Evaluating an expression in gekko

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Hello I have the following toy code that I am using to learn optimization in python

from gekko import GEKKO
m = GEKKO() # Initialize gekko
m.options.SOLVER=1  # APOPT is an MINLP solver

# optional solver settings with APOPT
m.solver_options = ['minlp_maximum_iterations 500', \
                    # minlp iterations with integer solution
                    'minlp_max_iter_with_int_sol 10', \
                    # treat minlp as nlp
                    'minlp_as_nlp 0', \
                    # nlp sub-problem max iterations
                    'nlp_maximum_iterations 50', \
                    # 1 = depth first, 2 = breadth first
                    'minlp_branch_method 1', \
                    # maximum deviation from whole number
                    'minlp_integer_tol 0.005', \
                    # covergence tolerance
                    'minlp_gap_tol 0.01']

# Initialize variables
x1 = m.Var(value=1,lb=1,ub=5)
x2 = m.Var(value=5,lb=1,ub=5)
# Integer constraints for x3 and x4
x3 = m.Var(value=5,lb=-5,ub=5,integer=True)
x4 = m.Var(value=1,lb=-5,ub=5,integer=True)
y = m.Var(value=1,lb=-5,ub=50,integer=True)
# Equations
m.Equation(x1*x2*x3*x4>=25)
m.Equations([y<x3/4,y>=x3/4+1e-8])
m.Equation(x1**2+x2**2+x3**2+x4**2==40)

#Expressions
F1 = x1*x4*(x1+x2+x3)
F2 = x3 + x4/10


m.Obj(F1 + F2) # Objective
m.solve(disp=False) # Solve
print('Results')
print('x1: ' + str(x1.value))
print('x2: ' + str(x2.value))
print('x3: ' + str(x3.value))
print('x4: ' + str(x4.value))
print('y: ' + str(y.value))
print('Objective: ' + str(m.options.objfcnval))

Now after optimization I got values of x1, x2, x3, x4 but I would like to evaluate the expression for F1, F2 without manual calculation. How can I do that ? Thanks in advance

gekko python-3.x
1 Answers

Create intermediates to get the F1 and F2 values.

#Expressions
F1 = m.Intermediate(x1*x4*(x1+x2+x3))
F2 = m.Intermediate(x3 + x4/10)

This shows the F1 and F2 values after the solve command.

print('F1: ' + str(F1.value[0]))
print('F2: ' + str(F2.value[0]))

Here is the complete script:

from gekko import GEKKO
m = GEKKO() # Initialize gekko
m.options.SOLVER=1  # APOPT is an MINLP solver

# optional solver settings with APOPT
m.solver_options = ['minlp_maximum_iterations 500', \
                    # minlp iterations with integer solution
                    'minlp_max_iter_with_int_sol 10', \
                    # treat minlp as nlp
                    'minlp_as_nlp 0', \
                    # nlp sub-problem max iterations
                    'nlp_maximum_iterations 50', \
                    # 1 = depth first, 2 = breadth first
                    'minlp_branch_method 1', \
                    # maximum deviation from whole number
                    'minlp_integer_tol 0.005', \
                    # covergence tolerance
                    'minlp_gap_tol 0.01']

# Initialize variables
x1 = m.Var(value=1,lb=1,ub=5)
x2 = m.Var(value=5,lb=1,ub=5)
# Integer constraints for x3 and x4
x3 = m.Var(value=5,lb=-5,ub=5,integer=True)
x4 = m.Var(value=1,lb=-5,ub=5,integer=True)
y = m.Var(value=1,lb=-5,ub=50,integer=True)
# Equations
m.Equation(x1*x2*x3*x4>=25)
m.Equations([y<x3/4,y>=x3/4+1e-8])
m.Equation(x1**2+x2**2+x3**2+x4**2==40)

#Expressions
F1 = m.Intermediate(x1*x4*(x1+x2+x3))
F2 = m.Intermediate(x3 + x4/10)

m.Obj(F1 + F2) # Objective
m.solve(disp=False) # Solve
print('Results')
print('x1: ' + str(x1.value[0]))
print('x2: ' + str(x2.value[0]))
print('x3: ' + str(x3.value[0]))
print('x4: ' + str(x4.value[0]))
print('y: ' + str(y.value[0]))
print('F1: ' + str(F1.value[0]))
print('F2: ' + str(F2.value[0]))
print('Objective: ' + str(m.options.objfcnval))

With the solution:

Results
x1: 1.3589086474
x2: 4.5992789966
x3: 4.0
x4: 1.0
y: 1.0
F1: 13.532267301
F2: 4.1
Objective: 17.632267301
user_23669410
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