Heuristic solution for continuous and binary variables

Good day.

I am solving optimization problem by Gurobi.

In the first case, I defined variables as binary using the following command:

x = [model.addVar(vtype=gp.GRB.BINARY, name="x%s" % i) for i in range(n)]
 
with the following Output:

Set parameter NonConvex to value 2
Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 0 rows, 100 columns and 0 nonzeros
Model fingerprint: 0xdf68950c
Model has 298 quadratic objective terms
Variable types: 0 continuous, 100 integer (100 binary)
Coefficient statistics:
  Matrix range     [0e+00, 0e+00]
  Objective range  [1e+00, 5e+00]
  QObjective range [2e+00, 4e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [0e+00, 0e+00]
Found heuristic solution: objective 222.0000000
Found heuristic solution: objective 227.0000000
Found heuristic solution: objective 288.0000000
Presolve removed 0 rows and 15 columns
Presolve time: 0.05s
Presolved: 249 rows, 334 columns, 747 nonzeros
Variable types: 0 continuous, 334 integer (334 binary)

Root relaxation: objective 3.000000e+02, 130 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0  300.00000    0   85  288.00000  300.00000  4.17%     -    0s
     0     0  293.50000    0  101  288.00000  293.50000  1.91%     -    0s
     0     0  289.83333    0  152  288.00000  289.83333  0.64%     -    0s
     0     0  289.63235    0  176  288.00000  289.63235  0.57%     -    0s
     0     0  289.63235    0  172  288.00000  289.63235  0.57%     -    0s
     0     0  289.63235    0   59  288.00000  289.63235  0.57%     -    0s
     0     0     cutoff    0       288.00000  288.00000  0.00%     -    0s

Cutting planes:
  Implied bound: 2
  Clique: 13
  MIR: 3
  Zero half: 32
  RLT: 7

Explored 1 nodes (918 simplex iterations) in 0.13 seconds (0.08 work units)
Thread count was 8 (of 8 available processors)

Solution count 3: 288 227 222 

Optimal solution found (tolerance 1.00e-04)
Best objective 2.880000000000e+02, best bound 2.880000000000e+02, gap 0.0000%

In the second case, I solved the same problem, but defined the variables as continuous to relax the problem using the following code:

x = [model.addVar(vtype=gp.GRB.CONTINUOUS, name="x%s" % i, lb=0, ub=1) for i in range(n)]

because I heard that the optimizers can solve the relaxed version more efficiently than the discrete one. I get the following output:

Set parameter NonConvex to value 2
Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])

CPU model: Apple M1
Thread count: 8 physical cores, 8 logical processors, using up to 8 threads

Optimize a model with 0 rows, 100 columns and 0 nonzeros
Model fingerprint: 0x295b0a6f
Model has 298 quadratic objective terms
Coefficient statistics:
  Matrix range     [0e+00, 0e+00]
  Objective range  [1e+00, 5e+00]
  QObjective range [2e+00, 4e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [0e+00, 0e+00]
Presolve removed 0 rows and 1 columns

Continuous model is non-convex -- solving as a MIP

Found heuristic solution: objective 222.0000000
Found heuristic solution: objective 227.0000000
Presolve removed 0 rows and 15 columns
Presolve time: 0.05s
Presolved: 249 rows, 334 columns, 747 nonzeros
Found heuristic solution: objective 240.0000000
Variable types: 0 continuous, 334 integer (334 binary)
Found heuristic solution: objective 252.0000000

Root relaxation: objective 3.000000e+02, 130 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0  300.00000    0   85  252.00000  300.00000  19.0%     -    0s
H    0     0                     270.0000000  300.00000  11.1%     -    0s
     0     0  293.50000    0   97  270.00000  293.50000  8.70%     -    0s
H    0     0                     278.0000000  293.50000  5.58%     -    0s
     0     0  291.00000    0  134  278.00000  291.00000  4.68%     -    0s
     0     0  291.00000    0  112  278.00000  291.00000  4.68%     -    0s
     0     2  291.00000    0  103  278.00000  291.00000  4.68%     -    0s
H    3     8                     281.0000000  290.50000  3.38%   123    0s
H    5     8                     287.0000000  290.25000  1.13%   122    0s
*   13     1               4     288.0000000  289.00000  0.35%  78.6    0s

Cutting planes:
  Gomory: 4
  MIR: 3
  Zero half: 57
  RLT: 6

Explored 21 nodes (1919 simplex iterations) in 0.15 seconds (0.10 work units)
Thread count was 8 (of 8 available processors)

Solution count 9: 288 287 281 ... 222

Optimal solution found (tolerance 1.00e-04)
Best objective 2.880000000000e+02, best bound 2.880000000000e+02, gap 0.0000%

As expected, the both cases arrive at the same solution.
However, at the initial steps before starting MIP, in the first case, the heuristic finds better objective (288.00) compared to the second case (252.00). Would you please let me know if there is a difference in heuristic method for binary and continuous variables?
Moreover, may I get some information in output log of heuristic method's process?
Thanks a lot

Official comment

Simranjit Kaur

Gurobi Staff

November 13, 2026 01:36

This post is more than two years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.

David Torres Sanchez

October 06, 2023 12:22

Hi,

Some heuristics can only run on certain types of variables (due to the assumptions made) or are more effective for certain types of variables.
The same thing for other parts of the solution process such as presolve, you can see in the MIP case we are able to remove more variables (15 vs 1).

There is no way of getting more information about the heuristics being run.
You can experiment with some heuristic-related parameters see the MIP section under parameters.

In any case, It seems that there is not much difference in solving time.

Lastly, there is a convenient function to relax the problem: model.relax().

Cheers,
David

Heuristic solution for continuous and binary variables

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