https://doi.org/10.31449/inf.v43i3.2914 Informatica 43 (2019) 409 –414 409 
Multi-objective Comprehensive Optimal Management of Construction 
Projects Based on Particle Algorithm 
Zijing Wang 
Luoyang Institute of Science and Technology, Luoyang, Henan 471023, China 
E-mail: wzjzijing@yeah.net 
Keywords: construction project management, particle swarm optimization, multi-objective optimization, genetic 
operator 
Received: July 25, 2019 
Construction industry is one of the pillars of rapid economic development. The optimization of 
construction project management can greatly optimize the cycle, cost and quality of projects. In this paper, 
the multi-objective management optimization model of construction projects and the particle swarm 
optimization (PSO) algorithm for calculating the optimal solution of the model are briefly introduced,  
genetic operators are  introduced into the PSO algorithm to prevent premature phenomenon, so as to 
improve the accuracy of the solution, and then case analysis is performed on a single-storey building 
project. The results show that the algorithm converges to stability and obtains the optimum solution set 
after 400 times of iterations and a total of 63250 seconds.  The construction period of each process of the 
solution with the shortest total construction period in the optimum solution set is shorter than that before 
optimization, the total construction period reduces by 56 days, the total cost reduces by 520,000 yuan, 
and the total quality increases by 3.58. In summary, the improved PSO algorithm can effectively optimize 
the management of construction projects. 
Povzetek: Predstavljen je izboljšani algoritem na osnovi delcev in večkriterijske optimizacije za 
izboljšanje vodenja gradbeniških projektov. 
 
1 Introduction 
Construction industry plays an indelible role in the rapid 
economic development [1]. In the construction process, 
whether building materials or labor force are disposable, 
different types of construction projects have different 
plans, and plans are also disposable. There is basically no 
case of modifying the plan after half of the construction 
according to the plan, so it needs to perform reasonable 
optimization allocation on the projects in the construction 
planning [2]. The main objectives of management 
optimization of construction projects are construction 
period, cost and quality, and the relevance between the 
optimization objectives is high. Finally, the problem of 
construction management optimization is transformed 
into a problem of multi-objective optimization, and the 
balance is obtained from the multi-objective to achieve 
the optimization effect of short construction period, low 
cost and high quality as far as possible [3].  
2 Related works of engineering 
projects 
Elbeltagi et al. [4] developed a multi-objective overall 
optimization model for project scheduling by using the 
new evolutionary strategy of particle swarm optimization 
and compromise solution based on Pareto optimal 
boundary. The experimental results showed that the 
model will help construction managers and decision 
makers to complete projects on time and reduce budgets 
through using existing information and resources. 
Senouci et al. [5] proposed a multi-objective optimization 
model for the problem of construction project scheduling 
under extreme weather conditions. The case analysis 
results showed that extreme weather had an impact on the 
construction period and cost, and the optimization model 
could minimize the time and cost of construction projects 
in extreme weather areas. Cheng et al. [6] proposed a 
multi-objective differential evolution algorithm based on 
objection to solve the problem of the time cost utilization 
and work-shift trade-off of the end of construction 
projects. The case analysis results verified the 
effectiveness of the algorithm. 
In this paper, the multi-objective management 
optimization model of construction projects and the 
particle swarm optimization (PSO) algorithm for 
calculating the optimal solution of the model are briefly 
introduced, genetic operators are introduced into the PSO 
algorithm to prevent "premature", so as to improve the 
accuracy of the solution, and then case analysis is 
performed on a single-story building project. 

410 Informatica 43 (2019) 409 –414 Z. Wang 
3 Multi-objective management 
optimization model for 
construction projects 
The multi-objective management of construction projects 
includes three objectives, namely, construction period, 
quality and cost respectively. The construction period 
represents the time required to complete the construction 
project, the quality represents the quality of the 
completed construction project, and the cost represents 
the cost required to complete the construction project. In 
the construction project management, the network plan 
chart is usually used to plan the construction period. In 
this study, the double code network chart [7] is used to 
represent the construction period plan of the construction 
project, the nodes in the double code network represent 
events, and the line arrows between nodes represent the 
working process. In actual construction projects, the 
network plan can not only have one line, which must have 
several branches, meaning that part of the construction 
process can be carried out simultaneously and finally 
converge at the end node. Therefore, the construction 
period in a construction project is determined by the key 
path which takes the longest time. The calculation 
formula of the construction period [8] is: 


=
N i
i
T T
,                              
(1) 
where  T represents the total construction period of the 
construction project, 
i
T represents the time consumed in 
the i-th working process, and N represents the set of 
work in the key path. 
For a construction project, the cost of its investment 
will greatly affect the schedule of the project, in other 
words, the length of the construction period can 
determine the cost of the investment. On the whole, the 
cost is negatively correlated with the construction period, 
and the relationship [9] is: 

=
− + + −  + =
n
i
C P C in i i in
T T T t t C C
1
2
) ( ] ) ( [  
, (2) 
where  
C
 represents the total cost, 
in
C
 represents 
the direct cost of the i-th job in the expected working 
time, 
i
∂
 represents the cost increment parameter of the i-
th job, 
i
t
 represents the actual working time of the  i-th 
job, 
in
t
 represents the estimated time of the  i-th job, 
β
 
represents the indirect cost parameter, 
C
T
 represents the 
actual total working time, 
γ
 represents the penalty 
coefficient, and 
P
T
represents the estimated total working 
time. 
Compared with the construction period and cost in 
the construction project, the quality of the construction is 
relatively difficult to quantify, and the relationship 
between the quality and the construction period of the 
construction is not a single positive (negative) 
correlation.  
In this study, the quality level index is used to 
evaluate the quality of each process in the project, and 
then the relationship between the construction period and 
the quality is established based on the reliability theory 
[10]: 















−
−
+
−
−
=
 − − =

=
is il
is il
q
is il
i
q
i
i
n
j
in
j
t t
et t e
t t
t e e
q
q q Q
il il
) (
ln
] ) 1 ( 1 [
1
,        (3) 
where 
Q
 represents the total quality of construction 
projects, 
i
q
 represents the quality level index of the i-th 
job, 
in
j
q
 represents the quality level index of the  j-th job 
before the i-th job, 
il
q
 represents the estimated quality 
level index of  the i-th job, and 
is il
t t ,
 represent the 
longest and shortest working time for the i-th job 
respectively. 
In the process of construction, construction 
companies always hope to complete construction projects 
faster, better and cheaper, but in fact, the construction 
period, cost and quality are mutually restricted by each 
other, i.e, the improvement of the quality will increase the 
cost and construction period, and the reduction of 
construction period will reduce the quality and increase 
the cost [11]. Therefore, the problem of management 
optimization of construction projects is a problem of 
multi-objective optimization, and the obtained final 
solution is the overall optimal solution of the three 
objectives compromising with each other instead of the 
optimal solution of one of them. Combining with the 
above, the multi-objective management optimization 
model of construction projects is: 
Objective function: 











 − − =
− + + −  + =
=



=
=

i
n
j
in
j
n
i
C P C in i i in
N i
i
q q Q
T T T t t C C
T T
] ) 1 ( 1 [ max
) ( ] ) ( [ min
min
1
1
2
 
, (4) 
Conditions:  





 
 
 
1
i is
il i is
il i is
q q
c c c
t t t
,                                (5) 
where 
il i is
c c c , ,
 represent the minimum cost, actual 
cost and maximum cost of the i-th job respectively, and 
i is
q q ,
 represent the worst quality and actual quality of 
the i-th job. 

Multi-objective Comprehensive Optimal Management... Informatica  43 (2019) 409 –414 411 
4 The improved PSO algorithm 
PSO algorithm [12] is also called "bird swarm foraging 
algorithm" as it is obtained by studying the foraging and 
migration behavior of birds. Its principle is to obtain the 
global optimal solution by tracing the current optimal 
solution. In the process of operation, the search direction 
of the optimal solution is determined by the value of 
fitness, the fitness is used to judge the quality of the 
solution, and the global optimal solution is found out by 
comparing the self-optimal solution with the current 
optimal solution. 
Through the iteration formula, the position and 
velocity of particles are updated continuously to find out 
the individual optimal solution and the overall optimal 
solution. The iteration formula [13] is: 



+ =
−   + −   + =
+
+
i i i
i i i i i i
V P P
P gbest x a P pbest x a V V
1
2 2 1 1 1
) ( ) (
, 
(6) 
where 
i i
V P ,
 represent the position and velocity of 
particle i respectively, 
i i
gbest pbest ,
 represent the 
individual optimal position and global optimal position 
respectively, 
2 1
, a a
 represent learning factors, and 
2 1
, x x
 
represent random numbers, which are evenly distributed 
between 0 and 1. When the optimal solution is searched 
or the preset maximum number of iterations is reached, 
the iteration stops. 
The basic principle of general PSO algorithm, as 
mentioned above, is relatively simple in implementation, 
but it is easy to converge to the local optimal solution 
prematurely in the process of searching for the optimal 
solution. In order to improve the performance of the PSO 
algorithm and make up for its shortcoming of 
"premature", in this study, crossover and mutation 
operators [14] in genetic algorithm are introduced to form 
an improved PSO algorithm. 
The operation flow of  the PSO algorithm improved 
by genetic algorithm is shown in Figure 1, and the steps 
are as follows: 
(1) The related parameters are input, including the 
size of particle swarm, the crossover and mutation 
probability, learning factors and the maximum times of 
iterations. The size of particle swarm is generally 
between 50 and 100, the probabilities of crossover and 
mutation are generally between 0.5 and 1, and then  
particles are randomly generated. The dimension of 
particles is determined by the number of working 
processes of the whole construction project, and a particle 
represents a set of time consuming of all processes of a 
construction project. After the particles are generated, the 
position and velocity of the particles are randomly 
initialized. 
(2) The value of fitness of the particle is calculated, 
and the individual and global optimal solution are 
selected from the particle swarm. In this study, the 
objective function above is used as the fitness function. 





−
=
) ( max
) ( min
) ( min
) ( min
X Q
X C
X T
X F
,                  (7) 
where ) (X F represents the value of fitness,  the final 
goal is to converge it to the minimum, and X represents 
particle swarm. At the same time, due to the difference of 
the units between the construction period, cost and 
quality in the objective function, the accuracy will be 
affected when evaluating, so it needs to standardize the 
value of fitness [15]. The equation is: 
s
x x
y
−
= ,                                  (8) 
where x represents the value of  fitness that needs 
standardization, y represents  the value of fitness after 
standardization, x represents the average of the fitness 
values of all particle, and s represents the variance of the 
fitness values of all particle. 
(3) The individual and global optimum solutions are 
selected by the values of  fitness, and equation (6) is used 
to update the velocity and position of particle swarm. 
Then the algorithm is judged whether the termination 
conditions is met,  including that the fitness function 
converges to stability and the maximum number of times 
of iterations is reached. If the termination condition is 
met, the results will be output directly; otherwise the next 
genetic operation for the particle swarm will be carried 
out. 
(4) Genetic operation, i.e., in this study, the 
phenomenon of "premature" of the traditional PSO 
algorithm is overcome by introducing crossover and 
mutation operations of genetic algorithm [16]. In the 
crossover operation in this paper, a random number 
between 0 and 1 is generated in each dimension of the 
particles. When the random number is less than the 
crossover probability, the parameters in the dimension of 
the particle will be exchanged with those in the same 
dimension of another particle to obtain a new individual 
particle. In the mutation operation, a random number 
between 0 and 1 is also generated in each dimension of 
 
Figure 1: The operation flow of the improved PSO algorithm. 

412 Informatica 43 (2019) 409 –414 Z. Wang 
the particles. When the random number is less than the 
mutation probability, the parameters in the dimension of 
the particle change randomly in a limited range to obtain 
a new individual. 
The steps (2), (3) and (4) are repeated until the 
algorithm reaches the termination condition, and the 
calculation results are output. 
5 Case analysis 
5.1 Case overview 
XX Construction Company undertook a single-storey 
construction project, the cost provided in the contract was 
2.8 million yuan, and the construction period was limited 
to 250 days. At the same time, in order to determine the 
quality of the building, the company invited 10 experts to 
evaluate the requirements of the contract and the quality 
of the project that the company can complete. The highest 
is 1, the lowest is 0,  the lowest qualified index of the  
quality of single work is 0.6, and finally the average value 
is taken. There are 16 working procedures in the 
construction project, and the plan of double code network 
is in Figure 2. 
5.2 Parameter setting 
According to the plan of the double code network in 
Figure 2, there are 16 processes in the construction 
project, and the related parameters of each process are in 
Table 1. The related parameters of PSO algorithm are as 
follows: the size of the population is 50, the dimension of 
the particle is 16, the learning factors,  are both set as 1.5, 
the maximum number of times of iterations is 400, and 
the probabilities of  crossover and mutation  in genetic 
operation are both 0.5.
Work 
serial 
number Work name is
t /day 
il
t /day 
is
c /ten 
thousand 
yuan 
il
c /ten 
thousand 
yuan is
q 
il
q 
A 
Construction 
preparation 
2 4 4 5 0.67 0.87 
B 
Foundation 
excavation 
8 10 6 10 0.65 0.89 
C Scaffolding 15 20 6 11 0.66 0.91 
D Column 7 11 11 16 0.69 0.91 
E Masonry 6 8 7 10 0.66 0.89 
F Roof panel 9 12 15 20 0.68 0.90 
G Roofing works 15 20 25 30 0.66 0.87 
H Polished exterior wall 30 40 36 50 0.68 0.91 
I 
Doors and windows 
construction 
7 10 10 15 0.66 0.89 
J Interior decoration 25 30 15 20 0.66 0.89 
K 
Door and window 
paint 
30 40 30 40 0.66 0.89 
L 
Piecemeal 
Engineering 
8 12 10 15 0.67 0.90 
M Backfill 3 5 3 5 0.66 0.89 
N 
Hydropower 
installation 
15 20 15 20 0.66 0.89 
O Operation detection 3 5 3 5 0.69 0.91 
P 
Check before 
acceptance 
1 2 1 3 0.66 0.89 
Table 1: Relevant parameters of single-storey construction projects.
1 2 3 4 6
10
11
7 13 16 5
9
12 15
8
14
A B C D E F
G
H
I
J
K
L
M N O P
  
Figure 2: The plan of the double code network. 
 

Multi-objective Comprehensive Optimal Management... Informatica  43 (2019) 409 –414 413 
5.3 Optimization results 
After 400 times of iterations of the improved PSO 
algorithm, the value of fitness of the objective function 
converges to stability, the set of optimal solution is 
obtained, and the total time consumed for optimization 
calculation is 63250 s. The first 25 sets of solutions in the 
set of optimal solution after the convergence of the fitness 
values are plotted with three objective functions as 
coordinate axes. Figure 3 shows that the x-axis is the 
objective function of the construction period, the y-axis 
is the objective function of the cost, and the z-axis is the 
objective function of the quality. There is no unique 
solution as the problem of management optimization of 
construction project is a problem of multi-objective 
optimization. Each blue point in Figure 3 represents a 
type of arrangement combination of project work,  and 
the curved surface formed by blue points is the set of 
optimal solution. 
The optimal construction period combination of 
construction projects is obtained by the improved PSO 
algorithm, that is, there are 25 groups of solutions in the 
optimal solution set. Due to the space limitation, it is 
impossible to list all the optimized schemes obtained by 
calculation. However, any solution in the solution set can 
be used as the optimal solution and are just selected 
according to the actual needs. Therefore, in this paper, 
one group of solutions is chose based on the shortest total 
construction period as the standard, and the comparison 
between the construction period of each process and the  
construction period before optimization in the project is  
in Figure 4. It can be seen from Figure 4 that the 
construction period of each process after optimization is 
less than that before optimization, and the construction 
project after optimization management can reduce the 
construction period. 
The optimization management of construction 
projects is a problem of multi-objective optimization, and 
the three optimization objectives, the construction period, 
cost and quality, interact with each other. Therefore, the 
total construction period, cost and quality of the 
construction project before and after optimization are 
compared. Table 2 shows that the total construction 
period of the construction project before optimization is 
249 days, the total cost is 2.75 million yuan, and the total 
quality level index is 10.67. After optimization, the total 
construction period is 193 days,  the total cost is 2.23 
million yuan, and the total quality level index is 14.25. It 
can be seen that the optimized construction project not 
only reduces the construction period of 56 days, but also 
reduces the cost of 520,000 yuan, and improves the 
quality level of 358. 
  Before 
optimization 
After 
optimization 
Total 
construction 
period/day 
249 193 
Total cost 
/10,000 yuan 
275 223 
Total quality 
level 
10.67 14.25 
Table 2: Total construction period, cost and quality 
before and after optimization. 
6 Conclusion 
In this paper, the multi-objective management 
optimization model of construction projects and the 
particle swarm optimization (PSO) algorithm for 
calculating the optimal solution of the model  are briefly 
introduced, genetic operators are introduced into the PSO 
algorithm to prevent "premature", so as to improve the 
accuracy of the solution,  and then case analysis is 
performed on a single-storey building project. The results 
are as follows. 
(1) After 400 times of iterations, the algorithm 
converges to stability taking a total time consumption of 
63250 s, and the optimal solution set is obtained. 
(2) The solution with the shortest total construction 
period is chose. Compared with the  construction period 
of each process, total construction period, total cost and 
total quality of the construction project before 
optimization, the construction period of each process 
after optimization is obviously reduced, the total 
construction period after optimization is 193 days with 
Figure 3: The scatter plot of the optimal solution of the 
improved PSO algorithm after optimization. 
 
Figure 4: The construction period of each process of the 
improved PSO algorithm before and after optimization. 

414 Informatica 43 (2019) 409 –414 Z. Wang 
the reduction of 56 days, the total cost is 2.23 million 
yuan with the reduction of 520,000 yuan, and the total 
quality is 1425 with the improvement of 358. 
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