       Re: Optimization with conditional restrictions

• To: mathgroup at smc.vnet.net
• Subject: [mg44593] Re: Optimization with conditional restrictions
• From: "Dana DeLouis" <delouis at bellsouth.net>
• Date: Mon, 17 Nov 2003 03:38:25 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```This is very similar to Danielâ?? solution.

equ = 3000*x11 + 55*x12 + 3000*x21 + 53*x22 +
3000*x31 + 53*x32;

var = Variables[equ]

{x11, x12, x21, x22, x31, x32}

We note the following constraint:

FullSimplify[25*x12 + 25*x22 + 25*x32 == 16000]

x12 + x22 + x32 == 640

const =
{x12 + x22 + x32 == 640,
0 <= x12 <= 336,
0 <= x22 <= 336,
0 <= x32 <= 336,
(x11 | x21 | x31) â?? Integers,
x11 == -DiscreteDelta[x12] + 1,
x21 == -DiscreteDelta[x22] + 1,
x31 == -DiscreteDelta[x32] + 1};

solution = Rationalize[NMinimize[{equ, const}, var]]

{40528,
{x11 -> 1, x12 -> 304, x21 -> 1, x22 -> 336, x31 -> 0, x32 -> 0}}

--
Dana DeLouis
Windows XP
Mathematica 5.0 for Windows
delouis at bellsouth.net
= = = = = = = = = = = = = = = = =

<guillerm at usal.es> wrote in message news:bovoca\$mj6\$1 at smc.vnet.net...
>
> Dear group,
> I wish minimize a function, ej:
> 55*x12 + 53*x22 + 53*x32 + 3000*x11 + 3000*x21 + 3000*x31
> including conditional restrictions, ej:
> x11 == If[x12 > 0, 1, 0] && x21 == If[x22 > 0, 1, 0] &&
> x31 == If[x32 > 0, 1, 0]},
> And other standars restrictions
>
> Here is an example:
>
> NMinimize[{55*x12 + 53*x22 + 53*x32 + 3000*x11 + 3000*x21 + 3000*x31,
> 25*x12 + 25*x22 + 25*x32 == 16000 && 0 <= x12 <= 336 &&
> 0 <= x22 <= 336 && 0 <= x32 <= 336 &&
> x11 Â?Â¸ Integers && x21 Â?Â¸ Integers && x31 Â?Â¸ Integers &&
> x11 == If[x12 > 0, 1, 0] && x21 == If[x22 > 0, 1, 0] &&
> x31 == If[x32 > 0, 1, 0]}, {x11, x12, x21, x22, x31, x32}]
>
> Out[]:= {42920.000, {x11 -> 1, x12 -> 2.078*^-7, x21 -> 1, x22 -> 323.29, x31 -
> > 1, x32 -> 316.7}}
>
> The out is wrong, if x12-> 0, should be x11-> 0. I have tested changing the
> restricions, writting: x11 == If[x12 > 0.01, 1, 0] && x21 == If[x22 > 0.01, 1,
> 0] && x31 == If[x32 > 0.01, 1, 0]
>
> Any help
>
> Guillermo Sanchez

```

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