Infeasible solution by AMPL solver..

[Dipankar Narayanan]

Hello Experts,

I am solving an optimization problem of which the .mod is given below:

reset;

param KNDC;

param KALL;

param N;

param PT;

param D {1..(KALL-KNDC)};

set TNDCSET:= {1..KNDC*N};

param H{1..KALL*N};

var C{1..KALL*N} binary;

var P{1..KALL*N} >= 0, <=PT;

var Q{1..KALL*N};

var Z{1..KALL*N};

###########     OPTION1: OBJ    #################

maximize OBJ: sum {t in 1..KNDC*N} ((1/card(TNDCSET)*(log(Q[t])/log(2))));

###########     OPTION2: OBJ    #################

maximize OBJ: prod {t in TNDCSET} (Q[t])^(1/card(TNDCSET));

subject to C10 {n in 1..N}: sum {t in n..KALL*N by N} C[t] = 1;

subject to C41 {t in 1..KALL*N}: Z[t] <= PT*C[t];

subject to C42 {t in 1..KALL*N}: Z[t] >= 0;

subject to C43 {t in 1..KALL*N}: Z[t] <= P[t];

subject to C44 {t in 1..KALL*N}: Z[t] >= P[t]-PT*(1-C[t]);

subject to C45: sum {t in 1..KALL*N} Z[t] == PT;

###########     OPTION1: CON50    #################

subject to C50 {k in {1..(KALL-KNDC)}}: sum {t in KNDC*N+1+(k-1)*N..KNDC*N+N+(k-1)*N} (((1/N)*(log(Q[t])/log(2)))) >= Rate_Req[k];

###########     OPTION2: CON50    #################

subject to C50 {k in {1..(KALL-KNDC)}}: prod {t in KNDC*N+1+(k-1)*N..KNDC*N+N+(k-1)*N} Q[t]^(1/N) >= D[k];

subject to C60 {t in 1..KALL*N}: Q[t]-min(P[t],PT*C[t])*H[t] <= 1 ;

Note that the objective can be written in two ways: OPTION: OBJ1 and OPTION: OBJ2.

When I run this program, for OPTION1: OBG and corresponding OPTION1: CON50, I get the following output:

Relative change in infeasible solution estimate < xtol.

objective 89.17063187; integrality gap 1e+20

1 nodes; 1 subproblem solves

suffix incumbent OUT;

suffix relaxbnd OUT;

However, for the OPTION2: OBJ and corresponding OPTION2: CON50, I get

KNITRO 9.0.1: Convergence to an infeasible point. Problem may be locally infeasible.

objective 5.125245003; integrality gap 1e+20

5 nodes; 5 subproblem solves

suffix incumbent OUT;

suffix relaxbnd OUT;

What is the problem and how can i fix this?

The .dat is given here:

data;

param KNDC:=2;

param KALL:=4;

param N:=10;

param PT:= 1;

param D:= 1 1.4 2 1.6;

param H  := 1 1366   2 1474   3 1690   4 1790   5 1881  6 1963  7 2036  8 2315  9 536 10 636 11 775  12 2350 13 1143 14 2041 15 1345 16 1420 17 1503 18 1698 19 1808 20 1335  21 2225 22 2327  23 1494   24 1523   25 1989   26  1796  27 1712   28  1493  29  1425  30  1364  31  1092  32  1034  33  1016  34  1024  35  1297  36  1035  37  1108  38  1107  39 1291  40 1288;

[Robert Fourer]

Both "Relative change in infeasible solution estimate < xtol" and "Convergence to an infeasible point" indicate that KNITRO could not find a feasible solution for your constraints. This could mean that your constraints are really infeasible: that there is no way to assign values to the variables that will satisfy all of the constraints. Or it could mean that KNITRO was unable to iterate to a feasible solution when starting from the initial solution that you gave.

It appears that you did not specify any initial values for the variables, so by default AMPL would have sent all zero values, which is often not a good start. You can specify your own initial values using the data file as for parameters, or by using a := express in the var declaration, or by using "let" statements to assign values. There's a discussion of initial values for nonlinear problems in the AMPL book here: http://ampl.com/BOOK/CHAPTERS/21-nonlinear.pdf#page=8.

Bob Fourer
am...@googlegroups.com

=======

From: am...@googlegroups.com [mailto:am...@googlegroups.com] On Behalf Of Dipankar Narayanan
Sent: Sunday, December 14, 2014 9:07 PM
To: am...@googlegroups.com
Subject: [AMPL 9762] Infeasible solution by AMPL solver..

I am solving an optimization problem of which the .mod is given below:

.......