GEKKO Documentation

GEKKO is an object-oriented Python library designed for machine learning and optimization of mixed-integer and differential algebraic equations. It interfaces with large-scale solvers for various programming types:

• LP: Linear Programming
• QP: Quadratic Programming
• NLP: Nonlinear Programming
• MILP: Mixed-Integer Linear Programming
• MINLP: Mixed-Integer Nonlinear Programming

Core Modes of Operation:

• Parameter regression
• Data reconciliation
• Real-time optimization
• Dynamic simulation
• Nonlinear predictive control

GEKKO's ML module allows you to import trained machine learning models from libraries like scikit-learn, gpflow, and tensorflow into the GEKKO optimization suite. This enables data-based optimization, model predictive control, and physics-informed hybrid modeling.

To use these features, import the ML subpackage:

from gekko import ML

GEKKO is optimization software designed for mixed-integer and differential algebraic equations. It supports linear, quadratic, nonlinear, and mixed integer programming (LP, QP, NLP, MILP, MINLP) by coupling with large-scale solvers.

Mathematical Modeling Abstractions

GEKKO uses a high-level abstraction for mathematical optimization. You define models using the following components:

• Constants, Parameters, and Variables: The fundamental values in your model.
• Intermediates or Equations: The relationships that connect values.
• Objective functions: Defined to either maximize or minimize specific values.
• Objects: Built-in collections of values and relationships that can utilize object-oriented relationships to build upon one another.

GEKKO supports several methods for calculating prediction uncertainty within interfaced models:

Gekko-MATLAB is a native MATLAB wrapper for the APMonitor optimization engine. It allows you to build models using a GEKKO-style interface directly in MATLAB without requiring Python.

Models are assembled into APMonitor sections such as Constants, Parameters, Variables, Intermediates, Equations, Connections, and Objects. You can solve these models either locally using the apm executable or remotely on the APMonitor server by setting m.remote = true.

The library provides several GEKKO-style math and object helpers implemented directly in MATLAB to handle non-linearities and complex structures.

Common helpers include:

• Nonlinearities: max2, max3, min2, min3, abs2, abs3, sign2, sign3, if2, if3.
• Splines: bspline, cspline, pwl (Note: these expect a GEKKO variable as dependent output).
• System/Control: state_space, arx, sysid, delay.
• Others: integral, periodic, sum, vsum, Array (returns cell arrays of GEKKO objects).

m = Gekko();
x = m.Var();
y = m.Var();
z = m.max2(x,y); % Example using max2 helper

m.Equation(x == 2);
m.Equation(y == -1);
m.solve();

disp(z.value)

The GEKKO solver extension module allows you to convert a GEKKO model into other mathematical optimization libraries, providing access to solvers not natively supported by GEKKO. Currently, it supports two converters:

1. AMPLPY: Converts the model to AMPL syntax for use with the AMPLPY library.
2. PYOMO: Converts the model to Pyomo syntax.

Important Limitations:

• remote=True is not supported when using the solver extension.
• Dynamic optimization features (e.g., m.time, derivatives) are not supported by either the AMPLPY or Pyomo converters at this time.
• Basic model building functions (variables, parameters, constants, intermediates, constraints, and objectives) are supported.

from gekko import GEKKO
m = GEKKO(remote=False)
# ... define model ...
m.options.SOLVER_EXTENSION = "AMPLPY" # or "PYOMO"
m.options.SOLVER = "solver_name"
m.solve()

If a model repeatedly fails to find a solution, you can automate a COLDSTART to reset the application.

• BAD_CYCLES (Integer, Input/Output): A counter that increments with each consecutive unsuccessful solution attempt. Defaults to 0.
• AUTO_COLD (Integer, Input): The threshold of BAD_CYCLES required to trigger a coldstart.
  • 0: No auto coldstart.
  • 1+: Triggers COLDSTART = 1 after the specified number of bad cycles.

Behavior: When the AUTO_COLD limit is reached, COLDSTART is set to 1 and remains on until a successful solution is found. Once successful, both COLDSTART and BAD_CYCLES are reset to 0.

The COLDSTART option defines the initialization mode for an application. This is useful for resetting an application after failure or handling difficult initialization.

• 0 (Default): Warm start (no specific initialization).
• 1: Cold start. Temporarily turns off all FV, MV, and CV STATUS values to reduce degrees of freedom, aiming for a feasible but suboptimal solution.
• 2: Decompose problem. An aggressive initialization that analyzes problem sparsity to create and solve a sequence of lower block triangular segments. This helps identify specific equations or variable bounds causing infeasibility.

Note: When COLDSTART >= 1, initialization values are taken from the file, the DBS file, and the CSV file (in that order), ignoring prior t0 files. Once a successful solution is found, COLDSTART is automatically reset to 0.

m.options.COLDSTART = 1

Traditional logical expressions (like if statements) cannot be used directly in gradient-based optimization because they create discontinuities in derivatives. GEKKO provides specialized logical functions that use either Mathematical Programs with Complementarity Constraints (MPCC, Type 2) or binary variables (Type 3) to provide differentiable workarounds.

Important: All Type 3 functions require a mixed-integer solver like APOPT (SOLVER=1). GEKKO will automatically switch the solver to APOPT if it detects these functions in your model.