I am learning about optimization problems and I'm interested in modeling the optimal design of wind power plants. I came up with an objective function that represents the capital cost per unit of power capacity of multiple power plants . The function takes the form:

$$ f(\mathbf{x}) = \frac{g(\mathbf{x})}{h(\mathbf{x})} $$

where $\mathbf{x}$ represents a vector of design variables, $f, g, h$ are all scalar functions, $f$ is the objective being minimized, $g$ represents the cost, and $h$ represents the average power per year delivered to load. The constraints are linear and mixed binary/continuous/discrete.

My question: (a) Is this an appropriate objective function or are there better ways to model this? (b) If this is an appropriate objective function, what kinds of algorithms can deal with the nonlinearity due to having a fraction in the objective function? (c) If this is not a good objective function, what would be a better one? (or how do you make a good objective function more generally?)

  • $\begingroup$ If you want to use this problem to learn I don't think this is a good cost function (but I can't suggest a better one). If you need to solve this problem there are many tools to find the minimum for this function, the easiest being Excel. $\endgroup$ – N74 Aug 23 '17 at 18:47
  • $\begingroup$ You could try to solve this with an MINLP solver (these are readily available). $\endgroup$ – Erwin Kalvelagen Aug 24 '17 at 6:25

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