Gekko (optimization software)

GEKKO

Developer(s)	Logan Beal and John Hedengren
Stable release	1.0.7 / March 5, 2024; 4 months ago (2024-03-05)
Repository	github.com/BYU-PRISM/GEKKO
Operating system	Cross-Platform
Type	Technical computing
License	MIT
Website	gekko.readthedocs.io/en/latest/

The GEKKO Python package^[1] solves large-scale mixed-integer and differential algebraic equations with nonlinear programming solvers (IPOPT, APOPT, BPOPT, SNOPT, MINOS). Modes of operation include machine learning, data reconciliation, real-time optimization, dynamic simulation, and nonlinear model predictive control. In addition, the package solves Linear programming (LP), Quadratic programming (QP), Quadratically constrained quadratic program (QCQP), Nonlinear programming (NLP), Mixed integer programming (MIP), and Mixed integer linear programming (MILP). GEKKO is available in Python and installed with pip from PyPI of the Python Software Foundation.

pip install gekko

GEKKO works on all platforms and with Python 2.7 and 3+. By default, the problem is sent to a public server where the solution is computed and returned to Python. There are Windows, MacOS, Linux, and ARM (Raspberry Pi) processor options to solve without an Internet connection. GEKKO is an extension of the APMonitor Optimization Suite but has integrated the modeling and solution visualization directly within Python. A mathematical model is expressed in terms of variables and equations such as the Hock & Schittkowski Benchmark Problem #71^[2] used to test the performance of nonlinear programming solvers. This particular optimization problem has an objective function ${\displaystyle \min _{x\in \mathbb {R} }\;x_{1}x_{4}(x_{1}+x_{2}+x_{3})+x_{3}}$ and subject to the inequality constraint ${\displaystyle x_{1}x_{2}x_{3}x_{4}\geq 25}$ and equality constraint ${\displaystyle {x_{1}}^{2}+{x_{2}}^{2}+{x_{3}}^{2}+{x_{4}}^{2}=40}$. The four variables must be between a lower bound of 1 and an upper bound of 5. The initial guess values are ${\displaystyle x_{1}=1,x_{2}=5,x_{3}=5,x_{4}=1}$. This optimization problem is solved with GEKKO as shown below.

from gekko import GEKKO

m = GEKKO()  # Initialize gekko
# Initialize variables
x1 = m.Var(value=1, lb=1, ub=5)
x2 = m.Var(value=5, lb=1, ub=5)
x3 = m.Var(value=5, lb=1, ub=5)
x4 = m.Var(value=1, lb=1, ub=5)
# Equations
m.Equation(x1 * x2 * x3 * x4 >= 25)
m.Equation(x1 ** 2 + x2 ** 2 + x3 ** 2 + x4 ** 2 == 40)
m.Minimize(x1 * x4 * (x1 + x2 + x3) + x3)
m.solve(disp=False)  # Solve
print("x1: " + str(x1.value))
print("x2: " + str(x2.value))
print("x3: " + str(x3.value))
print("x4: " + str(x4.value))
print("Objective: " + str(m.options.objfcnval))