I have a big Simulink model. I want to find the input to the system (which is a time series) that will maximize the output (which is another time series, like any other Simulink model).
Which command or toolbox should I use and how? Optimization toolbox, Neural networks, Fuzzy, Genetic algorithm?
as Mariano was suggesting you may consider using an optimization algorithm and run the Simulink model in your objective function. You can use the SIM command to run the simulation from the code with your different input vector. To understand what's the appropriate optimization function you need to consider which type of problem you are solving (as previously suggested FMINCON and FMINUNC are good starting points).
You may also consider using Simulink Parameter Estimation (offered in Simulink Design Optimization) to setup the optimization process directly in Simulink (although if you're extensively working with timeseries you may find it quicker to write all the code in MATLAB for your optimization routine).