## Generate a contour plot # Import some other libraries that we'll need # matplotlib and numpy packages must also be installed import matplotlib import numpy as np import matplotlib.pyplot as plt import random import math # define objective function def f(x): x1 = x x2 = x obj = 0.2 + x1**2 + x2**2 - 0.1*math.cos(6.0*3.1415*x1) - 0.1*math.cos(6.0*3.1415*x2) return obj # Start location x_start = [0.8, -0.5] # Design variables at mesh points i1 = np.arange(-1.0, 1.0, 0.01) i2 = np.arange(-1.0, 1.0, 0.01) x1m, x2m = np.meshgrid(i1, i2) fm = np.zeros(x1m.shape) for i in range(x1m.shape): for j in range(x1m.shape): fm[i][j] = 0.2 + x1m[i][j]**2 + x2m[i][j]**2 \ - 0.1*math.cos(6.0*3.1415*x1m[i][j]) \ - 0.1*math.cos(6.0*3.1415*x2m[i][j]) # Create a contour plot plt.figure() # Specify contour lines #lines = range(2,52,2) # Plot contours CS = plt.contour(x1m, x2m, fm)#,lines) # Label contours plt.clabel(CS, inline=1, fontsize=10) # Add some text to the plot plt.title('Non-Convex Function') plt.xlabel('x1') plt.ylabel('x2') ################################################## # Simulated Annealing ################################################## # Number of cycles n = 50 # Number of trials per cycle m = 50 # Number of accepted solutions na = 0.0 # Probability of accepting worse solution at the start p1 = 0.7 # Probability of accepting worse solution at the end p50 = 0.001 # Initial temperature t1 = -1.0/math.log(p1) # Final temperature t50 = -1.0/math.log(p50) # Fractional reduction every cycle frac = (t50/t1)**(1.0/(n-1.0)) # Initialize x x = np.zeros((n+1,2)) x = x_start xi = np.zeros(2) xi = x_start na = na + 1.0 # Current best results so far xc = np.zeros(2) xc = x fc = f(xi) fs = np.zeros(n+1) fs = fc # Current temperature t = t1 # DeltaE Average DeltaE_avg = 0.0 for i in range(n): print('Cycle: ' + str(i) + ' with Temperature: ' + str(t)) for j in range(m): # Generate new trial points xi = xc + random.random() - 0.5 xi = xc + random.random() - 0.5 # Clip to upper and lower bounds xi = max(min(xi,1.0),-1.0) xi = max(min(xi,1.0),-1.0) DeltaE = abs(f(xi)-fc) if (f(xi)>fc): # Initialize DeltaE_avg if a worse solution was found # on the first iteration if (i==0 and j==0): DeltaE_avg = DeltaE # objective function is worse # generate probability of acceptance p = math.exp(-DeltaE/(DeltaE_avg * t)) # determine whether to accept worse point if (random.random()