APOPT is finding a better local minimum to a MINLP problem when I use fewer nlp iterations. I was expecting the opposite result, what am I missing?

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I have the following boolean and continuous variables, where only some of the 'percents' have a status of 1.

status[i] = m.Array(m.Var, p, lb=0, ub=1, integer=True)
percent[i] = m.Array(m.FV, p, value=1, lb=0.6, ub=1.1)

I've used some intermediaries that use the min2 option that are fed into my contraint equation.

My objective is a linear summation of status, percent and a constant.

I am using the following solver options:

m = GEKKO(remote=False)
    # Options
    m.options.SOLVER = 1
    m.options.LINEAR = 0

    # optional solver settings with APOPT
    m.solver_options = ['minlp_maximum_iterations 10000',
                    'minlp_max_iter_with_int_sol 500',
                    'minlp_gap_tol 0.01',
                    'nlp_maximum_iterations 500',
                    'minlp_as_nlp 0',
                    'minlp_interger_leaves = 0',
                    'minlp_branch_method 1',
                    'minlp_integer_tol 0.01',
                    'minlp_print_level 2'
                    ]

My returned objective is: 2140.05, none of the constraints are violated and the solution is very good. However, by reducing the 'nlp_maximum_iterations' to 10, I can get an even better solution of 2138.67.

I would expect that my minimum would improve with increasing iterations. My plan was to find a balance between runtime and optimal cost, with the expectation that a long runtime would lead to a solution close to the global minimum, that I could use as a baseline.

In my testing of the problem, it seems that the nlp_max_iterations is the controlling factor on weather or not it finds the lower of the two costs. minlp_maximum_iterations, minlp_max_iter_with_int_sol,and minlp_gap_tol, did not seem to have an affect on the solution.

Any explanation of this behavior would be appreciated greatly.

gekko
1 Answers

Here are a few tips that may help:

  • Use min3 instead of min2. This uses a binary variable form instead of the MPCC form that can give false solutions.
  • APOPT should keep the best integer solution and return that if it reaches maximum iterations. Is the solution with objective 2138.67 an integer solution?
  • If it is a maximization problem then 2140.05 would be a better solution. Could you confirm that you are using m.Minimize() instead of m.Maximize()?

The APOPT solver uses a branch and bound method that solves Nonlinear Programming (NLP) problems while successively bounding variables at integer constraints. Here are methods for declaring binary, integer, and special ordered sets.

user_23669410
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