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ORIGINAL ARTICLE
A hybrid conceptual cost estimating model using ANN and GAfor power plant projects
Sanaz Tayefeh Hashemi1,2• Omid Mahdi Ebadati E.3 • Harleen Kaur4
Received: 1 August 2016 /Accepted: 14 August 2017 / Published online: 29 August 2017
� The Natural Computing Applications Forum 2017
Abstract Providing an accurate completion cost estimate
helps managers in deciding whether to undertake the pro-
ject due to cash in hand. Hence, MAPNA Group Co. as an
Iranian leading general contractor of power plant projects
is not an exception too. Cost prediction in these projects is
of great importance, whereas it can assist managers to keep
their overall budget under control. Literature has been
reviewed and influencing variables are explored. There-
after, an artificial neural network model is developed and
combined with genetic algorithm to select the best network
architecture. According to the literature reviewed, almost
all of the performed studies have selected the optimum
network architecture through a process of trial and error,
which makes the present method worthy of implementa-
tion. The best network architecture is capable of predicting
projects’ cost of accuracy equal to 94.71%. A sensitivity
analysis is then performed to test the significance degree of
model input variables.
Keywords MAPNA Group Co. � Artificial neural network(ANN) � Genetic algorithm (GA) � Construction cost �Early-stage cost estimation
1 Introduction
Power plants are industrial sites mainly constructed and
utilized to generate and distribute electric power. MAPNA
Group Co. is a leading Iranian company known as the first
and largest general contractor of power plants in the
Middle East and West Asia, which also operates in other
fields such as oil and gas, railway, wind farms and
investing projects as well as thermal power plants. Power
plant projects are basically classified into different cate-
gories across the worlds today. The main power plants
conducted by MAPNA Group Co. are as follows: gas tur-
bine power plant (GTPP), combined cycle power plant
(CCPP), combined cycle block (2 gas turbine ? 1 steam
turbine), hydroelectric, and Industrial Special (ISP) power
plant projects.
The main concern of construction project managers is to
undertake projects with allocating required resources,
regarding predefined criteria, within which cost is the most
important one, and delivering economic facilities while
meeting acceptable safety standards [1]. Hence, cost
management plays a vital role during project management
process and though early-stage cost estimation in projects
is a matter of great importance due to embedded uncer-
tainties because of lacking available accurate data.
Cost estimation is an excessively experience-oriented
process within which several matters such as relative
influencing factors and their interrelationships should be
considered based on adequate knowledge and expertise [2].
Traditional cost estimation methods in construction
& Harleen Kaur
1 Planning and Coordination Deputy of Power Division,
MAPNA Group Co, #231, Mirdamad Blvd.,
1918953651 Tehran, Iran
2 Department of Information Technology Management,
Kharazmi University, #242 Somayeh St., Between Qarani &
Vila, 15936-56311 Tehran, Iran
3 Department of Mathematics and Computer Science,
Kharazmi University, #242, Somayeh St., Between Qarani &
Vila, 15936-56311 Tehran, Iran
4 Department of Computer Science and Engineering, School of
Engineering Sciences and Technology, Hamdard University,
New Delhi 110062, India
123
Neural Comput & Applic (2019) 31:2143–2154
DOI 10.1007/s00521-017-3175-5
industry have long been noticed as methods fraught with
uncertainty, which needed major improvements regarding
the accuracy of prediction capabilities. The advent of
artificial neural networks has fulfilled this need in terms of
their capability of learning from nonlinear incomplete
datasets to predict novel cases with acceptable accuracy
even in the beginnings of projects [3].
Meta-heuristic algorithms such as genetic algorithm can
also enhance artificial neural networks performance, which
is based on simulated evolution. Application of genetic
algorithms in learning tasks has shown acceptable im-
provement as well as in optimization problems [4]. The
main objective of this study is to propose a model for
estimating power plant projects cost through the use of a
hybrid model, including artificial neural network optimized
by genetic algorithm.
This study has considered actual cost of finished power
plant projects with respect to their specific characteristics
regarding a financial view rather than taking into account
civil and construction factors. To the best of authors’
knowledge, the current studies done in the power plant
projects have implemented either just ANN [2] or a com-
parison between ANN and conventional regression analysis
[5], whereas the current study is the first one in the power
plant projects scope, which has taken into account the
implementation of ANN to estimate the costs within which
the best architecture is the result of subtle combination with
GA in order to set each parameter, including the number of
hidden layers, number of nodes per each hidden layer, and
corresponding weights and biases accurately. This research
has a novel approach of combining the actual cost in terms
of financial view with machine learning techniques in
power plant projects within which the best ANN topology
is the result of delicately combining GA to tune the cor-
responding network parameters.
The rest of paper is structured as follows: Sect. 2 con-
cisely reviews the literature on ANN and its hybrid models
to predict the cost of construction projects. Section 3
introduces the methodology and considers in detail the
variables, data gathering and data preparation for applying
them to the proposed method. Section 4 analyses the
results of the proposed method and conducts a sensitivity
analysis test. Finally, the paper is concluded in Sect. 5.
2 Related works
Nowadays, almost all businesses are based on a large
amount of data that in some cases predicting future per-
formance based on available past data is of great impor-
tance [6]. Predicting based on past data is not only crucial
to business success, but also inevitable in today’s com-
petitive economy. Therefore, construction industry is not
an exception too. As noted by [7] cost estimation in the
early stage of the project, when there neither exists enough
information nor the scope of work is finalized, has a major
impact on initial decision-making issues in construction
projects. Providing project managers with accurate cost
estimations prior to start of the project will assist them to
consider adequate and appropriate alternatives. As projects
progress, the level of accuracy increases due to more
information being available [8].
Conventional methods of predicting projects’ costs are
known to be faced with several deficiencies, including
inability to diagnose complex interrelationships between a
number of existing variables, neglecting inevitable uncer-
tainties and therefore, incapability of reaching reliable
forecasted final cost [9]. In return, artificial neural networks
with their successful experience in forecasting diverse
problems are among the most accurate and trustworthy
used models. Their ability to learn from incomplete data-
sets in order to predict the unseen section of data besides
their capability of modeling the problem with the least
available data and estimating almost all continuous func-
tions, have made them attractive enough to be used in
prediction problems [10].
Neural networks’ forecasting process is divided into two
sections. In the first section, the network is provided by a
set of data containing inputs and desired outputs and in the
second part, it tries to tune its parameters, including
weights and biases to reach desired output by minimizing
the difference between the generated output and desired
output known as the target in each iteration [11].
ANNs have been widely used in optimization problems
making them beneficial to tackle with problems instead of
conventional methods. Ye et al. [12] have taken advantage
of a specific type of neural network called projection neural
network to estimate the parameters of multiple-input
multiple-output (MIMO) models in predictive control
problems. Furthermore [13], has implemented an approach
called KDESOINN as a combination of kernel density
estimation (KDE) and self-organizing incremental neural
network (SOINN) as a density function estimator of big
data, out of which the neural network accounts for learning
from online noisy big data in order to be able to analyze
them. On the other hand, in aircraft industry [14], have
compared the use of multiple regression, GM(1,1) and a
combination of GM(1,N) and multi-layer perceptron
(MLP) neural network to estimate the development costs in
aircraft industry through which the later outperforms all. In
their study, the MLPNN is fed with GM(1,N) performance
and simulation data to optimize the forecasting process.
We can also see the use of neural networks in wind power
generation realm [15] through which a topographical
feedforward neural network is applied to predict the wind
speed in areas where wind speed measurements have not
2144 Neural Comput & Applic (2019) 31:2143–2154
123
been implemented. The neural network in this study has
been capable of predicting wind speed with an accuracy
equal to 96.6%.
ANNs have also been specifically used in studied related
to cost estimation. Cost estimation in different types of
projects has been the main study of many researchers, in
which some of them are listed below. Cost estimation is the
process of applying required art and technology to
approximate the extent to which the project is likely to
worth based on the current available data [16]. Application
of ANN has been investigated in manufacturing industry
[17–23]. Also in software cost estimation scope, [24] have
investigated a novel approach called cuckoo search
inspired by cuckoo’s breeding mechanism used to select
the best possible parameters of their cost estimation model.
A number of studies have also been conducted in con-
struction projects’ realm. The construction industry is
associated with some uncertainties among which cost
overrun and delays are the most important results of these
uncertainties [25]. Therefore, several researches have been
conducted to predict projects’ costs in early stages in order
to proactively deal with these uncertainties some of which
have studied this realm based on fuzzy logic [26–28], The
other researchers have investigated the subject through a
hybrid model of CBR and GA [29], as well as [30] which
have gone through the case with respect to a comparison
between an assembly-based data method and a historical-
based data method. Moreover [31], have gone into the
subject by developing ANN and support vector machine
(SVM) models. The work of [32] comprises a backpropa-
gation neural network used for predicting cost of school
buildings with two architectures, including a different
number of inputs, where the one with more inputs out-
performs the other, implying the influence of considering
more significant input parameters on the performance of
the network. Furthermore [33], in their study have devel-
oped six networks with distinct completed intervals of
construction projects as the networks’ inputs and the
remaining intervals up to projects’ completion representing
the networks’ outputs as a substitute approach for tradi-
tional cost flow forecasting methods. In [34], a comparison
between multiple regression analysis and artificial neural
networks is conducted to depict the superiority of neural
networks in estimating construction projects’ cost. In this
study, the best architecture of the neural network is defined
through a process of trial and error, and finally the opti-
mum network predicts the cost with 16.6 mean absolute
percentage error. A comprehensive attempt to investigate
situations under which artificial neural networks may per-
form better was done by [35] in building projects. In their
study, neural networks were fully examined by a different
number of inputs, various architectures, data transforma-
tion, data preparation, and different number of datasets.
Finally, analysis of variance (ANOVA) test was under-
taken in order to study the significant difference among
four different input sets.
Kim et al. [36] have conducted a comparative study
investigating advantages and disadvantages of three dif-
ferent approaches, including multiple regression analysis,
artificial neural networks, and case-based reasoning, in
estimating cost of construction projects, where they con-
clude that the last two methods perform much better than
the first one, while case-based reasoning (CBR) is less time
consuming and ANN produces results with smaller asso-
ciated error. The best architecture of ANN is also set by
trial and error. They propose the use of hybrid models of
ANN specially a combo with genetic algorithm for their
future research. Gunaydın and Dogan [37] have compared
regression analysis with backpropagation neural network in
early-stage cost estimation of structural systems of build-
ings where backpropagation neural network (BP ANN)
shows a better performance with an accuracy around 93%.
In [38], an ANN model was proposed for cost estimation
of highway projects and associated escalation in a future,
where the best architecture of the neural network is
determined by trial and error. Their study strongly advo-
cates the use of ANN over usual methods, for its superior
performance. Another study conducted by [11] outlines the
dominance of ANN over traditional earned value man-
agement (EVM) methods in cost estimation of sample
projects. Furthermore, [39] presents an ANN model to
predict installation projects’ cost, where the best corre-
sponding architecture is selected through a process of trial
and error, which leads to an accuracy around 80% that
shows a better performance compared to traditional meth-
ods. In addition, [40] in their study have investigated BP
ANN model compared with regression-based one in
buildings’ cost estimation, where the former within which
the best architecture is chosen after several trials, out-
weighs the latter. Further, [7] have developed a BP ANN
model to estimate building projects’ cost within which
again the best architecture is nominated after examining
different cases.
By comparing two types of neural networks, multi-layer
feedforward and general regression one, with the tradi-
tional methods of cost estimation, multiple regression
analysis [41], have proven that neural networks are more
reliable in tunnel construction cost prediction, with respect
to the reported accuracy (95.35%). Besides, the work of [3]
has shown an acceptable performance of BP ANN in cost
prediction of building projects. Furthermore [42], have
developed an ANN model for early cost estimation of
building projects in Gaza Strip with an accuracy equal to
94%. Roxas and Ongpeng [1] have also developed an ANN
model for cost estimation of building projects in the
Philippines. Moreover, [43] have applied BP ANN to
Neural Comput & Applic (2019) 31:2143–2154 2145
123
estimate the cost of projects, which yields an accuracy
around 92%. In [44] and [2], ANN models have been
implemented for cost estimation in construction projects
and water treatment plants projects, respectively, with
errors equal to 28.2 in the former, and 21.18% in the latter.
There have been studies conducted to investigate the
performance of neural networks, while combined by
genetic algorithm, which have reported positive influence
of genetic algorithm on the performance of proposed
models. Except [45], others have strongly proven this
correlation. In [45], a neural network model based on
Microsoft Excel is developed for cost estimation of high-
way projects, where the weights of the network are opti-
mized through three different methods, including Microsoft
Excel Solver (simplex method), application of genetic
algorithm, and backpropagation network, in which even-
tually the simplex method outperforms the others. As
opined by [41] neural networks are data-driven and there is
a strong correlation between the amount of training data
and model’s accuracy. Besides, we can see the study of
[46] presenting a hybrid model of BP ANN with genetic
algorithm that has successfully overcome the drawbacks of
BP ANN while implemented alone including the slow
convergence process and even the problem of network
being trapped in local minimums. It has also led to a lower
rate of error compared to BP ANN model alone, which is
worthy of comparison.
The learning ability of ANNs is extremely dependent on
its topology, and initial weights where choosing them
heuristically is highly time consuming [47]. Hence, genetic
algorithm because of its parallel searching ability, evolving
the best solution based on the population of solutions, and
being needless of any prior knowledge about the problem,
has been nominated as a method worthy of implementation
in selecting the best neural network topology in contrast to
other optimization methods [48]. This topic has been
investigated in the couple of studies [49, 50, 52–55]. In
[49], an attempt to determine the best architecture of
backpropagation neural network was made by proposing a
hybrid model incorporating genetic algorithm, which yields
results with error around 2.62%. In addition, [50] suggested
a hybrid model of genetic algorithm and backpropagation
neural network to estimate cost of building projects after
comparing it with two other models, including BP ANN
and a combo of ANN and genetic algorithm.
Recently [5], in their study have probed forecasting
hydroelectric power plant projects’ cost by means of ANN-
based model compared with multi-regression one, by
which three different architectures have been generated and
examined in the former, seeking the best performance.
They concluded that the ANN model is preferred to the
other in terms of forecasting error.
3 Research methodology
Research literature is reviewed to investigate different
techniques applied in predicting cost at completion of
projects of diverse types and specifically construction ones.
Main factors affecting the cost of power plant projects are
collected by conducting interviews with experts in this
domain. Thereafter, a hybrid model consisting of artificial
neural network and genetic algorithm as a meta-heuristic
algorithm for optimizing the network’s architecture is
applied. Research methodology is depicted in Fig. 1.
Historical data are needed to feed the model, and it is
collected and each project is divided into four main types
and four leading phases. EPC projects, as their name sug-
gests, are undertaken within 3 major phases, including
engineering, procurement, civil and commissioning; in this
study, due to different indexes needed for adjusting civil
works on one hand and commissioning works, on the other
hand, the civil and commissioning phase itself is divided
into two phases. Cost corresponding to each individual
phase is updated to the latest possible year (here 2015) by
applying appropriate indexes available due to statistical
indexes declared by Central Bank of Iran and Management
and Planning Organization (refer to Circular No. 1-9706/
54/2080). This step is conducted through applying opti-
mistic, most likely, and pessimistic scenarios, and thus the
final result is obtained via program evaluation review
technique (PERT). Besides, another way for updating the
cost is also applied according to inflation calculations (refer
to customer price index (CPI) provided by Central Bank of
Conducting Interviews with experts
Developing a Hybrid Model of ANN & GA
Choosing the Best Neural Network Architecture
Training the Model
Start
Testing the Model
Sensitivity Analysis Test
End
Data Preparation
(Classification & Adjustment)
Escalation-Based CostInflation-Based Cost
Fig. 1 Research methodology flowchart
2146 Neural Comput & Applic (2019) 31:2143–2154
123
Iran). The results of these two methods are considered as
ANN’s target values, and the factors affecting projects’
cost are the ANN’s inputs, while bearing this thought in
mind that what is estimated as the project cost is different
from tender price in that the tender price contains other
amounts, including company’s profit and contingency
reserve known as markup [51]. The best architecture for
ANN is selected by the GA algorithm trained and even-
tually is tested for further ability of the network to predict
new projects’ cost. As a final step, a sensitivity analysis is
performed to measure the significance of each of the model
inputs.
3.1 Variables’ identification
Factors affecting construction projects’ final cost have been
gathered through conducting interviews with experts within
which nine major influencing variables are finalized. These
factors are the input variables for ANN. Among these,
there are five factors that cause major changes in projects’
final cost, describing work packages, which are executed in
projects based on their contracts’ content and hence, they
should be considered in a cost estimating process:
• Substation construction (X1).
• Piling and soil stabilization (X2).
• Main cooling system type (X3).
• Number of fuel oil storage tanks (X4).
• Fuel type (fuel oil, gas or both) (X5).
There remain 4 other factors, which should be added to
aforementioned variables mainly defining the project’s
specifications:
• Power plant type (GTPP, CCPP, Block, and ISP) (X6).
• Project duration (in months) (X7).
• Number of units (X8).
• Projects phases (engineering, procurement, civil and
construction and commissioning) (X9).
In fact, the last item is added in order to be able to
consider the cost of each phase individually.
The indexes used in this study are retrieved from sta-
tistical data presented by Central Bank of Iran. These
indexes consist of escalation index and exchange rate, in
which the former is used for adjusting time in engineering,
civil and construction, and commissioning phases, and the
latter is applied for procurement phase. Another index is
the inflation index with respect to the year 2011 as the base
year, which is used for inflation-based method. The total
cost of a project is the output of the network, while bearing
this thought in mind that the presented cost is not a tender
price since the tender price contains other amounts,
including the profit and overheads known as markup and
indirect costs, respectively [51].
3.2 Historical data collection and preparation
Historical data of 39 projects are gathered in a database.
These projects are classified into four main types,
including GTPP, CCPP, Block and ISP. The input data
include both quantitative and qualitative variables. The
quantitative variables are remained unchanged, while the
qualitative ones (X1, X2, X3, X5, X6, and X9) are
transformed to scalar quantities and sorted with respect
to their influence on project cost as stated in [34]. Hence,
greater values show increasing effect on actual cost of
the project. For example, the procurement phase of
projects is regarded as the most expensive cost center,
while the engineering phase is at the opposite side of the
spectrum; therefore, the procurement phase acquires the
largest number, here 4, compared to engineering phase.
Time adjustment and location adjustment are performed
according to the method discussed by [54]. Since the
projects are undertaken in the different provinces of Iran,
in a primary step project’s cost is adjusted by location
indexes (provided in 1981 by Management and Planning
Organization formerly known as Budget and Planning
Organization). Hence, project’s cost is divided by
appropriate regional factors identified in the project’s
contract, related to the province in which the project is
undertaken and then multiplied by 1 as a base location
index associated with Tehran, the capital of Iran. Fur-
thermore, each project is executed within a period of
time starting with project’s start date and finished by
PAC (Provisional Acceptance Certificate) date. These
two milestones have specific indexes, in which each of
them is used for further time adjustment issue. Time
adjustment process consists of indexes in both, the time
of interest and time of reference. Each year’s index has
been monitored within 4 quarters. Time adjustment for
each phase has been done through two methods: esca-
lation-based and inflation-based adjustment method,
where the former is based on escalation indexes and
done through PERT technique, including optimistic, most
likely, and pessimistic scenarios, and the latter is
according to inflation indexes. The appropriate quarter
for the start date of each phase is considered regarding
that the project mainly starts as its civil phase is trig-
gered. In this way, the civil phase negotiations are made
and contracted about 3 months earlier than the project
start date due to experts’ opinions; since the engineering
phase starts on average 2 or 3 months prior to project
start date, it is assumed that the best time for this phase
is a quarter earlier than the project start date; usually,
procurement phase starts simultaneously on the project
start date, so the project can be led with needed materials
and equipment. Ultimately, the commissioning phase
starts 6 months later than the project start date since the
Neural Comput & Applic (2019) 31:2143–2154 2147
123
prerequisite tasks shall be completed in order to com-
mence this phase. Related index assumptions are shown
in Table 1.
Based on these hypotheses, location adjustment process
is performed by Eqs. (1) and (2):
C1 ¼ invoice
regional factorð1Þ
C2 ¼ invoiceþ escalation
regional factorð2Þ
CO¼C2 � Escalation Index time of interestð ÞEscalation Index time of referenceð Þ ð3Þ
CML ¼ C1 � Escalation Index time of interestð ÞEscalation Index time of referenceð Þ ð4Þ
CP ¼ C2 � Escalation Index time of interestð ÞEscalation Index time of referenceð Þ ð5Þ
CI ¼C1 � Inflation Index time of interestð ÞInflation Index time of referenceð Þ ð6Þ
The adjusted cost of each phase in escalation-based
method (pessimistic scenario) (CP) inflation-based method
(CI) and escalation-based method (most likely scenario)
(CML) is resulted by considering the start date of the
project as the time of reference, whereas in the escalation-
based method (optimistic scenario) (CO) the time of ref-
erence is set to the PAC date of project. This is mainly
because the indexes grow due to pass of time, which
consequently lead to greater indexes at the end of project
versus the start date, so smaller time of a reference index
leads to greater cost due to its inverse effect on time
adjustment process. The adjusted cost associated with
each of the methods is calculated by Eq. (3) through
Eq. (6).
The final cost in escalation-based method is calculated
by Eq. (7) based on PERT technique:
CE ¼ CO þ 4 � CML þ CP
6ð7Þ
Finally, cost resulted from pert technique applied to an
escalation-based method known as CE and cost resulted
from inflation-based method, are considered as target val-
ues in the ANN. Besides, the 9 aforementioned variables
are the networks’ input variables.
3.3 Neural network model design
Despite the black box mechanism of neural networks, they
have been widely used in prediction problems demon-
strating reasonable results as scrutinized in the literature.
Developing hybrid model of backpropagation neural net-
works and genetic algorithm will lead to more accurate
predictions and prevent the model from representing erro-
neous performance and hence can overcome encapsulated
shortcomings [23].
f ðhÞ ¼ 1
1þ e�hð8Þ
where h is obtained from multiplying neurons’ weights by
their input values, summed up with bias values. Due to
confidentiality of data and for better performance of the
network, data have been normalized into range [0, 1] with
the use of Eq. (9). Eventually, given the input parameters
for projects, the trained network is capable of estimating
project’s cost at the completion state (Table 2).
XðNormalizedÞ ¼ X �MinðXÞMaxðXÞ �MinðXÞ ð9Þ
3.4 Training and testing neural network model
Data are split into three parts, where 60 percent of data are
used for training the network, 20% for cross-validation and
the remaining part for testing the accuracy of the trained
network. The validation set is not used for training the
network. First of all, a primary ANN is initialized and is
then trained through the application of genetic algorithm,
which continuously searches for better network architec-
tures to achieve the lowest possible validation error. After
choosing the best network architecture by the application
of genetic algorithm, the efficiency of the model is exam-
ined through presenting novel cases in terms of test set to
the network.
3.5 Genetic algorithm implementation
GA accounts for choosing the best possible ANN archi-
tecture based on its evolution computing capabilities. For
this purpose, a global network is defined initially. The main
thought behind creating this global network is creating a
Table 1 Index assumptionsPhase Index Remarks
Engineering Escalation index Index1
Procurement Exchange rate (EURO/IRR) and (USD/IRR) Index2
Civil and construction Escalation index Index3
Commissioning Escalation index Index1
2148 Neural Comput & Applic (2019) 31:2143–2154
123
network once, rather than generating it each time in each
generation for each individual in the population which
drastically saves compiling time. Thus, this network is
recalled each time needed and is modified according to
each individual. This network is constructed as large as
possible, with 4 hidden layers and 8 nodes per each layer so
that it can cover all possible architecture within this range.
3.5.1 Initial population generation and encoding
A random initial population is generated initially within
which each chromosome contains 5 genes as follows:
1. Number of hidden layers
2. Number of nodes per each hidden layer
3. Input weights
4. Hidden layer weights
5. Biases
The chromosomes are populated and encoded by ran-
dom values in terms of continuous figures in the range of
[-1, 1]. The structure of each individual in the population
is depicted in Fig. 2:
3.5.2 Decoding process
Number of hidden layers is a two-gene chromosome where
random binary values are generated by MATLAB to define
it. These values are the encoded form of this gene, which is
interpretable by MATLAB. So it shall be decoded to
construct the desired network. The decoding process is a
conversion from binary to decimal values as follows
(Fig. 3):
Also the number of neurons per each hidden layer is a
three-gene chromosome where random binary values are
generated by MATLAB to define it. The corresponding
decoding process is a conversion from binary to decimal
values as follows (Fig. 4):
The other 3 genes are random values in the range of
[-1, 1] representing network weight initialization. They
are used just as they are generated in terms of input layer,
hidden layers and bias weights as much as needed.
3.5.3 Network construction and objective function
evaluation
Based on each individual in the population, a network is
constructed, respectively, which inherits its characteristics
from global network and the others such as the number of
hidden layers, nodes per each layer, and corresponding
weights for input layer, hidden layer, and biases modified
according to the chromosomes’ characteristics. Thereafter,
this network is examined in terms of its capability of pre-
dicting the cost with as low error as possible. Thus, each
chromosome has its corresponding cost and is sorted
according to it in an ascending order.
3.5.4 Evaluating the population
The population generated is evaluated by the ANN ability
to predict with reasonable accuracy. Thus, the performance
of ANN is the main concern, which is measured in terms of
mean squared error (MSE) of the results which is in turn
the fitness function of the problem. The final accuracy of
the network is calculated by Eqs. (2–4):
Accuracy ¼ 100�ffiffiffiffiffiffiffiffiffiffi
MSEp
100ð10Þ
Thereafter, the objective function which the problem
seeks to optimize is the reverse of fitness function:
Objective function ¼ 1
MSEð11Þ
3.5.5 Elitism and selection
About 25 percent of the population is reserved as elites. The
rest of the population is gone through selection operator,
here roulette wheel. The roulette wheel selection performs
Table 2 Best model parameters
based on trial and errorGenetic algorithm parameters Network parameters
Population 100 No. of training epochs 1000
Selection method Roulette wheel Training function Trainlm
Crossover probability 80% – –
Mutation probability 2% – –
No. of generations 50 – –
Number of hidden layers
Number of nodes per each hidden
layer
Input weights
Hidden layer weights
Biases weights
2 alleles 3*4 alleles 9*8 alleles 8*8*3+8 alleles 8*4+1 alleles
Fig. 2 Genetic algorithm
chromosome structure
Neural Comput & Applic (2019) 31:2143–2154 2149
123
as a fitness proportionate selection method where individ-
uals with higher fitness values will have the higher chances
to be selected while bearing this thought in mind that it is
not based on selecting the best and discarding the rest, so
that the weak have still the chance to be selected which is
considered as an advantage of this selection method.
3.5.6 Crossover and mutation operators
Crossover and mutation operators are presented in each
generation while bearing this thought in mind that they are
implemented based on probability values, which shall be
met as discussed earlier. New individuals are generated till
the population pool is filled for the next generation. The
new population is then evaluated based on the objective
function and goes for further evolution till the final number
of generations is met.
4 Results and analysis
The operations of the proposed method are built with
MATLAB version 2014b. The cost data with considering
aforementioned hypotheses are gathered in Microsoft
Excel and read in .dat format. The program is compiled for
40 times, and the final results are summarized in Table 3.
The networks chosen by GA along with the corre-
sponding range of errors in predicting projects cost are
depicted in this table. Thereafter, the results of each type of
neural network based on the number of hidden layers are
averaged according to Eq. (12) where Fi is the frequency of
observed error in each range and xi is the mean of the
corresponding range. According to these results, a two-
hidden layer network has yielded higher frequency of
errors in lower ranges and thus has shown a superior total
result toward the two other networks within which the best
architecture is shown in Fig. 5.
Binary Code Binary to Decimal Conversion
Summation with 1
Final Values
0 0 +1 10 1 +1 21 0 +1 31 1 +1 4
Fig. 3 Binary to decimal
conversion (number of hidden
layers)
Binary Code Binary to Decimal Conversion
Summation with 1
Final Values
0 0 0 +1 10 0 1 +1 20 1 0 +1 30 1 1 +1 41 0 0 +1 51 0 1 +1 61 1 0 +1 71 1 1 +1 8
Fig. 4 Binary to decimal
conversion (number of nodes
per each hidden layers)
Table 3 Summary of resultsRange of error One-hidden layer (%) Two-hidden layer Three-hidden layer
[4.4, 8] 72.73 77.78 44.44
[8, 11.7] 18.18 22.22 44.44
[11.7, 15.3] 4.55 – –
[15.3, 18.9] 4.55 – 11.11
Average error 7.67 6.99 9.02
Fig. 5 Best network
architecture
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123
Average Error ¼P
Fi � xi100
ð12Þ
The process of improving the network architecture via
GA, through which the aforementioned best network
architecture is resulted, is depicted in Fig. 6, and the final
accuracy of the network is calculated by Eq. (13).
Accuracy ¼ 100�ffiffiffiffiffiffiffiffiffiffi
MSEp
100ð13Þ
As shown in Fig. 6, the validation error decreases from
around 0.0059 to 0.0047 by applying GA algorithm. The
results of testing the model are depicted in Figs. 7 and 8.
Eventually, the model is able to predict project cost with
mean squared error (MSE) equal to 94.71% (Figs. 9, 10, 11).
Fig. 6 Genetic algorithm performance
Fig. 7 Test data (output versus target)
Fig. 8 Test data adaptability
Fig. 9 Network validation performance
Fig. 10 Network error histogram
Neural Comput & Applic (2019) 31:2143–2154 2151
123
4.1 Sensitivity analysis
In order to measure the impact of neural network’s inputs
on its performance, a sensitivity analysis is conducted
based on the method stated by [40]. Hence, the network is
compiled nine times in the absence of each of the nine
input parameters to monitor their significance level. Results
are shown in Fig. 12, in terms of the ratio of deteriorated
MSE due to the absence of each parameter, unto the
original best network MSE. As shown in Fig. 12, the type
of power plant project is the most influencing factor in
project cost, where establishing power distribution substa-
tion is the least important one. Furthermore, predicting
projects’ cost by considering it in phases will yield more
accurate results.
5 Conclusion
Early cost estimation is a vital process in project man-
agement as it helps project managers to make appropriate
decisions prior to undertake the projects. This study con-
tributes to this process by proposing a hybrid model con-
sisting of an artificial neural network and an optimization
algorithm for selecting the best network architecture. His-
torical data of MAPNA Group Co. power plant projects are
gathered and processed through two methods: escalation-
based and inflation-based methods, in which the former is
calculated through PERT technique, and the latter is the
result of incorporating the inflation index. Hence, the
model is provided with target value calculated through two
methods along with 9 input values. The best network
architecture is a two-hidden layer network with an accu-
racy equal to 94.71%. Eventually, a sensitivity analysis is
done to explore the effect of the network’s inputs on the
final result which shows that the type of power plant pro-
ject is the most influencing factor in the process of pre-
dicting projects’ cost.
Fig. 11 Network training
regression
4.36 4.033.47 3.26
2.441.70
1.17 1.02 0.82
0.00
1.00
2.00
3.00
4.00
5.00Input Variables Sensi�vity Analysis
Fig. 12 Input variables sensitivity analysis result
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123
Acknowledgements The authors would like to acknowledge with
great gratitude: MAPNA Group Co., where the case study is taken
place, Engineer Abolfazl Asgari Vice President of planning deputy
for continued support of this research, and Engineer Omid Mehdi-
zadeh for his invaluable recommendations during the study, which
would not have been possible without his supervision.
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