Integrate computation intelligence with Bayes theorem into complex construction installation: a heuristic two-stage resource scheduling optimisation approach

Abstract

The cost control challenge in construction and installation projects has always been a critical concern for construction entities. The complexity of task collaboration among various equipment and nodes during the installation process leads to extended construction duration, resulting in increased construction costs. To address this issue, this paper proposes a heuristic two-stage optimal deployment approach called MERD. The MERD approach incorporates intelligent computing principles from computer science into the resource scheduling of the construction process, modelling the installation scheduling problem into a combinatorial optimisation problem. Designing the probability method based on Bayes theorem, the MERD approach carries out an installation provisioning mechanism to optimise personnel and device allocation in the selected area. As a result, the MERD approach minimises construction hours and reduces labour costs in the construction process. Experimental results demonstrate the effectiveness and efficiency of the MERD approach in reducing work time and cost in engineering projects.

Keywords:

• Resource scheduling
• cost control
• intelligent computing
• heuristic two-stage optimal deployment approach

1. Introduction

Smart city has become a hot research topic in the field of Architecture (Long et al., 2021; Xiao & Xie, 2021). Building installation is an important link in the infrastructure construction of smart city, and the control of production cost is the key to realise the project profit in building installation.

In the control of the production cost of construction and installation projects, the dynamic flow of cost is the main concern of the project. Affected by the construction environment, the cost proportion in the production process is gradually increasing, and the labour cost is constantly increasing. The scheduling imbalance between multiple resources and nodes in the complex scene of the construction site makes the cost generated in the resource deployment become an indispensable part of the cost control of construction and installation. This problem will be reduced by optimising the scheduling of existing resources (Hartmann & Briskorn, 2022). Enterprises take high profit and low cost as their ideal goal. In order to achieve this goal, they need to make more effective use of limited resources, control project scheduling time and reduce total cost to maximise profits (Lin et al., 2018; Park & Yi, 2021). Most of the existing work is through the methods of construction organisation design and project management (Karunakaran et al., 2018), using fixed management methods to control and check cost consumption and expenditure. Although the purpose of cost control can be achieved to a certain extent, they still have some shortcomings. On the one hand, the control mode of traditional project management and construction organisation design focuses on the verification, accounting and control of project funds related costs (Yap et al., 2021). The macro planning formulated can not control the production costs in the actual work process, and it is difficult to flexibly deploy construction personnel according to the complexity of different areas, resulting in an increase in costs. On the other hand, affected by the workers' own factors (Lee et al., 2020), under the urgent construction period, the rework of high price and large number of devices will seriously lead to the problem of rising construction cost and delay of construction period (Love & Sing, 2013), which can not be effectively handled by the current cost control mode, and the lack of an interpretable device deployment strategy makes the randomness of the device installation and deployment process large, it is not conducive to effective construction and optimal allocation of resources (Kannimuthu et al., 2019). In summary, the problem to be studied in this paper can be expressed as how to adapt to the complexity of multi-equipment and multi-node task collaboration in the region during the resource scheduling process of equipment installation by designing a relevant scheme, so as to reduce the construction time and construction cost arising from the resource scheduling during the construction process. The motivation of this paper is to determine the research solution by setting the two main objects of the installation scheduling process designed for people and equipment. Based on the above two arguments, we first the potential factors leading to higher costs in the installation process is analysed, the construction process can be divided into personnel allocation and devices deployed in two stages, in the process of staffing put forward the thought of to optimise personnel structure, through the construction personnel age, experience, and physical relationship to build mathematical model to get the proficiency of age function, according to the proficiency of the workers and the complexity of the construction area, the construction personnel are deployed with the goal of minimising the man-hour consumption. In the device deployment phase, the deployment sequence of resources is planned according to the principle of reasonable allocation through the probability model to make up for the defects of random device deployment during the installation process.

This paper introduces a deployment approach of electrical resources in the process of building installation (MERD), which starts from the perspective of improving the construction quality and reducing the construction period to achieve the purpose of reducing the production cost. The MERD approach abstracts the actual construction scene into multiple areas to be operated. According to the different resource requirements and arrangement of each area, the implementation process is optimised by intelligent algorithm. The minimum installation time is taken as the problem to be solved, the near-optimal time cost is found, and the near-optimal personnel deployment mode is obtained by particle swarm optimisation algorithm, will stay deployment device data as the basis of the price and quantity as the main basis, constructing a Bayesian model, based on these two factors to solve the probability of the selected equipment installation, according to the different regional resources in the process of installation, the construction personnel to iterate through all the installation area, the purpose of minimising installation costs.

By analysing and calculating the influencing factors of a large number of preinstalled devices. MERD realises the rationality of device deployment process design, introduces the idea of combinational optimisation into specific engineering construction, realises the dynamic allocation of personnel organisation structure, and then considers the regional installation problem of deployed devices as the near-optimal problem of resource allocation. An near-optimal installation strategy is set up by integrating intelligent algorithm. A variety of electrical resources are reasonably allocated to complex practical projects by setting a sequence selection mechanism to achieve further optimisation of cost control.

The main contributions of this paper are as follows:

1. The classical Bayes theorem is introduced, and according to the analysis of processing events during the deployment of preinstalled devices, a scheduling algorithm using Bayes extension is designed to make the deployment of preinstalled devices more reasonable, so that the near-optimal installation of electrical resources has a mathematically interpretable solution.

2. This paper puts forward the idea of transforming the complicated resource installation and scheduling problem in practical engineering into a combinatorial optimisation problem, and obtains the near-optimal execution strategy through computational intelligence method, so as to further improve the actual work efficiency.

3. Combined with the installation requirements in the actual construction process, the cost saving problem is quantified as the problem of minimum objective function value, which makes up for the lack of cost control caused by less consideration of actual construction factors in the traditional way.

The rest of this paper is arranged as follows. The second part will briefly introduce the related work of cost control in construction and installation. The third part will introduce the scientific issues that need to be studied and the formal description of the relevant issues raised. In the fourth part, the overall idea, algorithm and implementation solution of the core content of this paper are introduced in detail. The fifth part introduces the experimental process and results. In the sixth part, we summarise the work of this paper.

2. Related work

The regulation of project costs in the process of construction has always been the focus of attention in engineering construction. The goal is to effectively control construction costs and maximise profits in engineering construction by regulating relevant elements in the process of construction. Many researchers have carried out relevant research around the cost control problem (Afshar-Nadjafi, 2021), and some of them have focused their research on the spatial processing of the work process. For example, Garcia-Nieves et al. (2019) proposes a mathematical model for repetitive project activities in the construction industry to optimise the construction schedule by considering the time and space conditions provided by repetitive projects to the maximum. Francis (2020) proposes that the site space-time modelling method of construction procedures is used for the progress of construction operations on construction sites. Francis (2019) also proposes a hybrid solution based on space-time technology, which combines graphics, programmes and algorithms to integrate space and operation, ensure the continuity of space and team use, and control and schedule building construction progress by giving priority to key spaces from the critical path. None of these approaches has been implemented to help decision makers structure projects in a way that maximises the sustainability performance of their construction projects while still meeting cost and time requirements.

The time problem in construction is also the main factor affecting the project cost. Many scholars have carried out research on the impact of time on the cost. Galagali (2017) proposes a practical construction project to study the trade-off between time, cost and quality, highlights the management solutions obtained, and points out the key problems and difficulties faced. By generating horizontal curves, we can make clear modelling and consider quality, time and cost for project scheduling decisions, and make correct decisions for specific situations. Yap and Skitmore (2020) pointed out the problem of project cost deviation due to ineffective coordination in the work process, and proposed a study on the nature of project communication and learning and their role in project time and cost control, but it only focused on the experience of a small group of relevant practitioners, which limited the universality of the research results. Deblaere et al. (2011) proposed a stochastic approach for determining project implementation policies and predicting activity start time vectors to minimise the cost function, and controlled the cost by weighting the expected activity start time deviation and delayed completion. Fahmy et al. (2020) proposes a dynamic planning model, which provides better resource management by optimising the cost, time, resources and cash flow used in the whole project construction process and real-time schedule planning. The control of project cost through time control in the construction process has produced a good effect, but unfortunately, the labour force, a potential influencing factor that will have a great impact on the construction cost, lacks necessary measures in the construction process, which can not solve the problem of reducing cost. In addition to the study of time factors, the labour factors related to engineering projects are also the focus of researchers' attention. Florez et al. (2013) proposes a new multi-objective mixed integer programming model, which helps project managers and decision makers to cope with the challenge of planning construction projects to achieve social sustainability by developing a multi-objective mixed integer programming. In order to reduce the impact on project performance of social objectives and achieve the sustainability objectives of the project. Biruk and Jaskowski (2017) created a mathematical model for optimising linear construction project plans in consideration of resource and work continuity constraints. The method proposed enables users to select the best personnel formation in the case of limited resources. Such studies pay attention to the allocation of construction personnel, which will have a positive effect on cost control, but pay less attention to task coordination in complex scenarios during construction.

In this paper, a heuristic two-stage optimisation MERD approach is proposed by drawing on the experience of related studies (Gawali & Shinde, 2018; Tsai et al., 2013), which first abstracts the actual construction scenario and takes the inter-domain resources in the construction and installation process of each region as the modelling variables and realises the optimisation of the distribution scheme in the process of regional distribution by setting the global traversal of the construction personnel. This approach takes into consideration the allocation of labour and minimising time cost into account, optimise its workers under different proficiency in the implementation process of the corresponding scene, overall construction time cost more balanced dynamic optimisation, from construction process optimisation to improve the quality of construction engineering construction, through mathematical model building of devices in the area of installation process reduce the randomness in the construction process, so as to achieve the optimisation of the total cost (Tables 1 and 2).

Table 1. Literature review list.

Author	Title
Garcia-Nieves, J Diego
Ponz-Tienda,J Luis
	Multipurpose linear programming optimisation model
Ospina-Alvarado, A
	for repetitive activities scheduling in construction projects
Bonilla-Palacios, M.(2019)
Francis, Adel(2020)	Chronographical site-spatial-temporal modelling of construction operations
Francis, Adel(2019)	Chronographical Spatiotemporal Scheduling Optimisation for Building Projects
Anagha Anirudh Galagali(2017)	Time-Cost-Quality Trade-off in Construction Project Management
Yap, Jbh	Ameliorating time and cost control with project learning and communication management:
Skitmore, M(2020)	Leveraging on reusable knowledge assets
Deblaere, Filip
Demeulemeester, Erik	Proactive policies for the stochastic resource-constrained project scheduling problem
Herroelen, Willy(2011)
Fahmy, Amer
Hassan, Tarek	Dynamic scheduling model for the construction industry
Bassioni, Hesham
McCaffer, Ronald(2020)
Florez, L
Castro-Lacouture, D	Sustainable workforce scheduling in construction programme management
Medaglia, A L(2013)
Biruk, S.	Scheduling Linear Construction Projects with Constraints
Jaskowski, P.(2017)	on Resource Availability
	Research on effective planning and scheduling of resources in the construction installation process

Table 2. Construction and installation equipment details.

	Type of the preinstalled device
Equipment category	One	Two	Three	Four
Monitoring	camera	display
Broadcasting	cable TV	acoustics
Communication	fixed telephone	broadband interface	routers
Ventilation and heating	Heating	ventilation	exhaust
Lighting	lighting lamp	sockets	switches	emergency lights
fire prevention	smoke sensor	temperature sensor	curtain doors	Sound optical alarm

3. The proposed problem and its formulation

3.1. Proposed problem

The key to profit in construction and installation engineering is to control the production cost in construction. Usually, the control of production cost is mainly carried out through construction organisation design and project management means. This cost control approach can not change in time with the change of construction activities, leading to the increase of cost. Due to the fixed management and control mode of construction organisation design and project management means, it is difficult to make dynamic regulation and control in the process of cost control, and the optimisation and integration of human resources and electrical resources cannot be carried out. In addition, in the actual installation process, the construction operation of multiple installation areas has a single work activity mode and large randomness in personnel allocation, which makes the work efficiency cannot be improved with the increase of the number of construction personnel. More importantly, due to the inherent limitations of the working mode, it is difficult to achieve the purpose of saving labour cost by using the traditional approach in the installation process, and it lacks a specific installation mechanism for the layout planning of electrical resources, so that the actual installation process will produce a large unnecessary time consumption. It is necessary to put forward a kind of can in the process of construction cost control methods, according to the practical construction of the resource requirements and regional job complexity is different, the construction personnel according to their different proficiency for task allocation, effective deployment into the corresponding operation area, install electrical resources deployment problems in the process of building form into a NP-Hard combinatorial optimisation problems (Immorlica et al., 2021), within the goal of minimising the time cost, the construction resources are optimally allocated, and the time consumption is minimised in the process of traversing and deploying all the devices to be installed, so as to achieve the purpose of cost saving. Figure 1 describes the task deployment process of electrical resources in building installation and construction.

Figure 1. Deployment tasks of electrical resources (Schematic representation of the resource allocation process).

3.2. Problem formulation

The problem of device deployment can be formally expressed as follows: according to the different properties of the installed devices they are divided into class i. there are j devices in the same class and the set of devices can be expressed as $A=\{A_{11},A_{12},\dots ,A_{ij}\}$, if there are n individuals in j devices under class i, then $A=\{x,x_2,\dots ,x_n\}$, the quantity is $N_{ij}=\sum _{k=1}^n{N}_{ik}$ the total number of devices is expressed as $N=\sum _{i=1}^n\sum _{k=1}^j{N}_{ik}$, according to the number of rooms in the construction space, it is divided into m installation areas. If the number of rooms is larger than the number of constructors, then divide the area to take root of the number of rooms. To meet the requirement that the number of constructors is much larger than the number of installation areas, the number of M areas can be expressed as $M=\{1,2,\dots ,m\}$, devices to be installed in each zone are represented by A, and the set of devices to be installed in the zone is represented by {$A_1^1$, $A_2^1,\dots ,A_n^1$},{$A_1^2$, $A_2^2,\dots ,A_n^2$},…,{$A_1^m$, $A_2^m,\dots ,A_n^m$}, $A_n^m$ is the nth device to be installed in the mth region. To ensure a reasonable characterisation of the working time of different devices, the time difference between devices is set to change on the basis of the base workload, which is expressed in K(work hours), different workloads during the installation of different devices are expressed by the weight C. The larger the weight, the greater the installation work consumption, and the workload set Q represents the installation workload of devices as $Q=\{c_{1}k,c_{2}k,\dots ,c_{n}k\}$, the construction operator can be represented as $X=\{X_1,X_2,\dots ,X_n\}$, their corresponding proficiency is $\{S_1,S_2,\dots ,S_n\}$ according to the actual construction situation, it is known that the ratio of workload to proficiency is proportional to the construction time, the higher the proficiency, the shorter the construction time, and the different working efficiency of workers of different age groups. This difference in working efficiency is mainly reflected in the worker's proficiency, which is measured by the worker's salary level, and the degree of proficiency is evaluated by the company's human resources department according to the employee data and performance. Skillfulness is expressed as: (1) $S=w_1{y}_1+w_2{y}_2.$(1) In formula (1(1) $S=w_1{y}_1+w_2{y}_2.$(1) ), $w_1$, $w_2$ represents the function measure weight, $w_1+w_2=1$, $w_1>w_2$, for ease of calculation, take here $w_1$=2/3, $w_2$=1/3. The setting of the weights comes from our detailed research and survey of the relevant companies, and the weights are obtained through repeated calculations and comparisons of the relevant data, according to the ratio of $w_1$ accounting for 2/3 of the overall, $w_2$ accounting for 1/3 of the overall. The age range of the constructors is $x\in [18,65]$. Building an age-physical endurance model function from basic data is as follows: (2) $y_1=C{X}^T$(2) The constant parameter C in the above formula is obtained from the neural network, and $C=[-5.8801,0.6451,-0.0165,0.0001,E-06,-E-08]$, $X=[x^0,x^1,x^2,x^3,x^4,x^5]$, The relationship between the age of related staff and the empirical function is constructed as follows: (3) $y_2=\frac{1}{1+[(x-18)/5{]}^{-2}}.$(3) Because differences in regional deployment among different constructors will lead to differences in construction time, in order to obtain the near-optimal scheduling scheme, the complexity and manual matching should be taken into account when dealing with the resource deployment problem. The human complexity matching problem can be abstracted as a task deployment problem in which n workers are assigned to m areas to achieve the near-optimal matching, a solution to a deployment task can be represented by an n-dimensional solution vector $X=\{X_1,X_2,\dots ,X_n\}$, each of these elements $X_i$ represents the destination area of the person i who will perform the task. Used to indicate to which operational area that builder will be deployed, the assignment process must also satisfy the following constraints:

1. The same worker can only select one area for construction at a time. Once the area is selected by the worker, it will not be changed, $q_i$ indicating the number of areas selected by the worker i, the constraint is denoted as $\sum _{q=1}^m{q}_i\le 1$.

2. The construction operation in the area can be completed by multiple workers at the same time, and $X_i$ represents the number of personnel i selecting the X Area.

3. At least one construction worker is required to carry out construction operations in the set are, the constraint is denoted as $\sum _{i=1}^n{X}_i\ge 1$.

4. The number of construction personnel is much larger than the number of construction areas, the constraint is denoted as n>>m.

5. There is no sequential constraint between the devices to be installed, and the complexity of device installation is expressed by the amount of work.

Considering the above constraints, we obtain the objective function of minimising working hours as follows: (4) $F=min\sum _{j=1}^m\sum _{x=1}^n\frac{\sum _{i=1}^{n^j}k{C}_i^j}{n{S}_x^j}.$(4) In the above formula,

where F is the total number of man-hours of the construction process; j is the area to be installed; i is selection of the area to be installed; $n^j$ is the total number of devices in the j area to be selected; $C_i^j$ is the unit complexity of selecting class i devices in the j area; $s_x^j$ is the proficiency of worker x in the j area to be selected; k is workload metric parameter; m is total number of installed areas; n is total number of installers.

In order to make the installation process more dynamic control and cost control, besides organising and deploying the constructors, it is necessary to ensure the rationality of device deployment. This paper establishes a selection mechanism by using Bayesian probability model (Liu et al., 2021), uses the posterior probability of device selection as a measure, and then selects the pre-installed devices based on the number and price of devices. According to the actual situation, the basic required devices are represented as follows: there are 6 categories of 18 devices in the Table 2, where the workload required for device installation is expressed as $\{C_{1}k,C_{2}k,C_{3}k,\dots ,C_{18}k\}$, from the actual construction process, the rate of cost loss due to misoperation of devices is positively related to the number and price of devices. As the fatigue of workers increases with time, the rate of misoperation increases. The higher the price of most devices, the lower the cost loss. Due to the uncertainty of device selection in the installation process, in order to ensure that the establishment of the model conforms to the actual working process, this paper adopts the Bayesian probability model to construct the ordering deployment model.

Assume that A, B, C are three random events.

Event A: select the jth device of class ith.

Event B: device installation is only based on the number of devices.

Event C: device installation is only based on device price.

The probability of selecting one of these i types of devices for installation can be expressed as Formula (5(5) $P(A)=\frac{1}{i}\frac{N_{ij}}{N_i}.$(5) ), in the scenario set in this paper, the value of variable i is 6. (5) $P(A)=\frac{1}{i}\frac{N_{ij}}{N_i}.$(5) Since the maximum quantity or price of each device is equally possible in advance, the task design process contains a total of j commonly used devices, and the probability of each device being selected may occur. The probability of selecting installed devices according to the quantity and price of devices can be expressed as Formula (6(6) $P(B)=P(C)=\frac{1}{j}.$(6) ), in the scenario set in this article, the value of j in the formula is 18. (6) $P(B)=P(C)=\frac{1}{j}.$(6) In the case of selection based on the number of devices, the probability of selecting a certain device for installation can be expressed as the ratio of the number of selected devices to the total number of devices. The possibility of selecting a certain device under the premise of considering the number of devices is expressed, that is, the prior probability of selecting installed devices based on the number of devices is expressed as: (7) $P(A|B)=\frac{N_{ij}}{N}.$(7) In the case of device price selection, the probability of selecting a device for installation can be expressed as the ratio of the amount of the selected device and the total amount of the device. The possibility of selecting a device on the premise of considering the price of the device is expressed, that is, the prior probability of selecting the installed device based on the price of the device is expressed as: (8) $P(A|C)=\frac{N_{ij}}{M}.$(8) In the formula (8(8) $P(A|C)=\frac{N_{ij}}{M}.$(8) ), $M=\sum _{i=1}^n\sum _{k=1}^j{M}_{ij},M_{ij}=\sum _{k=1}^j{d}_{ik}{A}_{ik}$. $M_{ij}$ denotes the price of j devices of class i, M denotes the total price. In actual construction, the number and price of devices should be considered as a whole to select devices. Based on these two conditions, the probability of selecting device installation needs to be solved by Bayesian formula.

The Bayesian theorem is as follows: (9) $P(B_i|A)=\frac{P(A|B_i)\ast P(B_i)}{\sum _{i=1}^{n}P(A|B_i)\ast P(B_i)}.$(9) In this algorithm, a device is selected based on a combination of two conditions. Therefore, using the generalisation of Bayesian theorem, the above formula is converted as follows: (10) $P(A|(BUC))=\frac{P(BUC|A)P(A)}{P(BUC)}.$(10) The expression $P(A|(BUC))$ is expressed as the posterior probability of device selection, which is determined by the conditional probability formula: (11) $P((BUC)|A)=\frac{P((BUC)A)}{P(A)}=\frac{P(AB)+P(AC)-P(ABC)}{P(A)}.$(11) In the formula above $P(B)>0$, $P(C)>0$, the same is true,when the number and price of the devices to be installed exist at the same time, the probability of the device being selected can be expressed as; (12) $P(A|BC)=\frac{P(ABC)}{P(BC)}.$(12) In this algorithm, event A is determined by event B and C. Event B and C are independent events when event A occurs, so $P(BC)=P(B)P(C)$. (13) $\begin{array}{rl}P(A|BC)& =\frac{P(A|B)P(A|C)}{P(A)}.\end{array}$(13) (14) $\begin{array}{rl}P(ABC)& =\frac{P(A|B)P(A|C)P(B)P(C)}{P(A)}.\end{array}$(14) Through the calculation of the above formula, it can be finally expressed as: (15) $P(A|BUC)=\frac{P(A|B)P(B)+P(A|C)P(C)-P(A|B)P(A|C)P(B)P(C)}{P(BUC)}.$(15)

3.3. Fundamentals of particle swarms

The basic idea of particle swarm optimisation algorithm (Song, 2022) comes from the research on the foraging behaviour of birds. It is an optimisation tool realised by imitating the clustering behaviour of birds and widely used in function optimisation problems. Each individual in the bird swarm is regarded as a particle, the potential solution of each optimisation problem can be imagined as a particle point in the multi latitude search space, the position of the particle is a candidate solution to the current problem. The state of a point of a particle in a multi-dimensional space is characterised by its position and velocity. According to the update mechanism of the particles themselves, the group interaction information and social communication behaviour, the optimal individual positions of the particles and the global optimal positions found by all particles are continuously updated and iterated, all particles in the particle swarm optimisation algorithm (Emambocus et al., 2021) have a fitness value determined by the objective function, and each particle has two iterative position and velocity vectors in the search space to move towards the optimal solution. Particles can be represented by vector groups as $(\overrightarrow{x_i}\overrightarrow{,v_i},\overrightarrow{p_i},\overrightarrow{g_i})$, where $\overrightarrow{x_i}=(x_{i1},x_{i2},\dots ,x_{id})$ and $\overrightarrow{v_i}=(v_{i1},v_{i2},\dots ,v_{id})$ represent the position and velocity vectors of the ith particle, $\overrightarrow{p_i}=(p_{i1},p_{i2},\dots ,p_{id})$ represents the individual optimal location of the particle, which we call $p_{best}$, and $\overrightarrow{g_i}=(g_{i1},g_{i2},\dots ,g_{id})$ represents the optimal location for population exploration, which is the global optimal vector, which we call $g_{best}$.

The position velocity update formula of the particle swarm optimisation algorithm: (16) $\{\begin{array}{l}{V}_i^{k+1}=w{v}_i^k+c_1{r}_1(p_{best}^k-x_i^k)+c_2{r}_2(g_{best}^k-x_i^k);\\ x_i^{k+1}=x_i^k+v_i^{k+1}.& \end{array}$(16) $r_1$ and $r_2$ are random numbers that are evenly distributed between 0 and 1, $c_1$ and $c_2$ are learning factors, represents the search ability of the particle itself, $c_2$ represents a social influence factor, and $c_1$ is usually equal to in values between 0 and 4, w is to avoid an unlimited increase in particle velocity with time-dependent inertial weights.

4. Proposed a heuristic two-stage optimisation approach of MERD

4.1. Algorithm of MERD

Aiming at the deployment of electrical resources in construction and installation engineering, this paper proposes a heuristic two-stage optimisation approach, namely MERD approach. Firstly, this approach constructs the working hours matrix according to the different construction complexity in the construction area and the man-hour consumption of workers in different areas, and takes it as the feasible domain to solve the problem. Then, the sequence of construction combinations of different construction areas selected by workers is considered as a particle, and the optimal particle in the feasible domain is found by solving the fitness function, and the idea of group intelligence (Rostami et al., 2021; Saberi-Movahed et al., 2022, November) is used to obtain the approximate optimal construction scheme. According to the optimal scheme, personnel with different proficiency levels are assigned to the region. The personnel with different proficiency are assigned to the area according to the near-optimal scheme. On the basis of the personnel allocation, the installation sequence (Rifai et al., 2022) relation of the devices to be installed in the area is determined by the mathematical model constructed, so as to reduce the randomness in the construction process. The overall purpose of reducing construction time is achieved through two-stage optimisation. The MERD approach is described as follows:

Step 1: Set the initial solution.

Give each particle a random solution to represent the worker's choice of area number arrangement, set Xi=$[x_1,x_2,\dots x_n]$ and the empty switching order are the initial velocities.

Step 2: Calculate the next position of each particle.

1. Firstly, the difference between the local optimal solution and the current particle position is calculated, and the result is treated as a commutative order $ss1=(p_{best}^k-x_i^k)$, finding the index of the same value between two particles will exchange the corresponding position values $ss=swapx(i,j)$, and retain the exchangers with probability u1. The difference between the particle's current position and the global optimal solution is then calculated and stored in the exchange order $ss2=(g_{best}^k-x_i^k)$, with probability u2.

2. Then, the current velocity of the merged particle, the exchange order $s{s}_1$ and the exchange order $s{s}_2$, and the merge result is updated according to Equation (16(16) $\{\begin{array}{l}{V}_i^{k+1}=w{v}_i^k+c_1{r}_1(p_{best}^k-x_i^k)+c_2{r}_2(g_{best}^k-x_i^k);\\ x_i^{k+1}=x_i^k+v_i^{k+1}.& \end{array}$(16) ).

3. Finally, the velocity is applied to the current position of the particle, and the position is updated according to Equation (16(16) $\{\begin{array}{l}{V}_i^{k+1}=w{v}_i^k+c_1{r}_1(p_{best}^k-x_i^k)+c_2{r}_2(g_{best}^k-x_i^k);\\ x_i^{k+1}=x_i^k+v_i^{k+1}.& \end{array}$(16) ), which means that a particle passes through the exchange sequence to get a new sequence.

Step 3: Calculate the particle function fitness.

Operate m construction areas, J indicates the area to be installed, $n^j$ represents the total number of devices in the selected J area, $C_i^j$ denotes the unit workload to select a class I device in J region, K denotes the measure, $s_x^j$ indicates proficiency in selecting worker X in area J. The fitness function of the particle is as follows: (17) $min\sum _{j=1}^m\sum _{x=1}^n\frac{\sum _{i=1}^{n^j}k{C}_i^j}{n{S}_x^j}.$(17)

Step 4: Complete the assignment if the global optimum does not meet the criteria, go back to step 3; otherwise, the output will end the iteration.

Step 5: Determine the ordering relationship according to formula (15(15) $P(A|BUC)=\frac{P(A|B)P(B)+P(A|C)P(C)-P(A|B)P(A|C)P(B)P(C)}{P(BUC)}.$(15) ).

The pseudocode of MERD's algorithm has been given as follows.

4.2. Discussion

In the process of construction installation and construction, cost control plays a key role in enterprise profitability, in most cases, the construction unit first thinks of cost control from the field of engineering management and carries out cost control through project management means. This traditional method makes people ignore the close connection between construction personnel, installation equipment and construction area in the construction process, and only think from the macro perspective of construction quality, labour expenditure, material cost and so on, and can not effectively deal with the cost output in the actual construction. Through analysis we find that the construction units usually separate workers and construction area, single handle electric resources from the angle of construction workers on the installation problem of the person, device, and the relationship between the construction area, if we can through the installation of construction personnel and operating area order relation, made under the same conditions to reduce the construction time consuming, this will be of great significance to the control of project cost, for which we introduce an installation and deployment strategy to optimise it.

On the whole, the process of MERD approach is consistent with the idea of heuristic algorithm, this is mainly because the solutions found by heuristic algorithms are not necessarily the best judgment. However, by constantly searching and modifying, it will become more and more accurate in its judgment of the target, from the point of view of the algorithm objective, it aims to realise the optimisation of the task allocation and scheduling problem in the construction process. Traditional approach that rely on the experience of the construction workers cannot achieve sufficient scheduling performance, so only through continuous optimisation of the construction scheme can we achieve a satisfactory accuracy, and MERD approach can ensure that in within a reasonable time to obtain the good results.The current handling of construction scheduling problems is all through manual random assignment, which organises the process in a chaotic and disorganised manner, in which a large number of redundant and repetitive processes are superimposed and the scheme is confusing. The proposed approach is novel in dealing with the resource scheduling process of construction and installation, and it achieves fusion innovation by combining traditional industry with new generation information technology, which makes a huge leap in the construction process. In the process of analysis we found that the installation problem can be seen as a specific environment resources deployment of near-optimal allocation strategy, different regional construction complexity combined with workers' proficiency, by combining combined particle swarm optimisation algorithm to the optimisation of different proficiency workers assigned to different areas, to find the near-optimal configuration order to make it a personnel under specific resources to achieve the effect of construction cost the near-optimal, thus minimising the cost of installation, and then selected area of the device by its quantity and price factors to calculate the selected probability, to calculate the probability value of reducing device selection of randomness so as to improve the work efficiency and work quality of installation.

5. Performance evaluation and analysis

We will evaluate the task assignment processing capabilities of the proposed MERD by comparing the performance of specific indicators of each approach. The MERD was tested by five different groups of experiments. The final result shows that the MERD shows better accuracy and stability in dealing with the construction task assignment and scheduling problems for installations in an area. The programme of the proposed MERD is implemented by Python Programming Software.

5.1. Comparison of construction time in the same construction area

In this section, we validate the feasibility of MERD through analysis and experiment, and compare the work hours generated by traditional random approach with those allocated by MERD according to the processing of related data, then evaluate and test them through comparative experiments. This experiment comprehensively compares the processing performance of each approach by observing the construction time of each approach under different data sizes, and verifies the processing performance of the proposed MERD in the experimental environment. As we all know, construction time is an important indicator of project progress, the construction time should be as short as possible and make it easier to popularise and use.The allocation of resources between tasks is determined by the functions required in the construction area, and the equipment needed to complete the functions is assigned through personnel. The difference between tasks is the amount of human resources, and the experiments conducted in this paper are to find this relationship.

Taking the construction area of a building as an example, the number of experiment assignments is 10 and the construction and installation area is 4, the construction electrical resources in the area are shown in the following Table 3:

Table 3. Proficiency of different workers.

Class	One	Two	Three	Four	Five	Six	Seven	eight	nine	ten
Personnel	1	2	3	4	5	6	7	8	9	10
Proficiency	1.5	2	1.75	1.6	0.75	1	1.6	1.5	0.74	0.5

The construction tasks in the construction area are shown in Table 4:

Table 4. Task volume in construction area.

Class	One	Two	Three	Four
Construction area	0	1	2	3
Tasks	73	74	64	55

The results under MERD are verified by comparing the construction time under traditional approach, the following Table 5 shows the order of some workers in the arrangement:

Table 5. Arrangement sequence of some workers.

X0	X1	X2	X3	X4	X5	X6	X7	X8	X9
1	0	1	2	3	3	0	2	3	3
2	2	1	0	1	0	0	3	3	1
2	1	0	2	1	1	1	3	3	1
0	0	1	0	1	2	2	3	1	0
3	2	0	1	1	1	2	0	3	1
0	1	0	2	0	2	3	3	0	0
1	0	2	0	1	3	0	2	3	1
2	1	0	2	2	2	3	3	3	2
2	1	0	2	1	1	2	3	3	1
1	0	1	2	1	1	0	0	3	1

The traditional approach achieves the near-optimal result of minimum construction amount 252.44. Using MERD approach to find the near-optimal variable for iteration under worker's arrangement order is 219.39.

In this set of experiments, a comparison experiment is set up to select the best result by comparing four parameters with the number of characteristic domains, and different population numbers and different iterations are taken respectively.

The near-optimal number of iterations was found by comparing the iteration curves of the algorithm under different iteration times, and then the accurate line of the approach was verified to expand the number of experimental assigned personnel and the construction and installation area. The division of the area is shown as follows (Tables 6 and 7).

Table 6. Task volume in construction area.

Class	One	Two	Three	Four	Five	Six	Seven	eight	nine	ten
Construction area	0	1	2	3	4	5	6	7	8	9
Tasks	94	73	83	65	98	78	95	66	89	54

Table 7. Arrangement sequence of some workers.

X0	X1	X2	X3	X4	X5	X6	X7	X8	X9
9	6	8	0	5	0	9	6	2	0
0	9	8	8	6	8	6	3	1	2
2	9	1	5	7	4	7	7	1	4
9	7	4	8	2	9	1	7	4	3
9	8	7	8	0	8	7	9	5	6
3	1	0	7	8	1	9	3	9	3
1	1	1	2	3	4	2	1	9	4
3	2	4	7	7	0	1	1	0	0
1	5	4	5	9	1	7	6	3	3
6	3	8	8	8	5	7	9	9	0

After the test value is updated, the experiment is verified again, the following table intercepts 10 of these data (Figures 2 and 3).

Figure 2. Iterative curve under different parameters. (a) 100 times. (b) 300 times. (c) 500 times. (d) 1000 times.

Figure 3. Construction scheme comparison experiment(Comparison of performance differences presented by different solutions in the construction process). (a) Construction time of different experimental schemes. (b) Comparison of minimum construction hours.

The experimental results obtained by the traditional approach are 649.7 and 596.3 working hours. It can be seen from the diagram that the time consumption produced by MERD under different personnel distribution is lower than that of traditional construction approach. It can be seen that there are significant numerical differences between MERD and traditional approach on the whole. By adjusting the construction volume and construction area to compare the difference of construction schemes under the same environment variable, the difference between the two schemes is relatively small when the personnel distribution is small. When the number of personnel allocation exceeds 20 people, the gap starts to show a big difference, the construction time of traditional approach increases to a large extent, and the growth of MERD is slower, with the increase of resources, the construction time of all methods starts to increase, but the increase of MERD time is slower. Based on the results of this set of experiments, the proposed MERD approach have better dispatch optimisation effect, and it has better performance when the number of samples increases, which can effectively improve the efficiency of the construction process.

We compare the construction time in a construction cycle by different approach, match and combine the relevant constructors with each other by random assignment to form an experimental scheme. Usually, the construction scenarios do not exceed single digits, and we set 500 sets of construction scenarios as input data for the experimental validation. We optimise the dispatch under the same construction conditions in the region, and finally compare the construction results of the experimental scheme. From the experimental results, it can be seen that the construction time generated by MERD scheme is at the minimum value marked in red, and the construction time generated by this scheme is the least compared with other construction schemes.

5.2. Performance comparison of resource allocation under different task loads

This experiment verifies the task processing performance of the proposed MERD approach in this experimental setting by comparing it with the traditional approach and observing the results of processing tasks under different task allocation volumes to perform a comparison of the final construction results. In this experimental scenario, we compare the performance of the stochastic and averaging approach used in today's construction process with MERD for processing task volumes, and the size of the scheduling increase reflects the model's ability to handle construction activities. By increasing the proportion of tasks in the experimental data to observe the processing performance of the algorithm in the face of the increase in pressure, the smaller the proportion of value added in task scheduling, the smaller the fluctuation value of the mobilisation of the construction personnel assigned in the scheduling process, which in turn shows its overall stability, and the use of its approach can reduce the waste of construction resources, thus better reducing the labour costs caused by staffing relationships and making the scheduling solution easier to popularisation and use.

The experimental results are as follows: Figure 4 shows that, with a small increase in task volume, the gap between MERD and traditional approach on construction task processing capacity is small. When the task volume increases to more than fifty percent,the processing performance of both approach increases significantly. As a whole, traditional approach and MERD can be seen, the difference between them increases gradually in the later period. MERD has a more prominent ability to dispatch multi-node resources, and the effect of increasing the construction process on MERD approach is small. This experiment shows that MERD has a good effect on personnel allocation in construction.

Figure 4. Performance curve of resource allocation under different task loads.

5.3. Cost comparison under different ranking relationships

The purpose of this experiment is to validate the cost control performance under the selected fold-down relationship in the region. The skillfulness of installers will increase with the accumulation of workload during the installation process, and different construction sequencing approach will have an impact on the growth of construction skillfulness. The skillfulness improvement process can be measured by the skillfulness function introduced by us. The skillfulness function (Peña et al., 2022) of installers is expressed as follows: $\theta =K{X}^{-\alpha }$, $\alpha =\frac{lg(1-p)}{lg2}$, the attenuation factor is related to the probability P of choosing the device.

The coefficient K is the working hour of installing the device, X is the total amount of installing a device, and the probability P of choosing the device is based on the price and the number of devices. Because the skillfulness generated by the installation process is determined by the probability of arranging the devices in the selected order, the skillfulness of the constructors is obtained based on the set folding relationship. It can be thought that the more a device is installed, the quicker the accumulation of proficiency in the installation process will be, and the price of components will affect the installation decision in the construction process and thus the project cost. Based on the construction proficiency function, we can measure the cost saved after the proficiency increase.

The traditional approach of random deployment of personnel and the average distribution approach have a poor ability to achieve the accumulation of personnel proficiency, and it is difficult for construction personnel to quickly accumulate experience from the work they are engaged in, as can be seen from Figure 5 below, there are obvious differences in construction costs from the scheduling of tasks in four different workload areas. From the experimental results, it can be seen that the highest construction cost is for the random assignment approach, and the second highest is for the average assignment approach, and it is obvious from the comparison of construction costs that the MERD scheme has a smaller construction volume compared with the random and average assignment approach, it can be seen that the MERD scheme reduces the construction volume by comparing the construction costs in different areas. In summary, this experiment demonstrates that the MERD has relatively good performance in workload control (Figure 6).

Figure 5. Cost comparison curves under different ranking relationships.

Figure 6. Time complexity comparison curve.

5.4. Time complexity comparison

This experiment verifies the processing performance of the algorithm in time frequency by comparing the time complexity of traditional approach in the process of installing and sorting. n is called the scale of the problem, when N changes constantly, it shows the law, we call it time complexity. Which is known to all, Running time complexity is an important indicator of the execution efficiency of construction scheduling model. The running time should be as short as possible to save computing resources and make it easier to popularise and use. The performance of the proposed MERD in solving device sequencing problems is verified by comparing the time complexity of the execution process. Perform device installation for N devices with N construction areas, in the process of construction, the time complexity of the traditional random approach to deal with the device sequencing problem is $n^2$, the principle of the average approach is similar to the idea of quick sorting, the time complexity of the average approach is logn, while the time complexity of the MERD approach is obviously lower than the traditional construction approach. The comparison of this performance clearly shows the awkwardness of the traditional approach in solving construction problems. With the increase of n, the traditional approach is far less than the MERD in solving sequencing problems. Considering the complexity of the algorithm, this approach has better processing performance.

5.5. Qualitative analysis

This experiment was to verify whether components distribution in the territory under the scheme on the properties of the cost control of contrast, we compare the construction processes in four regions considering the ordering approach. Based on the experimental results, it can be seen that the construction scheme optimised by sequence significantly reduces the construction cost. In the same construction environment, the construction cost is reduced due to the construction optimisation during installation phase. This happens because the MERD gives a determined installation order, which reduces the randomness of the construction process.

Comparing the construction process within the four regions, according to the experimental results, it can be seen that the construction plan after sequencing optimisation is adopted significantly reduces the construction cost, and the construction cost is reduced due to the adoption of construction optimisation in the installation phase in the same construction environment, and the reason for this situation is that the MERD approach gives a definite installation sequence, which reduces the randomness of the construction process, and the folding sequence relationship in the installation process is conducive to improving the proficiency of the installation and deployment operations during construction and increasing the productivity of the work process. Due to the disorderly nature of the installation process of the traditional construction scheme, the work proficiency of the installation personnel in the construction process is not accumulated, which is of little significance for the promotion of the overall project progress, and the construction approach of the installation process, which is subject to the assigned work of the construction organisation personnel, makes the work activities solidified and cannot be effectively fed back and programmed for optimisation.

Construction costs are reduced due to construction optimisation in the installation phase in the same construction environment. This happens because the MERD approach gives a defined installation sequence, which reduces the randomness of the construction process, and the installation process in a defined sequence relationship facilitates the improvement of the proficiency and efficiency of the construction personnel. The traditional construction installation process installer's work proficiency is not accumulated and the work activities are solidified, which prevents effective feedback and programme optimisation. The results are shown in Figure 7. By comparing the construction costs under four different construction complexities, it can be seen that the installation costs of the traditional random installation approach are always higher than the installation costs of the MERD approach when the construction volumes are different.

Figure 7. Construction cost under different schemes(Cost differences presented by different solutions in the construction process).

6. Conclusion and future work

This paper puts forward a approach of intelligent electric resources deployment by a two-phase heuristic optimisation thought to optimise the layout of the whole construction process, the approach on the whole used the ideas of swarm intelligence approach and combinatorial optimisation, formed a kind of on time the global optimisation of human resources cost control and construction workflow, It effectively solves the important basic problems related to engineering such as time cost control and optimal allocation of human resources. We explored the application of MERD approach in the task cooperation between multiple devices and multiple nodes in the process of building installation and construction, and achieved good results. The model introduced here can be used in the optimisation scheme scheduling of resources in related fields, so as to solve the scheduling problem in the construction process of this field by combining the optimisation of related labour and corresponding construction objects, so as to save the project cost.

In this paper, the feasibility of the algorithm is verified and analysed from five performance perspectives. The MERD approach proposed in this paper optimises the layout of the whole construction process by adopting the heuristic two-stage optimisation idea. The approach as a whole combines the use of swarm intelligence approach and combinatorial optimisation idea to optimise the scheduling process in the construction process to achieve the approximate optimal solution of the scheme. Then the installation selection sequence mechanism is established by Bayes' theorem to form a global optimal workflow, which effectively solves major engineering-related fundamental problems such as time cost control and optimal allocation of human resources, and the feasibility of the proposed scheme is verified by setting up comparative experiments. To promote the industrialisation and intelligent upgrading of the construction process has become the mainstream trend of today's development, the gap between the crude production approach of today's construction industry and the requirements of achieving high-quality development is large, in order to promote the high-quality development of the construction industry this paper has done relevant exploration in this direction.

This approach can largely save the construction time consuming in the process of mobilising and allocating related resources, can alleviate the limitation of human resources tension to a certain extent, promotes the intelligent upgrading of the industrial process, and to a certain extent promotes the integration and development of traditional industries with emerging technologies, which will generate huge economic benefits in industrial applications. If we want to optimise other scheduling problems in the future, we can adjust and reset the corresponding data parameters, which has a good reference and applicability for multi-stage resource scheduling problems, and can quickly promote the promotion and implementation of construction schemes.

The proposed MERD approach still has a large space for optimisation, which needs further research and improvement in dealing with the resource scheduling problem. Questions about the complexity of the skilled workers and construction scene, will be the next research work will be mixed in the practical process of a large number of interference factors into the MERD approach, we will continue to try in other implementation in practical engineering, in the follow-up work further for more types of data, and then optimise the MERD approach makes it more universal.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 61972054], the Key R & D Project of Changchun Science and Technology Development Plan [grant number 21ZY53], Jilin Higher Education Teaching Reform Research Project [grant number JLJY202168939653], the Theme Fund of Changchun Institute of Technology [grant number 320200052, 320200053], the Key R & D Project of Jilin Province Science and Technology Development Plan [grant number 20210201127GX], the Industrial Technology R & D Special Project of Jilin Provincial Development and Reform Commission [grant number 2021C045-6], the Fourth Batch of Jilin Province Youth S & T Talent Lift Project [grant number QT202001] and the Scientific Research Initiation Fund for Doctoral Innovation Team. We would like to thank the anonymous reviewers who helped us by commenting on this paper.