An Adaptive Memetic Algorithm With Dynamic Population Management for Designing HIV Multidrug Therapies
In this paper, a mathematical model of human immunodeficiency
virus (HIV) is utilized and an optimization problem is
proposed, with the final goal of implementing an optimal 900-day
structured treatment interruption (STI) protocol. Two type of commonly
used drugs in highly active antiretroviral therapy (HAART),
reverse transcriptase inhibitors (RTI) and protease inhibitors (PI), are
considered. In order to solving the proposed optimization problem an
adaptive memetic algorithm with population management (AMAPM)
is proposed. The AMAPM uses a distance measure to control the
diversity of population in genotype space and thus preventing the
stagnation and premature convergence. Moreover, the AMAPM uses
diversity parameter in phenotype space to dynamically set the population
size and the number of crossovers during the search process.
Three crossover operators diversify the population, simultaneously.
The progresses of crossover operators are utilized to set the number
of each crossover per generation. In order to escaping the local optima
and introducing the new search directions toward the global optima,
two local searchers assist the evolutionary process. In contrast to
traditional memetic algorithms, the activation of these local searchers
is not random and depends on both the diversity parameters in
genotype space and phenotype space. The capability of AMAPM in
finding optimal solutions compared with three popular metaheurestics
is introduced.
[1] T.W. Chun, L.W. Stuyver,S.B. Mizell, L.A. Ehler, J.A. Mican, M. Baseler,
A.L. Lloyd, M.A. Nowak and A.S. Fauci, Presence of an inducible HIV-1
latent reservoir during highly active antiretroviral therapy. Proc. Natl.
Acad. Sci. 94, 13193-13197, 1997.
[2] D. Finzi, M. Hermankova, T. Pierson, L.M. Carruth, C. Buck, R.E. Chaisson,
T.C. Quinn, K. Chadwick, J. Margolick, R. Brookmeyer and et
al., Identification of a reservoir for HIV-1 in patients on highly active
antiretroviral therapy. Science. 278, 1295-1300, 1997.
[3] J.K. Wong, M. Hezareh, H.F. Gunthard, D.V. Havlir, C.C. Ignacio,
C.A. Spina and D.D. Richman, Recovery of replication-competent HIV
despite prolonged suppression of plasma viremia. Science. 278, 1291-
1295, 1997.
[4] M.M. Hadjiandreou, R. Conejeros and V.S. Vassiliadis, Towards a longterm
model construction for the dynamic simulation of HIV infection.
Math. Biosci. Eng. 4, 489-504, 2007.
[5] A.S. Perelson, A.U. Neumann, M. Markowitz and et al., HIV-1 dynamics
in vivo: virion clearance rate, infected cell life-span, and viral generation
time. Math. Biosci. . Science. 271, 1582-1586, 1996.
[6] D. Wodarz, M.A. Nowak, Specific therapy regimes could lead to longterm
immunological control of HIV. Proc. Natl. Acad. Sci. 96, 14464-
14469, 1999.
[7] A. Landi, A. Mazzoldi, C. Andreoni, M. Bianchi, A. Cavallini, M. Laurino,
L. Ricotti, R. Iuliano, B. Matteoli and L. Ceccherini-Nelli, Modelling
and control of HIV dynamics. Computer methods and programs
in biomedicine. 89, 162-168, 2008.
[8] K.R. Fister, S. Lenhart and J.S. McNally, Optimizing chemotherapy in
an HIV model. Electronic Journal of Differential Equations. 32, 1-12,
1998.
[9] M.M. Hadjiandreou, R. Conejeros and D.I. Wilson, Specific therapy
regimes could lead to long-term immunological control of HIV. Chemical
Engineering Science. 64, 1600-1619, 2007.
[10] W. Garira, D.S. Musekwa and T. Shiri, Optimal control of combined
therapy in a single strain HIV-1 model. Electronic Journal of Differential
Equations.52, 1-22, 2005.
[11] J. Karrakchou, M. Rachik and S. Gourari, Optimal control and infectiology:
Application to an HIV/AIDS model. J. Appl. Math. Comput.177,
807-818, 2006.
[12] A. Heydari, M.H. Farahi and A.A. Heydari , Chemotherapy in an HIV
model by a pair of optimal control. Proceedings of the 7th WSEAS
International Conference on Simulation, Modelling and Optimization,
Beijing, China, 58-63, 2007.
[13] B.M. Adams, H.T. Banks, H.D. Kwon and H.T. Tran, Dynamic
multidrug therapies for HIV: optimal and STI control approaches. Math
Biosci Eng, 1, 223-241, 2004.
[14] F. Neri, J. Toivanen and R.A.E. Makinen, An adaptive evolutionary algorithm
with intelligent mutation local searchers for designing multidrug
therapies for HIV. Appl Intell, 27, 219-235, 2007.
[15] R. Culshaw, S. Ruan and R.J. Spiteri, Optimal HIV treatment by
maximizing immune response. J. Math. Biol, 48, 545-562, 2004.
[16] O. Krakovska and L.M. Wahl, Costs versus benefits: best possible and
best practical treatment regimens for HIV. J. Math. Biol, 54, 385-406,
2007.
[17] C.D. Myburgh and K.H.Wong, Computational Control of an HIV Model.
Annals of Operations Research, 133, 277-283, 2005.
[18] B.M. Adams, H.T. Banks, M. Davidian, H.D. Kwon, H.T. Tran,
S.N. Wynne and E.S. Rosenberg, HIV dynamics: modeling, data analysis,
and optimal treatment protocols. J. Comput. Appl. Math, 184, 10-49,
2005.
[19] J. Alvarez-Ramirez, M. Meraz and J. X. Velasco-Hernandez, Feedback
control of the chemotherapy of HIV. Int. J. Bifur. Chaos, 10, 2207-2219,
2000.
[20] S. Butler, D. Kirschner and S. Lenhart, Optimal control of chemotherapy
affecting the infectivity of HIV. In: Arino O, Axelrod D, Kimmel
M, Langlais M (eds) Advances in mathematical population dynamics:
molecules, cells, man. World Scientific, Singapore, 104-120, 2003.
[21] H. Shim, S.J. Han, C.C. Chung, S. Nam and J.H. Seo, Optimal
scheduling of drug treatment for HIV infection: continuous dose control
and receding horizon control. Int J Control Autom Syst, 1, 401-407,
2003.
[22] D. Kirschner, S. Lenhart and S. Serbin, Optimal control of the
chemotherapy of HIV infection: scheduling, amounts and initiation of
treatment. J. Math. Biol. 35, 775-792, 1997.
[23] U. Ledzewicz and H. Schattler, On optimal controls for a general
mathematical model for chemotherapy of HIV. In: Proceedings of the
2002 American control conference, 5, 3454-3459, 2002.
[24] G. Pannocchia, M. Laurino, and A. Landi, A Model Predictive Control
Strategy Toward Optimal Structured Treatment Interruptions in Anti-HIV
Therapy. IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING,
57, 1098-1101, 2010.
[25] R. Zurakowski, A.R. Teel and D. Wodarz, Enhancing immune response
to HIV infection using MPC-based treatment scheduling. In: Proceedings
of the 2003 American control conference, 2, 1182-1187, 2003.
[26] R. Zurakowski, A.R. Teel and D. Wodarz Utilizing alternate target cells
in treating HIV infection through scheduled treatment interruptions. In:
Proceedings of the 2004 American control conference, 1, 946-951, 2004.
[27] R. Zurakowski and A.R. Teel, A model predictive control based
scheduling method for HIV therapy. In: Proceedings of the 2003
American control conference, 2, 1182-1187, 2003.
[28] T. Banks, H.D. Kwon, J. Toivanen and H.T. Tran, An state dependent
Riccati equation based estimator approach for HIV feedback control.
Optim Control Appl Methods, 27, 93-121, 2006.
[29] M.A.L. Caetano and T. Yoneyama, Short and long period optimization
of drug doses in the treatment of AIDS. An Acad Bras Ci. 74, 379-392,
2002.
[30] A.M. Jeffrey, X. Xia and I.K. Craig, When to initiate HIV therapy: a
control theoretic approach. IEEE Trans Biomed Eng, 50, 1213-1220,
2003.
[31] J.J. Kutch, P. Gurfil, Optimal control of HIV infection with a
continuously-mutating viral population. In: Proceedings of the 2002
American control conference. 5, 4033-4038, 2002.
[32] F. Neri, J. Toivanen, G.L. Cascella, and Y.S. Ong, An Adaptive Multimeme
Algorithm for Designing HIV Multidrug Therapies. IEEE/ACM
TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS.
4, 1313-1328, 2007.
[33] S.H. Bajaria, G. Webb, D.E. Kirschner, Predicting differential responses
to structured treatment interruptions during HAART. Bull. Math. Biol.
66, 1093-1118, 2004.
[34] K. Sorensen, M. Sevaux, MAÔÇöPM: memetic algorithms with population
management. Computers and Operations Research. 33, 1214-1225, 2006.
[35] M. Sevaux, K. Sorensen, M. Sevaux, Permutation distance measures
for memetic algorithms with population management. Proc. The Sixth
Metaheuristics International Conference. 94, 22-26, 2005.
[36] V. Campos, M. Laguna, and R. Marti, Context-independent scatter
search and tabu search for permutation problems. INFORMS Journal
on Computing,, 17, 111-122,2005.
[37] Z. Michalewicz, Genetic Algorithms +Data Structures = Evolution
Program. Springer, Berlin, Heidelberg, New York, 1996.
[38] F. Glover, Tabu search part I. ORSA Journal on Computing. 1, 190-
206, 1989.
[1] T.W. Chun, L.W. Stuyver,S.B. Mizell, L.A. Ehler, J.A. Mican, M. Baseler,
A.L. Lloyd, M.A. Nowak and A.S. Fauci, Presence of an inducible HIV-1
latent reservoir during highly active antiretroviral therapy. Proc. Natl.
Acad. Sci. 94, 13193-13197, 1997.
[2] D. Finzi, M. Hermankova, T. Pierson, L.M. Carruth, C. Buck, R.E. Chaisson,
T.C. Quinn, K. Chadwick, J. Margolick, R. Brookmeyer and et
al., Identification of a reservoir for HIV-1 in patients on highly active
antiretroviral therapy. Science. 278, 1295-1300, 1997.
[3] J.K. Wong, M. Hezareh, H.F. Gunthard, D.V. Havlir, C.C. Ignacio,
C.A. Spina and D.D. Richman, Recovery of replication-competent HIV
despite prolonged suppression of plasma viremia. Science. 278, 1291-
1295, 1997.
[4] M.M. Hadjiandreou, R. Conejeros and V.S. Vassiliadis, Towards a longterm
model construction for the dynamic simulation of HIV infection.
Math. Biosci. Eng. 4, 489-504, 2007.
[5] A.S. Perelson, A.U. Neumann, M. Markowitz and et al., HIV-1 dynamics
in vivo: virion clearance rate, infected cell life-span, and viral generation
time. Math. Biosci. . Science. 271, 1582-1586, 1996.
[6] D. Wodarz, M.A. Nowak, Specific therapy regimes could lead to longterm
immunological control of HIV. Proc. Natl. Acad. Sci. 96, 14464-
14469, 1999.
[7] A. Landi, A. Mazzoldi, C. Andreoni, M. Bianchi, A. Cavallini, M. Laurino,
L. Ricotti, R. Iuliano, B. Matteoli and L. Ceccherini-Nelli, Modelling
and control of HIV dynamics. Computer methods and programs
in biomedicine. 89, 162-168, 2008.
[8] K.R. Fister, S. Lenhart and J.S. McNally, Optimizing chemotherapy in
an HIV model. Electronic Journal of Differential Equations. 32, 1-12,
1998.
[9] M.M. Hadjiandreou, R. Conejeros and D.I. Wilson, Specific therapy
regimes could lead to long-term immunological control of HIV. Chemical
Engineering Science. 64, 1600-1619, 2007.
[10] W. Garira, D.S. Musekwa and T. Shiri, Optimal control of combined
therapy in a single strain HIV-1 model. Electronic Journal of Differential
Equations.52, 1-22, 2005.
[11] J. Karrakchou, M. Rachik and S. Gourari, Optimal control and infectiology:
Application to an HIV/AIDS model. J. Appl. Math. Comput.177,
807-818, 2006.
[12] A. Heydari, M.H. Farahi and A.A. Heydari , Chemotherapy in an HIV
model by a pair of optimal control. Proceedings of the 7th WSEAS
International Conference on Simulation, Modelling and Optimization,
Beijing, China, 58-63, 2007.
[13] B.M. Adams, H.T. Banks, H.D. Kwon and H.T. Tran, Dynamic
multidrug therapies for HIV: optimal and STI control approaches. Math
Biosci Eng, 1, 223-241, 2004.
[14] F. Neri, J. Toivanen and R.A.E. Makinen, An adaptive evolutionary algorithm
with intelligent mutation local searchers for designing multidrug
therapies for HIV. Appl Intell, 27, 219-235, 2007.
[15] R. Culshaw, S. Ruan and R.J. Spiteri, Optimal HIV treatment by
maximizing immune response. J. Math. Biol, 48, 545-562, 2004.
[16] O. Krakovska and L.M. Wahl, Costs versus benefits: best possible and
best practical treatment regimens for HIV. J. Math. Biol, 54, 385-406,
2007.
[17] C.D. Myburgh and K.H.Wong, Computational Control of an HIV Model.
Annals of Operations Research, 133, 277-283, 2005.
[18] B.M. Adams, H.T. Banks, M. Davidian, H.D. Kwon, H.T. Tran,
S.N. Wynne and E.S. Rosenberg, HIV dynamics: modeling, data analysis,
and optimal treatment protocols. J. Comput. Appl. Math, 184, 10-49,
2005.
[19] J. Alvarez-Ramirez, M. Meraz and J. X. Velasco-Hernandez, Feedback
control of the chemotherapy of HIV. Int. J. Bifur. Chaos, 10, 2207-2219,
2000.
[20] S. Butler, D. Kirschner and S. Lenhart, Optimal control of chemotherapy
affecting the infectivity of HIV. In: Arino O, Axelrod D, Kimmel
M, Langlais M (eds) Advances in mathematical population dynamics:
molecules, cells, man. World Scientific, Singapore, 104-120, 2003.
[21] H. Shim, S.J. Han, C.C. Chung, S. Nam and J.H. Seo, Optimal
scheduling of drug treatment for HIV infection: continuous dose control
and receding horizon control. Int J Control Autom Syst, 1, 401-407,
2003.
[22] D. Kirschner, S. Lenhart and S. Serbin, Optimal control of the
chemotherapy of HIV infection: scheduling, amounts and initiation of
treatment. J. Math. Biol. 35, 775-792, 1997.
[23] U. Ledzewicz and H. Schattler, On optimal controls for a general
mathematical model for chemotherapy of HIV. In: Proceedings of the
2002 American control conference, 5, 3454-3459, 2002.
[24] G. Pannocchia, M. Laurino, and A. Landi, A Model Predictive Control
Strategy Toward Optimal Structured Treatment Interruptions in Anti-HIV
Therapy. IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING,
57, 1098-1101, 2010.
[25] R. Zurakowski, A.R. Teel and D. Wodarz, Enhancing immune response
to HIV infection using MPC-based treatment scheduling. In: Proceedings
of the 2003 American control conference, 2, 1182-1187, 2003.
[26] R. Zurakowski, A.R. Teel and D. Wodarz Utilizing alternate target cells
in treating HIV infection through scheduled treatment interruptions. In:
Proceedings of the 2004 American control conference, 1, 946-951, 2004.
[27] R. Zurakowski and A.R. Teel, A model predictive control based
scheduling method for HIV therapy. In: Proceedings of the 2003
American control conference, 2, 1182-1187, 2003.
[28] T. Banks, H.D. Kwon, J. Toivanen and H.T. Tran, An state dependent
Riccati equation based estimator approach for HIV feedback control.
Optim Control Appl Methods, 27, 93-121, 2006.
[29] M.A.L. Caetano and T. Yoneyama, Short and long period optimization
of drug doses in the treatment of AIDS. An Acad Bras Ci. 74, 379-392,
2002.
[30] A.M. Jeffrey, X. Xia and I.K. Craig, When to initiate HIV therapy: a
control theoretic approach. IEEE Trans Biomed Eng, 50, 1213-1220,
2003.
[31] J.J. Kutch, P. Gurfil, Optimal control of HIV infection with a
continuously-mutating viral population. In: Proceedings of the 2002
American control conference. 5, 4033-4038, 2002.
[32] F. Neri, J. Toivanen, G.L. Cascella, and Y.S. Ong, An Adaptive Multimeme
Algorithm for Designing HIV Multidrug Therapies. IEEE/ACM
TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS.
4, 1313-1328, 2007.
[33] S.H. Bajaria, G. Webb, D.E. Kirschner, Predicting differential responses
to structured treatment interruptions during HAART. Bull. Math. Biol.
66, 1093-1118, 2004.
[34] K. Sorensen, M. Sevaux, MAÔÇöPM: memetic algorithms with population
management. Computers and Operations Research. 33, 1214-1225, 2006.
[35] M. Sevaux, K. Sorensen, M. Sevaux, Permutation distance measures
for memetic algorithms with population management. Proc. The Sixth
Metaheuristics International Conference. 94, 22-26, 2005.
[36] V. Campos, M. Laguna, and R. Marti, Context-independent scatter
search and tabu search for permutation problems. INFORMS Journal
on Computing,, 17, 111-122,2005.
[37] Z. Michalewicz, Genetic Algorithms +Data Structures = Evolution
Program. Springer, Berlin, Heidelberg, New York, 1996.
[38] F. Glover, Tabu search part I. ORSA Journal on Computing. 1, 190-
206, 1989.
@article{"International Journal of Medical, Medicine and Health Sciences:53135", author = "Hassan Zarei and Ali Vahidian Kamyad and Sohrab Effati", title = "An Adaptive Memetic Algorithm With Dynamic Population Management for Designing HIV Multidrug Therapies", abstract = "In this paper, a mathematical model of human immunodeficiency
virus (HIV) is utilized and an optimization problem is
proposed, with the final goal of implementing an optimal 900-day
structured treatment interruption (STI) protocol. Two type of commonly
used drugs in highly active antiretroviral therapy (HAART),
reverse transcriptase inhibitors (RTI) and protease inhibitors (PI), are
considered. In order to solving the proposed optimization problem an
adaptive memetic algorithm with population management (AMAPM)
is proposed. The AMAPM uses a distance measure to control the
diversity of population in genotype space and thus preventing the
stagnation and premature convergence. Moreover, the AMAPM uses
diversity parameter in phenotype space to dynamically set the population
size and the number of crossovers during the search process.
Three crossover operators diversify the population, simultaneously.
The progresses of crossover operators are utilized to set the number
of each crossover per generation. In order to escaping the local optima
and introducing the new search directions toward the global optima,
two local searchers assist the evolutionary process. In contrast to
traditional memetic algorithms, the activation of these local searchers
is not random and depends on both the diversity parameters in
genotype space and phenotype space. The capability of AMAPM in
finding optimal solutions compared with three popular metaheurestics
is introduced.", keywords = "HIV therapy design, memetic algorithms, adaptivealgorithms, nonlinear integer programming.", volume = "5", number = "7", pages = "264-8", }
