Gekko non linear mixed integer programming. Problem setting up objective function

Question

I am new in using Gekko, I am setting up a problem as

def optimise():

    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 0.05', \
                    # covergence tolerance
                    'minlp_gap_tol 0.01']

    # Initialize variables
    x=[]
    for i in range(0,18) :
        x.append(m.Var(lb=4,ub=21,integer=True))

    #initialise objective
    m.Obj(simulate_game(x)) # Objective
    m.options.IMODE = 3 
    m.solve(disp=True) # Solve
    print('Results')
    print('Strategy:'+str(initialise_strategy(x)))
    print('Objective: ' + str(m.options.objfcnval))

where simulate_game(x) is an external function that given a parametrise strategy computes the performance in the game. When I run the solver I get the following output

apm 90.250.179.168_gk_model16 <br><pre> ----------------------------------------------------------------
 APMonitor, Version 0.9.2
 APMonitor Optimization Suite
 ----------------------------------------------------------------


 Warning: there is insufficient data in CSV file 90.250.179.168_gk_model16.csv

 --------- APM Model Size ------------
 Each time step contains
   Objects      :            0
   Constants    :            0
   Variables    :           18
   Intermediates:            0
   Connections  :            0
   Equations    :            1
   Residuals    :            1

 ________________________________________________
 WARNING: objective equation           1 has no variables
 ss.Eqn(1)
 0 = -0.06
 ________________________________________________
 Number of state variables:             18
 Number of total equations: -            0
 Number of slack variables: -            0
 ---------------------------------------
 Degrees of freedom       :             18

 ----------------------------------------------
 Steady State Optimization with APOPT Solver
 ----------------------------------------------
Iter:     1 I:  0 Tm:      0.00 NLPi:    1 Dpth:    0 Lvs:    0 Obj: -6.00E-02 Gap:  0.00E+00
 Successful solution

 ---------------------------------------------------
 Solver         :  APOPT (v1.0)
 Solution time  :   3.450000000884756E-002 sec
 Objective      :  -6.000000000000000E-002
 Successful solution
 ---------------------------------------------------

It seems to me that some of the warning in the output are telling what the problem is but I cannot really interpret them... I do not have equations because I do not have constraints in my problem... Any help is greatly appreciate. Apologies in advance for the beginner question.

John Hedengren · Accepted Answer · 2020-06-04 19:26:16Z

1

The problem is with m.Obj(simulate_game(x)) as you guessed. Gekko cannot use a black-box model but needs to constuct the model either from data (such as a c-spline, b-spline, machine learning, time series modeling) or with closed-form equations. If you need to use a black-box model, another optimizer may be better for your application. Here is a related question about integer variables in Python: Restrict scipy.optimize.minimize to integer values

answered Jun 4, 2020 at 19:26

John Hedengren

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1 Comment

lisa Over a year ago

That was my doubt indeed... thanks for confirming it! I'll look for an alternative as my function is a black box. Thanks for the link

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