Performance Evaluation of Sigmoid Functions with Hybrid Computational Method for Optimizing Lemon Grass Oil Production
Brajesh Kumar Singh1
Akash Punhani2
Department of Computer Science & Engineering F.E.T., R.B.S. College, Bichpuri Agra, India
[email protected]
Department of Computer Science & Engineering F.E.T., R.B.S. College, Bichpuri Agra, India
[email protected]
Shafiqulabidin3
Ritu Nigam4
Department of Information Technology Al Musanna College of Technology (Ministry of Manpower) Sultanate of Oman
Department of Computer Science & Engineering BMAS Engineering College Agra, India II.
Abstract— Two different Approaches are used to Optimize Lemon Grass Oil Production. Oil Production is compared and Production-Nutrient ratio comparison also shows that Logistic function is giving best result for production-nutrient ratio. So logistic Function proved to be better for optimizing results in our case.
In this paper, our main target is to find out the comparison of two different sigmoid functions based computational methods to solve the problem and these methods are applied on different combinations of N, P and Zn for better growth and oil production of lemon grass under salt stressed environment. Dose of K2O was common in all treatments. Many agricultural data are available which show the relationship between quantity of fertilizers used and lemon grass oil production obtained. We will use this data to develop two different mathematical models for predicting the lemon-grass oil production for a given combination of different fertilizers and then apply genetic algorithm for finding better solution, and finally will evaluate the performance of the two different function based computational methods.
Keywords- Back propagation neural network, fertilizers, Genetic algorithm, oil production.
I.
SOLUTION FOR A PROBLEM
INTRODUCTION
A Wide area in India comprising of Rajasthan, a part of Gujarat, Punjab, Haryana, Delhi, Uttar Pradesh, Madhya Pradesh, Maharashtra, Mysore, Andhra Pradesh and Tamil Nadu is arid or semi-arid. In such areas due to insufficient precipitation, irrigation is essential to meet the requirement of crop plants. Out of 23 million hectares total cropped area of the Uttar Pradesh about 7 million hectares, land is irrigated by various sources of irrigation and approximately 4 million hectares land is irrigated by under ground water sources. Most of the irrigation waters of semi-arid tract of Agra region have been reported to be of saline in nature. Continuous use of such waters would develop salinity hazards and salt sensitive or moderately tolerant plants grown under such condition show a remarkable decline in crop yield[1,2,3,4,5,7]. The maintenance of an optimum level of fertility (A suitable composition of fertilizers N+P2O5+K2O) is essential for better crop production in normal as well as under salt stressed conditions [13, 14]. For maintaining optimum level of fertility, farmers use fertilizers and perform test manually on a given soil. Perfect combinations of fertilizers are needed to increase the lemon-grass oil production. It is not easy for a farmer to perform manual test on every combination of fertilizers so that he can identify the perfect combination.
III.
BRIEF ABOUT METHODS FOR APPLICATION
As we are working on two different methods for same application so first of all we must know about the basics of methods and their workings. Activation function for a back propagation net should have several important characteristics: it should be continuous, differentiable, and monotonically non-decreasing. Furthermore, for computational efficiency, it is desirable that its derivative be easy to compute. For the most commonly used activation functions, the value of the derivative (at the particular value of the independent variable) can be expressed in terms of the value of the function (at the value of the independent variable). Usually, the function is expected to saturate, i.e., approach finite maximum and minimum values asymptotically. We have taken the two types of sigmoid functions into consideration as given below, 1. Logistic Activation Function 2. Hyperbolic Tangent Activation
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The logistic Function, a binary sigmoid function with range from 0 to 1, is often used as the activation function for neural nets in which the desired output values either are binary or are in the interval between 0 and 1(Fig. 1)
problems. First pioneered by John Holland in the 60s [9]. Genetic Algorithms have been widely studied, experimented and applied in many fields. In the literature, many papers have been published with research detailing new algorithms for solving single objective and multi objective optimization problems [10,11,12,17,18]. Genetic algorithm uses these three operators (Selection, Crossover and Mutation) to search the optimum value of a solution. B. Neural Network: An artificial neural network (ANN), also called neural network (NN) is an Inter connected group of artificial neurons that uses a mathematical or computational model for information processing based on a connectionist approach to computation. In most cases an ANN is an adaptive system that changes its structure based on external or internal information that flows through the network. In more practical terms neural networks are non-linear statistical data modeling or decision making tools. They can be used to model complex relationships between inputs and outputs or to find patterns in data. An artificial neural network involves a network of simple processing elements (artificial neurons) which can exhibit complex global behavior, determined by the connections between the processing elements and element parameters[6,8]. The back propagation algorithm was probably the main reason behind the re-popularization of neural networks after the publication of "Learning Internal Representations by Error Propagation" in 1986 (Though back propagation itself dates from 1974). The original network utilized multiple layers of weight-sum units of the type f = g (w'x + b), where g was a sigmoid function or logistic function such as used in logistic regression. Training was done by a form of stochastic steepest gradient descent. The employment of the chain rule of differentiation in deriving the appropriate parameter updates results in an algorithm that seems to 'back propagate errors', hence the nomenclature. It is a supervised learning method, and is an implementation of the Delta rule. It requires a human teacher, who knows, or can manually calculate, the desired output for any given input. It is most useful for feed-forward networks (networks that have no feedback, or simply, that have no connections that loop). The term is an abbreviation for "backwards propagation of errors". Back propagation requires that the transfer function used by the artificial neurons (or "nodes") be differentiable.
Figure-1: Logistic Function
It can be defined as f(x) = 1/(1+exp(- σ x)) (1) where σ is called the steepest parameter (also known as slope parameter). If f(x) is differentiated we get, f '(x) = σ f(x) [1- f(x)]. (2) Where Logistic function has been created for Dotted lines σ =3 and Hard lines σ = 1. The hyperbolic tangent function, a bipolar sigmoid function has the desired range of output values between -1 and 1 (Fig. 2).
Figure-2: Hyperbolic Function,
It can be defined as, b(x) = 2f(x) – 1 b(x) = 2 * (1/(1 + exp(- σ x))) -1 = (2 – 1 – exp(- σ x))/ (1+ exp(- σ x)) b(x) = (1- exp(- σ x)) / (1+ exp(- σ x))
(3) (4)
IV.
PROPOSED ALGORITHM FOR SOLVING PROBLEM
Algorithm for solving the same problem by two different activation functions can be explained in following steps[15,16,19,20]. 1. Train the neural network by using back propagation algorithm for the experimental Data 2. Set Generation counter equal to one. 3. Generate random Population (initial Population) N (P0) by assigning the binary string to different parameters.
A. Genetic Algorithms: The research on Genetic Algorithm has significantly concentrated and grown in recent years. The basic concept of GA is designed to simulate processes in natural system necessary for evolution, specifically those that follow the principles first laid down by Charles Darwin of survival of the fittest. Genetic Algorithms (GA) is adaptive heuristic search algorithm which is used to solve optimization
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4. 5. 6.
By applying proposed algorithm at same set of experimental data we generated and selected best twenty results given in table-2 and table-3,
Calculate the Fitness of population by using trained neural network. Apply selection, crossover and mutation to generate next Population. Increment of Generation counter by one. If total number of generation is greater than generation counter then repeat step 4-5 else stop. V.
Table-2 (Logistic activation function based proposed algorithmic data)
RESULT ANALYSIS
The data collected by Field experiments are stored in Table1.The input of data is different combination of fertilizers and output is oil production. Table: 1(Experimental Result)
Parameters for training a back propagation neural network, Number of Input Number of Output Neurons Iterations Total Error Momentum Learning Rate Tolerance Correctness
: : : : : : : : :
3 1 7 50000 1.986 0.2 0.3 95% 93%
The parameters of Genetic algorithm are explained below, Chromosomes sizes for N, P2O5 and ZnSO4 are 5, 5 and 5 respectively. No. of initial Populations : 10 No. of generations : 10 Random Seed : 0.15 Probability of Cross over : 0.7 Probability of Mutation : 0.3
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Table-3 (Hyperbolic tangent function based Proposed Algorithmic data set)
Comparison of Oil Production for two activation functions
Oil produc tion V a lue s
70 60
Hyperbolic tangent generated proposed algorithmic results results Logistic Function based proposed algorithmic results
50 40 30 20 10 0 1
3
5
7
9
11
13
15
17
19
number of data sets
Figure -3
Production-Neutrient Ratio comparison
Production-Neutrient ratio
0.40 0.35 0.30 0.25
Hyperbolic tangent results logistic function results
0.20 0.15 0.10 0.05 0.00 1
3
5
7
9
11
13
15
17
19
Number of Data sets
Figure-4
We use following parameters for training a back propagation neural network, Number of Inputs Number of Output Neurons Iteration Total Error Momentum Learning Rate Tolerance Correctness
: : : : : : : : :
Figure-3 shows the comparison of all sets of combinations with two different methods and it is seen that for all combinations, Logistic function based method is generating better results. Even in figure-4, Logistic function is giving best result for production-nutrient ratio. So logistic Function seems to be better for optimizing results in our case.
3 1 7 50000 2.086 0.2 0.3 95% 90%
VI.
CONCLUSION
Lemon Grass is an aromatic Grass and its cultivation is gaining importance because its oil is cheaper and rich source of Vitamin ‘A’. Numerous treatments have been tried under field conditions to suggest best possible solution for increasing the net return of the farmers. Simultaneously, field data have been used to predict more profitable nutrient applying Logistic and Hyperbolic Tangent activation function based proposed algorithm. Comparatively Logistic activation function based method proved most suitable to suggest appropriate combination of nutrients for producing Oil under present set of conditions.
The parameters of Genetic algorithm are explained below, Chromosomes sizes for N, P2O5 and ZnSO4 are 5,5 and 5 respectively. No. of initial Populations : 10 No. of generations : 05 Random Seed : 0.15 Probability of Cross over : 0.7 Probability of Mutation : 0.3
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Secondly, unnecessary expenditure on field trial may be saved and best possible predicted solution may be preferred even in the due course of time.
[13]
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M.A. Abdel-Salam, and S.A EI-Nour, “Interaction of Saline Water irrigation and Nitrogen fertilization on crop production in Calcareous Soils”, United Arab Rep. J. Soil Sci.,1965, 5:121-34. [2] J.S. Al- Abidi, and Z.S. Al-Rammah, “ The Effect of Soil Salinity on Cereal Crop in relation to Nutrients status of soil in the lower Mesopotamian”, Intern. Symp. Salt affected Soils, Karnal, 1980, 409-417. [3] A.K. Singh, and B. Pal, “Effect of Saline Water irrigation on Composition and Uptake of Nutrients by Palmarosa”, Indian Perfumer, 2000, 44 (1):29-33. [4] A.K. Singh, and B. Pal, “Effect of Chloride and Sulphate Salinity of Water on Growth, Herb, Dry metter and Oil Yield of Palmarosa”, Indian Perfumer, 2000, 44(3): 163-166. [5] L. Singh, and B. Pal, “Effect of Water Salinity and Fertility Levels on Yield and Yield characters of blonde psyllium”, Res. On Crops, 2000, 1(1):85-90. [6] K. Fukushima, “Cognitron: A Self-Organizing Multilayered Neural Network”, Biological Cybernetics, 1975, 20:121–136. [7] V. Singh, and J.S. Tomar, “Integrated Nutrient Management in rice wheat system”, Indian J. Agron., 1994,33(3):145-46. [8] Holland, J. H., Adoption in Natural and Artificial Systems, Ann Arbor: University of Michigan Press, 1975. [9] Goldberg, D.E., Genetic Algorithms for Search Optimization and Machine Learning, Reading, MA: Addison-Wesley, 1989. [10] D.E. Goldberg, and J. Richardson, “Genetic Algorithm with Sharing for Multimodel Function Optimization”, In Proceedings of the First International Conference on Genetic Algorithms and Their Applications, 1987, pp. 41-49. [11] D.E Goldberg, K. Deb, and D. Theirens, “Toward a better understanding of mixing in genetic algorithms”, Journal of SICE, 1993, 32, pp. 10-16. [12] R. Everson, and J. Fieldsend, “Multiobjective Optimization of Safety Related Systems: An Application to Short-Term Conflict Alert”,
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IEEE Transactions on Evolutionary Computation, 2006,Vol. 10, No. 2, pp. 187-198. Singh, Uma, Effect of Fertility levels and Quality Of Irrigation Water on The Growth,Compositon and Oil Production of Lemon Grass (Cymbopogon Flexuosus),.Ph.D. Thesis, Dr.B.R.Ambedkar Univ., Agra, 2001. B.R. Tripathi, and B. Pal , “The quality of irrigation water and its effect on soil characteristics and on the performance of wheat”, .intern. symp. Salt affected soils ,Karnal,1980 ,PP 376-81. Combining neural network, genetic algorithm and symbolic learning approach to discover knowledge from databases Zhou Yuanhui; Lu Yuchang; Shi Chunyi Systems, Man, and Cybernetics, 1997. apos;Computational Cybernetics and Simulationapos;., 1997 IEEE International Conference on Volume 5, Issue , 12-15 Oct 1997 Page(s):4388 - 4393 vol.5. Combining Neural Networks and Genetic Algorithms to Predict and Reduce Diesel Engine Emissions Alonso, J.M. Alvarruiz, F. Desantes, J.M. Hernandez, L. Hernandez,V. Molto, G. High Performance Networking & Comput. Group, Univ. Politecnica de Valencia. This paper appears in: Evolutionary Computation, IEEE Transactions on Publication Date: Feb. 2007, Volume: 11, Issue: 1 On page(s): 46-55 Brajesh Kumar Singh, K. K. Mishra ,Akash Punhani “Multiobjective Optimization of Rotary Furnace Using NSGA”Proceedings of 2009 Computing Conference(IACC IEEE international Advance 2009) PP. 565-568., ISBN: 978-981-08-2465-5 K.K. Mishra, Brajesh Kumar Singh, Akash Punhani and Lavkush Sharma “Optimizing melting Rate and Fuel Consumption of Rotary Furnace Using NSGA-II” in proceeding of CEC 2008, IEEE press, 2008,P.P. 3784-3788,ISBN 978-1-4244-1823-7 Mishra, K.K., Singh, Brajesh Kumar, Punhani,Akash and Singh, Uma.(2009) Combining Neural Networks and Genetic Algorithms to Predict and to Maximize Lemon Gras Oil Production. Proceedings of IEEE second international Joint Conference on Computational Sciences and Optimization(CSO 2009) held at Sanya, Hainan, China, 24-26 April 2009. PP. 297-299. A. K. Dubey (2008), A hybrid approach for multi-performance optimization of the electro-chemical honing process, The International Journal of Advanced Manufacturing Technology, Springer London, ISSN:0268-3768 (Print) 1433-3015.
