That is an impressive MINLP problem size. To determine how to make it faster on the pre-processing, you'll need to collect some additional information about where the time is used with `DIAGLEVEL>=1`.
```python
m.options.DIAGLEVEL = 1
```
This produces a report of how long it takes for each of the steps. Here is an [example MINLP problem (see #10)][1].
```python
from gekko import GEKKO
m = GEKKO() # Initialize gekko
m.options.SOLVER=1 # APOPT is an MINLP solver
m.options.DIAGLEVEL = 1
# 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
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=1,ub=5,integer=True)
x4 = m.Var(value=1,lb=1,ub=5,integer=True)
# Equations
m.Equation(x1*x2*x3*x4>=25)
m.Equation(x1**2+x2**2+x3**2+x4**2==40)
m.Obj(x1*x4*(x1+x2+x3)+x3) # Objective
m.solve(disp=True) # Solve
```
This produces the following timing results:
```
Timer # 1 0.03/ 1 = 0.03 Total system time
Timer # 2 0.02/ 1 = 0.02 Total solve time
Timer # 3 0.00/ 42 = 0.00 Objective Calc: apm_p
Timer # 4 0.00/ 29 = 0.00 Objective Grad: apm_g
Timer # 5 0.00/ 42 = 0.00 Constraint Calc: apm_c
Timer # 6 0.00/ 0 = 0.00 Sparsity: apm_s
Timer # 7 0.00/ 0 = 0.00 1st Deriv #1: apm_a1
Timer # 8 0.00/ 29 = 0.00 1st Deriv #2: apm_a2
Timer # 9 0.00/ 1 = 0.00 Custom Init: apm_custom_init
Timer # 10 0.00/ 1 = 0.00 Mode: apm_node_res::case 0
Timer # 11 0.00/ 1 = 0.00 Mode: apm_node_res::case 1
Timer # 12 0.00/ 1 = 0.00 Mode: apm_node_res::case 2
Timer # 13 0.00/ 1 = 0.00 Mode: apm_node_res::case 3
Timer # 14 0.00/ 89 = 0.00 Mode: apm_node_res::case 4
Timer # 15 0.00/ 58 = 0.00 Mode: apm_node_res::case 5
Timer # 16 0.00/ 0 = 0.00 Mode: apm_node_res::case 6
Timer # 17 0.00/ 29 = 0.00 Base 1st Deriv: apm_jacobian
Timer # 18 0.00/ 29 = 0.00 Base 1st Deriv: apm_condensed_jacobian
Timer # 19 0.00/ 1 = 0.00 Non-zeros: apm_nnz
Timer # 20 0.00/ 0 = 0.00 Count: Division by zero
Timer # 21 0.00/ 0 = 0.00 Count: Argument of LOG10 negative
Timer # 22 0.00/ 0 = 0.00 Count: Argument of LOG negative
Timer # 23 0.00/ 0 = 0.00 Count: Argument of SQRT negative
Timer # 24 0.00/ 0 = 0.00 Count: Argument of ASIN illegal
Timer # 25 0.00/ 0 = 0.00 Count: Argument of ACOS illegal
Timer # 26 0.00/ 1 = 0.00 Extract sparsity: apm_sparsity
Timer # 27 0.00/ 13 = 0.00 Variable ordering: apm_var_order
Timer # 28 0.00/ 1 = 0.00 Condensed sparsity
Timer # 29 0.00/ 0 = 0.00 Hessian Non-zeros
Timer # 30 0.00/ 1 = 0.00 Differentials
Timer # 31 0.00/ 0 = 0.00 Hessian Calculation
Timer # 32 0.00/ 0 = 0.00 Extract Hessian
Timer # 33 0.00/ 1 = 0.00 Base 1st Deriv: apm_jac_order
Timer # 34 0.01/ 1 = 0.01 Solver Setup
Timer # 35 0.00/ 1 = 0.00 Solver Solution
Timer # 36 0.00/ 53 = 0.00 Number of Variables
Timer # 37 0.00/ 35 = 0.00 Number of Equations
Timer # 38 0.01/ 14 = 0.00 File Read/Write
Timer # 39 0.00/ 0 = 0.00 Dynamic Init A
Timer # 40 0.00/ 0 = 0.00 Dynamic Init B
Timer # 41 0.00/ 0 = 0.00 Dynamic Init C
Timer # 42 0.00/ 1 = 0.00 Init: Read APM File
Timer # 43 0.00/ 1 = 0.00 Init: Parse Constants
Timer # 44 0.00/ 1 = 0.00 Init: Model Sizing
Timer # 45 0.00/ 1 = 0.00 Init: Allocate Memory
Timer # 46 0.00/ 1 = 0.00 Init: Parse Model
Timer # 47 0.00/ 1 = 0.00 Init: Check for Duplicates
Timer # 48 0.00/ 1 = 0.00 Init: Compile Equations
Timer # 49 0.00/ 1 = 0.00 Init: Check Uninitialized
Timer # 50 -0.00/ 13 = -0.00 Evaluate Expression Once
Timer # 51 0.00/ 0 = 0.00 Sensitivity Analysis: LU Factorization
Timer # 52 0.00/ 0 = 0.00 Sensitivity Analysis: Gauss Elimination
Timer # 53 0.00/ 0 = 0.00 Sensitivity Analysis: Total Time
```
APOPT stores the problem instance between NLP runs so it is fast to re-evaluate with different constraints as it performs branch and bound. APOPT uses a warm-start feature to rapidly evaluate the constrained NLP optimization problems. However, this warm-start feature isn't available to the Gekko user. There are other solvers available with Gekko (one that could be configured for MINLP) but they require a commercial license. There are also free MINLP solvers such as Couenne and Bonmin that are available from COIN-OR but they aren't supported yet. You can add a [feature request for Gekko][2] if you determine that APOPT pre-processing is the problem and you'd like to try another solver. Here is the optimization result that shows the timing for each iteration.
```
----------------------------------------------
Steady State Optimization with APOPT Solver
----------------------------------------------
Iter: 1 I: 0 Tm: 0.00 NLPi: 7 Dpth: 0 Lvs: 3 Obj: 1.70E+01 Gap: NaN
--Integer Solution: 1.75E+01 Lowest Leaf: 1.70E+01 Gap: 3.00E-02
Iter: 2 I: 0 Tm: 0.00 NLPi: 5 Dpth: 1 Lvs: 2 Obj: 1.75E+01 Gap: 3.00E-02
Iter: 3 I: 0 Tm: 0.00 NLPi: 6 Dpth: 1 Lvs: 2 Obj: 1.75E+01 Gap: 3.00E-02
--Integer Solution: 1.75E+01 Lowest Leaf: 1.70E+01 Gap: 3.00E-02
Iter: 4 I: 0 Tm: 0.00 NLPi: 6 Dpth: 2 Lvs: 1 Obj: 2.59E+01 Gap: 3.00E-02
Iter: 5 I: 0 Tm: 0.00 NLPi: 5 Dpth: 1 Lvs: 0 Obj: 2.15E+01 Gap: 3.00E-02
No additional trial points, returning the best integer solution
Successful solution
---------------------------------------------------
Solver : APOPT (v1.0)
Solution time : 1.649999999790452E-002 sec
Objective : 17.5322673012512
Successful solution
---------------------------------------------------
```
Here are a few things to try to diagnose or improve your solution time:
- Try the `IPOPT` solver for a non-integer solution. Does it still take 27 hours to complete the solution with this solver? This may be an indication that APOPT is doing pre-processing of the solution.
- Replace `gekko` constants and parameters with Python floats where possible. This reduces the amount of model processing time.
- Use [built-in gekko objects][3] such as `m.sum()` versus the Python `sum` function. This generally improves the model processing performance.
- Do automatic model reduction with `m.options.REDUCE=3` or manual model reduction with the use of [`Intermediate` variables][4].
[1]: https://apmonitor.com/wiki/index.php/Main/GekkoPythonOptimization
[2]: https://github.com/BYU-PRISM/GEKKO/issues
[3]: https://gekko.readthedocs.io/en/latest/model_methods.html#pre-built-objects
[4]: http://apmonitor.com/wiki/index.php/Main/Intermediates
Solvers such as APOPT or IPOPT use `m.solver_options` values if both `m.options` and `m.solver_options` are set. The [Gekko `m.options` values][1] are only a subset of all the solver options but also some of the most common configuration parameters that are adjustable for all solvers. Some of the common options are convergence tolerances (`RTOL` and `OTOL`), [maximum iterations][2] (`MAX_ITER`), and [maximum time][3] (`MAX_TIME`). Common solver results are also output such as [objective function value][3] (`OBJFCNVAL`), [solve time][4] (`SOLVETIME`), and [solution status][4] (`APPINFO`).
There are also specific options that are configurable by the solver type. For example, the APOPT solver is a Mixed Integer Nonlinear Programming (MINLP) solver. There are additional options that are configurable only from `m.solver_options` such as:
```python
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']
```
The IPOPT solver is a Nonlinear Programming (NLP) solver so it doesn't use the MINLP options.
[1]: https://gekko.readthedocs.io/en/latest/global.html
[2]: https://apmonitor.com/wiki/index.php/Main/OptionApmMaxIter
[3]: https://apmonitor.com/wiki/index.php/Main/OptionApmMaxTime
[4]: https://apmonitor.com/wiki/index.php/Main/OptionApmAppinfo
