APOPT Doesn't return lowest obj

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Mathias Sven

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Aug 30, 2021, 2:14:51 PM8/30/21

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Hello,

I am fairly new to Gekko and I was wondering if I have something misconfigured with my Mix-integer optimization problem. So basically the issue I am having is that during iterations one of the first few solutions is actually the best but the solver still gives a worse one as a solution, I can't exactly figure out why. Another thing I notice is that if I take obj function formula and divide it by 100 per se (so it is smaller), then the solution I get is actually better (Once I multiply the output by 100 again).

...

m.options.SOLVER = 1

m.solver_options = ['minlp_gap_tol 1.0e-200']

...

m.Maximize((..."formula to maximize"...) / 1)

m.solve(disp=True)

Output:

Iter: 1 I: 0 Tm: 0.00 NLPi: 4 Dpth: 0 Lvs: 3 Obj: -1.05E+06 Gap: NaN

--Integer Solution: -1.04E+06 Lowest Leaf: -1.05E+06 Gap: 9.67E-03

Iter: 2 I: 0 Tm: -0.00 NLPi: 2 Dpth: 1 Lvs: 2 Obj: -1.04E+06 Gap: 9.67E-03

Iter: 3 I: 0 Tm: 0.00 NLPi: 4 Dpth: 1 Lvs: 4 Obj: -1.06E+06 Gap: 9.67E-03

--Integer Solution: -1.05E+06 Lowest Leaf: -1.06E+06 Gap: 4.78E-03

Iter: 4 I: 0 Tm: 0.00 NLPi: 2 Dpth: 2 Lvs: 3 Obj: -1.05E+06 Gap: 4.78E-03

Iter: 5 I: 0 Tm: 0.00 NLPi: 3 Dpth: 2 Lvs: 5 Obj: -1.05E+06 Gap: 4.78E-03

Iter: 6 I: 0 Tm: 0.00 NLPi: 3 Dpth: 2 Lvs: 7 Obj: -1.05E+06 Gap: 4.78E-03

--Integer Solution: -1.05E+06 Lowest Leaf: -1.05E+06 Gap: 3.71E-03

Iter: 7 I: 0 Tm: -0.00 NLPi: 2 Dpth: 3 Lvs: 6 Obj: -1.05E+06 Gap: 3.71E-03

...

Iter: 47 I:-11 Tm: 0.00 NLPi: 2 Dpth: 13 Lvs: 3 Obj: -1.05E+06 Gap: 7.28E-04

Iter: 48 I: 0 Tm: 0.00 NLPi: 3 Dpth: 12 Lvs: 2 Obj: -1.05E+06 Gap: 7.28E-04

Iter: 49 I: 0 Tm: 0.00 NLPi: 3 Dpth: 12 Lvs: 1 Obj: -8.79E+05 Gap: 7.28E-04

No additional trial points, returning the best integer solution

Successful solution

Objective : -1050396.901745295

So as you can see Iter 3 should have been the solution.

Then if instead of m.Maximize((..."formula to maximize"...) / 1) I do

m.Maximize((..."formula to maximize"...) / 1000) instead, then the obj final becomes -1061.394773200687 which once multiplied by 1000 gives the correct "best solution" (I believe) to the original question.

Does anyone have any insight as for why this could be happening?

Thank you,

Mathias Sven

John Hedengren

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Aug 30, 2021, 2:31:31 PM8/30/21

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Mathias,

The Lowest Leaf is not a potential solution. It is the lowest non-integer solution and serves as a lower bound to the mixed-integer solution. The difference between the best integer solution and lowest leaf is used to calculate the Gap.