DOTcvpSB: a Matlab Toolbox for Dynamic Optimization in Systems ...

DOTcvpSB: a Matlab Toolbox for Dynamic Optimization in Systems BiologyLine: 21-44 There is a place for the constant parameters or for the formulas, e.g. conditions, description of the problem inthe ODE form, possible black box definition option, and the vector of the initial values. Note that the notationy(number), u(number), p(number) has to be used for the state, decision variables, and time-independentparameters, respectively. Next options serve for the definition of the number of state variables with theinitial and final time. The last group of the options is related with the settings for both, system and sensitivitymodule. In this place it is possible to initialize the ODE and sensitivities as for example nonlinear and linearsolver, linear multistep method, maximum number of steps, relative and absolute tolerance for the ODE andsensitivities. The last option in this part contains information about the sensitivities error control. When thisoption is set at the value of ’on’ then the CPU time will be larger and the sensitivities will be controlled.Note The last version of the DOTcvp toolbox was extended to solve black box models. The models haveto be defined as function in the form [J0,Ji]=FunctionName(x), where J0, Ji, and x represent thecost function, constraints violation in the vector form, and vector of optimized variables, respectively.Firstly, these models have to be copied to the following folder ’DOTcvp/src_black_box’ andthen run the toolbox installation file (to save all new paths into the MATLAB environment). Theuser can change the option regarding the black box models in the input file: ’data.odes.black_box =’None’,’1’,’FunctionName’’ where in the first part can be defined an argument ’None’ if ODE are providedor ’Full’ if black box function is defined. The second parameter is the penalty coefficient for thesummary of the constraints violation and the last one is the name of the black box function.Line: 46-73 This part of the input file contains options related with the NLP definition. First, the number of time intervalshas to be defined, then the minimization or maximization option is chosen. After the definition of the costfunction is done it is needed to define the upper and lower bounds of the decision variables and/or timeindependentparameters. Next the NLP or MINLP solver can be chosen together with the default input file(note that this file contains default settings for every MI/NLP solver, the user can change it), NLP tolerancelevel, gradient method, and maximum number of function evaluation. Next it is possible to set if free timeproblem is solved, if yes, then the upper and lower bounds have to be defined and the penalty function canbe enabled. In the next option it is possible to switch the piecewise constant (PWC) control trajectory to thepiecewise linear (PWL) control trajectory. Note, this option is available only for FMINCON and non-freetime problems. At the end of this group of options it is needed to define the number of decision, integervariables, and time-independent parameters.Note The number of state variables and decision, time-independent variables is counted automatically, butthe user can change it. The user can also introduce a non-constant initial control trajectories for theoptimization or simulation. If we consider two time intervals and two control variables, then the option’data.nlp.u0’ will be defined as follows: [u 011 u 012 ; u 021 u 022 ]Line: 75-83 This place is necessary for defining the number of the equality constraints with the time at which they areactive, i.e. after which segment. The penalty function for the equality constraints can also be active.Note The equality constraint of the type ’data.nl.eq.eq(1) = {’y(2)+0.1’}’ is active, the status is set on thevalue of ’on’ what means that the equationx 2 (t F ) = −0.1 (4.7)is active in the final segment ’data.nlp.eq.time(1) = data.nlp.RHO’. This direction – timing is equal tothe final time. If we would like to set the active equality constraint on the half time of the optimization,we have to define the before mentioned option on the value of 15 or ’data.nlp.RHO/2’.Line: 85-96 This part of the function contains information about the inequality constraints and their penalty functions.The user can insert the number of inequality constrains and choose type: ’>’ or ’=’ and ’