how can i use simulated annealing for calculating the regression coefficients?

Hello

I want to use simulated annealing method to calculate the coefficients of the following regression model:

dx=a0+a1x+a2y

dy=b0+b1x+b2y

my cost function is RMSE of this model. how can i use the simulated annealing for this problem?

I ask my friends to guide me.

Thanks you

Answer 1

[Torsten]

It's not simulated annealing, but most probably much faster.

M = [3979278.479	654200.79	35.38	-27.86
    4196516.825	554782.87	24.62	-18.59
    4232567.466	547982.05	19.88	-14.25
    4075226.435	613109.41	33.11	-27.08
    4118223.816	614123.66	23.23	-18.99
    4133106.88	563347.67	32.14	-23.61
    4178506.624	590038.35	15.94	-13.94
    4065198.758	626890.47	34.94	-26.97
    4155089.531	580988.82	24.37	-19.81
    4132633.258	579808.77	28.04	-20.78
    4080104.632	625582.59	32.2	-25.99
    4073897.357	640928.48	26.13	-17.13
    4055819.216	637942.92	34.4	-27.1
    4119454.841	626505.32	13.02	-12.83
    4203712.37	599359.61	10.45	-10.65
    3936616.293	740450.19	30.15	-24.09
    3969466.343	735778.54	26.27	-17.85
    3978570.896	688822.82	32.94	-26.24
    3989155.086	707440.89	32.72	-27.59
    4001583.747	690843.64	33.48	-27.14
    4006187.318	704299.83	11.6	-8.63
    3946774.43	747480.17	26.67	-21.59
    3967621.793	717309.19	32.47	-24.11
    3983606.726	731375.87	17.78	-11.25
    3978003.827	727514.86	28.17	-19.05
    3936119.58	761801.36	24.16	-20.79
    4301922.423	507200.19	16.87	-16.08
    4316922.001	555890.75	8.48	-8.54
    4101937.001	567780.19	35.27	-26.91
    4038480.372	608158.43	36.34	-27.97];
y = M(:,1);
x = M(:,2);
dy = M(:,3);
dx = M(:,4);
A = [ones(size(y,1),1) x y];
b = dx;
solx = A\b;
a0 = solx(1)

a0 = -587.0689

a1 = solx(2)

a1 = 1.4526e-04

a2 = solx(3)

a2 = 1.1618e-04

norm(A*solx-dx);
figure(1)
plot(1:numel(dx),[dx,a0+a1*x+a2*y])

b = dy;
soly = A\b;
b0 = soly(1)

b0 = 814.4896

b1 = soly(2)

b1 = -1.9792e-04

b2 = soly(3)

b2 = -1.6232e-04

norm(A*soly-dy);
figure(2)
plot(1:numel(dy),[dy,b0+b1*x+b2*y])

[Mary Tavoosi]

thanks for your answer. ut i want to know, is possible and good to use SA for this problem? or i should use other way such as LS for this problem.

[Torsten]

I did LS above.