Incorrect Solution When Squaring Gekko Integer Variables

Question

If I initialize a boolean variable as 0 I get an incorrect solution (0). If I initialize it as 1 I get the correct solution (1).

# Squaring doesn't work
#######################################################

m = GEKKO(remote=False)

b = m.Var(lb=0,ub=1,integer=True, value=0)

m.Maximize(b**2)


m.options.SOLVER = 1
m.solve(debug=0, disp=True)

Returns:

Successful solution
Objective:  0.

with b: [0]

This is a follow up to a previous question ( Gekko returning incorrect successful solution ) that concerns a model involving matrix multiplication of two gekko arrays with gekko integer variables. I believe I've traced that issue to this problem.

Answer 1

Try this:

from gekko import GEKKO
m = GEKKO()
b = m.Var(value=0, integer=True)
m.Equation(b>=0)
m.Equation(b<=1)
m.Maximize(b**2)
m.options.SOLVER = 1
m.solve(disp=False)
print(b.value)

Output:

[1.0]

See a demo in this colab .

In the gekko examples I saw that Obj() (which minimizes) is used along with Equation() , so I thought, well maybe the lower and upper bounds of the variable could be expressed as equations instead. Apparently, it works that way.

Answer 2

The APOPT solver is a local minimizer that assumes there is only one local minimum. It is also not checking the second derivative to differentiate between a local minimum and local maximum at x=0 . Hernán Alarcón gave a potential solution where inequality constraints are also solved. This causes the solver to not just accept the initial guess as a solution but to start a search and realize that there is a better solution. There are at least two other methods to find the correct solution.

Initialize with x>=1e-3

Instead of initializing at x=0 , try initializing x at any value that does not meet the KKT conditions .

from gekko import GEKKO
m = GEKKO(remote=False)
b = m.Var(lb=0,ub=1,integer=True, value=1e-3)
m.Maximize(b**2)
m.options.SOLVER=1
m.solve(disp=False)
print(-m.options.OBJFCNVAL)

Switch Solvers

This is an integer optimization problem but a Nonlinear Programming (NLP) solver such as IPOPT can also solve the problem with value=0 .

from gekko import GEKKO
m = GEKKO(remote=False)
b = m.Var(lb=0,ub=1,integer=True, value=0)
m.Maximize(b**2)
m.options.SOLVER=3
m.solve(disp=False)
print(-m.options.OBJFCNVAL)