nag_ip_bb (h02bbc) Example Program Results
Parameters to h02bbc
--------------------
Linear constraints............ 3 Number of variables........... 6
Number of integer variables... 6
prob.................... Nag_MILP
feas_tol............... 1.05e-08 machine precision...... 1.11e-16
inf_bound.............. 1.00e+20 max_iter................ 50
first_soln............. Nag_FALSE max_depth............... 10
max_nodes.............. ALL_NODES int_tol................ 1.00e-05
int_obj_bound.......... 1.00e+20 soln_tol............... 1.05e-08
nodsel......... Nag_MinObj_Search varsel............. Nag_First_Int
branch_dir....... Nag_Branch_Left crnames................. supplied
print_level............. Nag_Soln
outfile................. stdout
Memory allocation:
lower................... Nag
upper................... Nag
state................... Nag
lambda.................. Nag
Final solution:
Varbl State Value Lower Bound Upper Bound Lagr Mult Residual
OATMEAL EQ 4.00000e+00 4.0000e+00 4.0000e+00 3.000e+00 0.000e+00
CHICKEN LL 0.00000e+00 0.0000e+00 3.0000e+00 2.400e+01 0.000e+00
EGGS LL 0.00000e+00 0.0000e+00 2.0000e+00 1.300e+01 0.000e+00
MILK LL 5.00000e+00 5.0000e+00 8.0000e+00 9.000e+00 0.000e+00
PIE EQ 2.00000e+00 2.0000e+00 2.0000e+00 2.000e+01 0.000e+00
BACON LL 0.00000e+00 0.0000e+00 2.0000e+00 1.900e+01 0.000e+00
Constr State Value Lower Bound Upper Bound Lagr Mult Residual
ENERGY FR 2.08000e+03 2.0000e+03 None 0.000e+00 8.000e+01
PROTEIN FR 6.40000e+01 5.5000e+01 None 0.000e+00 9.000e+00
CALCIUM FR 1.47700e+03 8.0000e+02 None 0.000e+00 6.770e+02
Exit from branch and bound tree search after 27 nodes.
Optimal IP solution found.
Final IP objective value = 9.7000000e+01
Solve modified problem - use different tree search.
---------------------------------------------------
***Set options.list = Nag_FALSE
***Set options.int_obj_bound = 9.7001000e+01
***Set options.nodsel = Nag_Deep_Search
***Set options.print_level = Nag_Iter
Node Parent Obj Varbl Value Lower Upper Value Depth
No Node Value Chosen Before Bound Bound After
1 9.081e+01
2 1 9.165e+01 4 4.31e+00 0.00e+00 4.00e+00 4.00e+00 1
3 1 9.176e+01 4 4.31e+00 5.00e+00 8.00e+00 5.00e+00 1
4 2 9.206e+01 6 1.92e-01 0.00e+00 0.00e+00 0.00e+00 2
5 2 9.519e+01 6 1.92e-01 1.00e+00 2.00e+00 1.00e+00 2
6 4 9.385e+01 3 3.13e-01 0.00e+00 0.00e+00 0.00e+00 3
7 4 9.481e+01 3 3.13e-01 1.00e+00 2.00e+00 1.00e+00 3
8 6 Infeasible 2 2.44e-01 0.00e+00 0.00e+00 2.44e-01 4
9 6 1.033e+02 CO 2 2.44e-01 1.00e+00 3.00e+00 1.00e+00 4
10 7 9.606e+01 4 3.31e+00 0.00e+00 3.00e+00 3.00e+00 4
11 7 9.576e+01 4 3.31e+00 4.00e+00 4.00e+00 4.00e+00 4
12 10 9.785e+01 CO 3 1.31e+00 1.00e+00 1.00e+00 1.00e+00 5
13 10 9.881e+01 CO 3 1.31e+00 2.00e+00 2.00e+00 2.00e+00 5
14 11 1.116e+02 CO 5 1.74e+00 0.00e+00 1.00e+00 1.00e+00 5
15 11 9.800e+01 CO 5 1.74e+00 2.00e+00 2.00e+00 2.00e+00 5
16 5 1.039e+02 CO 4 2.69e+00 0.00e+00 2.00e+00 2.00e+00 3
17 5 9.562e+01 4 2.69e+00 3.00e+00 4.00e+00 3.00e+00 3
18 17 1.023e+02 CO 5 1.88e+00 0.00e+00 1.00e+00 1.00e+00 4
19 17 9.664e+01 5 1.88e+00 2.00e+00 2.00e+00 2.00e+00 4
20 19 9.838e+01 CO 1 3.55e+00 0.00e+00 3.00e+00 3.00e+00 5
21 19 9.800e+01 CO 1 3.55e+00 4.00e+00 4.00e+00 4.00e+00 5
22 3 9.444e+01 5 1.74e+00 0.00e+00 1.00e+00 1.00e+00 2
23 3 9.400e+01 5 1.74e+00 2.00e+00 2.00e+00 2.00e+00 2
*** Integer Solution ***
***IP objective value = 9.4000000e+01
Illustrate effect of supplying branching directions.
----------------------------------------------------
***Set options.branch_dir = Nag_Branch_InitX
Node Parent Obj Varbl Value Lower Upper Value Depth
No Node Value Chosen Before Bound Bound After
1 9.081e+01
2 1 9.176e+01 4 4.31e+00 5.00e+00 8.00e+00 5.00e+00 1
3 1 9.165e+01 4 4.31e+00 0.00e+00 4.00e+00 4.00e+00 1
4 2 9.400e+01 5 1.74e+00 2.00e+00 2.00e+00 2.00e+00 2
*** Integer Solution ***
5 2 9.444e+01 CO 5 1.74e+00 0.00e+00 1.00e+00 1.00e+00 2
6 3 9.206e+01 6 1.92e-01 0.00e+00 0.00e+00 0.00e+00 2
7 3 9.519e+01 CO 6 1.92e-01 1.00e+00 2.00e+00 1.00e+00 2
8 6 9.385e+01 3 3.13e-01 0.00e+00 0.00e+00 0.00e+00 3
9 6 9.481e+01 CO 3 3.13e-01 1.00e+00 2.00e+00 1.00e+00 3
10 8 Infeasible 2 2.44e-01 0.00e+00 0.00e+00 2.44e-01 4
11 8 1.033e+02 CO 2 2.44e-01 1.00e+00 3.00e+00 1.00e+00 4
***IP objective value = 9.4000000e+01
Obtain solution of root LP problem.
-----------------------------------
***Printout suppressed: options.print_level = Nag_NoPrint
***LP objective value = 9.0812500e+01
Finally, solve a related MIQP problem.
--------------------------------------
Parameters to h02bbc
--------------------
Linear constraints............ 3 Number of variables........... 6
Number of integer variables... 6
prob................... Nag_MIQP2
feas_tol............... 1.05e-08 machine precision...... 1.11e-16
inf_bound.............. 1.00e+20 max_iter................ 50
rank_tol............... 1.11e-14 max_df.................. 6
hrows................... 6
first_soln............. Nag_FALSE max_depth............... 10
max_nodes.............. ALL_NODES int_tol................ 1.00e-05
int_obj_bound.......... 1.00e+20 soln_tol............... 1.05e-08
nodsel......... Nag_MinObj_Search varsel............. Nag_First_Int
branch_dir....... Nag_Branch_Left crnames................. supplied
print_level........ Nag_Soln_Iter
outfile................. stdout
Memory allocation:
lower................... Nag
upper................... Nag
state................... Nag
lambda.................. Nag
(User-supplied callback qphess, first invocation.)
Node Parent Obj Varbl Value Lower Upper Value Depth
No Node Value Chosen Before Bound Bound After
1 -3.860e+01
2 1 -3.848e+01 4 4.31e+00 0.00e+00 4.00e+00 4.00e+00 1
3 1 -3.812e+01 4 4.31e+00 5.00e+00 8.00e+00 5.00e+00 1
*** Integer Solution ***
4 2 -3.847e+01 2 7.58e-02 0.00e+00 0.00e+00 0.00e+00 2
5 2 -3.750e+01 CO 2 7.58e-02 1.00e+00 3.00e+00 1.00e+00 2
6 4 -3.846e+01 3 8.58e-02 0.00e+00 0.00e+00 0.00e+00 3
7 4 -3.750e+01 CO 3 8.58e-02 1.00e+00 2.00e+00 1.00e+00 3
8 6 Infeasible 6 1.92e-01 0.00e+00 0.00e+00 1.92e-01 4
9 6 -3.750e+01 CO 6 1.92e-01 1.00e+00 2.00e+00 1.00e+00 4
Final solution:
Varbl State Value Lower Bound Upper Bound Lagr Mult Residual
OATMEAL FR 4.00000e+00 0.0000e+00 4.0000e+00 0.000e+00 0.000e+00
CHICKEN FR 0.00000e+00 0.0000e+00 3.0000e+00 0.000e+00 0.000e+00
EGGS FR 0.00000e+00 0.0000e+00 2.0000e+00 0.000e+00 0.000e+00
MILK LL 5.00000e+00 5.0000e+00 8.0000e+00 1.375e+00 0.000e+00
PIE FR 2.00000e+00 0.0000e+00 2.0000e+00 0.000e+00 0.000e+00
BACON FR 0.00000e+00 0.0000e+00 2.0000e+00 0.000e+00 0.000e+00
Constr State Value Lower Bound Upper Bound Lagr Mult Residual
ENERGY FR 2.08000e+03 1.9700e+03 None 0.000e+00 1.100e+02
PROTEIN FR 6.40000e+01 5.5000e+01 None 0.000e+00 9.000e+00
CALCIUM FR 1.47700e+03 8.0000e+02 None 0.000e+00 6.770e+02
Exit from branch and bound tree search after 9 nodes.
Optimal IP solution found.
Final IP objective value = -3.8125000e+01