Evolutionary Algorithm Problem 63

This is also a test example taken from [4], problem 63 on pg 85. Now we try something new by adding nonlinear constraints. The objective function is:

$\displaystyle f(x)= 1000 - x_{1}^2 - 2x_{2}^2 - x_{3}^2 - x_1x_2 - x_1x_3,
$

subject to the constraints:
$ 8x_1 + 14x_2 + 7x_3 - 56 = 0$
$ x_{1}^2 + x_{2}^2 + x_{3}^2 - 25 = 0$
$ x_i \ge 0 (i=1, 2, 3)$ ,

The previous best known solution in [4] was

$ \mathbf{x}^{*} = (3.512118414,  0.2169881741,  3.552174034)$ ,
and $ f(\mathbf{x}^{*}) = 961.7151721$ .

Same as the previous examples, we express one variable as two constrained functions of the remaining two variables. The optimal solution found by the CE algorithm was

$ \mathbf{x}^{*} = (3.51212143194203,  0.21698793435542,  3.55217106621256)$ ,
and $ f(\mathbf{x}^{*}) = 961.715172130052$ with sample size $ m=30$ , rarity paramter $ \varrho =0.1$ and smoothing parameter $ \alpha=0.2$ . This result was derived after 41 iterations in less than 8 sec of CPU time.

gen.m - generation of samples, satifying constraints.

normt1.m - generates truncated normals

opt.m - main program

S.m - objective function



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2004-12-17