Presented in the Second International Conference on Advanced Data and Information Engineering (DaEng-2015), Bali, Indonesi, April 25-26. To be published in LNEE-Springer (IN PRESS).
Bio-Inspired Algorithm Optimization of Neural Network for the Prediction of Dubai Crude Oil Price Haruna Chiroma1* , Sameem Abdul-kareem1, Abdullah Khan2, Adamu I. Abubakar3, Sanah Abdullahi Muaz4 , Abdulsalam Ya’u Gital5 and Liyana Mohd Shuib1 Faculty of Computer Science and IT University of Malaya, Malaysia * Department of Computer Science Federal College of Education (Technical), Gombe, Nigeria 2 Software and Multimedia Centre Universiti Tun Hussein Onn Malaysia 3 Department of Information system International Islamic University of Malaysia 5 Department of Computer Science Universiti Teknologi Malaysia 1
[email protected],
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[email protected] {sameem,tutut}@um.edu.my Abstract. Previous studies proposed several bio-inspired algorithms for the optimization of Neural Network (NN) to avoid local minima and to improve accuracy and convergence speed. To advance the performance of NN, a new bio- inspired algorithm called Flower Pollination Algorithm (FPA) is used to optimize the weights and bias of NN due to its ability to explore very large search space and frequent chosen of similar solution. The FPA optimized NN (FPNN) was applied to build a model for the prediction of Dubai crude oil price unlike previous studies that mainly focus on the West Texas Intermediate and Brent crude oil price benchmarks. Results suggested that the FPNN was found to improve the convergence speed and accuracy of the cuckoo search algorithm and artificial bee colony optimized NN in the prediction of Dubai crude oil price. The Middle East region that produces a significant amount of crude oil relies on the Dubai crude oil price to benchmark prices for exporting crude oil to Asian countries. Our model could be of help to the Middle East region for monitoring possible fluctuations in the Dubai crude oil market price so as to take better decision related to international crude oil price. Keywords: Flower Pollination Algorithm; Neural Network; Dubai Crude Oil Price Benchmark; West Texas Intermediate Crude Oil Price.
1
Introduction
There is a significant positive relationship between grain price and the prices of crude oil [1]. Therefore, fluctuation in the crude oil market can affect the prices of the grains. This implies that whenever the crude oil prices increases, the price of the grains can also increase. This can contribute to deficiencies in the food supply
because poorer nations cannot have the economic power to supply enough grains to their people. Thus, trigger hunger and possibly lost of human life for since food is required for human survival. The crude oil price is directly proportional to the cost of crop production, transportation, price of fertilizer, and fuel [1]. The increase in the prices of crude oil can significantly lead to serious patronage of the bio-fuel market, which in turn create hunger in poor countries and the crude oil imports of the poor countries can as well be affected negatively [2]. Crisis in the crude oil market created by Suez crises in 1956 – 1957, prompted shortage of gasoline, which causes cut in motoring, reduction in work weeks and threats of job cuts in automobile industries. In the USA, exportation of goods and services start diminishing and it was responsible for the 1957 USA economic recession. The production cost of the economy also well as the price of energy inputs increases which affect profit margins. In Britain, 70% of automobile services were closed down, driving on Sunday in Netherland, Switzerland and Belgium were banned and rationing was imposed in Britain, Denmark and France [3]. Many countries heavily depend on the international crude oil price benchmarks for the formulation of development frameworks and estimation of expected government revenues. For example, in Oman, 86% of revenue generated is derived from the sales of crude oil. Almost half of the Gross Domestic Product (GDP) in Kuwait and 70% of revenue derived are from the sales of crude oil. An estimated 90% of the Saudi Arabia economy depends on crude oil sales. The oil and gas account for 52% of the national budget of the Russian government. In Iran, 50% to 60% of the government revenue is derived from crude oil. In Nigeria, 96% government revenue is from crude oil sales, etc. [4]. Therefore, any significant crisis in the crude oil market can cause significant budget deficits in these countries [5], and can lead the world into economic recession [6]. Governments of countries require crude oil benchmarks for the formulation of prices related crude oil export/import. The formulation of the prices is based on reference to a particular crude oil price benchmark because the crude oil prices differ in different places in the world depending on the location. The availability of numerous types of crude oil makes buyers and sellers to price the crude oil at a discounted rate with reference to a certain benchmark. However, West Texas Intermediate (WTI), Brent and Dubai (see Figure 1) are the major crude oil benchmarks for formulating international oil pricing system [7]. To the best of our knowledge, prediction of crude oil price based on soft computing methodology mainly focuses on the WTI and Brent crude oil price benchmarks. The prediction of Dubai crude oil price is scarce despite the fact that in the Middle East, Dubai crude oil is the reference benchmarks for exporting crude oils to Asia [7]. Also, the Middle East region produces a significant amount of crude oil to the world [4]. The training of Neural Network (NN) using a new bio-inspired algorithm called Flower Pollination Algorithm (FPA) is scarce in the literature. In this paper, we propose to optimize the weights and bias of the NN using the FPA to build a model for the prediction of Dubai crude oil price in order to circumvent the possibility of being stuck in local minima and to improve accuracy and convergence speed. This can add a new soft computing method of oil prediction based on Dubai crude oil price benchmark to the existing WTI and Brent soft computing prediction methods. The PFA is chosen because the PFA has shown
improvement over the state of the art established bio-inspired algorithms such as genetic algorithm [8] particle swarm optimization [9], and Bat algorithm [10].
2
Related Work
Almost all the crude oil that is traded outside the USA and the Far East makes references to Brent crude oil price benchmarks while in the USA, the WTI is referenced as the benchmark. The WTI trades light/sweet crude oils as well as Brent but WTI sulfur content (0.24%) is slightly less than the Brent sulfur content (0.37%) making it better than the Brent. Dubai trades sour/heavy crude oil containing 2% of sulfur in the crudes [7]. Brent combined crude oil from 15 separate crude oil fields located in the North Sea [11]. Figure 1 showed the crude oil prices of the WTI, Brent and Dubai benchmarks between May 1987 to December, 2011. Researchers applied soft computing methods to propose models for the prediction of crude oil price. For example, Shu-ping et al. [12] decomposed WTI crude oil price data using empirical mode decomposition. Subsequently, a multi scale integrated model was created using NN, support vector machine (SVM) and statistical methods. The model was applied to predict WTI crude oil price. Shabri and Samsudin [13] used particle swarm optimization to optimized the parameters of the multiple linear regression to build a model for the prediction of WTI crude oil price. Similarly, Shabri, and Samsudin [14] integrated discrete wavelet transform and NN to build a model for the prediction of WTI and Brent crude oil price. Chiroma et al. [15] Applied the hybrid of NN and GA for the prediction of WTI crude oil price to deviate from the limitations of the backpropagation NN to improve prediction accuracy. It was found that the hybrid of NN and GA improved the prediction accuracy of the WTI crude oil price.
Figure 1: WTI, Brent, and Dubai crude oil price benchmarks A model based on Neuro Fuzzy NN with a robust performance [16] than the NN was used to build a model for the prediction of WTI and Brent crude oil price [17]. To improve convergence speed, an orthogonal wavelet and support vector machine were hybridized to create a model for the prediction of WTI crude oil price [18]. Gabralla and Abraham [19] proposed a multi step process of modeling to predict WTI crude oil
price. The steps include: feature selection, data partition and analysis. Multi-Layered Perceptron, Sequential Minimal Optimization for regression, Isotonic Regression, Multilayer Perceptron Regressor, Extra-Tree and Reduced Error Pruning Tree were the models proposed in the study. The models were applied to predict WTI crude oil price. In another study, the effectiveness of SVM kernel functions was investigated in WTI crude oil price to broaden the theoretical understanding of the SVM kernel functions. It found that the wave kernel function performs better than the other kernel functions [20]. Chiroma et al. [21] predicted WTI crude oil price based on organization for economic co – operation and development (OECD) inventories using co-active Neuro-fuzzy inference systems. In order to enhance the effectiveness of the artificial intelligence techniques, an ensemble machine learning approach was build for the prediction of crude oil price [22]. The review of the applications of soft computing methods in the prediction of crude oil price up to 2012 was covered in [2324]. The reviews showed that researchers mainly focused on the WTI and Brent crude oil price benchmarks for the prediction of crude oil price. 3. Proposed Methods 3.1 Flower Pollination Algorithm Yang [25] emulated the characteristic of the biological flower pollination in flowering plant to develop FP based on the rules listed as follows: 1. The global pollination processes are biotic and cross pollination in which the pollen transporting pollinators performs the levy flight. 2. Local pollination are viewed as abiotic and self pollination. 3. Reproduction probability is considered as flower constancy which is proportional to the resemblance of two flowers concerned. 4. The switching probability controlled both the local and global pollination p [0, 1]. Local pollination can have fraction p that is significant in the entire processes of the pollination because of physical proximity and wind. The plant can possess multiple flowers and every flower patch typically emits millions or even billions of pollen gametes in real life pollination practice. To simplify the proposed algorithm development, it was assumed that each plant has a single flower and each flower emit only a single pollen gamete. This resulted to the elimination of the need to differentiate a pollen gamete, plant or solution to a problem. This means that a solution xi to a problem is equivalent to a flower and pollen gamete. The major stages in the design of SFPA are global and local pollination. In the global pollination, the pollens of the flowers are moved by pollinators e.g. insects and pollens can move for a long distance since the insects typically fly for a long range of distance. This process guarantees pollination and reproduction of the fittest solution represented as g*. The flower constancy can be represented as:
xit 1 xit L( xit g* ) From Eq.(1),
(1)
xit , t, g* and L are pollen i or solution vector xi , iteration, the best
solution found in the current generation or iteration and strength of the
pollination(step size) respectively. The levy flight is used to represent movement of the insects, thus, L > 0 from a Levy distribution
L~
( ) sin( / 2) 1 , ( s so 0). s1
(2)
From Eq. (2), Γ(λ) represent the standard gamma function, and the distribution is valid for large steps s > 0. From rule 2, the local pollination and flower constancy is expressed as:
xit 1 xit ( xtj xkt ). where
(3)
x tj and xkt represent pollen from different flowers of the same species of
plant. Thus, mimic the flower constancy in a limited neighborhood. The p is used to switch between common global pollination to the intensive local pollination. The effectiveness of the PFA can be attributed to the following two reasons: (1) Insect pollinators can travel in long distances which enable the FPA to avoid local landscape to very large search space (explorations). (2) Ensure the similar species of the flowers are consistently chosen frequently, which guarantee fast convergence to the optimal solution (exploitation). 3. 2 Dataset The Dubai crude oil price dataset in $/barrel was collected on a monthly frequency because variables such as GDP can only be found on monthly frequency and using monthly dataset typically avoid the empty space created due to public holidays and weekends [26]. The dataset was collected spanning from May 1987 to December 2011 as shown in Figure 1. The window for the data was as a result of data availability of other variables such as OECD Crude Oil Ending Stocks, OECD Crude Oil Consumption, Organization of the Petroleum Exporting Countries (OPEC) Crude Oil Production World Crude Oil Production, US Crude Oil Supplied etc. That’s why the window was chosen since data availability determine the window of the collection period [27]. We transformed the dataset between -1 to 1 to improve both accuracy and convergence speed. The dataset was partition into 80% for training and 20% for evaluating the generalization ability of the model (test).
3. 3 Design of the Proposed FPNN The FPA was applied for optimization of the NN weights and bias. The number of the pollen gametes (n) represents the number of NN with bias. Before execution of the FPA to start running, FPA and the NN require initialization of parameters since they are both sensitive to parameters setting. The p of the FPA was set to 0.15 realized after trial-and-error, n was set to 20, dimension was set to 300 and maximum generation was 1000. The input neurons of the NN were 10 and the output neuron was set to one because the dataset contain 10 input attributes and the output target
attribute (Dubai crude oil price) was one. The hidden layer neurons were 5 realized after experimentation with small amount of dataset before implementation with the full size of the dataset in the actual experiment. The activation function in the hidden layer and output layer was logsig and linear respectively. Mean square error (MSE) was the fitness function for measuring the performance of the algorithms in the prediction of the Dubai crude oil price. The PFA was iterative run to explore and search for the optimal solution in the search space. The PFA searches for the FPNN with the minimum fitness value, optimal weights and bias as the best model for the prediction of Dubai crude oil price. The FPNN was run 10 times to ensure consistent findings and because there is no guarantee that the meta-heuristic algorithm can always produce the same results [28]. The FPNN was fixed to terminate if the maximum generation is reached. The best FPNN emerged as the optimal solution at the end the generation. The average of the CPU processing time and fitness values of the FPNN was computed over 10 runs for both training and testing. For comparison purpose, the artificial bee colony (ABC) with the following parameters: colony size of 50 adopted from [29] and cuckoo search algorithm (CS) with levy flight size and probability of the bad nest to be abandoned of 1 and 0.25 adopted from [30]. The experiment was repeated with the ABC and the CS to optimize the NN weights and bias to build ABCNN and CSNN respectively, for the prediction of Dubai crude oil price. The results were compared with that of the FPNN.
4. Results and Discussion The experiments described in the preceding section were implemented in MATLAB R2012b simulator on a machine (Intel Core (TM) 2 Quad CPU 2.33GHz, RAM 2GB, 32-bit operating system). The experiment has proven that it is possible to train a NN using bio-inspired algorithms. The numerical results of the prediction of Dubai crude oil price using FPNN, CSNN, and ABCNN are presented in Tables 1–3. The performance of the FPNN on training and test dataset were compared to the performance of the CSNN and ABCNN. In Tables 1 – 3, the first column represents the number of experimental trials, second column is the computation time in seconds during the training phase of the modeling process. The third column is the accuracy achieved by the algorithms (MSE) on training dataset. The fourth and fifth column is computation time, and accuracy of the algorithms of the test dataset. In the Tables 1 3 averages of cpu time and mse were computed over 10 experimental trials (Trials). Table 1. The performance of FPNN in the prediction of Dubai crude oil price Training Trials
Cpu Time
Test MSE
Cpu Time
MSE
1
4.583956
0.000378
4.551624
0.0000891
2
4.588453
0.000325
4.555924
0.0000876
3
4.592949
0.000312
4.560224
0.0000856
4
4.598529
0.000312
4.564550
0.0000898
5
4.632307
0.000312
4.568912
0.0000879
6
4.608011
0.000312
4.573195
0.0000873
7
4.612815
0.000393
4.577564
0.0000898
8
4.617398
0.000313
4.582168
0.0000981
9
4.622249
0.000305
4.586595
0.0007558
10
4.627053
0.000311
4.590875
0.0000898
Average
4.608372
0.000327
4.571163
0.0001560
Table 1. The performance of CSNN in the prediction of Dubai crude oil price Training
Test
Trial
Cpu Tim
MSE
Cpu Time
MSE
1
828.3859
0.000113
813.9725
0.000377
2
828.6547
0.000112
814.2331
0.000363
3
828.9231
0.000155
814.5080
0.000363
4
829.1863
0.000113
814.7643
0.000377
5
829.4590
0.000113
815.0238
0.000377
6
829.7231
0.000112
815.2787
0.000377
7
829.9892
0.000114
815.5436
0.000332
8
830.2491
0.000113
815.8014
0.000371
9
830.5134
0.000112
816.0661
0.000306
10
830.7766
0.000113
816.3244
0.000373
Average
829.5860
0.000117
815.1516
0.000362
3
Table 1. The performance of ABCANN in the Dubai crude oil price prediction 4
Training
Test
Trial
Cpu time
MSE
Cpu Time
MSE
1
755.4894
0.005159
753.5781
0.011184
2
755.7341
0.004159
753.8391
0.011188
3
755.9783
0.009075
754.0968
0.011146
4
756.2273
0.005346
754.3556
0.011146
5
756.4739
0.005146
754.6207
0.011159
6
756.7251
0.005587
754.8897
0.011189
7
756.9670
0.005159
755.147
0.011183
8
757.2096
0.005725
755.431
0.011146
9
757.4529
0.005153
755.6966
0.011184
10
757.6976
0.005346
755.9576
0.011185
Average
756.5955
0.005586
754.7612
0.011171
It can be observed that the result of all the algorithms in Tables 1 – 3 differs from one trial to another despite running the same algorithm on the same dataset. This is expected because meta-heuristic algorithms do not produce the same result when executed in different trials unlike deterministic algorithms [31]. The ABCNN converges to the optimal solution faster than the CSNN on both training and test dataset. However, the CSNN is more accurate than the ABCNN in terms of MSE on training and test dataset. Results in Tables 1-3 indicated that the proposed FPNN performs better than the CSNN and ABCNN in terms of average CPU time and MSE. The performance of the FPNN is consistent because it performs better than the CSNN and ABCNN in both training and test dataset. The performance of FA in this study is not surprising because FA were found to perform better than established biologically inspired algorithms such as GA and PSO in solving optimization problems [25]. The best explanation for the possible reason why the FPNN performs better than the CSNN and ABCNN in accuracy could probably because of the FPA ability to explore very large search space which may have contributed in searching for the optimal NN weights and bias. The possible reason why the FA converges faster than CS and ABC can probably be attributed to frequent chosen of a flower of the same species which could have makes the FA to converge to the optimum solution very fast and consistent. It was stated that no single algorithm is suitable for solving all types of problems [32]. Thus, possibly, the application of FPNN in different domain could produce contradictory results. The FPNN proposed in this paper can be reliable, consistent and promising in the prediction of Dubai crude oil price.
5. Conclusion This study has proven that it is possible to optimize the weights and bias of the NN using FP without being stuck in the local minima to build a model for the prediction of Dubai crude oil price. The proposed FANN was able to improve the accuracy and convergence speed of the prediction. This has added to the already discussed biologically inspired algorithms that were used for the optimization of NN weights and bias. The Middle East region that relies on the Dubai crude oil price in benchmarking price for exporting crude oil could use our model for the prediction of possible fluctuations in the Dubai crude oil price market. In addition, government in the Middle East region can also find our proposed model useful in the formulation of a national framework and international crude oil pricing system. Our prediction model is not to replace the human expert, but to complement their efforts in reaching a better decision that could lead to development and avoid a budget deficit. This study has added a novel method of crude oil price prediction based on Dubai crude oil price benchmark to the literature. As such, the methods of prediction in the three major crude oil price benchmarks using soft computing approach can be found in the literature. Further work will involve the inclusion of WTI and Brent crude oil price benchmarks to further expand the general application of the model in the major world crude oil price benchmarks.
Acknowledgment. This work is supported by University of Malaya High Impact Research Grant no vote UM.C/625/HIR/MOHE/SC/13/2 from Ministry of Higher Education Malaysia.
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