Firefly algorithm versus genetic algorithm as powerful ...

Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 170 (2017) 117–123

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Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy journal homepage: www.elsevier.com/locate/saa

Firefly algorithm versus genetic algorithm as powerful variable selection tools and their effect on different multivariate calibration models in spectroscopy: A comparative study Khalid A.M. Attia a, Mohammed W.I. Nassar a, Mohamed B. El-Zeiny b, Ahmed Serag a,⁎ a b

Pharmaceutical Analytical Chemistry Department, Faculty of Pharmacy, Al-Azhar University, 11751 Nasr City, Cairo, Egypt Analytical Chemistry Department, Faculty of Pharmacy, Modern University for Technology and Information (MTI), 12582 Al Hadaba Al Wosta, Cairo, Egypt

a r t i c l e

i n f o

Article history: Received 27 April 2016 Received in revised form 2 July 2016 Accepted 8 July 2016 Available online 10 July 2016 Keywords: Firefly algorithm Genetic algorithm Concentration residual augmented classical least squares Artificial neural network Support vector regression

a b s t r a c t For the first time, a new variable selection method based on swarm intelligence namely firefly algorithm is coupled with three different multivariate calibration models namely, concentration residual augmented classical least squares, artificial neural network and support vector regression in UV spectral data. A comparative study between the firefly algorithm and the well-known genetic algorithm was developed. The discussion revealed the superiority of using this new powerful algorithm over the well-known genetic algorithm. Moreover, different statistical tests were performed and no significant differences were found between all the models regarding their predictabilities. This ensures that simpler and faster models were obtained without any deterioration of the quality of the calibration. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Multivariate calibration has been widely applied in many fields, such as pharmaceutical, medical and environmental research to develop quantitative relations between variables and properties of interest [1]. Large number of variables compared with the number of samples is considered one of the greatest challenges in multivariate calibration [2]. So, selecting the most informative variables or eliminating the uninformative ones can still improve the performance of multivariate calibration models. Hence, variable selection techniques are considered one of the most promising areas of research in chemometrics. Greater efforts are directed to variable selection techniques based on swarm intelligence and nature inspired algorithms. The swarm intelligence algorithms are based on the interaction between agents from the same population, as well as, on the interaction with the environment which is their major advantage over other algorithms. So, they use crowd decision rather than random search. These agent-based algorithms are normally nature-inspired, e.g., the source of inspiration being ants' colonies [3], or flock of birds behavior [4]. For the first time, firefly as a variable selection algorithm [5–8] in UV spectral data was introduced in combination with three different multivariate models namely, concentration residual augmented classical least squares (CRACLS) [9,10], artificial neural network [11–13] (ANN) ⁎ Corresponding author. E-mail address: [email protected] (A. Serag).

http://dx.doi.org/10.1016/j.saa.2016.07.016 1386-1425/© 2016 Elsevier B.V. All rights reserved.

and support vector regression (SVR) [14–18]. Also, a comparative study was developed between this algorithm and the well-known genetic algorithm [19–21] on the same multivariate models. This study was applied for the determination of ciprofloxacin (CIP) Fig. 1 (a) in the presence of metronidazole (MET) as interferent Fig. 1 (b) in laboratory prepared mixtures and in their pharmaceutical dosage form. 2. Experimental 2.1. Materials and reagents A. Pure CIP (certified to contain 99.25%) and MET (certified to contain 99.65%) were kindly supplied by Minapharm Pharmaceutical Company, Cairo, Egypt. B. Ciprodiazole tablets nominally containing CIP (500 mg) and MET (500 mg) batch number EJE3135 were manufactured and supplied by MINAPHARM pharmaceuticals (Cairo, Egypt). C. Methanol; El-NASR Pharmaceutical Chemicals Co., Egypt.

2.2. Instruments SHIMADZU dual beam UV–visible spectrophotometer (Kyoto/ Japan), model UV-1800 PC connected to IBM compatible and a

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chosen concentrations for each compound is based on their linearity and the ratio between the two compounds involved in their pharmaceutical preparation. Table 1 represents the concentration design matrix while Fig. 2 shows the absorption spectra of these concentrations. Since, calibration data set selection based on optimal criteria improves the quality of multivariate models predictions, D-optimal selection algorithm was used for the calibration data set selection [24]. This algorithm improves the representativeness of the calibration data as shown by the 2D plot of the experimental space in Fig. 3. This plot shows the positioning of training set and the validation set samples. Fifteen mixtures of this design were used as a calibration set and the other ten mixtures were used as a validation set to test the predictability of the developed multivariate models. 3.3. Analysis of CIP in Ciprodiazole® tablets by the proposed methods Ten Ciprodiazole® tablets were weighed, powdered and mixed. The appropriate weight of powder equivalent to 20 mg of CIP was accurately transferred to 100-mL volumetric flask and the volume was made up to 100 mL with methanol. The solution was shaken vigorously for 15 min then sonicated for 30 min and filtered. Working solution was obtained by dilution of the stock solution with methanol to get solution labeled to contain (50 μg mL−1). Necessary dilutions were made with methanol to obtain the different concentrations of the studied drug. The spectra of these solutions were scanned, stored in the computer and analyzed by the proposed models. 4. Results and discussion 4.1. Variable selection by FA and GA

Fig. 1. Chemical structure of (a) ciprofloxacin and (b) metronidazole.

HP1020 laser jet printer. The spectral band was 2 nm and scanning speed is 2800 nm/min with 1 nm interval. 2.3. Software The bundled software, UV-Probe personal spectroscopy software version 2.43 (SHIMADZU) was used. All chemometric methods were implemented in Matlab 8.2.0.701 (R2013b). Grid search for optimum SVR parameters, CRACLS and FA were done with our own written codes in Matlab. The codes for the SVR algorithm were downloaded from the internet website http://onlinesvr.altervista.org/ [22]. ANNs were carried out by using Neural Network toolbox. The t-test and Ftest were performed using Microsoft® Excel. One way ANOVA test was performed using Graph Pad Prism version 5 (Graph Pad, San Diego, CA). 3. Procedures 3.1. Standard solutions A. CIP and MET standard stock solutions prepared to contain 200 μg mL−1 in methanol. B. CIP and MET standard working solutions prepared to contain 50 μg mL−1 in methanol.

3.2. Experimental design for chemometric models A 5-level, 2-factor design was performed using 5 concentration levels for each of the 2 compounds resulting in 25 mixtures [23]. The central level of the design is 5 μg mL−1 for each of CIP and MET. The

In order to increase the quality of the calibration, FA as a variable selection tool has been introduced here for the first time with three multivariate calibration models to solve the severe overlapping of CIP and MET as shown in Fig. 4. This powerful variable selection tool has been compared with the most widely used GA listing the advantages and the disadvantages of each method. FA was run on the calibration data to determine the selected variables using RMSE as a fitness function calculated by MLR model. It Table 1 The concentrations of CIP and MET in μg mL−1 in the used experimental design. Mixture number

CIP

MET

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

5 5 4 4 6 4.5 6 5 4.5 4.5 5.5 6 5.5 5 6 6 4 5.5 4 5 5.5 5.5 4.5 4 4.5

5 4 4 6 4.5 6 5 4.5 4.5 5.5 6 5.5 5 6 6 4 5.5 4 5 5.5 5.5 4.5 4 4.5 5

The shaded rows represent the calibration set.

K.A.M. Attia et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 170 (2017) 117–123

Fig. 2. The absorption spectra of the concentrations design.

Fig. 3. The 2D plot of the experimental space showing the positioning of training set (o) and the validation set (x) samples.

Fig. 4. Zero order absorption spectra of (5 μg mL−1) CIP (‫ )ـــــ‬and (5 μg mL−1) MET (........).

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K.A.M. Attia et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 170 (2017) 117–123 Table 2 Parameters of the FA used for variable selection applied to CIP raw variables: Parameter

Value

Number of fireflies Generations α β0 γ

30 200 0.2 1 1

Table 3 Parameters of the GA used for variable selection applied to CIP raw variables: Parameter

Value

Population size Maximum generations Mutation rate The number of variables in a window (window width) Percent of population the same at convergence % Wavelengths used at initiation Crossover type Maximum number of latent variables Cross validation Number of subsets to divide data into for cross validation Number of iterations for cross validation at each generation

36 48 0.005 3 100 50 Double 2 Random 4 2

should be noted that some parameters should be optimized in order to obtain the best performance of the algorithm. The absorption coefficient parameter “γ” is one of the most important parameters in the optimization process. This parameter controls the light intensity and consequently controls the fireflies' attractiveness. Its value is very important in determining the speed of the convergence and how the whole algorithm behaves. Another important parameter is the “α” parameter which provides a random movement to the fireflies. Without this random movement, the fireflies would possibly be attracted to a light that is not necessarily the brightest and the solution would be restricted to a local optimum, directly towards the best solution in the local search space. So with a proper use of this parameter, the search will escape from any local solution. This leads to a high chance of finding the global optima of the search. It should be noted that a high value of this parameter will disrupt the fireflies' movement resulting in a random search and the search loses its advantage. Also, a very low value does not give this step the importance it deserves and the fireflies will stick in their local optima. A trial and error method was used to find the adjusted FA parameters used during all the runs. The adjusted FA parameters were shown in Table 2.

GA was run on the calibration data to determine the selected variables using RMSE as a fitness function calculated by PLS model in our case. To optimize the GA parameters, a good balance between exploration (population size) and exploitation (number of generations) is required. A random search will be obtained if the search is too unbalanced towards exploration. On the other hand, if the search is too unbalanced towards exploitation, then a local search will be obtained and the population will stick to a local minimum. So, a number of independent short runs were used to find the best fitted population through compromising between the population size and number of generations. Another important parameter is the mutation rate which also allows the population to escape from local solutions through random altering of the genes of the selected chromosomes. This is the same idea as the random movement in the FA. The trial and error method was used to find the adjusted GA parameters used during all the runs. The adjusted GA parameters used during this study were shown in Table 3. The selected variables by both methods were used for building of CRACLS, ANN and SVR models. FA reduced the absorbance matrix to about 22% of the original matrix (31 variable for CIP of total 141 variable) as shown in Fig. 5. While, GA reduced the absorbance matrix to about 45% of the original matrix (63 variable for CIP of total 141 variable) as shown in Fig. 6. After the choice of the best parameters values for GA and FA, one hundred independent short runs were performed and the final variables were chosen by taking into account the frequency of appearance of these variables in all the runs in both FA and GA. Variables that appear in at least 50 runs are chosen to ensure that they are the most informative ones and not just chosen by chance.

4.2. Multivariate models In CRACLS method, the whole variables and those selected by FA and GA were used to build three CRACLS models using the CIP concentration vector. These models aim to quantify CIP in the presence of MET as interferent. Each model is allowed to iterate in order to minimize the error of the concentration matrix by using the RMSEV as the optimization criterion. So, the main goal is to determine the minimum number of iterations that can predict the concentration of the component of interest well without being affected with the presence of the interfering substance. F-test was used to find the least complex model by statistically comparing the results of the iteration with the minimum RMSEV with those of the previous iterations. The optimum iteration is the earliest one that shows no significant difference with the one with the minimum RMSEV.

Fig. 5. The chosen wavelengths by firefly algorithm (o) for (5 μg mL−1) of CIP.

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Fig. 6. The chosen wavelengths by genetic algorithm (o) for (5 μg mL−1) of CIP.

It was found that 2 iterations were sufficient to model the data and predict the concentration of CIP with sufficient accuracy in all the models. In ANN method, the whole variables and those selected by FA and GA were used to build three ANN models using the CIP concentration vector. The MET is considered as interferent. A trial and error method has to be used to find the best neural network architecture and for the optimization of neural network parameters [13,25]. In fact, the parameters are mutually related and selecting the optimum parameters values for constructing a network is not an easy task, so a compromise must usually be adopted. CIP concentration vector is the output layer and only a single hidden layer is considered sufficient to solve similar or more complex problems. Moreover, more hidden layers may cause overfitting. Among other ANN parameters, the hidden neurons number which is related to the converging performance of the output error function during the learning process. The root mean square error in prediction (RMSEP) was the optimization criterion for this parameter through a grid search since more neurons than necessary may cause overfitting of the network. Another parameter that should be optimized carefully is the transfer function pair. The nature of the data being analyzed determines the optimum transfer function pair. In this work, there is a linear correlation between absorbance and concentration so, purelin–purelin transfer function was implemented in all the models. The values of the optimized ANN parameters of all the models were shown in Table 4. In SVR method, the critical step is to find the optimum parameters for SVR models (ε and C). The optimum values for ε, C were obtained

by running a grid search based on K fold cross validation rather than leave one out cross-validation. This may help to avoid overfitting and accordingly increasing the robustness of the model and its generalization ability. The primary range of values for ε was (0.01–1) and for C was (30–1000). The grid search was performed in two stages, the first using a wide grid followed by a fine search. The values of C and ε that give the lowest RMSECV were selected for all the models. The optimum parameters of SVR models from grid search were shown in Table 5. The above discussion revealed that FA and GA are similar in some points as: • Both the FA and GA are nature inspired methods controlled by exploring the solutions (population) to find the best ones and then exploiting these promising solutions (generations). • Both methods avoid sticking to local optima by a random solution either by a randomization parameter in the firefly or mutation and crossover in the genetic algorithm. • Both methods used RMSE as a fitness function. However, FA shows some advantages over GA in this work which are: • FA is based on decreasing attraction and attractiveness with distance. This leads to the fact that the whole population can automatically subdivide into subgroups. Each group can swarm around each mode or local optimum to find all optima simultaneously. This is not the case in GA since the best solutions (chromosomes) are used to exploit and yield a new generation of child chromosomes so the optima can't be found in a simultaneous manner like FA.

Table 4 Optimized parameters of ANNs, FA-ANN and GA-ANN for CIP. Method

ANN

FA-ANN

GA-ANN

Architecture Hidden neurons number Transfer functions Learning rate Training function

141-8-1 8 Purelin–purelin 0.1 TRAINLM

31-4-1 4

63-4-1 4

100

100

Table 5 Optimized parameters of SVR, FA-SVR and GA-SVR for CIP. Method

SVR

FA-SVR

GA-SVR

C ε

300 0.02

150 0.06

100 0.05

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Table 6 Assay validation sheet of CIP by the proposed models. Model

RMSECa

RMSEPb

RRMSEPc

BCRMSEPd

r2e

Intercepte

Slopee

CRACLS FA-CRACLS GA-CRACLS ANN FA-ANN GA-ANN SVR FA-SVR GA-SVR

0.0643 0.0656 0.0616 0.0456 0.0515 0.10030 0.0366 0.0548 0.0538

0.0755 0.0741 0.0700 0.0426 0.05019 0.04020 0.0517 0.0546 0.0549

1.93 1.88 1.77 1.06 1.26 1.01 1.29 1.37 1.37

0.0057 0.0055 0.0049 0.0027 0.0025 0.0016 0.0027 0.0030 0.0030

0.993 0.993 0.994 0.996 0.996 0.991 0.997 0.994 0.995

−0.1249 −0.1635 −0.1671 −0.0588 −0.1365 −0.3812 −0.0088 0.0094 −0.0085

1.0245 1.0321 1.0328 1.0118 1.0292 1.0834 1.0027 0.999 1.0037

a b c d e

Root mean square error of calibration. Root mean square error of prediction. Relative root mean square error of prediction. Bias corrected mean square error of prediction. Data of the straight line plotted between predicted concentrations versus actual concentrations of the calibration set.

• FA introduced simpler models with less number of variables than GA. This led to decrease the complexity of the model and fasten the time required for the calculations. • FA parameters are less than those of GA. These parameters are easier to adjust to obtain the most informative variables than those of GA.

5. Method validation and statistical analysis 5.1. Method validation RMSEC, RMSEP and percentage of the relative root MSEP (RRMSEP) were used to measure the accuracy of the predictions [26] while bias corrected MSEP (BCMSEP) was used to measure the precision or variance of the predictions [27]. These parameters and other validation parameters were shown in Table 6. 6. Statistical analysis One way ANOVA test was done between all the models for each of the calibration and the validation sets to analyze the results. No significant differences were found as shown in Table 7. From Tables 6 and 7, it can be concluded that all the models almost maintain the same predictabilities and no significant differences were found. On the other hand, faster and simpler models were obtained in case of models based on variable selection. The ability of each one of the proposed models to determine CIP in pharmaceutical preparation with MET were compared by the reported method (derivative ratio) [28]. The results were subjected to statistical analysis as shown in Table 8. The calculated t and F values were less than the theoretical ones indicating that there were no significant differences between the proposed models and the reported method. Another statistical comparison of the obtained results by the proposed models and the reported method for determination of CIP in

Table 7 One-way ANOVA testing for the different proposed models used for the determination of CIP in calibration and validation sets.

Calibration Validation

Source

DF

Sum of squares

Mean square

F value

Between exp. Within exp. Between exp. Within exp.

8 126 8 81

5.514 192.040 18.644 108.634

0.689 1.524 2.330 1.341

0.452 (2.01)

The values between parentheses are the theoretical F values. The population means are not significantly different.

1.738 (2.05)

pharmaceutical product using one way ANOVA test was shown in Table 9. The results obtained by applying these models show no significant differences between all of them. 7. Conclusion Wavelength selection is a critical step in multivariate calibration. It is used to build simpler models with equivalent or better predictabilities when applied to spectral data. Up to now, many variable selection techniques have been developed but those based on swarm intelligence optimization methodologies are more interesting since they are usually inspired by nature such as insect life behavior and biological processes. The effect of FA and GA on three different chemometric models (CRACLS, ANN and SVR) was studied. FA had reduced the number of variables more than GA resulting in simpler and faster models. This leads to simpler and more robust models. Different types of statistical tests (t-test, F-test and ANOVA) were performed on all the models and good results were obtained.

Table 8 Statistical comparison for the results obtained by the proposed methods and the reported method for the analysis of CIP in Ciprodiazol® tablets. Value

Method

CRACLS FA-CRACLS GA-CRACLS ANN FA-ANN GA-ANN SVR FA-SVR GA-SVR Reported method (29)b

Mean

SD

N Variance Student's t testa F valuea (2.228) (5.050)

100.14 101.72 100.41 101.57 99.98 99.22 100.31 100.47 100.02 100.41

1.703 1.505 1.377 1.325 1.759 1.037 1.026 1.723 1.814 1.377

6 6 6 6 6 6 6 6 6 6

2.902 2.265 1.896 1.757 3.093 1.075 1.053 2.969 3.291 1.897

0.304 1.578 1.179 1.488 0.472 1.692 0.144 0.068 0.419

1.530 1.194 1.645 1.080 1.631 1.764 1.800 1.566 1.736

a The values in the parenthesis are the corresponding theoretical values of t and F at (P = 0.05). b Derivative ratio method for determination of CIP in presence of MET.

Table 9 One-way ANOVA testing for the different proposed models used for the determination of CIP in Ciprodiazol® tablets.

CIP

Source

DF

Sum of squares

Mean square

F value

Between exp. Within exp.

8 45

33.087 97.794

4.136 2.173

1.903 (2.15)

The values between parentheses are the theoretical F values. The population means are not significantly different.

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