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Parallel Computing in Optimization

APM is configured to run on heterogeneous networks and platforms. In this example application, we solve a series of optimization problems using Linux and Windows servers. The optimization problems are transferred to the servers in parallel, computed in parallel, and returned asynchronously to the MATLAB or Python script.

Multithreading in Python

In Python, parallelization is accomplished with multithreading. The following example shows how to create and run a program with 10 threads that each print a message.

import threading
import datetime
import time, random

class MyThread(threading.Thread):
    def __init__(self, id):
        self.id = id
        self.delay = random.random()
        threading.Thread.__init__(self)
    def run(self):
        time.sleep(self.delay)
        now = datetime.datetime.now()
        print("ID => %s: %s completes at %s\n" % \
              (self.id, self.getName(), now))

# Start threads
threads = []
for i in range(10):
    threads.append(MyThread(i))
    threads[i].start()
    print('Active threads: ' + str(threading.activeCount()))

# Print threads
print('All threads: \n')
print(threading.enumerate())

# Wait for all threads to complete
for t in threads:
    t.join()
print('Threads complete')

The next step is to embed a simple Nonlinear Programming (NLP) problem into the multi-threaded application. The tutorial examples are available for download below:


import numpy as np
import threading
import time, random
from gekko import GEKKO

class ThreadClass(threading.Thread):
    def __init__(self, id, server, ai, bi):
        s = self
        s.id = id
        s.server = server
        s.m = GEKKO()
        s.a = ai
        s.b = bi
        s.objective = float('NaN')

        # initialize variables
        s.m.x1 = s.m.Var(1,lb=1,ub=5)
        s.m.x2 = s.m.Var(5,lb=1,ub=5)
        s.m.x3 = s.m.Var(5,lb=1,ub=5)
        s.m.x4 = s.m.Var(1,lb=1,ub=5)

        # Equations
        s.m.Equation(s.m.x1*s.m.x2*s.m.x3*s.m.x4>=s.a)
        s.m.Equation(s.m.x1**2+s.m.x2**2+s.m.x3**2+s.m.x4**2==s.b)

        # Objective
        s.m.Obj(s.m.x1*s.m.x4*(s.m.x1+s.m.x2+s.m.x3)+s.m.x3)

        # Set global options
        s.m.options.IMODE = 3 # steady state optimization
        s.m.options.SOLVER = 1 # APOPT solver

        threading.Thread.__init__(s)

    def run(self):

        # Don't overload server by executing all scripts at once
        sleep_time = random.random()
        time.sleep(sleep_time)

        print('Running application ' + str(self.id) + '\n')

        # Solve
        self.m.solve(disp=False)

        # Results
        #print('')
        #print('Results')
        #print('x1: ' + str(self.m.x1.value))
        #print('x2: ' + str(self.m.x2.value))
        #print('x3: ' + str(self.m.x3.value))
        #print('x4: ' + str(self.m.x4.value))

        # Retrieve objective if successful
        if (self.m.options.APPSTATUS==1):
            self.objective = self.m.options.objfcnval
        else:
            self.objective = float('NaN')

# Select server
server = 'https://byu.apmonitor.com'

# Optimize at mesh points
x = np.arange(20.0, 30.0, 2.0)
y = np.arange(30.0, 50.0, 2.0)
a, b = np.meshgrid(x, y)

# Array of threads
threads = []

# Calculate objective at all meshgrid points

# Load applications
id = 0
for i in range(a.shape[0]):
    for j in range(b.shape[1]):
        # Create new thread
        threads.append(ThreadClass(id, server, a[i,j], b[i,j]))
        # Increment ID
        id += 1

# Run applications simultaneously as multiple threads
# Max number of threads to run at once
max_threads = 8
for t in threads:
    while (threading.activeCount()>max_threads):
        # check for additional threads every 0.01 sec
        time.sleep(0.01)
    # start the thread
    t.start()

# Check for completion
mt = 3.0 # max time
it = 0.0 # incrementing time
st = 1.0 # sleep time
while (threading.activeCount()>=1):
    time.sleep(st)
    it = it + st
    print('Active Threads: ' + str(threading.activeCount()))
    # Terminate after max time
    if (it>=mt):
        break

# Wait for all threads to complete
#for t in threads:
#    t.join()
#print('Threads complete')

# Initialize array for objective
obj = np.empty_like(a)

# Retrieve objective results
id = 0
for i in range(a.shape[0]):
    for j in range(b.shape[1]):
        obj[i,j] = threads[id].objective
        id += 1

# plot 3D figure of results
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
import numpy as np

fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(a, b, obj, \
                       rstride=1, cstride=1, cmap=cm.coolwarm, \
                       vmin = 12, vmax = 22, linewidth=0, antialiased=False)
ax.set_xlabel('a')
ax.set_ylabel('b')
ax.set_zlabel('obj')
ax.set_title('Multi-Threaded GEKKO')
plt.show()




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