You could perform a Bayesian (Gaussian Process) optimization. This is not ideal as it's manual, and a non smooth evaluation space will require many backtests to probe properly.
Spearmint-lite and other such programs were designed with just this in mind. You could automate the process with the non-lite Spearmint + Lean. Be warned, your evaluation method will determine how overfit the result is.
This project is not useful for this case, but the plots help explain the process very well/fast:
https://github.com/fmfn/BayesianOptimization