Hanging chain problem (GEKKO) - Revision history

JohnHedengren: /* Solver Results */

2019-03-14T17:25:21Z

Solver Results

← Older revision		Revision as of 17:25, 14 March 2019
Line 68:		Line 68:
	== Solver Results ==		== Solver Results ==

	An MINLP solution is calculated with IPOPT with an objective function value of ~~<math>~~5.13266~~</math>~~.		An MINLP solution is calculated with IPOPT with an objective function value of 5.13266.

	[[File:Hanging_chain_GEKKO.png]]		[[File:Hanging_chain_GEKKO.png]]

	[[Category:Gekko]]		[[Category:Gekko]]

JohnHedengren: /* Results with APOPT (MINLP) */

2019-03-14T17:25:05Z

Results with APOPT (MINLP)

← Older revision		Revision as of 17:25, 14 March 2019
Line 66:		Line 66:
	</source>		</source>

	== Results ~~with APOPT (MINLP)~~ ==		== Solver Results ==

	An MINLP solution is calculated with IPOPT with an objective function value of <math>5.13266</math>.		An MINLP solution is calculated with IPOPT with an objective function value of <math>5.13266</math>.

JohnHedengren: Add GEKKO Python solution

2019-03-13T19:27:36Z

Add GEKKO Python solution

New page

This page contains a solution of the energy minimization of the [[Hanging chain problem]] in [https://gekko.readthedocs.io/en/latest/ GEKKO] Python format. The GEKKO package is available with '''pip install gekko'''. The Python code uses orthogonal collocation and a simultaneous optimization method. The end point constraints are imposed as soft constraints (objective terms).

<source lang="Python">
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt

n = 51
Lp = 4
b = 3
a = 1
m = GEKKO()
m.time = np.linspace(0, 1, n)

x1 = m.Var(value=a, lb=0, ub=10)
x2 = m.Var(value=0, lb=0, ub=10)
x3 = m.Var(value=0, lb=0, ub=10)

u = m.MV(value=0, lb=-10, ub=20) # integer=True,

tmp = np.zeros(n)
tmp[-1] = 1

final = m.Param(value=tmp)

m.Equation(x1.dt() == u)
m.Equation(x2.dt() == x1 * (1+u**2)**0.5)
m.Equation(x3.dt() == (1+u**2)**0.5)
# m.Equation((x1-b)*final == 0)
# m.Equation((x3-Lp)*final == 0)

m.Obj(1000*(x1-b)**2*final)
m.Obj(1000*(x3-Lp)**2*final)

#m.fix(x1, n-1, b)
#m.fix(x3, n-1, Lp)

m.options.SOLVER = 3
m.options.NODES = 3
m.options.IMODE = 6
m.Obj(x2*final)

# initialize
m.options.TIME_SHIFT = 0
u.STATUS = 0
m.solve()

# solve
u.STATUS = 1
u.DCOST = 1e-3
m.solve()

plt.subplot(2,1,1)
plt.plot(m.time,x1.value,'r--',label=r'$x_1$')
plt.plot(m.time,x2.value,'g-',label=r'$x_2$')
plt.plot(m.time,x3.value,'k:',label=r'$x_3$')
plt.ylabel('x')
plt.legend()
plt.xlim([0,1])
plt.subplot(2,1,2)
plt.plot(2,1,2)
plt.plot(m.time,u.value,'k-',label=r'$u$')
plt.ylabel('u')
plt.xlim([0,1])
plt.show()
</source>

== Results with APOPT (MINLP) ==

An MINLP solution is calculated with IPOPT with an objective function value of <math>5.13266</math>.

[[File:Hanging_chain_GEKKO.png]]

[[Category:Gekko]]