JohnHedengren at 19:17, 13 March 2019

2019-03-13T19:17:01Z

← Older revision		Revision as of 19:17, 13 March 2019
Line 56:		Line 56:
	</source>		</source>

	An MINLP solution is calculated with [https://apopt.com APOPT] with an objective function value of <math>x_2(t_f) = 1.36</math>.		An MINLP solution is calculated with [https://apopt.com APOPT] with an objective function value of <math>x_2(t_f) = 1.349497</math>.

	[[File:Volterra_fishing_GEKKO.png]]		[[File:Volterra_fishing_GEKKO.png]]

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

JohnHedengren: Create results page with Python GEKKO

2019-03-13T19:15:50Z

Create results page with Python GEKKO

New page

This page contains a solution of the MIOCP [[Lotka Volterra fishing problem]] in [https://gekko.readthedocs.io/en/latest/ GEKKO] Python format. The model in Python code for a fixed control discretization grid using orthogonal collocation and a simultaneous optimization method. The GEKKO package is available with '''pip install gekko'''.

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

m = GEKKO() # create GEKKO model

# Add 0.01 as first step
# 0,0.01,0.1,0.2,0.3,...11.9,12.0)
m.time = np.insert(np.linspace(0,12,121),1,0.01)

# change solver options
m.solver_options = ['minlp_gap_tol 0.001',\
'minlp_maximum_iterations 10000',\
'minlp_max_iter_with_int_sol 100',\
'minlp_branch_method 1',\
'minlp_integer_tol 0.001',\
'minlp_integer_leaves 0',\
'minlp_maximum_iterations 200']

c0 = 0.4
c1 = 0.2

last = m.Param(np.zeros(122))
last.value[-1] = 1

x0 = m.Var(value=0.5,lb=0)
x1 = m.Var(value=0.7,lb=0)
x2 = m.Var(value=0.0,lb=0)
w = m.MV(value=0,lb=0,ub=1,integer=True)
w.STATUS = 1

m.Obj(last*x2)

m.Equations([x0.dt() == x0 - x0*x1 - c0*x0*w,\
x1.dt() == - x1 + x0*x1 - c1*x1*w,\
x2.dt() == (x0-1)**2 + (x1-1)**2])

m.options.IMODE = 6
m.options.NODES = 3
m.options.SOLVER = 1
m.options.MV_TYPE = 0
m.solve()

plt.figure(1)
plt.step(m.time,w.value,'r-',label='w (0/1)')
plt.plot(m.time,x0.value,'b-',label=r'$x_0$')
plt.plot(m.time,x1.value,'k-',label=r'$x_1$')
plt.plot(m.time,x2.value,'g-',label=r'$x_2$')
plt.xlabel('Time')
plt.ylabel('Variables')
plt.legend(loc='best')
plt.show()
</source>

An MINLP solution is calculated with [https://apopt.com APOPT] with an objective function value of <math>x_2(t_f) = 1.36</math>.

[[File:Volterra_fishing_GEKKO.png]]

[[Category:Gekko]]

Lotka Volterra fishing problem (GEKKO) - Revision history

JohnHedengren at 19:17, 13 March 2019

JohnHedengren: Create results page with Python GEKKO