FindMinimum might be getting caught in a local minimum. If you're looking for a global minimum, you could try using NMinimize instead of FindMinimum. FindMinimum only searches for a local minimum. NMinimize doesn't guarantee a global minimum, and it's slower, but it finds a better solution (333.399) in a little over a minute on my system (2011 laptop):
In[51]:= NMinimize[
{Total[...] + ...,
0.001 <= u <= 1,
5 <= l0 <= 10,
0.001 <= m0 <= 1,
0.001 <= tc <= 3.7},
{u, l0, m0, tc, c1, c2, c3, c4}
]
Out[51]= {333.399, {u -> 0.206876, l0 -> 5.14977, m0 -> 0.260959,
tc -> 3.31495, c1 -> -0.183037, c2 -> -1.67226, c3 -> 2.09666,
c4 -> 0.623773}}
You can also specify different Methods for NMinimize to use. The above is the default ("NelderMead" for your problem). I tried the other three with their default options and got these results:
Method->"SimulatedAnnealing" did better (156.368) in about 6 minutes:
In[54]:= NMinimize[
{Total[...] + ...,
0.001 <= u <= 1,
5 <= l0 <= 10,
0.001 <= m0 <= 1,
0.001 <= tc <= 3.7},
{u, l0, m0, tc, c1, c2, c3, c4} ,
Method -> "SimulatedAnnealing"
]
Out[54]= {156.368, {u -> 0.288779, l0 -> 7.41511,
m0 -> 0.350708, tc -> 3.31493, c1 -> -0.766559, c2 -> 0.490018,
c3 -> 0.128281, c4 -> -1.55951}}
Method->"DifferentialEvolution" did slightly better still (145.673), but it took 16 minutes:
In[53]:= NMinimize[
{Total[...] + ...,
0.001 <= u <= 1,
5 <= l0 <= 10,
0.001 <= m0 <= 1,
0.001 <= tc <= 3.7},
{u, l0, m0, tc, c1, c2, c3, c4} ,
Method -> "DifferentialEvolution"
]
Out[53]= {145.673, {u -> 0.432289, l0 -> 6.63203,
m0 -> 0.289599, tc -> 3.31489, c1 -> 0.670817, c2 -> -0.835306,
c3 -> 10.1536, c4 -> -6.43342}}
Finally, Method->"RandomSearch" did the best (6.30799), but it ran for over an hour with the default options:
In[55]:= NMinimize[
{Total[...] + ...,
0.001 <= u <= 1,
5 <= l0 <= 10,
0.001 <= m0 <= 1,
0.001 <= tc <= 3.7},
{u, l0, m0, tc, c1, c2, c3, c4} ,
Method -> "RandomSearch"
]
Out[55]= {6.30799, {u -> 0.620098, l0 -> 6.82731,
m0 -> 0.27329, tc -> 3.3149, c1 -> 3.81016, c2 -> -9.4462,
c3 -> 316., c4 -> -3155.41}}
You might be able to speed it up by using some of the other sub-options described at the bottom of this page: Numerical Nonlinear Global Optimization.