Objective value is higher when integers are used

[willigott]

I ran this example from the documentation and got the same output:

 ---------------------------------------------------
 Solver         :  APOPT (v1.0)
 Solution time  :   1.639999999315478E-002 sec
 Objective      :    17.5322673012512     
 Successful solution
 ---------------------------------------------------

Results
x1: [1.358909]
x2: [4.599279]
x3: [4.0]
x4: [1.0]
Objective: 17.5322673

I then checked how the solution would look like when all xi would be integers, so I changed the definitions for x1 and x2 to

# Initialize variables
x1 = m.Var(value=1, lb=1, ub=5, integer=True)
x2 = m.Var(value=5, lb=1, ub=5, integer=True)

which then gives

 Successful solution

 ---------------------------------------------------
 Solver         :  APOPT (v1.0)
 Solution time  :   0.103800000011688      sec
 Objective      :    82.0000000000000     
 Successful solution
 ---------------------------------------------------

Results
x1: [4.0]
x2: [4.0]
x3: [2.0]
x4: [2.0]
Objective: 82.0

As one can see, the constraints are fulfilled, however, the objective value is now almost 5 times higher than before when x1 and x2 were not restricted to be integers.

Why is this solution not picked up when x1 and x2 are not constrained to be integers? Which optimization parameters would I have to fine-tune to avoid this local optimum?

[abe-mart]

Gekko actually minimizes the objective function, so constraining the variables to be integers produces a solution that is five times worse than the unconstrained version.

On Sun, Dec 2, 2018, 9:05 AM willigott <notifications@github.com wrote:

I ran this example https://gekko.readthedocs.io/en/latest/examples.html#mixed-integer-nonlinear-programming from the documentation and got the same output:

---

Solver : APOPT (v1.0) Solution time : 1.639999999315478E-002 sec Objective : 17.5322673012512 Successful solution

Results x1: [1.358909] x2: [4.599279] x3: [4.0] x4: [1.0] Objective: 17.5322673

I then checked how the solution would look like when all xi would be integers, so I changed the definitions for x1 and x2 to

Initialize variables

x1 = m.Var(value=1, lb=1, ub=5, integer=True) x2 = m.Var(value=5, lb=1, ub=5, integer=True)

which then gives

Successful solution

---

Solver : APOPT (v1.0) Solution time : 0.103800000011688 sec Objective : 82.0000000000000 Successful solution

Results x1: [4.0] x2: [4.0] x3: [2.0] x4: [2.0] Objective: 82.0

As one can see, the constraints are fulfilled, however, the objective value is now almost 5 times higher than before when x1 and x2 were not restricted to be integers.

Why is this solution not picked up when x1 and x2 are not constrained to be integers? Which optimization parameters would I have to fine-tune to avoid this local optimum?

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[willigott]

Ooops, of course, stupid me. Thanks for the immediate reply!