[Fwd: Re: How can regions be modeled in which different objective functions apply?]

-------- Forwarded Message --------
From: Thomas Schwabhäuser <[email protected]>
To: [email protected]
Subject: Re: How can regions be modeled in which different objective
functions apply?
Date: Thu, 28 Sep 2017 16:11:54 +0200

Dear Optimizers  --

 

It was not even hard to figure out that the quoted Problem is equivalent
to

 

var X{i in 0..1};

var Y{j in 0..1};

 

maximize energy: ObjF;

 

s.t. AllRegions{i in I,j in I}: ObjF <= ObjF[i,j];

s.t. EachRegion{i in I,j in I}: ObjF[i,j] = F[i,j,X[i,j],Y[i,j]];

s.t. Region1X: X[0,0] <= S;

s.t. Region1Y: Y[0,0] <= T;

s.t. Region2X: X[1,0] >= S;

s.t. Region2Y: Y[1,0] <= T;

s.t. Region3X: X[0,1] <= S;

s.t. Region3Y: Y[0,1] >= T;

s.t. Region4X: X[1,1] >= S;

s.t. Region4Y: Y[1,1] >= T;

 

provided F[i,j,x,y] dispatches to/is replaced by the functions F[x,y],
G[x,y], H[x,y], andK[x,y] according to the Indices i and j which are
assumed to take the value 0 or 1. This variant uses 8 variables X[i,j]
and Y[i,j] each pair (X,Y) is bound to the desired region above or below
the thresholds. However, once the maximum energy is determined we do not
necessarily need to tell for which values of X and Y the objective
function takes its maximum but at least for which combination of i and j
the maximum was found.

      * Could anybody tell how to find the right values of i and j,
        please?

2017-09-28 11:02 GMT+02:00 Thomas Schwabhäuser
<[email protected]>:
        Dear All --
        
         
        
        
        I need to find the maximum energy which is given by 4 GMPL
        expressions F[x,y], G[x,y], H[x,y], K[x,y], say. These
        expressions apply to different regions determined by thresholds
        S and T. According to Re: [Help-glpk] Multiple LP problem
        solving I was going to solve the following Problem:
         
        
             maximize Energy: ObjF;
        
         
        
             subject to Region1: x >= S or y >= T or ObjF <= F[x,y] ;
        
             subject to Region2: x <= S or y >= T or ObjF <= G[x,y];
        
             subject to Region3: x >= S or y <= T or ObjF <= H[x,y];
        
             subject to Region4: x <= S or y <= T or ObjF <= K[x,y];
        
         
        
        Unfortunately the Messages when parsing this are
        
         
        
        Reading model section from models\RLMF.mod...
        
        models\Regions.mod:79: syntax error in constraint statement
        
        Context: ...ize Energy : Z ; subject to Region1 : XM >= Thresh_M
        or
        
         
        
             1. Can somebody explain this error?
             2. I suspect a logical or is not allowed in constraints. Is
                that true?
             3. If so, could anybody propose an alternative?
        
         
        
        Thanks, Thomas
        
        




-- 
Mit freundlichen Grüßen

Thomas Schwabhäuser,
Melittastrasse 9,
70597 Stutttgart

Tel.  + 49 (0) 711 - 76 22 41,
Cel.  + 49 (0) 171 - 491 50 96

[email protected]
http://www.cip.mathematik.uni-stuttgart.de/~schwabts/




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