# Re: [eclipse-clp-users] Q: Linear Programming with Disjunction constraints

From: Kim Lai <kim73327_at_...6...>
Date: Fri, 25 Apr 2008 06:52:36 +0800
```hi, your reply is a great help for me. thanks.I use lib(eplex) to
reformulate my problem as follow. and it really got a solution.
But after I port the following code to C++. I'm getting trouble with ""How
to extract the variables result"".
A result like this
"A2{0.0 .. 1.7976931348623157e+308 _at_ 1.1999999992549422}"
I'd like to extract A2=1.199 = 1.2
But it's not even a string...
in C++: I usually use "EC_word(Vars[i]).is_double(&d) == EC_succeed"
to get a double or long int .....And this didn't work..
------------eclipse code------------------------
- lib(eplex).

solve(Vars, Cost) :-

model(Vars, Obj),

eplex_solver_setup(min(Obj)),

eplex_solve(Cost),

printf("%f %f %f", Vars ).

model(Vars, Obj) :-

Vars = [A1, A2, A3 ],

Vars \$:: 0..inf,

M = 10000000,

B1 :: 0..1,

B2 :: 0..1,

Obj \$>= A1 + 1.2,

Obj \$>= A2 + 2.3,

Obj \$>= A3 + 1.3,

A2 - A1 + B1*M \$=< -0.2 + M,

A2 - A1 + (1-B1)*M \$>= 1.2 + M,

A3 - A2 + B2*M \$=< -0.4 + M,

A3 - A2 + (1-B2)*M \$>= 1.5 + M.
--------------------------------------------------------------------------

thanks for ur reply :)

On Thu, Apr 24, 2008 at 12:52 AM, Kish Shen <kisshen_at_...5...> wrote:

> Hi Kim,
>
> Kim Lai wrote:
>
>>
>>
>> ---------- Forwarded message ----------
>> From: *Kim Lai* <kim73327_at_...6... <mailto:kim73327_at_...6...>>
>> Date: Apr 23, 2008 10:56 PM
>> Subject: Q: Linear Programming with Disjunction constraints
>> To: eclipse-clp-users_at_...105... <mailto:eclipse-clp-users@...105...
>> >
>>
>> hi, I'm new to eclipse. Here looks for a great HELP.
>> after studying the documents... I still have trouble with my problem.
>> I don't know how to use lib(eplex) for 1. disjunctive constraints
>> 2. get a maximum among lots Varables
>>
>>  The ECLiPSe documentation on eplex is not really designed to teach you
> linear programming, or even constraint programming You would need to read
> other source material (e.g. textbooks on linear programming and constraint
> programming) for this.
>
> However, the issue of disjunctive constraint (which are non-linear, and
> therefore cannot be directly modelled in linear programming) is discussed in
> the ECLiPSe tutorial, in the chapter `Building Hybrid Algorithms' (section
> 'Handling Disjunctions').
>
> A well known aproach in linear programming to model disjunctions is to use
> `Big-M constraints' -- this is discussed in the tutorial chapter.
>
> For your point 2, see below.
>
>  I'd like to formulate a problem like this:
>>
>> ------------------------------------------------------------------------------
>> Vars = [ t1, t2, t3 ]
>> Vars :: 0.0..inf
>>
>> % constraints
>> (t1 - t2 <= -10.2  or  t1 - t2 >= 15.6) and
>> (t2 - t3 <= -3.1 or t2 - t3 >= 9.8 )
>> % goal ( cost )
>> try to minimize( Maximum among( t1 + 14.5, t2+1.4, t3+ 4.5 ) )
>> -------------------------------------------------------------------------
>>
>
> Looking at your example, you seem to be trying to model some sort of job
> scheduling problem. The standard technique to model the minimum time to
> complete a schedule is to add a `dummy' task that can only start after all
> the other tasks have completed, and minimise the start time of this task as
> your objective.
>
> If you are to model this in ic, you probably want to use finite domain
> rather than real intervals -- to do this you need to have integers only, so
> you need to choose your time unit so that they are integer, for your
> example, this would seem to be in units of 0.1 seconds rather than seconds.
>
> This sort of problem can also be modelled as a linear problem using Big-M
> constraints.
>
> The example page of the ECLiPSe website has several scheduling examples
> (under the Planning and Scheduling section) which you might find useful to
> look at:
>
> http://www.eclipse-clp.org/examples/index.html
>
> I will take a look at your specific code to see why you are getting the
> error you are getting, but you should not need to use maxlist/2 with the
> dummy task approach.
>
> Cheers,
>
> Kish
>
>

--
....Best Regards
by Kim Lai, 賴廣甫
Welcome to visit http://kimklai.blogspot.com
```
Received on Thu Apr 24 2008 - 15:52:38 CEST

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