How use bounding restrictions in Baron

Support
1

Hello, I’m trying to solve a nonlinear problem with Baron in NEOS. Without an optional bounding restriction, I get solutions. However, when I try to use it, I don’t get any solution. Any idea why this might happen?

The model is for a square packing problem, and the bounding restriction tries to limit the area of the box.

Here’s the model:
nero.run (611 Bytes)
MGC.mod (2.3 KB)
MecfG.dat (2.0 KB)

Best regards

2

Here’s what I see when I run on NEOS with a time limit of 100 seconds. When the bounding restriction is not included, BARON’s preprocessing heuristics find a feasible solution with objective value 35.6983. The subsequent search does not find any better solution, so the feasible solution found by preprocessing is returned:

Doing local search
 Solving bounding LP
 Starting multi-start local search
 Preprocessing found feasible solution with value 35.6983
 Done with local search
===========================================================================
  Iteration       Time (s)     Mem   Lower bound     Upper bound   Progress
          1          22.39    28MB     0.625000E-01    35.6983        0.02%
         15          54.65    28MB     0.625000E-01    35.6983        0.04%
        127          88.36    28MB     0.625000E-01    35.6983        0.05%
        382         100.02    37MB     0.625000E-01    35.6983        0.05%

                    *** Max. allowable time exceeded ***   
.......

BARON 24.5.8 (2024.05.08): 382 iterations, CPU time limit reached.
Objective 35.69833937

When you add the bounding restriction,

s.t. tes4: (W)*(H)<=25.00;

the previous solution with objective value (W)*(H) equal to 35.6983 is no longer feasible. Neither the preprocessing nor the search is able to find any feasible solution at all before BARON reaches the time limit:

 Doing local search
 Solving bounding LP
 Starting multi-start local search
 Done with local search
===========================================================================
  Iteration       Time (s)     Mem   Lower bound     Upper bound   Progress
          1          47.02    28MB     0.625000E-01   0.100000E+52    NA
          3+         80.26    28MB     0.625000E-01   0.100000E+52    NA
          4         100.01    28MB     0.625000E-01    25.0000        0.00%

                    *** Max. allowable time exceeded ***     

                   *** No feasible solution was found ***

Thus no solution is returned.

Since you are seeing the same behavior even with a much higher time limit, it may be that there is no feasible solution at all with (W)*(H)<=25.00. Or there may be a feasible solution satisfying this constraint, but it is very hard for BARON to find.