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

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DOTcvpSB: a Matlab Toolbox for Dynamic Optimization in Systems Biologyor we can talk about the path constraints. These constrains are solved by the conversion to the integralform which must be relaxed by some tolerance level. This can be done in the option: ’data.nlp.ineq.Tol= 0.0005’. If there is a problem with the convergence, we can set an active penalty function, same asin the equality constraints, the value of which is implemented in the option: ’data.nlp.ineq.PenaltyCoe= [1 1]’. This penalty function is incorporated directly into the cost function.Line: 98-112 There are settings for the output. The first option in this part is related with the display of the intermediateresults. Other settings are connected with the figures which show the state, control or convergence curves orsave the results into the ’.dat’ file. There is an option to insert additional commands for the depicted picturesand an option for the turning ’on/off’ of the profiler function. If the profiler function is set to the value of’on’ the toolbox after the optimization shows all parts with the relevant CPU time. Note that if this option isactive, this has an impact on the total CPU time.Line: 114 In this option the user can choose a flag for the single optimization, sucessive re-optimization, hybrid strategyor for the simulation. The re-optimization is secured by modified mesh refining algorithm [1] and theprinciple lies in refinition of the control trajectory, so the number of control variables together with the IVPand NLP tolerances is increased. This method is described in detail in the next chapter 5. The hybrid strategy[3] is characterized by the combination of the stochastic and deterministic method. If the simulationmodule is selected the system will be integrated during the whole time. The default settings for all modulesare shown in the chapter 11.Line: 116-119 Here the main function of the toolbox is called together with the data input structure.Several parts of this input function contain information which is described in detail in the manuals forSUNDIALS, IPOPT, FMINCON, SRES, DE, ACOmi, MISQP, MITS, and that is the reason for the absence oftheir description.4.1.3 Initialization, final results, and optimal trajectories1 ________________________________________________________23 DOTcvp: Dynamic Optimization Toolbox with CVP approach4 for handling continuous and mixed-integer DO problems56 Main author: Tomas Hirmajer, thirmajer@gmail.com7 Coauthors: Eva Balsa-Canto and Julio R. Banga8 Web pages: http://www.iim.csic.es/~dotcvp/9 http://www.iim.csic.es/~dotcvpsb/10 Core version: DOTcvp_R2010_E311 ________________________________________________________1213 ________________________________________________________1415 DOTcvp - a Module for Single Optimization16 ________________________________________________________1718 Saving of the ODE ................................................. done!19 Saving of the inequality constraints .............................. done!20 Generation of the file: cvm_rhs.m (ODE - MATLAB) .................. done!21 Saving of the parameters .......................................... done!22 Generation of the file: cvm_d/bjac.m (Jacobian - MATLAB) .......... done!23 Saving of the cost function (J0) .................................. done!24 Generation of the gradients (J0) .................................. done!25 Generation of the file: cvm_rhsS.m (sensitivities - MATLAB) ....... done!26 Saving of the in/equality constraints (Ji) ........................ done!27 Generation of the gradients (Ji) .................................. done!28 Generation of the file: temp_cvfdx.m (main IVP file) .............. done!29 Optimizing of the process (N=30; min(J0); FMINCON; VanDerPolOscillator) ... in progress30 Default settings are loading ...................................... done!31 Generation of the file: cvm_rhs.m (ODE - MATLAB) .................. done!32 Generation of the file: temp_cvfdx.m (main IVP file) .............. done!33 Simulation of the process ......................................... done!34 Save of the data .................................................. done!35 Deleting of the temporary files ................................... done!36 ____________________________37 Final results [single-optimization]:38 ............. Problem name: VanDerPolOscillator39 ...... NLP or MINLP solver: FMINCON40 . Number of time intervals: 3041 ... IVP relative tolerance: 1.000000e-00742 ... IVP absolute tolerance: 1.000000e-00743 . Sens. absolute tolerance: 1.000000e-00744 ............ NLP tolerance: 1.000000e-00545 ....... Final state values: 1.892634e-002 -1.000018e-001 2.924821e+00046 ...... 1th optimal control: -1.927935e-001 2.017685e-001 5.470906e-001 8.083584e-001 9.140475e-001 9.387560e-001 9.207990e-00147 8.861899e-001 8.577802e-001 8.471769e-001 8.308007e-001 7.890242e-001 7.335549e-001 6.662662e-00148 5.923498e-001 5.156350e-001 4.392108e-001 3.655986e-001 2.967516e-001 2.342226e-001 1.792525e-00149 1.318771e-001 9.175374e-002 5.884850e-002 3.270859e-002 1.294192e-002 -8.947570e-004 -8.743508e-00350 -9.794536e-003 -1.106268e-003Page – 21
x 2DOTcvpSB: a Matlab Toolbox for Dynamic Optimization in Systems Biology51 . 1th inequality constrain violation [without the penalty coefficient]: 5.003195e-00452 . 2th inequality constrain violation [without the penalty coefficient]: 1.995099e-00553 ____________________________54 ............ Final CPUtime: 4.98437500 seconds55 . Cost function [min(J_0)]: 2.924824685657 The detailed information is saved to the workspace structure with the name 'data'.5859 data =6061 name: 'VanDerPolOscillator'62 compiler: 'None'63 odes: [1x1 struct]64 sens: [1x1 struct]65 nlp: [1x1 struct]66 options: [1x1 struct]67 version: 'DOTcvp_R2010_E3'68 output: [1x1 struct]69 p: [-0.0011 30 -5.0000e-004 -1.9905e-005]70 gradJ0: [1x32 double]71 gradJi: [3x32 double]72 J0: 2.9248min J 0=2.92482468 [FMINCON: 1e−005; CVODEs: 1e−007; N=30; MATLAB]min J 0=2.92482468 [FMINCON: 1e−005; CVODEs: 1e−007; N=30; MATLAB]31.2x 1u 12.5120.8State Variables, x1.51Controls, ux 30 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.60.40.50.200−0.50 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Time−0.2TimeFigure 4.1 – Optimal state trajectories (left) and the optimal control profile (right) for the van der Pol oscillator.The Figures 4.1 show the constrained state trajectories and the optimal control trajectory for the scenarioN = 30 on the basis of the settings presented in the subsection 4.1.2. These are the figures from the DOTcvpoutput. It is possible to see in the title of figures the value of the cost function and the resulting settings for NLP astolerance level, number of time intervals, name of the MI/NLP solver, used gradient method and settings for IVPas tolerance level, nonlinear solver, sensitivity correction method, LMM, and compiler. This information can bedone with the option: ’data.output.title’.The above mentioned problem with the presented settings, as well as other problems presented in the nextsections is possible to run directly from the toolbox. The names of the van der Pol oscillator problem in theDOTcvp toolbox are the following: cdop_VanDerPolOscillator_simple; cdop_VanDerPolOscillatorPage – 22
Page 1 and 2: TECHNICAL REPORTDOTcvpSB: a Matlab
Page 3 and 4: Main Web PageIt is possible to get
Page 5 and 6: DOTcvpSB: a Matlab Toolbox for Dyna
Page 13 and 14: CHAPTER 2Optimal control problem2.1
Page 17: DOTcvpSB: a Matlab Toolbox for Dyna
Page 30 and 31: CHAPTER 7GUI for DOTcvp7.1 STEP BY
Page 42 and 43: CHAPTER 9Biochemical engineering pr
Page 50 and 51: CHAPTER 11Default settingsThe user

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