Mixed-integer non-linear optimal control in systems biology and biotechnology: numerical methods and a software toolbox

Here we consider the problem of optimal manipulation of biological or biotechnological systems, formulated as a class of mixed-integer optimal control problems. We describe the current state of the art regarding the numerical solution of these problems, and a software implementation developed in our group (DOTcvp toolbox, based on Matlab). DOTcvp combines the control vector parameterization approach with a number of local deterministic and global stochastic and hybrid (mixed-integer) non-linear programming solvers and suitable dynamic process simulation methods so as to cover the solution of a wide class of problems. The performance of DOTcvp is illustrated considering representative set of benchmark problems, including the problem of drug displacement in a patient, the optimal operation of a fed-batch bioreactor, and the optimal control of intracellular calcium oscillations. The DOTcvp toolbox is freely available to academic users.