial construction plan generation method to determine the construction process of each activity on the construction unit;

[0023] S2.3, if the generated construction plan meets the expected construction period constraint, then output the initial construction plan; if it does not meet the expected construction period constraint, then go to step S2.4;

[0024] S2.4. Use the backward-forward adjustment method to adjust the construction plan generated in step S2, and use the adjusted construction plan as the initial construction plan.

[0025] Furthermore, the relaxation problem generation method of step S4 is as follows: the activity set A is divided into two sets OA and MA using the rolling horizon method, where OA is composed of three subsets IA, OLA and RA. According to the construction start time SD of activity i on construction unit j in the construction plan, i,j and end time ED i,j , identify the activities in three subsets; except for the activities in OA, the rest of the activities belong to MA.

[0026] Furthermore, the activity subset IA is determined as follows: if the construction process of activity i in construction unit j is completely within the time window, then the sub-activity (i, j) belongs to IA, that is, IA = {(i, j)∈A×U i |SD i,j ≥st∧ED i,j ≥et}.

[0027] Furthermore, the method for determining the activity subset OLA is as follows: if the construction process of activity i in construction unit j overlaps with the time window, then the sub-activity (i, j) belongs to OLA; there are two specific overlapping situations: the construction start time of activity i in construction unit j is earlier than the start of the time window and the construction is completed within the time window; or the construction starts within the time window and the construction ends later than the end of the time window, that is, OLA = {(i, j)∈A×U i |(SD i,j <st∧ED i,j ≤et)∨(SD i,j ≤st∧ED i,j >et)}.

[0028] Furthermore, the method for determining the activity subset RA is as follows: if the construction process of activity i in construction unit j is compactly constructed with the activities in OLA, then the sub-activity (i, j) belongs to RA; compact construction means: the sum of the construction end time of activity i in construction unit j and the interval time between activities is equal to the construction start time of activity i' in construction unit j in OLA, or the construction start time of activity i in construction unit j is equal to the sum of the construction end time of activity i' in construction unit j in OLA and the interval time between activities, that is, RA = {(i, j)∈A×U i |ED i,j +Lag i,i' =SD i',j ∨SD i,j =ED i',j +Lag i,i' ,(i',j)∈OLA}.

[0029] Furthermore, the solution method of step S5 is as follows: construct the following constraint programming model, and solve the constraint programming model with the help of Cplex CPOptimizer. The specific formula is as follows:

[0030] Objective function of total project cost:

[0031]

[0032] The objective function must meet the following conditions:

[0033] Construction logic constraints:

[0034] End-Start: Start-Start: Start-End: End-End: If work group k is working on a construction unit, work group k can only adopt one construction mode:

[0035]

[0036] If work group k is constructing on a construction unit, the construction mode of the construction unit is the same as that of the work group:

[0037]

[0038] Each construction unit of the activity can only be constructed by one work group:

[0039]

[0040] Ensure that there is no overlap in the construction process of the work groups:

[0041]

[0042] Calculate the construction interruption time of work group k in activity i:

[0043]

[0044] Resource constraints and duration constraints:

[0045]

[0046] Matching constraints between work groups and construction units:

[0047]

[0048] If the work group must perform construction according to a fixed logic, the following constraints need to be added:

[0049]

[0050] Compared with the prior art, this solution has the following beneficial effects:

[0051] 1. This scheme considers the impact of work group resource allocation on the construction plan. Existing studies usually assume that the construction plan can be prepared in advance with the known work group resource allocation. In reality, the work group resource allocation needs to be decided by the manager. In addition, in theory, a more flexible rather than fixed resource allocation can obtain a more cost-effective construction plan. This scheme incorporates the decision-making process of work group resource allocation into the construction plan preparation process, and expands the traditional two-dimensional construction mode-activity-related planning framework into a three-dimensional construction mode-work group-activity-related planning framework, making the model more practical while providing the possibility of exploring a more cost-effective construction plan.

[0052] 2. This scheme comprehensively considers various construction strategies that may be adopted by work groups under multiple work groups, multiple modes and resource constraints. For example, work groups can use soft logic or fixed logic for construction; work groups can have construction interruptions or maintain construction contact; the construction workload of work groups can be variable, etc., so that the model has the ability to adaptively select reasonable construction strategies for work groups for different types of repetitive construction projects.

[0053] 3. Compared with the integer programming method, the constraint programming method has significant advantages when applied to the solution of the optimization problem of the preparation of construction plans for repetitive construction projects in large-scale scenarios. However, considering the NP-hard properties of the optimization problem of the preparation of construction plans for repetitive construction projects under resource constraints, simply relying on the classical constraint programming method still cannot obtain a satisfactory construction plan within a reasonable time. The present invention introduces the optimization idea of ​​relaxation solution into the solution of this problem for the first time, adopts the rolling time domain strategy to generate the corresponding relaxation problem based on the initial construction plan, and uses the constraint programming method to realize the characterization and solution of the relaxation problem, and obtains a better construction plan through continuous iteration. The proposal of this innovative relaxation strategy that integrates rolling time domain and constraint programming should be the first application in the preparation of construction plans for repetitive construction projects, and at the same time provides new ideas for the design of algorithms based on the idea of ​​relaxation optimization.

[0054] 4. In order to strike a balance between solution time and solution quality, this solution designs a relaxation solution algorithm (CP-R&S) based on constraint programming and integrated with rolling horizon strategy. Based on an initial construction plan, this algorithm uses the rolling horizon strategy to generate a relaxation problem, and reconstructs the relaxation problem into a constraint programming model and solves it using the constraint programming method. Through multiple iterations, the initial plan is improved to generate a better construction plan. Through case analysis, the effectiveness of the CP-R&S algorithm in obtaining approximate / optimal construction plans for different construction scenarios is verified, as well as its superiority in solution quality and solution time compared to classic integer programming and constraint programming methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a sensitivity analysis result diagram under the original scale case in the present invention;

[0056] Figure 2 It is the construction plan diagram corresponding to the construction scene 1 in the present invention;

[0057] Figure 3 It is the construction plan corresponding to the construction scene 2 in the present invention;

[0058] Figure 4 It is the construction plan diagram corresponding to the construction scene 3 in the present invention;

[0059] Figure 5It is the construction plan diagram corresponding to the construction scene 4 in the present invention;

[0060] Figure 6 It is the construction plan diagram corresponding to the construction scene 5 in the present invention;

[0061] Figure 7 It is the construction plan diagram corresponding to the construction scene 6 in the present invention;

[0062] Figure 8 It is the construction plan diagram corresponding to the construction scene 7 in the present invention;

[0063] Fig. 9 It is the construction plan diagram corresponding to the construction scene 8 in the present invention;

[0064] Fig.10 It is the construction plan diagram corresponding to the construction scene 9 in the present invention;

[0065] Fig.11 It is a construction plan diagram corresponding to the construction scene 10 in the present invention;

[0066] Fig.12 It is the construction plan diagram corresponding to the construction scene 11 in the present invention;

[0067] Fig.13 It is a construction plan diagram corresponding to the construction scene 12 in the present invention;

[0068] Fig.14 It is a framework diagram for generating a forward serial construction plan in the present invention;

[0069] Fig.15 It is a framework diagram of the backward-forward adjustment method in the present invention. Fig.16 It is a schematic diagram of the construction process of the work group in the present invention. DETAILED DESCRIPTION

[0070] The present invention is further described in detail below through specific embodiments:

[0071] Explanation of terms:

[0072] Repetitive construction projects: The repetitive construction projects described in the present invention refer to construction projects that include construction activities with repetitive characteristics, that is, in repetitive construction projects, the construction team needs to move from one construction unit (section) to another construction unit (section) to complete the same construction task. Typical repetitive construction projects include: for example: linear repetitive projects such as railways and highways, and vertical repetitive construction projects such as high-rise buildings.

[0073] Soft logic: The soft logic of the present invention refers to the flexible change of the construction sequence of the same type of construction activities in different construction units in repetitive construction projects, that is, synchronous construction, sequential construction, or partial synchronous and partial sequential construction. Taking residential construction projects, a typical repetitive construction project, as an example, for activities such as frame structure construction, the construction sequence between different houses is variable, rather than having to be constructed in order from small to large according to the house number.

[0074] Parameter Description:

[0075] (1) Index

[0076] iActivity Index

[0077] jConstruction Unit Index

[0078] k-group index

[0079] mConstruction mode index

[0080] tTime Index

[0081] r can update resource index

[0082] (2) Collection

[0083] A collection of activities in a project

[0084] U i The construction unit set of activity i

[0085] K i The set of available construction groups for activity i

[0086] M i Construction mode collection for activity i

[0087] T project expected duration collection

[0088] R Updatable Resource Collection

[0089] P i The set of predecessor activities of activity i

[0090] S i The set of subsequent activities of activity i

[0091] (3) Parameters

[0092] Expected duration of DL project

[0093] RL r The amount of renewable resource r available on day t

[0094] Lag p,i The construction time interval between activity i and its predecessor activity p

[0095] di,j,m The construction duration of activity i on construction unit j when construction mode m is adopted

[0096] c i,m,r Direct cost of construction on construction unit j when activity i adopts construction mode m

[0097] re i,m,r When activity i adopts construction mode m, the daily usage of resource j can be updated

[0098] Unit interruption cost of inc project, work unit / yuan / day

[0099] Unit indirect cost of ic project, RMB / day

[0100] N is the number of activities

[0101] B is a large positive number

[0102] O virtual construction unit means that the work team starts construction from this virtual construction unit and returns to this virtual construction unit after completing all construction tasks.

[0103] (4) Intermediate variables

[0104] v i,k,m Whether the work group k of activity i adopts mode m for construction, if yes, the value is 1, otherwise, the value is 0;

[0105] iti i,k,j,j' The interruption duration caused when work group k of activity i moves from construction unit j to construction unit j';

[0106] Decision variables:

[0107] x i,j,m,t Whether construction unit j of activity i uses construction mode m to complete construction on day t, if yes, the value is 1, otherwise, the value is 0;

[0108] y i,k,j,j' Whether the work group k of activity i moves from construction unit j to construction unit j'. If yes, the value is 1, otherwise, the value is 0.

[0109] Example

[0110] A method for optimizing repetitive construction project costs comprises the following steps:

[0111] S1, parameter setting: initialization time window start time (st = 0), algorithm iteration number (k = 0);

[0112] S2. Generate an initial construction plan, and mark the construction period of the initial construction plan as Dmax. The method for generating the initial construction plan is as follows:

[0113] S2.1. Determine the number of work groups used for each activity and the construction mode used by each work group;

[0114] S2.2, use the forward serial construction plan generation method to determine the construction process of each activity on the construction unit;

[0115] S2.3, if the generated construction plan meets the expected construction period constraint, then output the initial construction plan; if it does not meet the expected construction period constraint, then go to step S2.4;

[0116] S2.4. Use the backward-forward adjustment method to adjust the construction plan generated in step S2, and use the adjusted construction plan as the initial construction plan.

[0117] This embodiment uses a two-stage constructive heuristic method to generate an initial construction plan. The first stage is used to determine the number of work groups used in the activity and the construction mode of the work group. For the number of work groups, in order to ensure that the generated plan meets the construction period as much as possible, the number of work groups used in the activity is the maximum number of available work groups. For the construction mode, this embodiment sorts the modes from high to low according to the resource usage of the modes, and selects the mode corresponding to the median as the construction mode of the work group, so as to ensure that the resource usage is relatively small while avoiding the work group's construction time on the construction unit being too long.

[0118] In the second stage, the heuristic method adopts the compilation idea of ​​the forward serial construction plan generation framework to generate the initial construction plan. Specifically, the forward serial construction plan generation framework starts from the first activity and determines the construction process of each construction unit in each activity, that is, the work group working on the construction unit, the construction start and end time of the work group, so that it meets the logical constraints and resource constraints until the construction process of the last activity in the project is arranged. For the construction arrangement within the activity, the construction strategy of the work group is first come first served. According to the workload of each construction unit, it starts from the construction unit with the smallest workload and then carries out the construction in sequence. If the construction period corresponding to the initial plan is longer than the established construction period, the backward-forward adjustment method is used to adjust the initial plan to meet the construction period constraint.

[0119] Taking a project with four activities as an example, we will explain how to use the second stage of the heuristic method to implement the construction plan of the project. Fig.14 and Fig.15As shown. In the forward serial construction plan generation framework, the construction process of each activity is determined in sequence according to the sequence relationship of the activities. First, the construction process of activity A is determined, as follows: Activity A uses 2 construction groups, and the workload on each construction unit is ranked from small to large as 4-2-1-3. Therefore, the construction process of the construction unit is determined in the order of 4-2-1-3. For construction unit 4, work group 1 is selected for construction. Since activity A is the first activity, that is, activity A has no preceding activity, the construction start time of work group 1 on construction unit 4 is 0. According to the construction mode of work group 1, the construction duration of the work group on the construction unit is determined, and the construction end time of the work group on the construction unit is calculated (construction end time = construction start time + construction duration). For construction unit 2, at this time, work group 1 is constructing on construction unit 4, and work group 2 has no construction tasks. Therefore, according to the principle of "first come, first served", work group 2 is arranged to construct on construction unit 2, and the construction process of work group 2 is determined according to the construction mode of work group 2. For construction unit 1, work group 1 completed the construction on day 1, and work group 2 completed the construction on day 2. According to the principle of "first come, first served", work group 1 is arranged to work on construction unit 1. Similarly, it can be determined that construction unit 3 is to be constructed by work group 2. After determining the construction process of activity A on each unit (such as Fig.14 As shown in (a), the construction process of activities B, C, and D is determined in sequence to ensure that the construction process of each activity meets the logical constraints. If there is a situation where the resource constraints are not met, the start time of the work group on the construction unit is adjusted according to the serial scheduling method so that the construction process of the work group meets the resource constraints. Finally, the initial construction plan is generated, as shown in Fig.14 As shown in (c).

[0120] Since the duration of the generated initial construction plan is 20 days, which does not meet the expected duration of 19 days, the backward-forward adjustment method is needed to adjust the initial plan. In the post-sequence adjustment process, the original construction post-sequence relationship ABCD is flipped to DCBA, that is, the construction process of each activity is determined in sequence starting from activity D. The determination of the construction process of each activity is still based on the principle of "first come, first served". The resulting construction plan is as follows Fig.15 At this time, the initial construction plan does not start construction on the first day, so the overall plan is moved back by one day, forming the following Fig.15 The construction plan in (c) that satisfies the expected construction period constraint is used as the initial solution of the algorithm.

[0121] S3. If the start time st of the time window is greater than the difference between the construction period of the initial construction plan and the length of the time window, that is, st>Dmax-L, the start time of the time window is set to 0, that is, st=0.

[0122] S4. Use the rolling time domain method to generate the corresponding relaxation problem. In the relaxation problem, activities belonging to OA can be optimized freely, and activities belonging to MA need to pre-arrange the construction tasks of the work groups, that is, to pre-assign some work groups to certain construction units for construction. The start time of the time window is st and the length is L. In the initial stage of the algorithm, st is set to 0. In each iteration, the time window moves forward ml units, and st is updated to st+ml. It should be noted that the start and end of the time window are not necessarily integers. The number of iterations of the algorithm Iter is given by Calculated, where D max The duration of the initial feasible construction plan.

[0123] The parameter overlap represents the difference between the length L of the time window and the displacement ml, that is, overlap = L-ml. If overlap = 0, it means that during the iteration process, there is no overlap between the current time window and the time window corresponding to the previous iteration. Correspondingly, the activities that need to be optimized between iterations may not overlap at all. During the optimization process, the loss of construction information of the preceding activities can easily cause the algorithm to fall into a local optimum. Therefore, L and overlap are the two most important parameters in the algorithm and need to be set by the user. The relaxation problem generation method is as follows: Use the rolling time domain method to divide the activity set A into two sets, OA and MA, that is, A = OA∪MA. Among them, OA is composed of three subsets, IA, OLA and RA, according to the construction start time SD of activity i on construction unit j in the construction plan i,j and end time ED i,j , identify activities in three subsets:

[0124] The method for determining the activity subset IA is as follows: if the construction process of activity i in construction unit j is completely within the time window, then the sub-activity (i, j) belongs to IA, that is, IA = {(i, j)∈A×U i |SD i,j ≥st∧ED i,j ≥et}.

[0125] The method for determining the activity subset OLA is as follows: if the construction process of activity i on construction unit j overlaps with the time window, then the sub-activity (i, j) belongs to OLA; there are two specific overlapping situations: the construction start time of activity i on construction unit j is earlier than the start of the time window and the construction is completed within the time window; or the construction starts within the time window and the construction ends later than the end of the time window, that is, OLA = {(i, j)∈A×U i |(SD i,j <st∧ED i,j ≤et)∨(SD i,j ≤st∧ED i,j >et)}.

[0126] The method for determining the activity subset RA is as follows: if the construction process of activity i in construction unit j is compactly constructed with the activities in OLA, then the sub-activity (i, j) belongs to RA; compact construction means: the sum of the construction end time of activity i in construction unit j and the interval time between activities is equal to the construction start time of activity i' in construction unit j in OLA, or the construction start time of activity i in construction unit j is equal to the sum of the construction end time of activity i' in construction unit j in OLA and the interval time between activities, that is, RA = {(i, j)∈A×U i |ED i,j +Lag i,i' =SD i',j ∨SD i,j =ED i',j +Lag i,i' ,(i',j)∈OLA}.

[0127] Except for the activities in OA, all other activities belong to MA.

[0128] S5. Solve the relaxation problem of step S4 using constraint programming method. Constraint programming method is a unique modeling and solving method that requires reconstruction of the problem. During the reconstruction process, the constraint programming method uses interval variables to describe the activity construction process. Interval variables contain parameters such as start value, end value, and variable length (size), which are used to represent a time interval in the construction plan. For example: Assume that the construction start time of activity i in the construction unit is 8, the construction end time is 10, and the construction duration is 2. Correspondingly, the interval variable activity_unit i,j The starting value, ending value and length of are 8, 10, and 2 respectively. The important feature of interval variables is selectivity, that is, in the optimization results, some interval variables can be empty. Table 1 shows the decision variables in the constraint programming method. At the same time, for various constraints involved in MRCRPSP-MCSL, the constraint programming method needs to use some OPL functions to characterize them. The definitions of each OPL function are shown in Table 2.

[0129] Table 1 Decision variables in constraint programming

[0130]

[0131] Table 2 OPL function definition

[0132]

[0133]

[0134] According to the decision variables and OPL functions, for the relaxation problem, the following constraint programming model is constructed, and the constraint programming model is solved with the help of CplexCP Optimizer. The specific formula is as follows:

[0135] Objective function of total project cost:

[0136]

[0137] The objective function must meet the following conditions:

[0138] Construction logic constraints:

[0139] Finish-to-Start (FS):

[0140]

[0141] Start-to-Start (SS):

[0142]

[0143] Start-to-Finish (SF):

[0144]

[0145] Finish-to-Finish (FF):

[0146]

[0147] If work group k is working on a construction unit, work group k can only adopt one construction mode:

[0148]

[0149]

[0150] If work group k is constructing on a construction unit, the construction mode of the construction unit is the same as that of the work group:

[0151]

[0152] Each construction unit of the activity can only be constructed by one work group:

[0153]

[0154] Ensure that there is no overlap in the construction process of the work groups:

[0155]

[0156] Calculate the construction interruption time of work group k in activity i:

[0157]

[0158] If the work group is required to maintain continuous construction, formula (13) is 0.

[0159] Resource constraints and duration constraints:

[0160]

[0161] Matching constraints between work groups and construction units:

[0162]

[0163] If the work group must perform construction according to a fixed logic, the following constraints need to be added:

[0164]

[0165] S6. Update the number of iterations, that is, k=k+1; and update the start time of the time window, that is, st=st+L–overlap.

[0166] S7, repeat steps S3-S6 until the iteration condition is met, stop the iteration and output the optimal solution in the iteration process. Case analysis:

[0167] This embodiment sets up a total of 1 case, and 14 construction scenarios are derived from this case. The purpose of case analysis is to verify the effectiveness of the model proposed in this embodiment based on actual data. All cases are run on a desktop computer with a Windows 10 operating system and an Intel(R) Xeon(R) Silver 4110CPU@2.10GHz and 16GB RAM.

[0168] Project Overview: The case study is a school renovation project, the main work is to renovate 7 classrooms in 7 different schools into 7 laboratories. There are 10 repetitive activities in the renovation project. The name of each repetitive activity, the standard construction duration corresponding to the selectable construction mode, the standard direct cost and resource usage, the number of available work groups, the sequence relationship, etc. are shown in Table 3 below. The unit indirect cost of the project is 5,000 yuan / day, and the daily resource availability is 25. For each work group, the interruption cost is 200 yuan / day. The construction duration of the activity on the construction unit is the product of the standard duration corresponding to the construction mode selected for the activity and the construction unit factor (as shown in Table 4 below). Similarly, the direct cost of the activity on the construction unit is the product of the standard direct cost corresponding to the construction mode selected for the activity and the construction unit factor.

[0169] Table 3 Case analysis parameter values

[0170]

[0171] Table 4 Construction unit factors

[0172]

[0173] Based on the engineering case, this embodiment derives 14 case scenarios, of which 12 are original case scale scenarios, and the remaining 2 are medium and large-scale case scenarios (as shown in Table 5 below). The medium-scale case is to expand the number of activities and the number of sections in the original case by 2 times. At this time, the number of sub-activities in the project changes from the original 70 to 280, assuming a construction period of 300 days. The large-scale case is to expand the number of both by 4 times. At this time, the number of sub-activities in the project changes to 1120, assuming a construction period of 1000 days. The other types of information involved in the original case, such as the logical relationship between activities, the number of available work groups for activities, the construction mode, the daily available resources, etc., are not changed.

[0174] Sensitivity analysis:

[0175] The algorithm proposed in this embodiment needs to perform sensitivity analysis on the time window length (L) and the overlap with the time window of the previous iteration process. The value ranges of the two parameters are L∈{0.2D max ,0.4D max ,0.5D max ,0.6D max ,0.8D max}, overlap∈{0.2L,0.4L,0.5L,0.6L,0.8L}. Sensitivity analysis is conducted on three cases of different scales, and the evaluation indicators are mainly average gap and average running time. The average gap corresponding to each set of L and overlap values ​​is calculated as follows: For each scenario under different scale cases, determine the optimization result obtained by the CP-R&S algorithm for each set of L and overlap values, denoted as The minimum value of the objective function is selected from all optimization results as the optimal solution in this scenario, denoted as . The average difference corresponding to different parameter values ​​can be calculated according to the following formula.

[0176]

[0177] Figure 1 The results of the sensitivity analysis for the original scale case are shown. Figure 1As can be seen from the figure on the left, no matter how much L is, as the overlap value increases, the average gap shows a downward trend, and finally when overlap = 0.8L, the average gap is the smallest. In addition, in most cases, the average gap is less than 0.35%, reflecting the good stability of the CP-R&S algorithm. Figure 1 As can be seen from the figure on the right, no matter what the value of L is, as the overlap value increases, the average running time of the algorithm increases. When the overlap value is the same, the average running time corresponding to L = 0.2Dmax is significantly higher than the average running time under other L values. Combined with the calculation formula of the number of algorithm iterations, it can be seen that the smaller the L value and the larger the overlap value, the more iterations will be added, and accordingly, the algorithm running time will be extended. It is worth noting that when and only when overlap = 0.8L, the longer the algorithm running time, the lower the value of the average gap.

[0178] In summary, this embodiment uses the average gap as the main parameter selection indicator to determine the values ​​of each parameter corresponding to the original, medium and large-scale cases as follows: L = 0.5Dmax, overlap = 0.8L; L = 0.2Dmax, overlap = 0.6L; L = 0.5Dmax, overlap = 0.5L.

[0179] Solution explanation:

[0180] The optimization results of each scenario under different scale cases are shown in Table 5 below. The construction period under all construction scenarios meets the specified completion time, reflecting the effectiveness of the CP-R&S algorithm. In the table, construction scenarios 1-6 consider the resource allocation of the work group, and construction scenarios 7-12 do not consider the resource allocation of the work group, that is, the active work groups need to adopt the same construction mode. When the work group maintains continuous construction, there is no interruption cost. In the construction scenarios 1-12 corresponding to the original scale cases, the construction mode used by the work group is detailed in Table 6 below. This embodiment draws the construction plan diagram corresponding to construction scenarios 1-12 (such as Figure 2-13 In the figure, letters represent activities and numbers represent work group numbers.

[0181] Table 5 Optimization results under different construction scenarios

[0182]

[0183] Table 6 Construction scenarios 1-12 corresponding to the construction group-construction mode in the construction plan

[0184]

[0185]

[0186] This embodiment provides specific values ​​of various costs in different scenarios, as shown in Table 7 below, among which direct costs account for the highest proportion and interruption costs account for the lowest proportion.

[0187] (1) In terms of direct costs, except for construction scenarios 4 and 5, the direct costs of the remaining construction scenarios are all 2,729,750 yuan. As shown in Table 6, in all scenarios, three work groups are used for construction of each activity. Except for construction scenarios 4 and 5, each work group in the remaining construction scenarios uses mode 1 for construction between sections. Therefore, the direct costs of each sub-activity in the remaining construction scenarios are the lowest, and accordingly, the total direct costs are the minimum, that is, 2,729,750 yuan.

[0188] (2) In terms of indirect costs, construction scenarios 2 and 8 have the shortest construction period, both 63 days, and the lowest indirect costs; construction scenario 10 has the longest construction period, 70 days, and the highest indirect costs.

[0189] (3) In terms of interruption costs, among the construction scenarios where construction interruption is allowed, construction scenario 6 (such as Figure 7 The total construction interruption time of the construction group (as shown in Figure 2) is 11 days, and the interruption cost is the highest, which is 2,200 yuan. Figure 3 In the example shown in Figure 1, there is a one-day interruption when the work group 3 of activity D moves from construction unit 7 to construction unit 1. Fig. 9 As shown in Table 6, there is a one-day interruption when the work group 2 of activity D moves from construction unit 4 to construction unit 1. The interruption cost of the two construction scenarios is the shortest, which is 200 yuan. In addition, according to Table 6 and Figure 2-13 It can be seen that the construction period of the project in this case is relatively loose, so when each work group uses Mode 1 for construction, a construction plan that meets the construction period can still be generated.

[0190] Table 7 Cost structure under different construction scenarios

[0191]

[0192]

[0193] Furthermore, this embodiment discusses the impact of different factors or construction strategies on the total project cost by comparing the optimization results between different scenarios.

[0194] (1) Impact of work group resource allocation: The results of paired comparisons (1 and 7, 2 and 8, 3 and 9, 4 and 10, 5 and 11, 6 and 12) show that the total costs of construction scenarios 1, 4, and 5 are better than those of construction scenarios 7, 10, and 11, and the total costs of construction scenarios 2 and 3 are the same as those of construction scenarios 8 and 9. As shown in Table 7, the interruption cost of construction scenario 1 is better than that of construction scenario 7. In construction scenario 1 (e.g. Figure 2In construction scenario 7 (as shown in Figure 2), there is a construction interruption between activities B and D, and the interruption duration is 7 days. Figure 8 As shown in Figure 2, there is a construction interruption in activities A, B, F, and G, and the interruption duration is 9 days. The direct costs of construction scenarios 4 and 5 are higher than those of the corresponding construction scenarios 10 and 11. Figure 5 and Figure 6 The above results show that when the construction period is relatively loose, the consideration of internal resource allocation of the work group has no significant effect on the reduction of direct costs, but it can help to flexibly schedule the construction process of the work group, shorten the construction period and construction interruption time, and reduce the total cost of the project.

[0195] (2) Impact of construction sequence: The optimization results of construction scenarios 1 and 6, construction scenarios 3 and 4, construction scenarios 7 and 12, and construction scenarios 9 and 10 are compared one by one. The total project cost of construction scenarios 1, 3, 7, and 9 using soft logic is lower, and the construction period is also shorter. In particular, both construction scenarios 3 and 4 require construction continuity, and the project cost is only composed of direct and indirect costs. Comparing the construction plan diagrams of the two, construction scenario 4 (such as Figure 5 There are sub-activities with shorter construction duration, namely A-3 and J-6, and the duration is longer than that of construction scenario 3 (as shown in Figure 4 As shown). Therefore, the direct and indirect costs of construction scenario 4 are greater than those of construction scenario 3. It can be seen that when the construction team uses soft logic for construction, it can effectively shorten the construction period and reduce indirect costs, which is also beneficial to the reduction of direct costs.

[0196] (3) Impact of construction continuity: The optimization results of construction scenarios 1 and 3, construction scenarios 6 and 4, construction scenarios 7 and 9, and construction scenarios 12 and 10 are compared one by one. The total project cost of construction scenarios 1, 6, 7, and 12 that do not maintain construction continuity is lower. Figure 2 , 8 , 13) than construction scenarios 3, 9, and 10 (as shown in Figure 4 , 10 , 11) are 1, 1, and 2 days shorter, respectively, which is consistent with the classic theory that not maintaining construction continuity is conducive to shortening the construction period. In this case, the unit indirect cost (5,000 yuan / day) is much greater than the unit interruption cost (200 yuan / day / work group). Obviously, compared with the reduction of interruption time, shortening the construction period is more conducive to reducing project costs. Considering that maintaining construction continuity is conducive to improving construction efficiency, when optimizing costs, it is necessary to find a balance between maintaining construction continuity and shortening the construction period.

[0197] (4) Impact of resource constraints: The optimization results of construction scenarios 1 and 2, construction scenarios 4 and 5, construction scenarios 7 and 8, and construction scenarios 10 and 11 are compared one by one. The total project cost and construction period of construction scenarios 2, 5, 8, and 11 without resource constraints are lower. Combined with the corresponding construction plan diagrams of these four construction scenarios (such as Figure 3 , 6 , 9, and 12), it can be seen that the absence of resource constraints makes the construction process between activities in the same construction unit more compact. Figure 3 and Fig. 9 As shown in FIG. 3 , the construction process of each activity on construction unit 3 embodies this feature. Therefore, regardless of resource constraints, the construction period of the project is shorter and the indirect costs are less.

[0198] Based on the comparative analysis of the above optimization results, this embodiment provides the following management enlightenment for the preparation of repetitive construction project construction plans:

[0199] (1) Without changing the construction strategy (fixed / soft logic) of the work group, detailed consideration of the internal resource allocation of the work group will be conducive to more flexible arrangement of the work group's construction tasks and reduce the total project cost.

[0200] (2) For the following construction projects, such as scattered house renovation, which have no requirements for the construction sequence, managers can adopt more flexible work group construction strategies, including: allowing work groups to have construction interruptions, and work groups can carry out construction according to soft logic, etc., so as to reduce the total cost of the project.

[0201] (3) For construction projects such as new housing projects, which require construction to be carried out in a fixed sequence, managers may allow some active work groups to have construction interruptions, thereby shortening the construction period and reducing the total project cost.

[0202] (4) If managers pay more attention to the regularity of construction organization, they can let the work team carry out construction according to a fixed logic and maintain construction continuity.

[0203] Algorithm comparison analysis:

[0204] In this embodiment, Python is used to directly call docplex on a computer with the same configuration to solve the Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) models respectively, and the differences in solution results and running time of the three methods are compared, as shown in Table 8 below.

[0205] The MILP model is as follows:

[0206] Constraints:

[0207] Unit construction constraints:

[0208] The activity has one and only one work group on each construction unit using one mode to complete the construction on a certain day.

[0209]

[0210] Construction logic constraints: Activity i and the preceding activity p, in the same construction unit, need to satisfy four possible logical relationships, namely Finish-to-Start (FS), Start-to-Start (SS), Start-to-Finish (SF), and Finish-to-Finish (FF). The corresponding constraints are:

[0211]

[0212] Non-negative construction start time constraint: The construction start time of any construction unit of the first activity is greater than or equal to 0.

[0213]

[0214] First-day construction constraint: The first activity contains a construction unit whose construction start time is 0, i.e., the first day of construction.

[0215]

[0216] Work group construction process constraints: For activity i, if work group k has construction tasks, it needs to start from virtual construction unit O and return to virtual unit O after completing all construction tasks. When work group k moves from construction unit j to construction unit j' for construction, the construction start time of construction unit j' is greater than or equal to the completion time of construction unit j. Fig.16 As shown, work group 1 starts from the virtual unit, constructs according to construction unit 1-5-2, and returns to the virtual unit after completing the construction task. Therefore, the construction start time of construction unit 5 is greater than or equal to the construction end time of construction unit 1.

[0217]

[0218] Work group construction sequence constraint: After work group k in activity i completes the construction task on construction unit j, it needs to leave the construction unit and go to the next construction unit. At the same time, the work group construction sequence (path) cannot have loops, that is, after moving from construction unit j to construction unit j', it can't return from construction unit j' to construction unit j. Fig.16As shown, there is no loop in the construction sequence (path) of work group 1 and work group 2.

[0219]

[0220] Resource constraint: The daily resource usage of the project must not exceed the resource supply.

[0221]

[0222] Duration constraint: The project needs to be completed within the expected duration.

[0223]

[0224] Variable value range constraint: specifies the value range of variables in the model.

[0225]

[0226] Interruption time constraint: The model takes into account the construction interruption cost when calculating the cost. The determination of the construction interruption time is the premise for calculating the construction interruption cost. The calculation method of the construction interruption time of each work group in the activity is as follows:

[0227]

[0228] Since this constraint is a nonlinear constraint, in order to facilitate the solution of the model, it needs to be linearized. The linearized constraint is expressed as follows:

[0229]

[0230]

[0231] Optimization goal: The optimization goal of the model is to minimize the cost of repetitive construction projects, where the project cost is composed of direct cost DC, indirect cost IC and interruption cost INC. Direct cost DC is the sum of the direct costs corresponding to the construction mode used for each sub-activity, indirect cost IC is the product of the construction period and the unit indirect cost, and interruption cost INC is the product of the sum of the interruption time of each work group in the activity during the construction process and the unit interruption cost.

[0232]

[0233] By referencing the intermediate variable D and adding corresponding constraints, the calculation process of indirect costs can be expressed linearly, namely:

[0234]

[0235] The only difference between the CP model and the CP-R&S model of this embodiment is that the CP model does not include a model for the "work group-construction unit" matching constraint (i.e., it does not include Formula 16). According to the case size from small to large, the running time of docplex directly solving the two types of models is set to 1h, 3h, and 6h respectively. If the optimal solution is obtained within the preset time, the running time is the time to obtain the optimal solution. The solution result of the constraint programming-based relax and solve algorithm (CP-R&S) algorithm of this embodiment is the optimal solution obtained in the sensitivity analysis. If a method fails to obtain a feasible solution within the preset solution time, the solution result is represented by "*".

[0236] Table 8 Comparison of optimization results of different methods

[0237]

[0238]

[0239] As shown in Table 8, within the preset solution time, MILP only obtains feasible solutions in scenarios 8, 11, and 12, and the objective function value is much larger than the solutions of CP and CP-R&S. For CP, feasible solutions can be generated within the preset solution time for any scenario, among which the optimal solution is obtained in 708s for scenario 11. Regardless of any scenario, the running time of CP-R&S is much shorter than the preset solution time of MILP and CP. For the 12 scenarios corresponding to small-scale cases, the solution results of CP-R&S in 9 scenarios are better than CP, and the solution results in scenarios 9 and 11 are the same as CP. When solving medium-scale and large-scale cases, CP is better than CP-R&S as the running time increases. However, for medium-scale cases, the running time of CP-R&S is 0.12 times that of CP, and the solution result is only 0.24% worse than CP. For large-scale cases, the running time of CP-R&S is 0.13 times that of CP, and the solution is only 0.28% worse than that of CP. Therefore, CP-R&S can obtain solution results that are similar to or even better than CP in a solution time much shorter than CP.

[0240] In summary, compared with MILP, CP is easier to obtain feasible solutions. CP-R&S can obtain better solutions than CP in most scenarios in a shorter time. As the running time increases, CP can obtain better results. Compared with MILP and CP, the CP-R&S designed in this study can obtain relatively satisfactory solutions within a reasonable time, reflecting its good balance between solution time and solution quality, indicating that the algorithm has certain potential when applied to the preparation of construction plans and the solution of optimization problems of repetitive construction projects.

[0241] The above are only embodiments of the present invention, and the common knowledge such as the known specific structures and / or characteristics in the scheme are not described in detail here. It should be pointed out that for those skilled in the art, several deformations and improvements can be made without departing from the structure of the present invention, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A method for optimizing the cost of repetitive construction projects, characterized in that: The steps include: S1, parameter setting: initialization time window start time, algorithm iteration times; S2, generating an initial construction plan; S3. If the start time st of the time window is greater than the difference between the duration of the initial construction plan and the length of the time window, the start time of the time window is set to 0; S4, using the rolling horizon method to generate the corresponding relaxation problem; S5, solving the relaxation problem of step S4 using constraint programming method; S6. Update the number of iterations and the start time of the time window; S7. Repeat steps S3-S6 until the iteration condition is met, stop the iteration and output the optimal solution in the iteration process.

2. A repetitive construction project cost optimization method according to claim 1, characterized in that: The method for generating the initial construction plan in step S2 is as follows: S2.

1. Determine the number of work groups used for each activity and the construction mode used by each work group; S2.2, use the forward serial construction plan generation method to determine the construction process of each activity on the construction unit; S2.3, if the generated construction plan meets the expected construction period constraint, then output the initial construction plan; if it does not meet the expected construction period constraint, then go to step S2.4; S2.

4. Use the backward-forward adjustment method to adjust the construction plan generated in step S2, and use the adjusted construction plan as the initial construction plan.

3. A repetitive construction project cost optimization method according to claim 2, characterized in that: The relaxation problem generation method of step S4 is as follows: the activity set A is divided into two sets OA and MA using the rolling horizon method, where OA consists of three subsets IA, OLA and RA. According to the construction start time SD of activity i on construction unit j in the construction plan, i,j and end time ED i,j , identify the activities in three subsets; except for the activities in OA, the rest of the activities belong to MA.

4. A repetitive construction project cost optimization method according to claim 3, characterized in that: The method for determining the activity subset IA is as follows: if the construction process of activity i in construction unit j is completely within the time window, then the sub-activity (i, j) belongs to IA, that is, IA = {(i, j)∈A×U i |SD i,j ≥st∧ED i,j ≥et}.

5. The method for optimizing the cost of repetitive construction projects according to claim 3, characterized in that: The method for determining the activity subset OLA is as follows: if the construction process of activity i on construction unit j overlaps with the time window, then the sub-activity (i, j) belongs to OLA; there are two specific overlapping situations: the construction start time of activity i on construction unit j is earlier than the start of the time window and the construction is completed within the time window; or the construction starts within the time window and the construction ends later than the end of the time window, that is, OLA = {(i, j)∈A×U i |(SD i,j <st∧ED i,j ≤et)∨(SD i,j ≤st∧ED i,j >et)}.

6. A method for optimizing repetitive construction project costs according to claim 5, characterized in that: The method for determining the activity subset RA is as follows: if the construction process of activity i in construction unit j is compactly constructed with the activities in OLA, then the sub-activity (i, j) belongs to RA; compact construction means: the sum of the construction end time of activity i in construction unit j and the interval time between activities is equal to the construction start time of activity i' in construction unit j in OLA, or the construction start time of activity i in construction unit j is equal to the sum of the construction end time of activity i' in construction unit j in OLA and the interval time between activities, that is, RA = {(i, j)∈A×U i |ED i,j +Lag i,i' =SD i',j ∨SD i,j =ED i',j +Lag i,i' ,(i',j)∈OLA}.

7. A method for optimizing repetitive construction project costs according to any one of claims 3 to 6, characterized in that: The solution method of step S5 is as follows: construct the following constraint programming model, and solve the constraint programming model with the help of Cplex CP Optimizer. The specific formula is as follows: Objective function of total project cost: The objective function must meet the following conditions: Construction logic constraints: End-Start: Start-Start: Start-End: End-End: If work group k is working on a construction unit, work group k can only adopt one construction mode: If work group k is constructing on a construction unit, the construction mode of the construction unit is the same as that of the work group: Each construction unit of the activity can only be constructed by one work group: Ensure that there is no overlap in the construction process of the work groups: Calculate the construction interruption time of work group k in activity i: Resource constraints and duration constraints: Matching constraints between work groups and construction units: If the work group must perform construction according to a fixed logic, the following constraints need to be added:

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