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Antiviral therapy using a fuzzy controller optimized by modified evolutionary algorithms: a comparative study

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Abstract

Hepatitis is usually caused by a viral infection or metabolic diseases. Hepatitis type B virus (HBV) infection is among the most common causes of hepatitis and can result in serious liver diseases. Several dynamic models have been developed to mathematically describe the HBV infection and antiviral therapy. In addition, different control strategies have been reported in the literature to deal with optimal antiviral therapy problem of infectious diseases. In this paper, a set of optimized closed-loop fuzzy controllers are employed for optimal treatment of basic HBV infection. To optimize the proposed scheme, five modified and modern optimization algorithms are investigated. After designing the controller, some parameters of the HBV infection model are considered to be unknown, and the robustness of the optimized controller is studied. Experimental results show that the covariance matrix adaptation–evolution strategy-based optimized closed-loop fuzzy controller has the best performance in terms of total cost of an objective function defined based on maximization of uninfected target cells, minimization of free HBVs and minimization of drug usage. In addition, the execution time of this optimization algorithm is only 8 % more than the execution time of imperialist competition algorithm as the investigated algorithm with the best convergence speed.

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References

  1. Ribeiro RM, Lo A, Perelson AS (2002) Dynamics of hepatitis B virus infection. Microbes Infect 4:829–835

    Article  Google Scholar 

  2. Pan CQ, Duan ZP, Bhamidimarri KR, Zou HB, Liang XF, Li J, Tong MJ (2012) An algorithm for risk assessment and intervention of mother to child transmission of hepatitis B virus. Clin Gastroenterol Hepatol 10:452–459

    Article  Google Scholar 

  3. Kapoor A, Bhatia V, Gopalan S, Sibal A (2011) Hepatitis B in children-current status. Apollo Med 8:287–293

    Article  Google Scholar 

  4. Michelin A, Henderson DK (2010) Infection control guidelines for prevention of health care-associated transmission of hepatitis B and C viruses. Clin Liver Dis 14:119–136

    Article  Google Scholar 

  5. Ganem D (1996) Fields virology. In: Fields BN, Knipe DM, Howley PM (eds) Lippincott-Raven, Philadelphia, pp 2703–2737

    Google Scholar 

  6. Feitelson MA, Larkin JD (2001) New animal models for hepatitis B and C. ILAR J 42:127–138

    Article  Google Scholar 

  7. Landi A, Mazzoldi A, Andreoni C, Bianchi M, Cavallini A, Laurino M, Ricotti L, Iuliano R, Matteoli B, Ceccherini-Nelli L (2008) Modeling and control of HIV dynamics. Comput Methods Prog Biomed 89:162–168

    Article  Google Scholar 

  8. Debroy S (2010) Evaluating treatment of hepatitis C for hemolytic anemia management. Math Biosci 225:141–155

    Article  MathSciNet  MATH  Google Scholar 

  9. Nowak M, Bonhoeffer S, Hill AM, Boehme R, Thomas HC, McDade H (1996) Viral dynamics in hepatitis B virus infection. Proc Natl Acad Sci USA 93:4398–4402

    Article  Google Scholar 

  10. Tsiang M, Rooney J, Toole J, Gibbs C (1999) Biphasic clearance kinetics of hepatitis B virus from patients during adefovir dipivoxil therapy. Hepatology 29:1863–1869

    Article  Google Scholar 

  11. Lau G, Tsiang M, Hou J, Yuen S, Carman W, Zhang L, Gibbs C, Lam S (2000) Combination therapy with lamivudine and famciclovir for chronic hepatitis B infected Chinese patients: a viral dynamics study. Hepatology 32:394–399

    Article  Google Scholar 

  12. Lewin S, Ribeiro R, Walters T, Lau G, Bowden S, Locarnini S, Perelson A (2001) Analysis of hepatitis B viral load decline under potent therapy: complex decay profiles observed. Hepatology 34:1012–1020

    Article  Google Scholar 

  13. Colombatto P, Civitano L, Bizzarri R, Oliveri F, Choudhury S, Gieschke R, Bonino F, Brunetto MR (2006) A multiphase model of the dynamics of HBV infection in HBeAg-negative patients during pegylated interferon-α2a, lamivudine and combination therapy. Antivir Ther 11:197–212

    Google Scholar 

  14. Hattaf K, Rachik M, Saadi S, Yousfi N (2009) Optimal control of treatment in a basic virus infection model. Appl Math Sci 3:949–958

    MathSciNet  MATH  Google Scholar 

  15. Costanza V, Rivadeneira PS, Biafore FL, D’Attellis CE (2009) A closed-loop approach to antiretroviral therapies for HIV infection. Biomed Signal Process Control 4:139–148

    Article  Google Scholar 

  16. Zurakowski R, Teel AR (2006) A model predictive control based scheduling method for HIV therapy. J Theor Biol 238:368–382

    Article  MathSciNet  Google Scholar 

  17. Pannocchia G, Laurino M, Landi A (2010) A model predictive control strategy toward optimal structured treatment interruptions in anti-HIV therapy. IEEE Trans Biomed Eng 57:1040–1050

    Article  Google Scholar 

  18. Coban R (2011) A fuzzy controller design for nuclear research reactors using the particle swarm optimization algorithm. Nucl Eng Design 241:1899–1908

    Article  Google Scholar 

  19. Frantti T (2012) Expert system for open-loop power control of wireless local area networks. Expert Syst Appl 39:10191–10201

    Article  Google Scholar 

  20. Zeuzem S, de Man RA, Honkoop P, Roth WK, Schalm SW, Schmidt JM (1997) Dynamics of hepatitis B virus infection in vivo. Hepatology 27:431–436

    Article  Google Scholar 

  21. Bonhoeffer S, May RM, Shaw GM, Nowak MA (1997) Viral dynamics and drug therapy. Proc Natl Acad Sci USA 94:6971–6976

    Article  Google Scholar 

  22. Tsiang M, Lau GKK, Cheeseman L, Murray A, Gibbs CS (2000) Viral dynamics analysis of HBV clearance under different antiviral treatment regimens using a mathematical model. Antiviral Res 46:A57

    Google Scholar 

  23. Su Y, Min L (2006) P.083 A mathematical model for adefovir dipivoxil anti-HBV infection treatment. J Clin Virol 36(Supplement 2):S86

    Article  MathSciNet  Google Scholar 

  24. Fournier C, Zoulim F (2007) Antiviral therapy of chronic hepatitis B: prevention of drug resistance. Clin Liver Dis 11:869–892

    Article  Google Scholar 

  25. Wu YT, Su YM, Min LQ (2011) PP-097 A time delay anti-HBV infection treatment mathematical model with adefovir. Int J Infect Dis 15(Supplement 1):S72

    Article  Google Scholar 

  26. Perelson AS, Neumann AU, Markowitz M, Leonard JM, Ho DD (1996) HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time. Science 271:1582–1586

    Article  Google Scholar 

  27. Nowak MA, Bangham CRM (1996) Population dynamics of immune responses to persistent viruses. Science 272:74–79

    Article  Google Scholar 

  28. Bonhoeffer S, Coffin JM, Nowak MA (1997) Human immunodeficiency virus drug therapy and virus load. J Virol 71:3275–3278

    Google Scholar 

  29. Huang Y, Rosenkranz SL, Wu H (2003) Modeling HIV dynamics and antiviral response with consideration of time-varying drug exposures, adherence and phenotypic sensitivity. Math Biosci 184:165–186

    Article  MathSciNet  MATH  Google Scholar 

  30. Gao T, Wang W, Liu X (2011) Mathematical analysis of an HIV model with impulsive antiretroviral drug doses. Math Comput Simul 82:653–665

    Article  MathSciNet  MATH  Google Scholar 

  31. Lam NP, Neumann AU, Gretch DR, Wiley TE, Perelson AS, Layden TJ (1997) Dose-dependent acute clearance of hepatitis C genotype 1 virus with interferon alpha. Hepatology 26:226–231

    Article  Google Scholar 

  32. Zeuzem S, Schmidt JM, Lee J-H, von Wagner M, Teuber G, Roth WK (1998) Hepatitis C virus dynamics in vivo: effect of ribavirin and interferon alpha on viral turnover. Hepatology 28:245–252

    Article  Google Scholar 

  33. Martin NK, Vickerman P, Foster GR, Hutchinson SJ, Goldberg DJ, Hickman M (2011) Can antiviral therapy for hepatitis C reduce the prevalence of HCV among injecting drug user populations? A modeling analysis of its prevention utility. Hepatology 54:1137–1144

    Article  Google Scholar 

  34. Martin NK, Vickerman P, Hickman M (2011) Mathematical modelling of hepatitis C treatment for injecting drug users. J Theor Biol 274:58–66

    Article  MathSciNet  Google Scholar 

  35. Min L, Su Y, Kuang Y (2008) Mathematical analysis of a basic model of virus infection with application to HBV infection. Rocky Mt J Math 38:1573–1585

    Article  MathSciNet  MATH  Google Scholar 

  36. Sheikhan M, Ghoreishi SA (2012) Application of covariance matrix adaptation-evolution strategy to optimal control of hepatitis B infection. Neural Comput Appl (article in press, available online 8 July 2012. doi:10.1007/s00521-012-1013-3)

  37. Das S, Pan I, Das S, Gupta A (2012) A novel fractional order fuzzy PID controller and its optimal time domain tuning based on integral performance indices. Eng Appl Artif Intell 25:430–442

    Article  Google Scholar 

  38. Oh SK, Kim WD, Pedrycz W (2012) Design of optimized cascade fuzzy controller based on differential evolution: simulation studies and practical insights. Eng Appl Artif Intell 25:520–532

    Article  Google Scholar 

  39. Meidanshahi V, Karimi G (2012) Dynamic modeling, optimization and control of power density in a PEM fuel cell. Appl Energy 93:98–105

    Article  Google Scholar 

  40. Kumbasar T, Eksin I, Guzelkaya M, Yesil E (2011) Adaptive fuzzy model based inverse controller design using BB-BC optimization algorithm. Expert Syst Appl 38:12356–12364

    Article  Google Scholar 

  41. Oh SK, Jang HJ, Pedrycz W (2011) Optimized fuzzy PD cascade controller: a comparative analysis and design. Simul Model Pract Theory 19:181–195

    Article  Google Scholar 

  42. Oh SK, Jang HJ, Pedrycz W (2011) A comparative experimental study of type-1/type-2 fuzzy cascade controller based on genetic algorithms and particle swarm optimization. Expert Syst Appl 38:11217–11229

    Article  Google Scholar 

  43. Cococcioni M, Lazzerini B, Marcelloni F (2011) On reducing computational overhead in multi-objective genetic Takagi-Sugeno fuzzy systems. Appl Soft Comput 11:675–688

    Article  Google Scholar 

  44. Pan I, Das S, Gupta A (2011) Handling packet dropouts and random delays for unstable delayed processes in NCS by optimal tuning of PIλDμ controllers with evolutionary algorithms. ISA Trans 50:557–572

    Article  Google Scholar 

  45. Das S, Pan I, Das S, Gupta A (2012) Improved model reduction and tuning of fractional-order PIλDμ controllers for analytical rule extraction with genetic programming. ISA Trans 51:237–261

    Article  Google Scholar 

  46. dos Santos Coelho L, Wicthoff Pessôa M (2011) A tuning strategy for multivariable PI and PID controllers using differential evolution combined with chaotic Zaslavskii map. Expert Syst Appl 38:13694–13701

    Google Scholar 

  47. Sundareswaran K, Srinivasarao Nayak P (2012) Ant colony based feedback controller design for soft-starter fed induction motor drive. Appl Soft Comput 12:1566–1573

    Article  Google Scholar 

  48. Sheikhan M, Shahnazi R, Hemmati E (2012) Adaptive active queue management controller for TCP communication networks using PSO-RBF models. Neural Comput Appl (article in press, available online 4 Jan. 2012. doi:10.1007/s00521-011-0786-0)

  49. Sheikhan M, Shahnazi R, Garoucy S (2011) Hyperchaos synchronization using PSO-optimized RBF-based controllers to improve security of communication systems. Neural Comput Appl (article in press, available online 16 Dec. 2011. doi:10.1007/s00521-011-0774-4)

  50. Sheikhan M, Shahnazi R, Garoucy S (2011) Synchronization of general chaotic systems using neural controllers with application to secure communication. Neural Comput Appl (article in press, available online 19 July 2011. doi:10.1007/s00521-011-0697-0)

  51. Roeva O (2006) A modified genetic algorithm for a parameter identification of fermentation processes. Biotechnol Biotechnol Equip 20:202–209

    Google Scholar 

  52. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: The proceedings of the IEEE international conference on neural networks, vol 4, pp 1942–1948

  53. Shi Y, Eberhart R (1998) Parameter selection in particle swarm optimization. In: The proceedings of the international conference on evolutionary programming, pp 591–601

  54. Sheikhan M, Garoucy S (2012) Fast codebook search for ACELP coders based on intelligent optimization techniques. Int J Innovative Comput Inform Control (article in press, Tokai University, Japan)

  55. Hansen N, Ostermeier A (2001) Completely derandomized self-adaptation in evolution strategies. Evolut Comput 9:159–195

    Article  Google Scholar 

  56. Hansen N, Müller SD, Koumoutsakos P (2003) Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evolut Comput 11:1–18

    Article  Google Scholar 

  57. Atashpaz-Gargari E, Lucas C (2007) Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In: The proceedings of the IEEE congress on evolutionary computation, pp 4661–4667

  58. Shah NA, Moffitt RA, Wang MD (2007) Modified genetic algorithm for parameter selection of compartmental models. In: The proceedings of the IEEE international conference on Engineering in Medicine and Biology Society, pp 143–146

  59. Sridharan B (2010) Modifications in genetic algorithm using additional parameters to make them computationally efficient. In: The proceedings of the IEEE international conference on advance computing, pp 55–59

  60. Rani MR, Selamat H, Zamzuri H, Ibrahim Z (2012) Multi-objective optimization for PID controller tuning using the global ranking genetic algorithm. Int J Innovative Comput Inform Control 8:269–284

    Google Scholar 

  61. Wakasa Y, Tanaka K, Akashi T, Nishimura Y (2010) PSO-based simultaneous tuning method for PID controllers and dead-zone compensators and its application to ultrasonic motors. Int J Innovative Comput Inform Control 6:4593–4604

    Google Scholar 

  62. Karakuzu C (2010) Parameter tuning of fuzzy sliding mode controller using particle swarm optimization. Int J Innovative Comput Inform Control 6:4755–4770

    Google Scholar 

  63. Ali M, Pant M, Singh VP (2010) Two modified differential evolution algorithms and their applications to engineering design problems. World J Modell Simul 6:72–80

    Google Scholar 

  64. Willjuice Iruthayarajan M, Baskar S (2010) Covariance matrix adaptation evolution strategy based design of centralized PID controller. Expert Syst Appl 37:5775–5781

    Article  Google Scholar 

  65. Atashpaz-Gargari E, Rajabioun R, Hashemzadeh F, Salmasi FR (2009) A decentralized PID controller based on optimal shrinkage of Gershgorin bands and PID tuning using colonial competitive algorithm. Int J Innovative Comput Inform Control 5:3227–3240

    Google Scholar 

  66. van den Bergh F, Engelbrecht AP (2006) A study of particle swarm optimization particle trajectories. Inf Sci 176:937–971

    Article  MATH  Google Scholar 

  67. Engelbrecht AP (2007) Computational intelligence- an introduction, chapter 16, 2nd edn. Wiley, England, pp 289–357

    Book  Google Scholar 

  68. Ratnaweera A, Halgamuge SK, Watson HC (2004) Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Trans Evolut Comput 8:240–255

    Article  Google Scholar 

  69. Ghosh S, Das S, Roy S, Minhazul Islam SK, Suganthan PN (2012) A differential covariance matrix adaptation evolutionary algorithm for real parameter optimization. Inf Sci 182:199–219

    Article  MathSciNet  Google Scholar 

  70. Kern S, Müller S, Hansen N, Büche D, Ocenasek J, Koumoutsakos P (2004) Learning probability distributions in continuous evolutionary algorithms- a comparative review. Nat Comput 3:77–112

    Article  MathSciNet  MATH  Google Scholar 

  71. Storn R, Price K (1997) Differential evolution- a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359

    Article  MathSciNet  MATH  Google Scholar 

  72. Goldberg DE (1989) Genetic algorithms in search, optimization and learning, 1st edn. Addison Wesley, Boston

    MATH  Google Scholar 

  73. Back T, Hoffmeister F, Schwefel H (1991) A survey of evolution strategies. In: The proceedings of the international conference on genetic algorithms and their applications, pp 2–9

  74. Fogel L (1994) Evolutionary programming in perspective: the top–down view. In: Zurada JM, Marks R Jr, Robinson C (eds) Computational intelligence: imitating life. IEEE Press, Piscataway

    Google Scholar 

  75. Fan HY, Lampinen J (2003) A trigonometric mutation operation to differential evolution. J Glob Optim 27:105–129

    Article  MathSciNet  MATH  Google Scholar 

  76. Bergey PK, Ragsdale C (2005) Modified differential evolution: a greedy random strategy for genetic recombination. Omega 33:255–265

    Article  Google Scholar 

  77. Kaelo P, Ali MM (2006) A numerical study of some modified differential evolution algorithms. Eur J Oper Res 169:1176–1184

    Article  MathSciNet  MATH  Google Scholar 

  78. Rahnamayan S, Tizhoosh HR, Salama MMA (2007) Opposition based differential evolution. IEEE Trans Evolut Comput 12:1–16

    Google Scholar 

  79. Yang Z, He J, Yao X (2007) Making a difference to differential evolution. In: Michalewicz Z, Siarry P (eds) Advances in Metaheuristics for hard optimization. Springer, Berlin, pp 415–432

    Google Scholar 

  80. Ali MM (2007) Differential evolution with preferential crossover. Eur J Oper Res 181:1137–1147

    Article  MATH  Google Scholar 

  81. Salman A, Engelbrecht AP, Omran MGH (2007) Empirical analysis of self adaptive differential evolution. Eur J Oper Res 183:785–804

    Article  MATH  Google Scholar 

  82. Pant M, Ali M, Singh VP (2008) Differential evolution with parent centric crossover. In: The proceedings of the second UKSIM European symposium on computer modeling and simulation, pp 141–146

  83. Mandal A, Das AK, Mukherjee P, Das S, Suganthan PN (2011) Modified differential evolution with local search algorithm for real world optimization. In: The proceedings of the IEEE congress on evolutionary computation, pp 1565-1572

  84. Ying H (1998) General SISO Takagi-Sugeno fuzzy systems with linear rule consequent are universal approximators. IEEE Trans Fuzzy Syst 6:582–587

    Article  Google Scholar 

  85. Guidotti LG, Rochford R, Chung J, Shapiro M, Purcell R, Chisari FV (1999) Viral clearance without destruction of infected cells during acute HBV infection. Science 284:825–829

    Article  Google Scholar 

  86. Zoulim F (2001) Detection of hepatitis B virus resistance to antivirals. J Clin Virol 21:243–253

    Article  Google Scholar 

  87. Chen X, Li Y (2007) A modified PSO structure resulting in high exploration ability with convergence guaranteed. IEEE Trans Syst Man Cybernet B Cybernet 37:1271–1289

    Article  Google Scholar 

  88. Cai X, Cui Z, Zeng J, Tan Y (2008) Particle swarm optimization with self-adjusting cognitive selection strategy. Int J Innovative Comput Inform Control 4:943–952

    Google Scholar 

  89. Lin C, Liu Y, Lee C (2008) An efficient neural fuzzy network based on immune particle swarm optimization for prediction and control applications. Int J Innovative Comput Inform Control 4:1711–1722

    Google Scholar 

  90. Zeng G, Jiang Y (2010) A modified PSO algorithm with line search. In: The proceedings of the international conference on computational intelligence and software engineering, pp 1–4. doi:10.1109/CISE.2010.5677031

  91. Nafar M, Gharehpetian GB, Niknam T (2012) Using modified fuzzy particle swarm optimization algorithm for parameter estimation of surge arresters models. Int J Innovative Comput Inform Control 8:567–582

    Google Scholar 

  92. Niknam T, Taherian Fard E, Pourjafarian N, Rousta A (2011) An efficient hybrid algorithm based on modified imperialist competitive algorithm and K-means for data clustering. Eng Appl Artif Intell 24:306–317

    Article  Google Scholar 

  93. Ebrahimzadeh A, Addeh J, Rahmani Z (2012) Control chart pattern recognition using K-MICA clustering and neural networks. ISA Trans 51:111–119

    Article  Google Scholar 

  94. Mohamed AW, Sabry HZ (2012) Constrained optimization based on modified differential evolution algorithm. Inf Sci 194:171–208

    Article  Google Scholar 

  95. Weihmann L, Martins D, dos Santos Coelho L (2012) Modified differential evolution approach for optimization of planar parallel manipulators force capabilities. Expert Syst Appl 39:6150–6156

    Article  Google Scholar 

  96. Dorigo M, Gambardella LM (1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evolut Comput 1:53–66

    Article  Google Scholar 

  97. Baskan O, Haldenbilen S, Ceylan H, Ceylan H (2009) A new solution algorithm for improving performance of ant colony optimization. Appl Math Comput 211:75–84

    Article  MathSciNet  MATH  Google Scholar 

  98. Pham DT, Ghanbarzadeh A, Koç E, Otri S, Rahim S, Zaidi M (2006) The bees algorithm- a novel tool for complex optimisation problems. In: The proceedings of innovative production machines and systems conference, pp 454–461

  99. Akay B, Karaboga D (2012) A modified artificial bee colony algorithm for real-parameter optimization. Inf Sci 192:120–142

    Article  Google Scholar 

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  1. Electrical Engineering Department, Faculty of Engineering, Islamic Azad University, South Tehran Branch, P.O. Box: 11365-4435, Tehran, Iran

    Mansour Sheikhan & S. Amir Ghoreishi

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Sheikhan, M., Ghoreishi, S.A. Antiviral therapy using a fuzzy controller optimized by modified evolutionary algorithms: a comparative study. Neural Comput & Applic 23, 1801–1813 (2013). https://doi.org/10.1007/s00521-012-1146-4

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