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I need to find an optimal set of "n" parameter values that minimize an objective function (a 2-hr simulation of a system). I have looked at genetic algorithm and simulated annealing methods, but was wondering if there are any better algorithms and guidance on their merits and limitations.

With the above optimization methods I can find the optimal parameter values that hold true for the entire simulation duration. Incase, I want to find the optimal "time varying" parameter values (parameter values change with time during the 2-hr simulation), are there any methods/ideas other than making each time varying parameter value a variable to optimize? Any thoughts?

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Some thoughts:

  • There is something called local regression ("loess" for short, pronounced Low-Ess). Whether that's helpful is for you to decide.

  • I work on products for doing non-linear mixed effects modeling (NLME) in the context of pharmacometrics. So, for example, each subject can have a parameter called V, for volume of distribution (basically blood plasma volume) that affects the observed concentration after a dose of drug. In some models, V may change over time. If so, we try to find a time-varying input datum called a "covariate", such as body weight W. Then we might make a model where V = V0 + k W, where V0 is some kind of base volume, and k determines how much weight affects volume. So we're estimating non-time-varying parameters V0 and k, even though V is time-varying.

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