MINLP non optimal solution

GAMS
1

dear sir,

Consider the following code:

SOC(time)… soc(time) =e= (1-alpha)*soc(time-1)$(ord(time)1)

  • (1-alpha)*soc_ini$(ord(time)=1)
  • (P(time)/cap)U(time)U(time)0.5(deltainj(1 + U(time))+(U(time)-1)/(delta*ext));

ptotal(time)… Ptot(time) =e= w(time) - P(time)*U(time);

*U.fx(“3”) = -1;
U.lo(time) = -1;
U.up(time) = 1;
obj… Z =e= sum(time, mcp(time)*Ptot(time));

The obj has to be maximized using MINLP. The optimal obj solution is 600, U is an integer variable, P is a positive variable, w is a parameter matrix, but if U(3) is forced to -1; the optimal value of the objective function is 900.

Can anyone help me with it? It seems that the CONOPT/SBB solver is not able to optimize.

With regards,
Subir

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2

Hi all,

Attached is the marginal values for the above problem solved using two solvers,

using SBB (licensed):
Simple B&B Sep 3, 2003 WIN.SB.SB 21.2 011.026.041.VIS

Relaxed problem gives integer solution.

---- EQU SOC_batt Battery soc level

LOWER LEVEL UPPER MARGINAL

1 0.495 0.495 0.495 EPS
2 . . . EPS

---- EQU Ptotal total power supplied

LOWER LEVEL UPPER MARGINAL

1 10.000 10.000 10.000 EPS
2 20.000 20.000 20.000 EPS

LOWER LEVEL UPPER MARGINAL

---- EQU obj 501.788 501.788 501.788 1.000

---- VAR Ptot total flow

LOWER LEVEL UPPER MARGINAL

1 . 10.000 30.000 .
2 . 20.000 30.000 .

---- VAR soc SOC of battery

LOWER LEVEL UPPER MARGINAL

1 0.200 0.495 0.800 .
2 0.200 0.490 0.800 .

LOWER LEVEL UPPER MARGINAL

---- VAR Z -INF 501.788 +INF .

Z obj function

---- VAR P_Batt Battery output

LOWER LEVEL UPPER MARGINAL

1 . . 40.000 EPS
2 . . 40.000 EPS

---- VAR U_Batt

LOWER LEVEL UPPER MARGINAL

1 -1.000 . 1.000 EPS
2 -1.000 . 1.000 EPS


**** REPORT SUMMARY : 0 NONOPT
0 INFEASIBLE
0 UNBOUNDED
0 ERRORS


EXECUTION TIME = 0.000 SECONDS 0.8 Mb WIN212-136



using BARON (demo):

Baron 5.0 Sep 3, 2003 WIN.BA.NA 21.2 005.000.000.VIS P3PC

Branch And Reduce Optimization Navigator
Nikolaos Sahinidis and Mohit Tawarmalani
The Optimization Firm, LLC.

Total time elapsed : 000:00:00, in seconds: 0.02
on parsing : 000:00:00, in seconds: 0.00
on preprocessing: 000:00:00, in seconds: 0.02
on navigating : 000:00:00, in seconds: 0.00
on relaxed : 000:00:00, in seconds: 0.00
on local : 000:00:00, in seconds: 0.00
on tightening : 000:00:00, in seconds: 0.00
on marginals : 000:00:00, in seconds: 0.00
on probing : 000:00:00, in seconds: 0.00


Total no. of BaR iterations: 1
Best solution found at node: 1
Max. no. of nodes in memory: 1


Solution = 800.004 found at node 1
Best possible = 800.004
Absolute gap = 0 optca = 0
Relative gap = 0.00000 optcr = 0.1

— Using CONOPT to complete solution

CONOPT iterations = 4
CONOPT time = 0.055 seconds
CONOPT max rmove = 7.76E-07
CONOPT rel norm2 = 9.21E-07


---- EQU SOC_batt Battery soc level

LOWER LEVEL UPPER MARGINAL

1 0.495 0.495 0.495 680.000
2 . . . 686.869

---- EQU Ptotal total power supplied

LOWER LEVEL UPPER MARGINAL

1 10.000 10.000 10.000 EPS
2 20.000 20.000 20.000 -9.899

LOWER LEVEL UPPER MARGINAL

---- EQU obj 501.788 501.788 501.788 1.000

---- VAR Ptot total flow

LOWER LEVEL UPPER MARGINAL

1 . 19.822 30.000 .
2 . 30.000 30.000 9.899

---- VAR soc SOC of battery

LOWER LEVEL UPPER MARGINAL

1 0.200 0.351 0.800 .
2 0.200 0.200 0.800 -686.869

LOWER LEVEL UPPER MARGINAL

---- VAR Z -INF 800.004 +INF .

Z obj function

---- VAR P_Batt Battery output

LOWER LEVEL UPPER MARGINAL

1 . 9.822 40.000 .
2 . 10.000 40.000 .

---- VAR U_Batt

LOWER LEVEL UPPER MARGINAL

1 -1.000 -1.000 1.000 168.162
2 -1.000 -1.000 1.000 172.945


**** REPORT SUMMARY : 0 NONOPT
0 INFEASIBLE
0 UNBOUNDED
0 ERRORS


EXECUTION TIME = 0.000 SECONDS 0.8 Mb WIN212-136

I think while using SBB the integer variables are remaining at 0. Can anyone give any insight about it?

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