TY - JOUR
T1 - Optimization problems in chemical reactions using continuous-time Markov chains
AU - Carrillo, Lizeth
AU - Escobar, Jesica A.
AU - Clempner, Julio B.
AU - Poznyak, Alexander S.
N1 - Publisher Copyright:
© 2016, Springer International Publishing Switzerland.
PY - 2016/6/1
Y1 - 2016/6/1
N2 - In this paper we generalize two models for chemical reactions, based on continuous-time Markov chains, into continuous-time Markov decision process. We propose a mathematical optimization approach for solving an average optimality criterion in state-discrete continuous-time Markov decision process. Our proposal extends the c-variable method used in discrete-time decision process by introducing a new linear constraint for continuous time. The advantage of our approach is that it reduces the continuous-time Markov decision process to a discrete-time Markov decision process where the linear constraints make the problem computationally tractable. The usefulness of the method is illustrated in chemical reactions where the concentration dynamics is modelled as a continuous-time Markov chain. The first application is a single reversible reaction for the formation of the amidogen radical where we found the optimal temperature that minimizes the average expected rate of H formation at steady state. The second is a chemical reaction network for the proton transfer, hydration and tautomeric reaction of anthocyanin pigments, in this case we found an optimal strategy over a set of values of H + that minimizes the average expected total number of molecules at steady state.
AB - In this paper we generalize two models for chemical reactions, based on continuous-time Markov chains, into continuous-time Markov decision process. We propose a mathematical optimization approach for solving an average optimality criterion in state-discrete continuous-time Markov decision process. Our proposal extends the c-variable method used in discrete-time decision process by introducing a new linear constraint for continuous time. The advantage of our approach is that it reduces the continuous-time Markov decision process to a discrete-time Markov decision process where the linear constraints make the problem computationally tractable. The usefulness of the method is illustrated in chemical reactions where the concentration dynamics is modelled as a continuous-time Markov chain. The first application is a single reversible reaction for the formation of the amidogen radical where we found the optimal temperature that minimizes the average expected rate of H formation at steady state. The second is a chemical reaction network for the proton transfer, hydration and tautomeric reaction of anthocyanin pigments, in this case we found an optimal strategy over a set of values of H + that minimizes the average expected total number of molecules at steady state.
KW - C-variable method
KW - Chemical reactions
KW - Continuous-time Markov decision process
KW - Long run average reward
UR - http://www.scopus.com/inward/record.url?scp=84959142718&partnerID=8YFLogxK
U2 - 10.1007/s10910-016-0620-0
DO - 10.1007/s10910-016-0620-0
M3 - Artículo
SN - 0259-9791
VL - 54
SP - 1233
EP - 1254
JO - Journal of Mathematical Chemistry
JF - Journal of Mathematical Chemistry
IS - 6
ER -