Applying the hybrid model to optimize the construction cost index

Thuy-Linh Le Applying The Hybrid Model To Optimize The Construction Cost Index Thuy-Linh Le The University of Danang, University of Technology and Education, Da Nang, Vietnam lttlinh@ute.udn.vn Abstract. Construction usually involves risks and uncertainty since its complicated operations require huge capital, long time, and intensive labor resources. The cost of construction is always a major concern of owners and contractors. Thus, the ability to accurately forecast future trends in the Construction Cost Index (CCI) is critical for construction cost managers in order to prepare accurate budgets and proper bids. However, CCI forecasting accuracy is affected by simultaneous fluctuations in many factors (e.g., domestic economic conditions, supplies and equipment expenses, gasoline prices, or economic indica- tors). The main contribution of this research is a hybrid model using an artificial neural network optimized by the Particle Swarm algorithm intelligence to help cost engineers deal with the variability of CCI. A stratified 10-fold cross-validation method was adopted to compare the average performance of the mod- els. This research uses 17 potentially significant factors and 50 CCI data set were used to build the pro- posed model. To increase the objectivity of the study, the employed Algorithm accuracy is the average accuracy of the ten models in ten validation rounds. This study is a useful proposal for cost engineers and project managers to draw up more accurate budgets, to offer reasonable prices to reduce construction costs during the operation process. Keywords. construction cost index, Artificial neural network, Particle Swarm Optimization, cross-vali- dation method. 1 Introduction Construction activities not only usually take a long time to complete, but usually, start months or even years after cost estimates are made. This situation increases the risk of construction projects are encountered. To perform a construction project effectively, which obtains some basic requirements such as saving time, good qualification, and getting a significant profit is really challenged for contractors and shareholders. Thus, an accurate estimation for construction costs has become the vital goal of the contractors. In CCI research for the Taiwan construction index, Cheng indicated many projects losing profits due to excess costs due to unforeseen changes in construction-related costs [1]. In another study, Shahandashti and Ashuri showed that approximately one-third of contractors identify variability in construction costs as a significant factor affecting profits [2]. Hence, the ability to accurately forecast price trends for resource inputs is essential to successfully estimate and manage construction costs. The construction cost index is a weighted composite index of the price of constant quantities of labor, materials, and equipment. This index provides a tool to estimate cost changes that apply to most construction projects [3]. CCI is widely used for calculating construction costs, the eg planning phase of projects, estimat- ing construction costs, and controlling costs during the construction phase. Furthermore, the CCI allows sys- tematic and relatively accurate projections of future project costs, facilitating budget decision making of capital projects, and improving bid accuracy [4, 5]. However, due to the instability of the CCI index, accurate prediction of CCI is always a challenging issue for cost engineers. The numerous factors that potentially impact the CCI, especially the unique economic conditions and construction environment in each country, which would severely hamper the accuracy of the CCI forecasting process [6]. For instance, it is clear that if using unique economic conditions and construction environments in each market (e.g., geographic region, country) then the factors associated with the CCI and the impact of each may differ significantly from market to market [7]. Prior studies on CCI may be classified into two principal categories: statistical methods and causal meth- ods [8, 9]. The former works to identify and analyze the factors that significantly affect CCI [8] while [9] 75 KỶ YẾU HỘI THẢO KHOA HỌC QUỐC GIA CITA 2020 “CNTT VÀ ỨNG DỤNG TRONG CÁC LĨNH VỰC” focus to compare the relative importance of each factor. They indicate the superior performance of the re- gression model than other existing methods. However, the relationships between CCI and its main factors of influence may be nonlinear and complex. Thus, research in this category has been limited because of applying inefficiently to CCI-related factors [8]. Artificial neural network (ANN) is a superior tool in artificial intelligence (AI)-based inference models offer a viable alternative approach to the cost-estimation problem [10]. AI-based inference models simulate the human inference processes, inferring new facts from previously acquired information, and changing adap- tively in response to changes in the historical data. AI-based inference models are thus a powerful data- modeling tool capable of capturing and representing complex input-output relationships. In another area, ANNs are the most widely used AI models in the applications of building energy predic- tion, thermal simulation, and assessing building material properties. A major disadvantage of ANN is a huge number of control parameters required to construct the network, including the number of hidden layers and neurons in hidden layers, learning rate, and momentum. Moreover, the ANN training process must be ob- tained via a gradient descent algorithm on the error space, which can be very complex and may contain many local solutions that prevent an ANN model from converging on an optimal solution [11]. Therefore, to optimize the prediction and assessment processes mentioned above, particle swarm optimi- zation (PSO) algorithm can be used combining with ANN. This is a new trend to obtain more accuracy in predicting uncertain values such as forecasting CCI and other applications. This study intends to use PSO to optimize two parameters of ANN that include learning rate (η-eta) and momentum constant (α-alpha) to predict CCI in Taiwan. The remaining sections of this paper are organized as follow: the next introduces the PSO-ANNs model; the third validates and discusses PSO-ANNs performance; and the last presents conclusions and recommends the use of the proposed model. 2 Methodologies 2.1 Artificial neural network Warren McCulloch and Walter Pitts created a computational model for neural networks based on mathemat- ics and algorithms called threshold logic [12]. In which they considered human brains as a well-structured computer which is consists of countless neurons. Artificial Neural Network is the information processing model that is modeled on the operation of the nervous system of the organism, including large numbers of neurons that are linked to information processing [10]. ANN has been applied successfully and highly ap- praised in various application domains, such as prediction, controlling, system modeling and identification, signal processing, and pattern classification. k kj jnet w O= å and 1 ( ) 1 k k netk y f net e- = = + (1) where netk is the activation of kth neuron; j is the set of neurons in the preceding layer; wkj is the connection weight between neuron k and neuron j; Oj is the output of neuron j; and yk is the sigmoid or logistic transfer function. 1 ( ) 1 k net f net e- = + (2) The formula for training and updating weights kjw in each cycle t is: ( ) ( 1) ( )kj kj kjw t w t w t= - +D (3) The change value ( )kjw tD is calculated as: ( ) ( 1)kj pj pj kjw t o w thd aD = + D - (4) where h is learning rate parameter, pjd is the propagated error, pjo is the output of neuron j for record p, α is the momentum parameter, and ( 1)kjw tD - is the change value for wkj in the previous cycle. 76 Thuy-Linh Le 2.2 Particle Swarm Optimization Developed by Kennedy and Eberhart (1995) [13], PSO is a well-known population-based stochastic global optimization Algorithm and widely used in simulation and forecasting. PSO is a metaheuristic algorithm based on the concept of swarm intelligence capable of solving complex mathematical problems existing in engineering. It consists of a set of particles moving around a search space, and is affected by their own best past location and the best past location of any particle in the swarm or a close neighbor. The velocity of each particle is updated in every iteration. ( ) ( ) ( )( )( ) ( )( )( )1 21 () ()besti i i i gbest iv t v t c ran p p t c rand p p tj+ = ´ + ´ ´ - + ´ ´ - (5) where vi(t+1) is the new velocity of the ith particle; φ is the inertia weight; c1 and c2 are the weighting coeffi- cients for the personal best and global best positions respectively; pi(t) is the position of the ith particle at time t; p is the best known position of the ith particle so far, and pgbest is the best position of any particle in the swarm so far. The rand() function generates a uniformly random variable ∈[0,1]. Variants on this update equation consider the best positions within the local neighborhood of a particular at time t and ( ) ( ) ( )1i i ip t p t v t+ = + (6) The position of a particular is updated using Eq. (6). By using tent mapping, the PSO provides a highly diverse initial population. The tent map is a recurrence relation, written as 1 1 0 2 1 1 2 n n n x x x x x m m m + ì £ £ïï = í ï - £ £ ïî for 0 ≤ μ ≤ 2 and 0 ≤ x ≤ 1 (7) where μ is a positive real constant. In the iterating procedure, any point x0 in the interval is assumed a new subsequent position as described, generating a sequence xn in [0,1]. The initial settings range of C and Ơ are [10-3; 1012] and [10-3; 103] respectively. Population size of the PSO is 50, max generation is 25 and PSO learning parameters c1 and c2 are 2.05. 2.3 Cross-fold validation method A stratified 10-fold cross-validation method to compare the average performance of the models and increase the objectivity of the study. The average prediction results for 10 testing folds can then be used to appraise model performance. To do so, randomly selected data were divided into 10 distinct folds. Each fold was used in turn as testing set with the remaining folds used as a training set to ensure all data instances were applied in both training and testing phases. Algorithm accuracy is then expressed as the average accuracy of the ten models in ten validation rounds. 2.4 PSO_ANN model This section provides a detailed description of the proposed PSO_ANN model which is established by fusing PSO and ANN, for forecasting CCI. As presented earlier, PSO is integrated into ANN to automatically de- termine the optimal number of learning rate (η) and momentum constant (α) in order to improve ANN per- formance. The PSO_ANN model is illustrated in Fig.1. Fig.1. Flowchart of PSO_ANN model process 77 KỶ YẾU HỘI THẢO KHOA HỌC QUỐC GIA CITA 2020 “CNTT VÀ ỨNG DỤNG TRONG CÁC LĨNH VỰC” 3 Experimental Results and Discussion 3.1 Database of Taiwan Construction Cost Index The PSO-ANN model uses Taiwan construction cost index data that is published monthly by the Taiwan Economic Data Center. This index uses aggregate measures of materials and labor costs in the construction to capture current general construction costs and control the fluctuations of these costs over time. This study uses 17 potentially important influence factors as the initial input variables. These factors have been applied in Cheng Cheng work [28] because of their potential effects on CCI Taiwan. The factors are classified into four groups: economy, energy, finance, and the stock market. Table 1 describes information about each input and output variable and provides additional corresponding sources where the input/output variable is taken. Table 1. Factors of Influence and Data Sources Variable X Influence Factors Field 1 Five major banks in lending rates Financial 2 NT-US exchange rate Financial 3 International oil prices Energy 4 Wholesale Price Index Economic 5 Consumer Price Index Economic 6 Leading indicator Economic 7 Coincident indicators Economic 8 Monitoring indicator Economic 9 Manufacturing New Orders Index Economic 10 Taiwan Weighted Stock Index Stock market 11 NASDAQ Composite Index Stock market 12 U.S. Dow Jones Industrial Average Stock market 13 Singapore’s Straits Times Index Stock market 14 Thailand’s SET Stock Index Stock market 15 Tokyo’s Nikkei NK-225 Stock market 16 Hong Kong’s Hang Seng Index Stock market 17 South Korea’s Weighted Stock Index Stock market Variable Y Construction Cost Index Construction market The global economy is closely interconnected, especially neighboring economies of Taiwan. Thus, this research considers the stock markets in the South Korea, China, Japan, and the United States. The proposed forecasting model has used 50 historical data sets from January 2010 to January 2015. 3.2 Experimental Results and Discussion After analyzed the data by K-fold cross validation model, we got 10 different data folds. Then, each data set of 50 Taiwan CCI data was divided into two data sets: training set of 40 cases which established the inference model, and a testing set of 10 cases (equivalent with 10% of data) which evaluated the performance of that model. 78 Thuy-Linh Le Table 2. Ten-fold cross-validation Table 3. ANN and PSO_ANN results Folds MAPE ANN PSO_ANN Fold 1 17.40% 6.10% Fold 2 15.20% 3.97% Fold 3 12.80% 6.58% Fold 4 16.70% 6.70% Fold 5 13.80% 6.13% Fold 6 13.10% 5.41% Fold 7 13.20% 9.35% Fold 8 14.80% 6.98% Fold 9 18.70% 5.53% Fold 10 13.70% 7.27% Min 12.80% 4.00% Max 18.70% 9.30% Average 14.92% 6.40% Std deviation 2.04% 1.40% Fig.2. Comparison of ANN and PSO_ANN results 14,92% 6,40% 0% 2% 4% 6% 8% 10% 12% 14% 16% ANN PSO-ANN MAPE Performance of ANN & PSO_ANN ANN PSO-ANN 79 KỶ YẾU HỘI THẢO KHOA HỌC QUỐC GIA CITA 2020 “CNTT VÀ ỨNG DỤNG TRONG CÁC LĨNH VỰC” In practice, identifying the most suitable set of control parameters is an optimization problem. Hence, combining ANN with PSO search engine may offer an efficient solution parameter-setting problem. Table 3 and Fig 1 display the dominance of PSO-ANN model than ANN model. It is clear that the average MAPE results from ANN model are nearly 15% which is higher than 10% that means ANN model did not give an accurate prediction. Whereas, the average MAPE value of PSO_ANN model is over 6% which represents highly accurate of PSO_ANN in its predictions. It is expected that parameter analysis will provide a clear insight into the CCI response to changes in influencing parameters, which will be highly useful information to control construction project costs. The PSO-ANN model is a useful tool for cost engineers consider and extend these ranges to find the correlation of the CCI with each parameter. 4 Conclusions CCI is a weighted aggregate index of the prices of constant quantities of the 3 main factors of construction projects: labor, materials, and equipment. By providing the estimating cost changes which are applicable for most construction project, CCI is a great concern in investment projects. Therefore, high quality of CCI forecasting helps saving a significant amount of project costs. The proposed PSO_ANN model is highly accurate in its efficacy with the value of MAPE index less than 10%. The PSO_ANN model has increased the accuracy of CCI index predictions compared to the ANN model by reducing MAPE value from over 14% to over 6%. The PSO_ANN model assists cost engineers to estimate the budget accurately and the financial advisor to consult precise decisions to their owners. References 1. M.-Y. Cheng, N.-D. Hoang, and Y.-W. 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