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commentaires et refactorisation

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Dumbobelix 2023-12-11 11:20:44 +01:00
parent 66cb5f32a7
commit 75488c3fee
1 changed files with 37 additions and 21 deletions
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opti_prod.py
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@ -2,6 +2,7 @@ import numpy as np
import matplotlib.pyplot as plt import matplotlib.pyplot as plt
import PyQt5 as qt import PyQt5 as qt
# Valeurs des constantes de l'exemple du cours
ptot = 1000 # [MW] ptot = 1000 # [MW]
p2max = 400 # [MW] p2max = 400 # [MW]
p23max = 500 p23max = 500
@ -15,15 +16,19 @@ def C2(x):
return 20*x + 0.02*x**2 return 20*x + 0.02*x**2
def f(x): def f(x):
# Lagrangien pour une optimisation simple de la production
return C1(x[0]) + C2(x[1]) + x[2] * (ptot - x[0] - x[1]) return C1(x[0]) + C2(x[1]) + x[2] * (ptot - x[0] - x[1])
def f2(x): def f2(x):
# Lagrangien pour une optimisation avec contrainte de production max
return f(x[0:3]) - abs(x[3]) * (p2max - x[1]) return f(x[0:3]) - abs(x[3]) * (p2max - x[1])
def f3(x): def f3(x):
# Lagrangien pour une optimisation avec contrainte de production et de transport max
return f(x[0:3]) - abs(x[3]) * (p23max - t21 * x[0] - t22 * x[1]) return f(x[0:3]) - abs(x[3]) * (p23max - t21 * x[0] - t22 * x[1])
def grad(f, x, h=1e-4): def grad(f, x, h=1e-4):
# Il y a surement des librairies qui font ça mieux, mais c'était plus rapide d'écrire cette fonction que de chercher dans la doc
res = [] res = []
for i in range(len(x)): for i in range(len(x)):
delta = f(x[:i] + [x[i] + h / 2] + x[i+1:]) - f(x[:i] + [x[i] - h / 2] + x[i+1:]) delta = f(x[:i] + [x[i] + h / 2] + x[i+1:]) - f(x[:i] + [x[i] - h / 2] + x[i+1:])
@ -31,57 +36,68 @@ def grad(f, x, h=1e-4):
return res return res
def norm(x): def norm(x):
# Idem, flemme d'utiliser des arrays et de lire la doc np
n = 0 n = 0
for d in x: for d in x:
n += d**2 n += d**2
return np.sqrt(n) return np.sqrt(n)
def g(x): def adaptation_f(f):
return norm(grad(f, x, h=1e-5)) # Permet de lancer la descente de gradient sur la norme du gradient du lagrangien
l = lambda x : norm(grad(f, x, h=1e-6)) # Un pas plus faible va créer des divergences
def g2(x): return l
return norm(grad(f2, x, h=1e-6))
def g3(x):
return norm(grad(f3, x, h=1e-6))
def minimize(f, x0, h=1e-4, step=1e-1, tol=1e-8, N=1e4, echo=False): def minimize(f, x0, h=1e-4, step=1e-1, tol=1e-8, N=1e4, echo=False):
# Initialisation
x = x0 x = x0
g = grad(f, x, h) g = grad(f, x, h)
n = 0 n = 0
prev = norm(g) + 2*tol prev = norm(g) + 2*tol # Très moche mais j'ai pas le temps de faire un truc plus élégant
while abs(norm(g) - prev) > tol: while abs(norm(g) - prev) > tol:
n += 1 # Mise à jour de la variable de suivi de convergence
prev = norm(g) prev = norm(g)
for i in range(len(x)):
x[i] -= g[i] * step # Calcul
for i in range(len(x)): # Moche mais flemme de rendre ça joli
x[i] -= g[i] * step # Descente de gradient classique
g = grad(f, x, h) g = grad(f, x, h)
# Print pour debug
if (n % 100 == 0) and echo: if (n % 100 == 0) and echo:
print("Itération ", n) print("Itération ", n)
print("norm(g) = ", norm(g)) print("norm(g) = ", norm(g))
print("prev = ", prev) print("prev = ", prev)
print("x = ", x) print("x = ", x)
print("g = ", g) print("g = ", g)
# Système anti boucle infinie
if n > N: if n > N:
return x return x
n += 1
return x return x
def custom_minimize(f, x0): def custom_minimize(f, x0, echo=False):
res_app = minimize(f, x0, step=5e-1) res_app = minimize(f, x0, step=5e-1)
if echo:
print(res_app) print(res_app)
res_app = minimize(f, res_app, step=1e-3, tol=1e-12, h=1e-5) res_app = minimize(f, res_app, step=1e-3, tol=1e-12, h=1e-5)
if echo:
print(res_app) print(res_app)
res_app = minimize(f, res_app, step=1e-5, tol=1e-14, h=1e-5) res_app = minimize(f, res_app, step=1e-5, tol=1e-14, h=1e-5)
if echo:
print(res_app) print(res_app)
res_app = minimize(f, res_app, step=1e-6, tol=1e-16, h=5e-6) res_app = minimize(f, res_app, step=1e-6, tol=1e-16, h=5e-6)
if echo:
print(res_app) print(res_app)
return res_app return res_app
print("Cas sans contraintes")
print(custom_minimize(adaptation_f(f), [0, 0, 0]))
print(minimize(g, [0, 0, 0])) print("Cas avec contrainte de production")
print(custom_minimize(adaptation_f(f2), [0, 0, 0, 0.01]))
custom_minimize(g2, [0, 0, 0, 0.01]) print("Cas avec contraintes de production et de transport")
print(custom_minimize(adaptation_f(f3), [0, 0, 0, 0.01]))
custom_minimize(g3, [0, 0, 0, 0.01])