Indonesian Journal of Electrical Engineering and Computer Science V ol. 8, No . 1, October 2017, pp . 27 35 DOI: 10.11591/ijeecs .v8.i1.pp27-35 27 Optimisation of Bioc hemical Systems Pr oduction using Hybrid of Ne wton method, Diff erential Ev olution Algorithm and Cooperative Coe v olution Algorithm Mohd Arfian Ismail *1 , Vitaliy Mezhuy e v 1 , K ohbalan Moor th y 1 , Shahreen Kasim 2 , and Ashraf Osman Ibrahim 3,4 1 F aculty of Computer Systems and Softw are Engineer ing, Univ ersiti Mala ysia P aha ng, P ahang, Mala ysia 2 Soft Computing and Data Mining Centre , F aculty of Computer Science and In f or mation T echnology , Univ ersiti T un Hussein Onn, Johor , Mala ysia 3 F aculty of computer Science and Inf or mation T echnology , Alzaiem Alazhar i Univ ersit y , Khar toum Nor th 13311, Sudan 4 Ar ab Open Univ ersity , Khar toum, Sudan *Corresponding author , e-mail: arfian@ump .edu.m y Abstract This paper present a h ybr id meth od of Ne wton method, Diff erential Ev olution Algor ithm (DE) and Cooper ativ e Coe v olution Algor ithm (CCA). The proposed method is used to solv e the optimisation prob lem in optimise the production of biochemical systems . The prob lems are maximising the biochemical systems pro- duction and sim ultaneously minimising the total amount of chemical reaction concentr ation in v olv es . Besides that, the siz e of biochemical systems also contr ib uted to the prob lem in optimising the biochemical systems production. In the proposed method, the Ne wton method is used in dealing biochemical system, DE f or opti- misation process while CCA is used to increase the perf or mance of DE. In or der to e v aluate the perf or mance of the proposed method, the proposed method is tested on tw o benchmar k bioche mical systems . Then, the result that obtained b y the proposed method is compare with other w or ks and the finding sho ws that the proposed method perf or ms w ell compare to the other w or ks . K e yw or ds: Ne wton method, Diff erential Ev olution Algor ithm, Cooper ativ e Coe v olut ioan Algor ithm, Biochem- ical systems , Computational Intelligence Cop yright c 2017 Institute of Ad v anced Engineering and Science . All rights rese r ved. 1. Intr oduction Biomass is a good alter nativ e to produce the biofuel. This is because the biomass is a plant-based resource that can be used to replace the limited biofuel. No w ada ys , the demand of biomass is increase where it leads to competition of land and plant [1, 2, 3]. Recently , man y re- searchers ha v e f ocus on manipulating the microorganism activity in order to produce the biomass r ather than really on increasing the land a nd plant. This is because manipulating the microorgan- ism is f ar cheaper and reduce time r ather than increase the land or plant. But, the biomass that e xtr acted from manipulating the microorganism activity has a limitation where the production is lo w [4, 5]. Due to that, man y researcher ha v e f ocus on optimisation the production of biomass . One w a y to impro v e the biomass production is the optimisation of biochemical systems production b y fine-tuning the reactions v alue in biochemical systems . The optimisation of the production in biochemical systems can be perf or med because the biochemical system can be represented b y a nonlinear equations system. In the nonlinear equa- tions system, each v ar iab le is used to represent each reactions of biochemical systems . The process of fine-tuning the reactions v alue can be perf or med b y change the v ar iab les v alue . Fine- tuning process of the v ar iab les in nonlinear equat ions system becomes a hard task if in v olv es a large biochemical systems . This is because a large biochemical systems contains with man y reac- tions and in v olv es man y inter action betw een reaction. In order to o v ercome this situation, this paper Receiv ed Ma y 6, 2017; Re vised September 2, 2017; Accepted September 15, 2017 Evaluation Warning : The document was created with Spire.PDF for Python.
28 ISSN: 2502-4752 present an automated method to fine-tuning the v ar iab les in nonlinear equations system. The pro- posed method h ybr id the Ne wton method, Diff erential Ev olution Algor ithm (DE) and Cooper ativ e Coe v olution Algor ithm (CCA). In optimisation of biochemical systems production, the biochemical systems can be mod- elled b y mathematical model, which is gener alised mass action (GMA) model. Dur ing the opti- misation, there are se v er al constr aints in v olv e which are steady state condition and reaction con- centr ation constr ain t. The steady stat e condition mak e all the equations in GMA model equal to 0 where it mak e the optimisation process become the process of solving a nonlinear equations system. There are v ar ious methods that can be used in solving a nonlinear equations system such as Ne wton method, Secant method and Bisection method. In this study , Ne wton method is used because Ne wton method is f ast in solving the system [6], simple to used [7, 8] and v er y widely used in solving nonlinear equations system [9, 10, 11]. F or fine-tuning the reactions v alue in biochemical systems , an optimisation method is needed. The reason of fine-tuning is to disco v er the suitab le v alue that produce the high pro- duction of biochemical systems . The fine-tuning process become complicated when in v olv es a comple x biochemical system where contains with man y reactions and in v olv es man y inter action betw een them. Because of that, an optimisation method is need. There are v ar ious method can be applied such as genetic algor ithm (GA), DE, and P ar ticle Sw ar m Optimisation (PSO) algor ithm. This study used DE because DE off er se v er al adv antages such as DE in v olv es f e w par ameters [12, 13] and DE is more rob ust on se v er al prob lems when compare to other [14]. In the optimisation of biochemical systems production, tw o f actors that need to be con- sidered which are the production and the total of chemical reaction concentr ations in v olv es . In addition, a large of biochemical systems th at content with man y reactions and inter action betw een them also contr ib ute to the difficulty in optimisation process . Because of these f actors , this mak e the representation of the solution become comple x. This mak e the optimisation proses become hard and complicated. In order to o v ercome these issues , this study use CCA in order to simplify the representation of the solution b y dividing the complete into m ultiple sub-solutions . In this paper , the h ybr id of Ne wton method, GA and CCA is proposed and discuss in detail. The aim of the proposed method is to solv e the prob lems in optimisation of biochemical systems production which are to impro v e the biochemical systems production and at the same time reduce the total of chemical reaction concentr ations in v olv es . In the proposed method, the function of Ne wton method is to solv e the nonlinear equations system, DE is used in optimisation process where DE is used to fine-tuning process while CCA is utilised to impro v e the perf or mance of DE. In the f ollo wing section, the e xplanation of the proposed method is discussed in detail. Then, the model and e xper imental data is descr ibe in detail where tw o benchmar k biochemical systems are used namely the Saccharom yces cere visiae ( S .cere visiae ) pathw a y and the Escher ichia Coli ( E.coli ) pathw a y . After that, the e xper imental result and discussion is presented bef ore this paper w as conclude in conclusion. 2. A Hybrid Method of Ne wton Method, Diff erential Ev olution Algorithm and Cooperative Coe v olution Algorithm This section is about the discussion of the proposed method. The proposed method h ybr id Ne wton method, DE and CCA. In the proposed method, Ne wton method is utilised to deal with nonlinear equations system, DE is used in optimisation process and CCA is embodied into DE in order to impro v e the perf or mance of DE b y simplifies the chromosome representation. Figure 1 sho ws the proposed method in flo wchar t f or m. The detail steps in the proposed method are as f ollo ws: Step 1: Gener ate the initial solution. In the first step , the first gener ation of m solution is gen- er ated separ ately in n sub-population (the n umber of sub-population is equal to the n umber of v ar iab les that need to be tuned). The v ar iab le (in non linear equations system) is represented b y sub-chromosome . The sub-chromoso me is in binar y f or mat. The sub-chromosome is gener ated r andomly and in a specific f or mat (depends on the v alue of chemical reaction concentr ation). Step 2 : F or m the complete chromosome . The complete solution is f or m in this step b y combine all IJEECS V ol. 8, No . 1, October 2017 : 27 35 Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS ISSN: 2502-4752 29 Figure 1. The flo wchar of the proposed method sub-chromosomes from all sub-populations . The sub-chromosome is selected based on their fit- ness v alue where the sub-chromosome that has lo w est fitness v alue is select ed and then combine with other sub-chromosome from each sub-population. This is because the selection process is in- tended to minimise the total amount of chemical reaction concentr ation in v olv es . Figure 2 depicted the gener ation of sub-chromosome until the f or mation of complete chromosome . Step 3: Ev aluate the complete chromosome . In this step , the complete chromosome is decoded into v ar iab les f or m. At this stage , the Ne wton method is used in solving t he nonlinear equations system. Besides that, tw o ter mination conditions are applied which are; the maxim um n umber of gener ation is reach and all the chemical reaction concentr ation v alue is in their r ange . The process mo v e f orw ard to Step 6 if these conditions are meet, otherwise the process enter the ne xt step . Step 4: Decompose the complete chromosome . In this step , the complete chromosome is decom- posed into m ultiple sub-chromosomes . After that, all sub-chromosomes w ent bac k into their o wn sub-population f or reproduction process . Step 5: Pr oduce ne w gener ation. This step is intended to impro v e the solution b y producing the ne xt gener ation of the solution. This step happens in all sub-population. The m utation and crosso v er process are applied on all sub-chromosome . Step 6: Retur n the best solution. This is the final step . In this step , the best so lution is giv en. 3. Model and Experimental Data In order to test the perf or mance of the proposed method, tw o benchmar k biochemical sys- tems are used which are the optimisation of the ethanol production in S . cere visiae pathw a y and the optimization of the tr p biosynthesis in E. Coli . A J a v a prog r am based on J AMA v ersion 1.0.3 and jMetal [15] are used. The J AM A prog r am is used in dealing with nonlinear equations system while Optimisation of biochemical systems production using h ybr id of Ne wton method, ... (M.A. Ismail) Evaluation Warning : The document was created with Spire.PDF for Python.
30 ISSN: 2502-4752 Figure 2. The process of f or mation the complete chromosome jMetal f or optimisation process . The J AMA can be obtained from http://math.nist.go v/ja v an umer ics/jama/ and jMetal can be do wnloaded from http://jmetal.sourcef orge .net. The detail descr iption of tw o benchmar k biochemical systems are descr ibe in the ne xt sub section. 3.1. Optimisation of the ethanol pr oduction in Sacc har om yces cere visiae pathwa y The proposed method is used to optimise the ethanol production in S .cere visiae pathw a y . The detail descr iption of this pathw a y can be f oun d in [16]. In this pathw a y , the nonlinear equations system can be represented as f ollo ws: V in V H K = 0 V H K V P F K V C ar b = 0 V P F K V GAP D 0 : 5 V Gr o = 0 (1) 2 V GAP D V P K = 0 2 V GAP D + V P K V H K V C ar b V P F K V AT P ase = 0 where at steady state conditions , these chemical reaction concentr ations (denoted b y V ) ha v e the f ollo wing v alue: V in = 0 : 8122 X 0 : 2344 2 Y 1 V H K = 2 : 8632 X 0 : 7464 1 X 0 : 0243 5 Y 2 V P F K = 0 : 5232 X 0 : 7318 2 X 0 : 3941 5 Y 3 V C ar b = 8 : 904 10 4 X 8 : 6107 2 Y 7 (2) V GAP D = 7 : 6092 10 2 X 0 : 6159 3 X 0 : 1308 5 Y 4 V Gr o = 9 : 272 10 2 X 0 : 05 3 X 0 : 533 4 X 0 : 0822 5 Y 8 V P K = 9 : 471 10 2 X 0 : 05 3 X 0 : 533 4 X 0 : 0822 5 Y 5 V AT P a se = X 5 Y 6 IJEECS V ol. 8, No . 1, October 2017 : 27 35 Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS ISSN: 2502-4752 31 In this biochemical system, the ethanol production is giv en b y V P K and it became the fitness function of complete chromosome . This lead to the impro ving the production as f ollo ws: max F 1 ( v ) = V P K (3) F or the total of chemical reaction concentr ations in v olv es , it can be f or m ulated as f ollo w: min F 2 = 5 X j =1 X j + 6 X j =6 Y j (4) where the r ange of X is set betw een 0.2 to 1.2 and Y in the r ange of 0 to 50 [17, 18]. 3.2. Optimisation of the tr yptophan biosynthesis in Esc heric hia Coli pathwa y In this pathw a y , the proposed method is used to optimise the tr p production. Xiu et al. has e xplained in detail of this pathw a y[19]. F or this pathw a y , the nonlinear equations system can be f or m ulated as f ollo ws: V 11 V 12 = 0 V 21 V 22 = 0 (5) V 31 V 32 V 33 V 34 = 0 All reaction concentr ation (denoted b y V ) has the f ollo wing v alues at steady state condition: V 11 = 0 : 6403 X 5 : 87 10 4 3 X 0 : 8332 5 V 12 = 1 : 0233 X 1 X 0 : 0035 4 X 0 : 9965 11 V 21 = X 1 V 22 = 1 : 4854 X 2 X 0 : 1349 4 X 0 : 8651 12 (6) V 31 = 0 : 5534 X 2 X 0 : 5573 3 X 0 : 5573 6 V 32 = X 3 X 4 V 33 = 0 : 9942 X 7 : 0426 10 4 3 X 7 V 34 = 0 : 8925 X 3 : 5 10 6 3 X 0 : 9760 4 X 8 X 0 : 0240 9 X 3 : 5 10 6 10 The tr p production is giv en b y reaction V 34 thus it become the fitness function of the com- plete chromosome . This lead to the impro ving the production as f ollo ws: max F 1 = V 34 (7) F or the total of chemical reaction concentr ations in v olv es , it can be f or m ulated as f ollo w: min F 2 = 6 X j =1 X j + X 8 (8) where the r ange of X 1 to X 3 is betw een 0.8 to 1.2, X 4 betw een 0 to 0.00624, X 5 betw een 4 to 10, X 6 betw een 500 to 5000 and betw een X 8 0 to 1000 [17, 18]. 4. Experimental results and discussions In producing the best result, se v er al e xper iments are perf or med. T ab le 1 list the DE pa- r ameters setting used. F or CCA, the n umber of sub-populations depend on the v ar iab les in non- linear equations system the need to be tuned. F or the S .cere visiae pathw a y , the n umber of sub- populations is 11 while f or E.coli pathw a y , the n umber of sub-population s is 7. F or the Ne wton Optimisation of biochemical systems production using h ybr id of Ne wton method, ... (M.A. Ismail) Evaluation Warning : The document was created with Spire.PDF for Python.
32 ISSN: 2502-4752 P ar ameter S .cere visiae pathw a y E.coli pathw a y Mutation (Scaling f actor) 0.8 0.7 Crosso v er 0.2 0.2 T ab le 1. The DE par ameters method, fix ed par ameter used f or both pathw a y; the n umber of iter ation is 100 and the toler ance v alue is 10 6 . In S .cere visiae pathw a y , the best result obtained b y the proposed method is 52.7269 in maximising the ethanol production while 295.2405 in minimising the total of chemical concentr ation in v olv es . The detail result, a v er age result and compar ison with other methods are listed in T ab le 2. F rom T ab le 2, it can be obser v ed that the perf or mance of the proposed method is outperf or m the result from other w or ks in maximising the ethanol production and at the same time minimising the total amount of chemical reaction concentr ation in v olv es . P ar ameter This w or k W or k b y [20] W or k b y [18] W or k b y [21] X 1 1.113 1.14 1.102 1.11 X 2 1.053 1.05 1.046 1.03 X 3 1.127 1.15 1.141 1.13 X 4 1.164 1.17 1.171 1.18 X 5 0.92 1. 12 1.113 51.14 Y 1 49.972 49.97 50 49.99 Y 2 49.810 44.77 45.953 45.83 Y 3 49.90 49.89 50 49.92 Y 4 47.333 47.26 47.772 47.97 Y 5 48.062 48 48.366 48.30 Y 8 49.792 49.75 50 49.79 F 1 52.727 52.084 52.512 52.57 F 2 295.241 295.28 297.664 297.384 T ab le 2. The detail result obtained b y the proposed method in S .cere visiae pathw a y Meanwhile , the best result produce b y the proposed method in E.coli pathw a y is 3.9988 in maximising the tr p production and 6015.5871 in minimising the total of chemical concentr ation in v olv es . The detail result, a v er age result and compar ison with other methods are listed in T ab le 3. Same obser v ation with S .cere visiae pathw a y , the perf or mance of the proposed method also perf or m better when it compare to other w or ks . P ar ameter This w or k W or k b y [22] W or k b y [23] W or k b y [18] W or k b y [21] X 1 1.191 1.19 1.2 1.2 1.11 X 2 1.119 1.15 1.15 1.12 1.114 X 3 0.8 0.8 0.8 0.8 0.8 X 4 0.0054 0.0041 0.004 0.0054 0.0054 X 5 4.037 4 4 4.011 4.75 X 6 5000 5000 5000 5000 5000 X 8 1000 1000 1000 1000 1000 F 1 3.999 3.06 3.06 3.95 3.98 F 2 6015.5871 6016.38 6016.57 6016.57 6016.22 T ab le 3. The detail result obtained b y the proposed method in E.coli pathw a y Besides that, the compar ison betw een m ulti sub-population that used in this study with single population (dont use CCA). The pur pose of CCA is to enhance the perf or mance of DE in minimising the total amount of chemical reaction concentr at ion in v olv es . Se v er al e xper iments are IJEECS V ol. 8, No . 1, October 2017 : 27 35 Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS ISSN: 2502-4752 33 conducted using par ameters setting in T ab le 1. Figure 3 and Figure 4 depicted the bar g r aph of the compar ison betw een m ulti sub-population with single population in S .cere visiae pathw a y and E.coli pathw a y . F rom that figures , it can be seen clear ly that all the results of m ulti sub-population are lo w er compare to the results obtained b y single population. It can be conclu ded that, the CCA ab le to impro v e the perf or mance of DE in minimising the total amount of chemical reaction concentr ation in v olv es . Figure 3. The compar ison of m ulti population and single population in S .cere visiae pathw a y Figure 4. The compar ison of m ulti population and single population in E.coli pathw a y In order to sho w the consistency in apply CCA, the proposed method is compared with the method that not use CCA (only use Ne wton method and DE). About 100 indep endent e xper iments are perf or med. Figure 5 and Figure 6 sho w the compar ison in bo x pl ot f or m. Figure 5 sho w the ethanol production in S .cere visiae pathw a y while Figure 6 sho w the tr p production in E.coli pathw a y . F rom the figures , the result produce b y the proposed method are not too wide compare to the result that not use CCA. F rom t his obser v ation, it can be e xplained that the propose method ab le to produce a consistent result if the e xper iment r un se v er al times . Figure 5. The bo xplot of the ethanol production Optimisation of biochemical systems production using h ybr id of Ne wton method, ... (M.A. Ismail) Evaluation Warning : The document was created with Spire.PDF for Python.
34 ISSN: 2502-4752 Figure 6. The bo xplot of the tr p production 5. Conc lusion This paper has proposed a h ybr id method of Ne wton method, DE and CCA. The proposed method is proposed to o v ercome the prob lems in optimisation of biochemical systems where the prob lems are to maximise the biochemical systems production and sim ultaneously minimise the total amount of chemical reaction concentr ation in v olv es . The proposed method w or ks b y vie w the biochemical systems as nonlinear equation system. Firstly , the Ne wton method is used to solv e the nonlinear equations system. Then, DE is used in optimisation process . The perf or mance of DE is drop when applied on alrge and comple x biochemical systems and CCA is utilised to impro v e the perf or mance of DE. Th e proposed method is applied on benchmar k biochemical systems and the e xper imental result sho w that the perf or mance is outperf or m the other w or ks . Ac kno wledg ement Special thanks and appreciation to the editor and anon ymous re vie w ers that re vie w ed this paper . The author also w ould thanks to the sponsor from RDU Gr ant V ot No . RDU1603115 f or m Univ ersiti Mala ysia P ahang. Ref erences [1] A. Ajano vic , “Biofuels v ersus f ood production: Does biofuels production increase f ood pr ices?” Energy , v ol. 36, no . 4, pp . 2070–2076, 2010. [2] M. Har v e y , “The ne w competition f or land: F ood, energy , and climate change, F ood P olicy , v ol. 36, no . 1, pp . S40—-S51, 2010. [3] S . Haus , S . J ab bar i, T . Millat, H. J anssen, R.-J . Fischer , H. Bahl, J . R. King, and O . W olk en- hauer , “A systems biology approach to in v estigate the eff ect of pH-induced gene regulation on solv ent production b y Clostr idium acetob utylicum in contin uous culture , BMC Systems Biology , v ol. 5, no . 10, 2011. [4] M. Caspers , U . Broc kmeier , C . Deger ing, T . Egger t, and R. F reudl, “Impro v ement of Sec- dependent secretion of a h eterologous model protein in Bacillus subtilis b y satur ation m utage- nesis of the N-domain of the Am yE signal peptide .” Applied microbiology and biotechnology , v ol. 86, no . 6, pp . 1877–85, ma y 2010. [5] Y .-S . J ang, J . Lee , A. Mala viy a, D . Y . Seung, J . H. Cho , and S . Y . Lee , “Butanol production from rene w ab le biomass: Redisco v er y of metab olic pathw a ys and metabolic engineer ing, Biotechnology Jour nal , v ol. 7, no . 2, pp . 186–198, 2011. [6] C .-S . Liu, “A modified Ne wton method f or solving non-linear algebr aic equations, Jour nal of Mar ine Science and T echnology , v ol. 17, no . 3, pp . 238–247, jun 2009. [7] M. Al-T o w aiq and Y . A. Hour , “T w o Impro v ed Methods Based on Bro yden’ s Ne wton Methods f or the Solution of Nonlinea r System of Equations, Jour nal of Engineer ing and Applied Sciences , v ol. 11, pp . 2344–2348, 2016. [8] C .-S . Liu and S . N. Atlur i, “A no v el time integ r ation method f or solving a large system of non- linear algebr aic equations, Computer Modeling in Engineer ing and Sciences , v ol. 31, no . 2, pp . 71–83, jan 2008. IJEECS V ol. 8, No . 1, October 2017 : 27 35 Evaluation Warning : The document was created with Spire.PDF for Python.
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