Let's say I have some data to adjust to this model:
$$V=V_0 +K_1(\cos (\omega_1 +f_1)+e_1\cos(\omega_1)) + K_2(\cos (\omega_2 +f_2)+e_2\cos(\omega_2)), $$
with $V_0$, $K_1$, $K_2$, $\omega_1$, $\omega_2$, $e_1$, $e_2$, $T_1$, $T_2$ parameters of the problem, $f_1(f_2)$ depends on $T_1(T_2)$ and $e_1(e_2)$. Note the model is just a sum of two sinusoidal waves.
I was trying to fit these parameters using the dual-annealing function in Python, which doesn't require no initial parameters but just bounds to each one of the parameters. That made me think, does it mean that in a global minimum problem like this the solution doesn't depend on the initial guesses of the parameters? And if so, does it affect the accuracy of the solutions?
Simulated annealing methods are stochastic methods inspired in the metal annealing with cooling process. It can be considered a stochastic gradient method and it's application doesn't depends on the initial point but depends on the search region size. See this short introduction.