Genetic Algorithm Combining Operation Tree (GAOT) for concrete performance

Genetic Algorithm Combining Operation Tree (GAOT) was constructed to estimate the slump flow of high-performance concrete (HPC) by using seven concrete ingredients. HPC is a highly complex material; because modeling its behavior is extremely difficult, robust optimization techniques are required. GAOT is a type of evolutionary algorithm that simultaneously optimizes functions and their associated coefficients and is suitable for automatically discovering relationships between nonlinear systems. In a case study, it was observed that for estimating HPC slump flow, the GAOT is more accurate than regression model and back-propagation neural networks (BPNN). Introduction High performance concrete (HPC) is a highly complex material manufactured of four to ten different components and its behavior is thus difficult to model. HPC incorporates supplementary cementitious materials, including fly ash, blast furnace slag, and chemical admixtures, such as superplasticizers [1]. Traditional approaches model performance of concrete assuming an analytical equation followed by a regression analysis using experimental data to determine unknown coefficients in the equation [2]. In recent years, artificial neural networks (ANNs) performed exceptionally as regression tools because they are more direct than traditional statistical methods [3]. Moreover, ANNs are highly nonlinear and can capture complex interactions between input/output variables in a system, without prior knowledge about the nature of interactions. However, such “black box” models do not easily generate analytical equation forms [4]. The references [5, 6] proposed using genetic operation trees (GOT) to study concrete strength. The main purpose of this paper is based on GOT to improve the modeling techniques of estimating HPC parameters by Genetic Algorithm Combining Operation Tree (GAOT). Because of the complex nonlinear relationship between several ingredients and the slump flow of HPC, GOT usually suffers from premature convergence which cannot acquire satisfying solutions. The results show GAOT is better, compared with regression model and back-propagation neural networks (BPNN). Genetic Algorithm Combining Operation Tree (GAOT) Genetic Algorithm (GA). Genetic algorithm (GA) is an optimization method that employs a unique search algorithm which can jump from a local optimum to close to the global optimum. The concept of GA was derived from Darwin’s theories on natural selection and survival of the fittest. GA can generate an optimal solution by considering the optimization problem as an evolution problem. [7] Operation Tree (OT). Operation tree is a tree structure which represents a mathematical formula. A five-layered operation tree model is shown in Fig. 1. N1 is the root node denoted a mathematical operation (addition, subtraction, multiplication, division, natural logarithm, or exponentiation). N2–N15 are interior nodes denoted a variable, a constant, or a mathematical operation. N16 N31 are leaf nodes denoted a variable or a constant [8]. Fig. 2, shows an example of operation tree model is following Eq. 1. 5th International Conference on Information Engineering for Mechanics and Materials (ICIMM 2015) © 2015. The authors Published by Atlantis Press 445 ( ) D C B A Y + = (1) Fig. 1 A five-layered operation tree Fig. 2 the parse tree of Eq. 1 Mathematical operations, variables and constants in the root, branches, and leaves of the operation tree. When the tree-style structure is set up to represent a specific mathematical formula, operation tree can generate predicted output value for each data by substituting the input values of data into the variables on branches or leafs of the tree-style structure. The conventional regression analysis requires predetermined formula structure and is only allowed to adjust the regression coefficients in the predetermined structure. The disadvantage can be overcome by operation tree. Operation tree is a tree-style data structure which represents a flexible mathematical formula and optimizing the structure to fit the data best is a discrete optimization problem. Therefore, the optimization of operation tree cannot be solved with conventional mathematical programming. Genetic algorithm, that can solve discrete optimization problem, is adopted in this study to optimize the operation trees to fit the data best. Genetic Algorithm Combining Operation Tree. This study employed operation tree to express a regression formula, and genetic algorithms to optimize the operation tree to fit the data set to produce a self-organized regression formula. Operation tree performance can be evaluated with root mean squared error (RMSE) between predicted and actual output values. A five-layered operation tree was employed in this study as shown in Fig. 1. Table 1 lists the gene codes of mathematical operations, variables, and constants. Table 1 genetic code of mathematical operations, variables, and constants Code 1 2 3 4 5 6 7 Meaning + × ÷ x ln C Code 8 9 10 11 12 13 14 Meaning x1 x2 x3 x4 x5 x6 x7 Case Study Concrete is a complex material widely used due to its strong capacity to withstand compression [9]. In addition to the three basic ingredients in conventional concrete, i.e., Portland cement, fine and coarse aggregates, and water, HPC incorporates supplementary cementitious materials, including fly ash, blast furnace slag, and chemical admixtures, such as superplasticizers [1]. The use of fly ash, blast furnace slag, and other replacement materials contributes to better workability [10]. Therefore, the model consisted of seven input variables, including cement (C), fly ash (FL), slag (SL), water (W), N1 N3 N2 N4 N5 N6 N7 N8 N9 N10 N11 N13 N14 N12 N15 N16 N17 N26 N27 N20 N21 N28 N29 N30 N31 N22 N23 N24 N25 N18 N19