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

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DOTcvpSB: a Matlab Toolbox for Dynamic Optimization in Systems Biology2. FMINCON [10] (Find MINimum of CONstrained nonlinear multivariable function) is a part of theMATLAB optimization toolbox which uses sequential quadratic programming (SQP);3. MISQP [14] (Mixed-Integer Sequential Quadratic Programming) solves mixed-integer non-linear programmingproblems by a modified sequential quadratic programming method;• stochastic global1. DE [30] (Differential Evolution) uses population based approach for minimizing the performance index;2. SRES [26] (Stochastic Ranking Evolution Strategy) uses an evolution strategy combined with an approachto balance objective and penalty functions;• and hybrid metaheuristics1. ACOmi [29] (Ant Colony Optimization for Mixed Integer nonlinear programming problems) is inspiredby ants foraging behavior and for the local search it uses MISQP;2. MITS [13] (Mixed-Integer Tabu Search algorithm) is based on extensions of the metaheuristic TabuSearch algorithm and for local search it uses MISQP too;where the deterministic MISQP solver and all hybrid solvers are able to handle mixed-integer problems directly.The problem is automatically reformulated on the basis of user’s option.1.4 NUMERICAL SIMULATION METHOD (IVP SOLVERS)Forward integration of the ODE, Jacobian, and sensitivities if it is needed is ensured by CVODES, a part ofSUNDIALS [17], which is able to perform the simultaneous or staggered sensitivity analysis too. The IVP problemcan be solved with the Newton or Functional iteration module and with the Adams or BDF linear multistep method(LMM). The Adams method is recommended for solving of the non-stiff problems while BDF is recommendedfor solving of the stiff problems. Note that the sensitivity equations are provided analytically and the error controlstrategy for the sensitivity variables could be enabled.Figure 1.1 – Organization of the toolbox code.Page – 9
DOTcvpSB: a Matlab Toolbox for Dynamic Optimization in Systems BiologyThe organization of the toolbox code is shown in Figure 1.1 where the toolbox files have the name: ’dotcvp_’and the temporary files: ’temp_’. Note that the temporary files are generated and later deleted automatically,because they are problem dependent. Finally it is needed to emphasize that DOTcvp contains packages that are anopen-source.1.5 RECOMMENDED OPERATING PROCEDUREIt should be noted that, for a general MIDO formulation, there is no a priori way to distinguish if theresulting MINLP will be convex or not, so the user has no clue on which optimization strategy should be using.Thus, we recommend that, for any new problem, the user follows this protocol:• Step 1: try solving the problem with the single optimization strategy and a local deterministic method, suchas FMINCON or IPOPT for DO problems, or MISQP for MIDO problems, using a rather crude controldiscretization (e.g. 10 elements). After obtaining a solution, repeat changing the initial guess for the controlvariable. If a rather different solution is obtained, suspect multimodality and go to step 2 below. If not, solvethe problem again using a finer discretization. For faster and more satisfactory results regarding controldiscretization, use the successive re-optimization module.• Step 2: solve the problem using the multi-start optimization module. In general 100 runs is a sensiblenumber for this task, but for costly problems the user might want to reduce this. Plotting an histogram ofthe resulting set of solutions will give a good view of the problem multimodality. For clearly multimodalproblems, go to step 3. If not, stop, or go back to step 1 if e.g. more refined control levels are desired.• Step 3: use the single optimization strategy as in step 1, but use a global stochastic method, like DE or SRESfor DO problems, or ACOmi or MITS for MIDO problems. If satisfactory results are obtained in reasonablecomputation times, stop. If the computational cost is excessive, go to step 4.• Step 4: use a hybrid global-local strategy. More advanced users can tweak the different options to increaseefficiency and/or robustness.This protocol is especially recommended for novel users who are not familiar with numerical optimizationmethods. Advanced users can tweak the hybrid strategy options, or even create their own strategies combiningcalls to the different solvers in a MATLAB script.1.6 TOOLBOX DOWNLOADThe toolbox can be downloaded from the afore mentioned web page. The name of the toolbox is as follows:’DOTcvp_RXXXX_YN.zip’. The letters mean:XXXX - [number] represents the toolbox year versionY - [letter] represents the major changes, usually the changes in the input fileN - [number] represents the minor changes1.7 TOOLBOX INSTALLATIONThe installation procedure consists of several steps listed below:1. If you have an older installation of DOTcvp, please remove it. This helps to avoid possible compatibilityproblems.2. Unzip the packed file into any directory. To unzip the toolbox the user needs a password which is free toreceive. The unziped file contains the name and date when the ’zip’ package was created. This helps torecognize a new package of the toolbox. It is recommended to use the latest version of the toolbox.3. You can try to download and use some demonstrative examples from afore mentioned web page and extractthem into a ’dotcvp_examples’ directory. Of course any different directory can be used.4. The next step is the toolbox installation. First, you should start MATLAB and change to the directory whereDOTcvp was unpacked, and then run ’dotcvp_install.m’ install file. If everything is all right the user will seethe following output procedure:Page – 10
Page 1 and 2: TECHNICAL REPORTDOTcvpSB: a Matlab
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DOTcvpSB: a Matlab Toolbox for Dyna
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