I am using Cplex to solve the Set Partitioning Problem from your documentation.
I receive the following output, which shows that the problem is solved using Branch & Cut first and after that the "MILP problem relaxed to LP with fixed integer variables using
incumbent solution" is solved again using dual simplex. Why is it solved twice? I'm calling Cplex via "prob.solve(CPLEX_CMD(msg=1)).
Welcome to IBM(R) ILOG(R) CPLEX(R) Interactive Optimizer 12.10.0.0
with Simplex, Mixed Integer & Barrier Optimizers
5725-A06 5725-A29 5724-Y48 5724-Y49 5724-Y54 5724-Y55 5655-Y21
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CPLEX> Problem '/var/folders/rm/ncy_nf_932l2h58hjq1vjddm0000gn/T/7fd8c3f1c9a54deb9a30af67efede4cf-pulp.lp' read.
Read time = 0.01 sec. (0.29 ticks)
CPLEX> Version identifier: 12.10.0.0 | 2019-11-26 | 843d4de
Tried aggregator 1 time.
MIP Presolve modified 697 coefficients.
Reduced MIP has 18 rows, 3213 columns, and 14365 nonzeros.
Reduced MIP has 3213 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.03 sec. (24.12 ticks)
Found incumbent of value 44.000000 after 0.08 sec. (54.94 ticks)
Tried aggregator 1 time.
Detecting symmetries...
Reduced MIP has 18 rows, 3213 columns, and 14365 nonzeros.
Reduced MIP has 3213 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.02 sec. (23.18 ticks)
Probing time = 0.02 sec. (7.05 ticks)
Clique table members: 17.
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: deterministic, using up to 4 threads.
Root relaxation solution time = 0.01 sec. (3.92 ticks)
Nodes Cuts/
Node Left Objective IInf Best Integer Best Bound ItCnt Gap
* 0+ 0 44.0000 0.0000 100.00%
* 0 0 integral 0 12.0000 12.0000 28 0.00%
Elapsed time = 0.14 sec. (93.80 ticks, tree = 0.00 MB, solutions = 2)
Root node processing (before b&c):
Real time = 0.14 sec. (93.92 ticks)
Parallel b&c, 4 threads:
Real time = 0.00 sec. (0.00 ticks)
Sync time (average) = 0.00 sec.
Wait time (average) = 0.00 sec.
------------
Total (root+branch&cut) = 0.14 sec. (93.92 ticks)
Solution pool: 2 solutions saved.
MIP - Integer optimal solution: Objective = 1.2000000000e+01
Solution time = 0.14 sec. Iterations = 28 Nodes = 0
Deterministic time = 93.93 ticks (654.94 ticks/sec)
CPLEX> MILP problem relaxed to LP with fixed integer variables using
incumbent solution.
CPLEX> Version identifier: 12.10.0.0 | 2019-11-26 | 843d4de
Parallel mode: deterministic, using up to 4 threads for concurrent optimization:
* Starting dual Simplex on 1 thread...
* Starting Barrier on 3 threads...
Tried aggregator 1 time.
LP Presolve eliminated 18 rows and 3213 columns.
All rows and columns eliminated.
Presolve time = 0.00 sec. (1.26 ticks)
Dual simplex solved model.
Dual simplex - Optimal: Objective = 1.2000000000e+01
Solution time = 0.01 sec. Iterations = 0 (0)
Deterministic time = 1.71 ticks (307.89 ticks/sec)
CPLEX> Solution written to file '/var/folders/rm/ncy_nf_932l2h58hjq1vjddm0000gn/T/7fd8c3f1c9a54deb9a30af67efede4cf-pulp.sol'.
CPLEX> The maximum happiness is: 12.0
The table order is:
('M', 'N')
('E', 'F', 'G')
('A', 'B', 'C', 'D')
('I', 'J', 'K', 'L')
('O', 'P', 'Q', 'R')
Any help is welcome, thanks in advance.