An Adaptive Memetic Algorithm With Dynamic Population Management for Designing HIV Multidrug Therapies

Authors: Hassan Zarei, Ali Vahidian Kamyad, Sohrab Effati

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331393

References:

[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.