A method for optimizing the cost of repetitive construction projects

Abstract

The present invention patent discloses a method for optimizing the cost of repetitive construction projects, specifically relating to the field of engineering construction. It includes the following steps: S1, parameter setting: initializing the start time of the time window and the number of algorithm iterations; S2, generating an initial construction plan; S3, if the start time 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, then setting the start time of the time window to 0; S4, using the rolling time domain method to generate the corresponding relaxation problem; S5, using the constraint programming method to solve the relaxation problem of step S4; S6, updating the number of iterations and updating the start time of the time window; S7, repeating steps S3-S6 until the iteration conditions are met, and outputting the optimal solution in the iterative process. The technical solution of the present invention solves the problem that the existing construction plan compilation method with cost as the optimization target cannot be applied to different construction scenarios. At the same time, when solving medium and large-scale cases, it can obtain an approximate optimal solution within a reasonable time.

Description

Technical Field

[0001] The present 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 established construction period. In the context of the current global economic recovery slowdown, how to effectively reduce project costs has become the focus of all project participants. The construction plan compilation problem with cost as the optimization target aims to obtain a construction plan with the lowest project cost within a given construction period. Currently, 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 multiple modes and multiple work groups; 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 research.

[0003] During construction planning, resource selection and allocation are crucial for reducing project costs and shortening construction schedules. In reality, construction projects are typically delivered by contractors upon completion. Driven by profit, contractors may undertake multiple projects simultaneously, requiring them to rationally allocate construction resources to ensure on-time completion while minimizing costs. Specifically, for any project, contractors must determine the number of work teams to be used for each activity, as well as the resource allocation for each team, based on their available 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 commonly overlooked during construction planning: Construction planning and optimization for repetitive construction projects often assumes that the work group resource allocation (construction mode) for an activity is known. Alternatively, when a work group can choose multiple construction modes, all work groups for the same activity must adopt the same construction mode. In real-world scenarios, contractors rely on their own construction resources to determine the number of work groups for an activity and the resource allocation for each work group, i.e., the construction mode.

[0006] 2. Failure to thoroughly explore the impact of different construction strategies of work teams on project costs when multiple construction factors coexist: During the construction plan preparation process, construction is usually carried out according to a fixed construction sequence, that is, a fixed logic, ignoring the fact that work teams can adopt soft logic construction strategies for some types of construction projects (for example, multi-building residential construction projects). Some studies that allow work teams to adopt soft logic construction strategies are usually only aimed at implementing construction plans for repetitive construction projects in single work teams or single-mode scenarios. When multiple real-world factors coexist, how each factor or different construction strategy affects project costs, including the various costs that make up the project costs (direct costs and indirect costs), still requires in-depth discussion.

[0007] 3. Failure to explore the application of different modeling methods or modeling ideas in the construction plan preparation process: The integer programming method is mainly used to characterize the problem. The modeling idea for 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 solving speed, but their solution quality cannot guarantee optimality and may even show significant differences in different scenarios.

[0009] 5. Although integer programming or constraint programming methods (relying solely on solvers such as Gurobi and Cplex) can theoretically obtain optimal solutions, 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, there is an urgent need 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 compilation 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 number;

[0014] S2. Generate an initial construction plan;

[0015] S3. If the start time of the time window st 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. Solve the relaxation problem of step S4 using a 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 method for generating the initial construction plan in step S2 is as follows:

[0021] S2.1. Determine the number of work groups to be used for each activity and the construction mode to be 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, the initial construction plan is output; if not, the process proceeds 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, wherein OA is composed of three subsets IA, OLA and RA, and the construction start time SD of activity i on construction unit j in the construction plan is used. i,j and end time ED i,j , identify the activities in the 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 time 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 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 that 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-Begin: 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 duration of the construction interruption of 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 existing technology, this solution has the following beneficial effects:

[0051] 1. This proposal considers the impact of work group resource allocation on the construction plan. Existing studies typically assume that construction plans are prepared based on a known work group resource allocation in advance. In reality, work group resource allocation decisions must be made by managers. Furthermore, in theory, a more flexible, rather than fixed, resource allocation approach can yield a more cost-effective construction plan. This proposal incorporates the decision-making process of work group resource allocation into the construction plan preparation process, expanding the traditional two-dimensional construction mode-activity-linked planning framework to a three-dimensional construction mode-work group-activity-linked planning framework. This makes the model more practical and opens up the possibility of exploring more cost-effective construction plans.

[0052] 2. This solution 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 connections; and the construction workload of work groups can be variable. This enables the model to have 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 compilation of construction plans for repetitive construction projects in large-scale scenarios. However, considering the NP-hard properties of the optimization problem of the compilation 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 on the basis of 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 to the compilation of construction plans for repetitive construction projects, and at the same time provides a new idea for the design of algorithms based on the idea of ​​relaxation optimization.

[0054] 4. 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 a rolling horizon strategy. Based on an initial construction plan, this algorithm utilizes a rolling horizon strategy to generate a relaxation problem. This relaxation problem is then reconstructed into a constraint programming model using constraint programming methods and solved. Through multiple iterations, the initial plan is improved, resulting in a more optimal construction plan. Case studies demonstrate the effectiveness of the CP-R&S algorithm in obtaining approximate / optimal construction plans for different construction scenarios, as well as its superiority in solution quality and time compared to classic integer programming and constraint programming methods. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

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

[0058] Figure 4 This is the construction plan corresponding to construction scenario 3 in the present invention;

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

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

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

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

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

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

[0065] Figure 11 It is the construction plan corresponding to the construction scene 10 in the present invention;

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

[0067] Figure 13 It is the construction plan corresponding to the construction scene 12 in the present invention;

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

[0069] Figure 15 It is a framework diagram of the backward-forward adjustment method in the present invention.

[0070] Figure 16 It is a schematic diagram of the construction process of the work group in the present invention. DETAILED DESCRIPTION

[0071] The present invention will be further described in detail below through specific embodiments:

[0072] Explanation of terms:

[0073] Repetitive Construction Projects: Repetitive construction projects, as defined in this disclosure, refer to projects involving repetitive construction activities. Specifically, in repetitive construction projects, construction teams must move from one construction unit (section) to another to complete the same construction tasks. Typical repetitive construction projects include linear repetitive projects such as railways and highways, and vertical repetitive construction projects such as high-rise buildings.

[0074] Soft Logic: The soft logic described in this invention refers to the flexible alteration of the construction sequence of the same type of construction activities in different construction units within repetitive construction projects, allowing for simultaneous construction, sequential construction, or partial synchronization and partial sequential construction. For example, in a typical repetitive construction project, such as a residential building project, the construction sequence of frame structure construction can be varied between different residences, rather than being strictly numbered from smallest to largest.

[0075] Parameter Description:

[0076] (1) Index

[0077] iActivity Index

[0078] jConstruction Unit Index

[0079] k-group index

[0080] mConstruction mode index

[0081] t time index

[0082] rUpdateable resource index

[0083] (2) Collection

[0084] A collection of activities in project A

[0085] U i Construction unit set for activity i

[0086] K i The set of available construction groups for activity i

[0087] M i Construction mode set for activity i

[0088] T project expected duration collection

[0089] R updateable resource collection

[0090] P i The set of predecessor activities of activity i

[0091] S i The set of subsequent activities of activity i

[0092] (3) Parameters

[0093] Expected duration of DL project

[0094] RL r The amount of renewable resource r available on day t

[0095] Lag p,i The construction time interval between activity i and its predecessor activity p

[0096] di,j,m When activity i adopts construction mode m, the construction duration on construction unit j

[0097] c i,m,r Direct cost of construction on construction unit j when activity i adopts construction mode m

[0098] re i,m,r When activity i adopts construction mode m, the daily usage of resource j can be updated

[0099] Unit interruption cost of the project, work unit / yuan / day

[0100] Unit indirect cost of IC project, RMB / day

[0101] N The number of activities

[0102] B is a large positive number

[0103] 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.

[0104] (4) Intermediate variables

[0105] 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;

[0106] iti i,k,j,j' The duration of the interruption caused when worker group k of activity i moves from construction unit j to construction unit j';

[0107] Decision variables:

[0108] 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;

[0109] y i,k,j,j' Whether the work group k of activity i moves from construction unit j to construction unit j', the value is 1 if yes, otherwise the value is 0.

[0110] Example

[0111] A method for optimizing repetitive construction project costs comprises the following steps:

[0112] S1. Parameter setting: initialization time window start time (st=0), algorithm iteration number (k=0);

[0113] S2. Generate an initial construction plan, and mark the duration of the initial construction plan as Dmax. The method for generating the initial construction plan is as follows:

[0114] S2.1. Determine the number of work groups to be used for each activity and the construction mode to be used by each work group;

[0115] S2.2. Use the forward serial construction plan generation method to determine the construction process of each activity on the construction unit;

[0116] S2.3. If the generated construction plan meets the expected construction period constraint, the initial construction plan is output; if not, the process proceeds to step S2.4.

[0117] 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.

[0118] This embodiment uses a two-stage constructive heuristic approach to generate an initial construction plan. The first stage determines the number of work teams used in an activity and the work team's construction mode. Regarding the number of work teams, to ensure that the generated plan meets the construction deadline as much as possible, the maximum number of work teams used in an activity is used. Regarding the construction mode, this embodiment ranks the modes based on their resource usage, from high to low. The mode corresponding to the median is selected as the work team's construction mode. This ensures relatively low resource usage while also preventing the work team from spending excessive time on a construction unit.

[0119] In the second phase, the heuristic method employs the principles of a forward-based serial construction plan generation framework to generate an initial construction plan. Specifically, starting with the first activity, the framework determines the construction process for each construction unit within each activity, specifically the work group working on that construction unit, and the start and end times of the work group's construction, ensuring that the work is consistent with both logical and resource constraints, until the construction process for the last activity in the project is scheduled. Within activities, the work group's construction strategy is first-come, first-served, with each unit's workload prioritized, starting with the unit with the smallest workload and proceeding sequentially. If the initial plan's duration exceeds the established duration, a backward-forward adjustment method is used to adjust the initial plan to meet the duration constraints.

[0120] Taking a project with four activities as an example, we will explain how to use the second stage of the heuristic method to prepare the construction plan for the project. Figure 14 and Figure 15As shown in Figure 1. In the forward serial construction plan generation framework, the construction process of each activity is determined sequentially based on the activity sequence. First, the construction process of Activity A is determined as follows: Activity A uses two construction teams, and the workload on each construction unit is ranked from smallest to largest as 4-2-1-3. Therefore, the construction process of each construction unit is determined in the order 4-2-1-3. For Construction Unit 4, Work Team 1 is selected for construction. Since Activity A is the first activity, meaning that Activity A has no predecessor activities, Work Team 1's construction start time for Construction Unit 4 is 0. Based on Work Team 1's construction mode, the duration of this work team's construction on this construction unit is determined, and the end time of this work team's construction on this construction unit is calculated (Construction end time = Construction start time + Construction duration). For Construction Unit 2, Work Team 1 is currently working on Construction Unit 4, and Work Team 2 has no construction tasks. Therefore, based on the "first come, first served" principle, Work Team 2 is assigned to Construction Unit 2. Based on Work Team 2's construction mode, the construction process of Work Team 2 is determined. For construction unit 1, work group 1 completes the construction on day 1, and work group 2 completes the construction on day 2. Based on the principle of "first come, first served", work group 1 is scheduled 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 Figure 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 Figure 14 As shown in (c).

[0121] Since the initial construction plan has a construction period of 20 days, which does not meet the expected construction period 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 construction process of each activity is still determined according to the principle of "first come, first served". The resulting construction plan is as follows Figure 15 As shown in (b) in the figure, the initial construction plan does not start construction on the first day, so the plan is shifted back one day, forming the following Figure 15 The construction plan in (c) that meets the expected construction period constraint is used as the initial solution of the algorithm.

[0122] 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.

[0123] 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 determined by Calculated, where D max The duration of the initial feasible construction plan.

[0124] 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 within three subsets:

[0125] 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}.

[0126] 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 time 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 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)}.

[0127] 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 that 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}.

[0128] Except for the activities in OA, the rest of the activities belong to MA.

[0129] S5. Use the constraint programming method to solve the relaxation problem of step S4. The constraint programming method is a unique modeling and solving method that requires the problem to be reconstructed. 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 and ending values ​​and lengths of are 8, 10, and 2, respectively. An important characteristic of interval variables is their selectivity; that is, some interval variables can be empty in the optimization results. Table 1 below shows the decision variables used in the constraint programming method. Furthermore, the constraint programming method requires the use of some OPL functions to characterize the various constraints involved in MRCRPSP-MCSL. The definitions of these OPL functions are shown in Table 2.

[0130] Table 1 Decision variables in constraint programming

[0131]

[0132] Table 2 OPL function definition

[0133]

[0134]

[0135] According to the decision variables and OPL functions, for the relaxation problem, the following constraint programming model is constructed and solved with the help of CplexCP Optimizer. The specific formula is as follows:

[0136] Objective function of total project cost:

[0137]

[0138] The objective function must meet the following conditions:

[0139] Construction logic constraints:

[0140] Finish-to-Start (FS):

[0141]

[0142] Start-to-Start (SS):

[0143]

[0144] Start-to-Finish (SF):

[0145]

[0146] Finish-to-Finish (FF):

[0147]

[0148] If work group k is working on a construction unit, work group k can only adopt one construction mode:

[0149]

[0150]

[0151] 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:

[0152]

[0153] Each construction unit of the activity can only be constructed by one work group:

[0154]

[0155] Ensure that there is no overlap in the construction process of the work groups:

[0156]

[0157] Calculate the duration of the construction interruption of group k in activity i:

[0158]

[0159] If the work group is required to maintain construction continuity, formula (13) is 0.

[0160] Resource constraints and duration constraints:

[0161]

[0162] Matching constraints between work groups and construction units:

[0163]

[0164] If the work group must perform construction according to a fixed logic, the following constraints need to be added:

[0165]

[0166] S6. Update the number of iterations, i.e., k=k+1; and update the start time of the time window, i.e., st=st+L–overlap.

[0167] 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:

[0168] This example presents one case study, from which 14 construction scenarios are derived. The purpose of this case study analysis is to verify the effectiveness of the model proposed in this example using real-world data. All cases were run on a desktop computer running Windows 10, equipped with an Intel(R) Xeon(R) Silver 4110 CPU @ 2.10 GHz and 16 GB of RAM.

[0169] Project Overview: The case study is a school renovation project, the main work of which 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, and the sequence relationship 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.

[0170] Table 3 Case analysis parameter values

[0171]

[0172] Table 4 Construction unit factors

[0173]

[0174] Based on the engineering case, this embodiment derives 14 case scenarios, 12 of which are original case scale scenarios, and the remaining two 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. All other 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., remains unchanged.

[0175] Sensitivity analysis:

[0176] The algorithm proposed in this embodiment needs to perform sensitivity analysis on the two parameters of the time window length (L) and the overlap with the time window of the previous iteration. 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 was conducted on three cases of different scales, and the main evaluation indicators were average gap and average running time. The average gap corresponding to each set of L and overlap values ​​was calculated as follows: For each scenario under different scale cases, the optimization result obtained by the CP-R&S algorithm for each set of L and overlap values ​​was determined, denoted as The minimum value of the objective function is selected from all optimization results as the optimal solution for this scenario, denoted as . The average difference corresponding to different parameter values ​​can be calculated using the following formula.

[0177]

[0178] Figure 1 The results of the sensitivity analysis for the original scale case are presented. Figure 1As can be seen from the left graph, regardless of the value of L, the average gap shows a downward trend as the overlap value increases, and finally reaches the minimum when overlap = 0.8L. 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 shown in the right-hand graph, regardless of the value of L, the average runtime of the algorithm increases as the overlap value increases. For the same overlap value, the average runtime corresponding to L = 0.2Dmax is significantly higher than the average runtime for other L values. Combined with the formula for calculating the number of algorithm iterations, it can be seen that smaller L values ​​and larger overlap values ​​both increase the number of iterations and, accordingly, extend the algorithm runtime. Notably, when overlap = 0.8L, the algorithm runtime increases and the average gap decreases.

[0179] 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: L = 0.5Dmax, overlap = 0.8L; L = 0.2Dmax, overlap = 0.6L; L = 0.5Dmax, overlap = 0.5L.

[0180] Solution explanation:

[0181] 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 allocation of work group resources, and construction scenarios 7-12 do not consider the allocation of work group resources, 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 (as shown in Figure 2-13 In the figure, letters represent activities and numbers represent group numbers.

[0182] Table 5 Optimization results under different construction scenarios

[0183]

[0184] Table 6 Construction scenarios 1-12 corresponding to the work group-construction mode in the construction plan

[0185]

[0186]

[0187] This embodiment provides specific values ​​of various expenses in different scenarios, as shown in Table 7 below, among which direct expenses account for the highest proportion and interruption expenses account for the lowest proportion.

[0188] (1) In terms of direct costs, except for construction scenarios 4 and 5, the direct costs of the remaining construction scenarios are all RMB 2,729,750. As shown in Table 6, in all scenarios, three work groups are used to carry out construction for each activity. Except for construction scenarios 4 and 5, each work group in the remaining construction scenarios uses mode 1 to construct 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, RMB 2,729,750.

[0189] (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.

[0190] (3) In terms of interruption costs, among the various construction scenarios where construction interruption is allowed, construction scenario 6 (e.g. Figure 7 The total construction interruption time of the work 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. Figure 9 In the example shown in Figure 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, from 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.

[0191] Table 7 Cost structure under different construction scenarios

[0192]

[0193]

[0194] Furthermore, this embodiment discusses the impact of different factors or construction strategies on the total project cost by comparing optimization results between different scenarios.

[0195] (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 the construction scenario 7 (shown as Figure 8 As shown in Figure 2, there are construction interruptions in activities A, B, F, and G, and the duration of the interruption 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 indicate that, given a relatively flexible construction schedule, resource allocation within the work group does not significantly reduce direct costs. However, it can help flexibly schedule the work group's construction process, shorten the construction period and construction interruption time, and reduce the total project cost.

[0196] (2) Influence 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 less, and the construction period is also shorter. In particular, construction scenarios 3 and 4 both require construction continuity, and the project cost is only composed of direct costs 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 in Figure 4, the direct and indirect costs of construction scenario 4 are greater than those of construction scenario 3. Therefore, when the construction team uses soft logic for construction, it can effectively shorten the construction period, reduce indirect costs, and also help reduce direct costs.

[0197] (3) Impact of construction continuity: Comparing 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 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) were reduced by 1, 1, and 2 days, respectively, which is consistent with the classic theory that not maintaining construction continuity is beneficial for shortening the construction period. In this case, the unit indirect cost (5,000 yuan / day) far exceeded the unit interruption cost (200 yuan / day / work group). Clearly, shortening the construction period is more conducive to reducing project costs than reducing interruption time. Considering that maintaining construction continuity is conducive to improving construction efficiency, when optimizing costs, it is necessary to strike a balance between maintaining construction continuity and shortening the construction period.

[0198] (4) Impact of resource constraints: Comparing 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 one by one, the total project cost and construction period corresponding to 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) we can see that the absence of resource constraints makes the construction process between activities within the same construction unit more compact. Figure 3 and Figure 9 As shown in Figure 3, the construction process of each activity on construction unit 3 reflects this feature. Therefore, regardless of resource constraints, the project duration is shorter and the indirect costs are reduced.

[0199] Based on the comparative analysis of the above optimization results, this embodiment provides the following management implications for the compilation of repetitive construction project construction plans:

[0200] (1) Without changing the construction strategy of the work group (fixed / soft logic), 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.

[0201] (2) For the following construction projects, such as scattered house decoration, which have no requirements on 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.

[0202] (3) For the following construction projects, such as new housing projects, which require construction to be carried out in a fixed sequence, managers can allow some active work groups to have construction interruptions, thereby shortening the construction period and reducing the total project cost.

[0203] (4) If managers pay more attention to the regularity of construction organization, they can let the work team construct according to a fixed logic and maintain construction continuity.

[0204] Algorithm comparison analysis:

[0205] In this example, 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. The differences in solution results and running time of the three methods are compared, as shown in Table 8 below.

[0206] The MILP model is as follows:

[0207] Constraints:

[0208] Unit construction constraints:

[0209] The activity is that there is only one work group on each construction unit using one mode to complete the construction on a certain day.

[0210]

[0211] Construction logic constraints: Activity i and the preceding activity p must satisfy four possible logical relationships in the same construction unit: Finish-to-Start (FS), Start-to-Start (SS), Start-to-Finish (SF), and Finish-to-Finish (FF). The corresponding constraints are:

[0212]

[0213] Construction start time non-negative constraint: The construction start time of any construction unit of the first activity is greater than or equal to 0.

[0214]

[0215] First-day construction constraint: The first activity contains a construction unit with a construction start time of 0, which is the first day of construction.

[0216]

[0217] 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' must be greater than or equal to the completion time of construction unit j. Figure 16 As shown, work group 1 starts from the virtual unit and constructs according to construction unit 1-5-2. After completing the construction task, it returns to the virtual unit. Therefore, the construction start time of construction unit 5 is greater than or equal to the construction end time of construction unit 1.

[0218]

[0219] Work group construction sequence constraint: After completing the construction task on construction unit j in activity i, work group k needs to leave the construction unit and move 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', and then returning from construction unit j' to construction unit j. Figure 16As shown, there is no loop in the construction sequence (path) of work group 1 and work group 2.

[0220]

[0221] Resource constraints: The project's daily resource usage must not exceed the resource supply.

[0222]

[0223] Duration constraint: The project needs to be completed within the expected duration.

[0224]

[0225] Variable value range constraint: specifies the value range of variables in the model.

[0226]

[0227] Interruption time constraint: The model takes into account the construction interruption cost when calculating the cost. Determining the construction interruption time is the prerequisite for calculating the construction interruption cost. The construction interruption time of each work group in the activity is calculated as follows:

[0228]

[0229] Since this constraint is nonlinear, it needs to be linearized to facilitate the solution of the model. The linearized constraint is expressed as follows:

[0230]

[0231]

[0232] Optimization objective: The optimization objective of the model is to minimize the cost of repetitive construction projects, where the project cost is composed of direct costs (DC), indirect costs (IC), and interruption costs (INC). Direct costs (DC) are the sum of the direct costs corresponding to the construction mode used for each sub-activity, indirect costs (IC) are the product of the construction period and the unit indirect cost, and interruption costs (INC) are the product of the sum of the interruption time of each work group during the construction process and the unit interruption cost.

[0233]

[0234] By referencing the intermediate variable D and adding corresponding constraints, the calculation process of indirect costs can be linearized, namely:

[0235]

[0236] 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 scale 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 "*".

[0237] Table 8 Comparison of optimization results of different methods

[0238]

[0239]

[0240] Table 8 shows that within the preset solution time, MILP only achieved feasible solutions for scenarios 8, 11, and 12, and the objective function values ​​were significantly greater than those of the CP and CP-R&S solutions. For all scenarios, CP generated feasible solutions within the preset solution time, achieving the optimal solution in 708 seconds for scenario 11. The runtime of CP-R&S was significantly shorter than the preset solution times for both MILP and CP in all scenarios. For the 12 scenarios corresponding to small-scale cases, CP-R&S outperformed CP in nine, achieving the same results as CP in scenarios 9 and 11. For medium- and large-scale cases, CP outperformed CP-R&S as the runtime increased. However, for the medium-scale case, CP-R&S ran in 0.12 times the time of CP, achieving a solution that was only 0.24% inferior to CP. For large-scale cases, CP-R&S runs in 0.13 times the time of CP and achieves a solution that is only 0.28% worse than CP. This shows that CP-R&S can achieve solutions that are similar to or even better than CP in a much shorter solution time.

[0241] In summary, compared to MILP, CP is more likely to obtain a feasible solution. CP-R&S achieves better solutions than CP in a shorter time in most scenarios. CP achieves even better results as runtime increases. Comparing MILP and CP, the CP-R&S designed in this study achieves relatively satisfactory results within a reasonable timeframe, demonstrating a good balance between solution time and solution quality. This suggests that the algorithm has potential for solving repetitive construction project planning and optimization problems.

[0242] The above are only embodiments of the present invention, and common knowledge such as the specific structure and / or characteristics of the scheme are not described in detail here. It should be pointed out that for those skilled in the art, without departing from the structure of the present invention, several variations and improvements can be made, which should also be regarded as the scope of protection 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 repetitive construction project costs, characterized in that: The steps include: S1. Parameter setting: initialization time window start time, algorithm iteration number; S2. Generate an initial construction plan; S3. If the start time of the time window st If it 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. Solve the relaxation problem of step S4 using a 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; The method for generating the initial construction plan in step S2 is as follows: S2.

1. Determine the number of work groups to be used for each activity and the construction mode to be 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, the initial construction plan is output; if not, the process proceeds to step S2.

4. S2.

4. Using a backward-forward adjustment method, adjust the construction plan generated in step S2, and use the adjusted construction plan as the initial construction plan; The relaxation problem generation method of step S4 is as follows: the activity set Divided into and Two sets, where Depend on 、 and Three subsets are composed according to the activities in the construction plan In the construction unit Construction start time and end time , identify activities within three subsets; except All other activities except those in ; The solution method of step S5 is as follows: construct the following constraint programming model and solve it with the help of Cplex CP Optimizer. The constraint programming model includes the total project cost objective function and preset constraints. The total project cost objective function is: （1）； : Optional interval variable, indicating activity In the construction unit Upper adoption model Construction is underway, the length of ; : Used to judge interval variables If it exists, the value is 1, otherwise the value is 0; : Unit indirect cost of the project, yuan / day; : Used to obtain interval variables The end value is used to obtain the construction end time of the activity on the construction unit; : interval variable, indicating activity Construction unit ; : Unit interruption cost of the project, work unit / yuan / day; The preset constraints include construction logic constraints, resource constraints, construction period constraints, and matching constraints between work groups and construction units.

2. The method for optimizing repetitive construction project costs according to claim 1, characterized in that: Activity subset The method of determining is as follows: If the activity In the construction unit The construction process is completely within the time window, then the sub-activity belong ,Right now .

3. The method for optimizing repetitive construction project costs according to claim 1, wherein: Activity subset The method of determining is as follows: If the activity In the construction unit If the construction process on the time window overlaps, the sub-activity belong ; There are two specific overlapping situations: activities In the construction unit The construction start time 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 end time is later than the end of the time window, that is, .

4. The method for optimizing repetitive construction project costs according to claim 3, characterized in that: Activity subset The method of determining is as follows: If the activity In the construction unit The construction process and If there is a compact construction of activities within the sub-activity belong ; Compact construction means: activity In the construction unit The sum of the construction completion time and the interval time between activities is equal to Activities In the construction unit Construction start time, or activity In the construction unit The construction start time is equal to Activities In the construction unit The sum of the construction completion time and the interval time between activities, that is, .

5. A method for optimizing repetitive construction project costs according to any one of claims 1 to 4, characterized in that: The construction logic constraints are: End-Begin: （2）； Start-Start: （3）； Start-End: （4）； End-End: （5）； : used to represent interval variables and The end-beginning logical relationship of existence; : used to represent interval variables and The end-end logical relationship of existence; : used to represent interval variables and The logical relationship of beginning and end exists; : used to represent interval variables and The beginning-beginning logical relationship of existence; : interval variable, indicating activity Construction unit ; If the work group Construction on the construction unit, the work group Only one construction mode can be used: （6）； （7）； : Boolean variable, indicating activity Middle Workers Group Whether to adopt the model If it is 1, it is 0; : Optional interval variable, indicating activity In the construction unit Upper by the work group Carry out construction; If the work group When construction is carried out on a construction unit, the construction mode of the construction unit is the same as that of the work group: （8）； （9）； :Used to indicate if interval variable exists, then in a set of interval variables There is only one interval variable , so that the interval variable With interval variables Synchronization start and synchronization end are used to express various uniqueness constraints; : Used to express if conditions If established, then the condition Also established; Each construction unit of the activity can only be constructed by one work group: （10）； Ensure that there is no overlap in the construction process of the work groups: （11）； : used to represent a set of interval variables The beginning and end of each interval variable in do not overlap, which is used to indicate that the construction process of a single work group does not overlap; Computing activities Middle Workers Group Length of construction interruption: （12）； （13）； : Optional interval variable, indicating activity Adopting a working group construction; : used to represent interval variables Start with a set of interval variables The first non-empty interval variable in the same way, the interval variable The end with a set of interval variables The end of the last non-empty interval variable in is the same, which is used to calculate the interruption time of the working group; : Used to obtain interval variables The length of is used to obtain the construction duration of the activity on the construction unit; The resource constraints and duration constraints are: （14）； （15）； : Used to represent the resource usage value of an interval variable, used to calculate the daily resource usage of the project; : Renewable resources In the The daily availability; : Expected duration of the project; The matching constraints between the work group and the construction unit are: （16）； If the work group must perform construction according to a fixed logic, the following constraints need to be added: （17）。

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