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a1208.py
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import copy
import numpy as np
import matplotlib.pyplot as plt
from gurobipy import GRB
import gurobipy as gp
def ev2ms(m,v):
return np.log(m**2/(v+m**2)**.5),np.log(v/m**2+1)**.5
def gsum(a):
return gp.quicksum(a)
np.random.seed(1)
mu = np.array([67,135,105,80,79,72])
nss = len(mu)
samples = 3000 # a sample is a full rand process
xi = np.zeros((samples,2,nss)) # scene,e/d,t
for sce in range(samples):
for t in range(nss):
m,s = ev2ms(1,.25)
xi[sce,0,t] = np.random.lognormal(m,s)
m,s = ev2ms(mu[t],((t+1)/20*mu[t])**2)
xi[sce,1,t] = np.random.lognormal(m,s)
perfInfoObj = np.zeros(samples) # = 17499.933728562126 (rdseed = 1, samples = 3000);
# PerfInfoObj_LPrelax = 5984.709179172252;
# used to generate initial pai
for sm in range(samples):
m = gp.Model('extensive')
Y = m.addVars(nss)
p = m.addVars(nss,ub=897)
n = m.addVars(nss)
x = m.addVars(nss)
D = m.addVars(nss)
o = m.addVars(nss,ub=201.75)
y = m.addVars(nss,ub=1,vtype=GRB.BINARY) # vtype=GRB.BINARY
m.setObjective(gsum(15*p[t]+30*n[t]+6456*y[t]+100*o[t] for t in range(nss)) + 120*n[nss-1])
m.addConstr(n[0] - p[0] - D[0] + 60 == 0)
m.addConstr(-Y[0] +.6 * 1 + .4 * xi[sm, 0, 0] == 0) # random param
for t in range(1,nss): # 1,2,3,4,5
m.addConstr(n[t]-p[t]-D[t]+p[t-1]-n[t-1]+x[t-1] == 0)
m.addConstr(-Y[t] + .6*Y[t-1] + .4*xi[sm,0,t] == 0) # random param
for t in range(nss):
m.addConstr(D[t] == .6*mu[t]*Y[t] + .4*xi[sm,1,t]) # random param
for t in range(nss):
m.addConstr(22.4 * y[t] + x[t] - o[t] <= 807)
m.addConstr(538 * y[t] - x[t] >= 0)
m.addConstr(p[t] + x[t] <= 897)
m.setParam('OutputFlag',0)
m.optimize()
if m.status != 2:
print('m.status =',m.status)
exit(3)
perfInfoObj[sm] = m.ObjVal
# for t in range(nss):
# print('t=%2d:y %8g|x %8g|n %8g|p %8g|Y %8g|D %8g|o %8g' % (t,y[t].X,x[t].X,n[t].X,p[t].X,Y[t].X,D[t].X,o[t].X))
# print('\n')
beta = np.zeros(96)
for bite in range(300000000):
# begin conv opt program
# scenario_time decomposition
valMat = np.zeros((samples, nss + 1))
grad = np.zeros_like(beta)
for sm in range(samples):
addTerm = 0 # additional term (without x)
t = 0
m = gp.Model('extensive')
Y = m.addVar()
p = m.addVar(ub=897)
n = m.addVar()
x = m.addVar()
D = m.addVar()
o = m.addVar(ub=201.75)
y = m.addVar(vtype=GRB.BINARY)
# next stage base --> use conditional Expectation
base = np.array([1,xi[sm,0,0],xi[sm,1,0]])
pai_0,pai_1 = np.dot(base,beta[:3]),np.dot(base,beta[3:6])
pen = pai_0*(n-p-D) + pai_1*-Y
baseNxt = np.array([1,xi[sm,0,0],xi[sm,1,0],1,mu[t+1]])
pai_Nxt_0,pai_Nxt_1 = np.dot(baseNxt,beta[6:11]),np.dot(baseNxt,beta[11:16])
penNxt = pai_Nxt_0*(p-n+x) + pai_Nxt_1*.6*Y
cost = 15*p+30*n+6456*y+100*o
m.setObjective((cost+pen+penNxt)/samples)
m.addConstr(D == .6 * mu[t] * Y + .4 * xi[sm, 1, t]) # random param
m.addConstr(22.4 * y + x - o <= 807)
m.addConstr(538 * y - x >= 0)
m.addConstr(p + x <= 897)
m.setParam('OutputFlag', 0)
# m.setParam('DualReductions', 0)
m.optimize()
if m.status != 2:
print('m.status =', m.status)
exit(3)
valMat[sm,t] = m.ObjVal
grad[:3] += base * (n.X-p.X-D.X) / samples
grad[3:6] += base * (-Y.X) / samples
grad[6:11] += baseNxt * (p.X - n.X + x.X) / samples
grad[11:16] += baseNxt * (.6 * Y.X) / samples
addTerm += (pai_0*60 + pai_1*(.6 + .4*xi[sm,0,t]) + pai_Nxt_1*.4*xi[sm,0,t+1])/samples
grad[:3] += base*60/ samples
grad[3:6] += base*(.6 + .4*xi[sm,0,t])/ samples
grad[11:16] += baseNxt * .4*xi[sm,0,t+1]/ samples
t = 1
m = gp.Model('scena')
Y = m.addVar()
p = m.addVar(ub=897)
n = m.addVar()
x = m.addVar()
D = m.addVar()
o = m.addVar(ub=201.75)
y = m.addVar(vtype=GRB.BINARY)
base = np.array([1,xi[sm,0,0],xi[sm,1,0],xi[sm,0,1],xi[sm,1,1]])
pai_0,pai_1 = np.dot(base,beta[6:11]),np.dot(base,beta[11:16])
pen = pai_0*(n-p-D) + pai_1*-Y
baseNxt = np.array([1,xi[sm,0,0],xi[sm,1,0],xi[sm,0,1],xi[sm,1,1],1,mu[t+1]])
pai_Nxt_0,pai_Nxt_1 = np.dot(baseNxt,beta[16:23]),np.dot(baseNxt,beta[23:30])
penNxt = pai_Nxt_0*(p-n+x) + pai_Nxt_1*.6*Y
cost = 15*p+30*n+6456*y+100*o
m.setObjective((cost+penNxt+pen)/samples)
m.addConstr(D == .6 * mu[t] * Y + .4 * xi[sm, 1, t]) # random param
m.addConstr(22.4 * y + x - o <= 807)
m.addConstr(538 * y - x >= 0)
m.addConstr(p + x <= 897)
m.setParam('OutputFlag',0)
m.optimize()
if m.status != 2:
print('m.status =',m.status)
exit(3)
valMat[sm,t] = m.ObjVal
grad[6:11] += base * (n.X-p.X-D.X) / samples
grad[11:16] += base * (-Y.X) / samples
grad[16:23] += baseNxt * (p.X - n.X + x.X) / samples
grad[23:30] += baseNxt * (.6 * Y.X) / samples
addTerm += (pai_1*.4*xi[sm,0,t] + pai_Nxt_1*.4*xi[sm,0,t+1])/samples
grad[11:16] += base * .4*xi[sm,0,t] / samples
grad[23:30] += baseNxt * .4*xi[sm,0,t+1] / samples
t = 2
m = gp.Model('scena')
Y = m.addVar()
p = m.addVar(ub=897)
n = m.addVar()
x = m.addVar()
D = m.addVar()
o = m.addVar(ub=201.75)
y = m.addVar(vtype=GRB.BINARY)
base = np.array([1,xi[sm,0,0],xi[sm,1,0],xi[sm,0,1],xi[sm,1,1],xi[sm,0,2],xi[sm,1,2]])
pai_0,pai_1 = np.dot(base,beta[16:23]),np.dot(base,beta[23:30])
pen = pai_0*(n-p-D) + pai_1*-Y
baseNxt = np.array([1,xi[sm,0,0],xi[sm,1,0],xi[sm,0,1],xi[sm,1,1],xi[sm,0,2],xi[sm,1,2],1,mu[t+1]])
pai_Nxt_0,pai_Nxt_1 = np.dot(baseNxt,beta[30:39]),np.dot(baseNxt,beta[39:48])
penNxt = pai_Nxt_0*(p-n+x) + pai_Nxt_1*.6*Y
cost = 15*p+30*n+6456*y+100*o
m.setObjective((cost+penNxt+pen)/samples)
m.addConstr(D == .6 * mu[t] * Y + .4 * xi[sm, 1, t]) # random param
m.addConstr(22.4 * y + x - o <= 807)
m.addConstr(538 * y - x >= 0)
m.addConstr(p + x <= 897)
m.setParam('OutputFlag',0)
m.optimize()
if m.status != 2:
print('m.status =',m.status)
exit(3)
valMat[sm,t] = m.ObjVal
grad[16:23] += base * (n.X-p.X-D.X) / samples
grad[23:30] += base * (-Y.X) / samples
grad[30:39] += baseNxt * (p.X - n.X + x.X) / samples
grad[39:48] += baseNxt * (.6 * Y.X) / samples
addTerm += (pai_1*.4*xi[sm,0,t] + pai_Nxt_1*.4*xi[sm,0,t+1])/samples
grad[23:30] += base * .4*xi[sm,0,t] / samples
grad[39:48] += baseNxt * .4*xi[sm,0,t+1] / samples
t = 3
m = gp.Model('scena')
Y = m.addVar()
p = m.addVar(ub=897)
n = m.addVar()
x = m.addVar()
D = m.addVar()
o = m.addVar(ub=201.75)
y = m.addVar(vtype=GRB.BINARY)
base = np.array([1, xi[sm, 0, 0], xi[sm, 1, 0], xi[sm, 0, 1], xi[sm, 1, 1], xi[sm, 0, 2], xi[sm, 1, 2], xi[sm, 0, 3], xi[sm, 1, 3]])
pai_0, pai_1 = np.dot(base, beta[30:39]), np.dot(base, beta[39:48])
pen = pai_0 * (n - p - D) + pai_1 * -Y
baseNxt = np.array([1, xi[sm, 0, 0], xi[sm, 1, 0], xi[sm, 0, 1], xi[sm, 1, 1], xi[sm, 0, 2], xi[sm, 1, 2], xi[sm, 0, 3], xi[sm, 1, 3], 1, mu[t+1]])
pai_Nxt_0, pai_Nxt_1 = np.dot(baseNxt, beta[48:59]), np.dot(baseNxt, beta[59:70])
penNxt = pai_Nxt_0 * (p - n + x) + pai_Nxt_1 * .6 * Y
cost = 15*p+30*n+6456*y+100*o
m.setObjective((cost+penNxt+pen)/samples)
m.addConstr(D == .6 * mu[t] * Y + .4 * xi[sm, 1, t]) # random param
m.addConstr(22.4 * y + x - o <= 807)
m.addConstr(538 * y - x >= 0)
m.addConstr(p + x <= 897)
m.setParam('OutputFlag',0)
m.optimize()
if m.status != 2:
print('m.status =',m.status)
exit(3)
valMat[sm,t] = m.ObjVal
grad[30:39] += base * (n.X - p.X - D.X) / samples
grad[39:48] += base * (-Y.X) / samples
grad[48:59] += baseNxt * (p.X - n.X + x.X) / samples
grad[59:70] += baseNxt * (.6 * Y.X) / samples
addTerm += (pai_1 * .4 * xi[sm, 0, t] + pai_Nxt_1 * .4 * xi[sm, 0, t + 1]) / samples
grad[39:48] += base * .4 * xi[sm, 0, t] / samples
grad[59:70] += baseNxt * .4 * xi[sm, 0, t + 1] / samples
t = 4
m = gp.Model('scena')
Y = m.addVar()
p = m.addVar(ub=897)
n = m.addVar()
x = m.addVar()
D = m.addVar()
o = m.addVar(ub=201.75)
y = m.addVar(vtype=GRB.BINARY)
base = np.array([1, xi[sm, 0, 0], xi[sm, 1, 0], xi[sm, 0, 1], xi[sm, 1, 1], xi[sm, 0, 2], xi[sm, 1, 2], xi[sm, 0, 3],xi[sm, 1, 3],xi[sm, 0, 4],xi[sm, 1, 4]])
pai_0, pai_1 = np.dot(base, beta[48:59]), np.dot(base, beta[59:70])
pen = pai_0 * (n - p - D) + pai_1 * -Y
baseNxt = np.array([1, xi[sm, 0, 0], xi[sm, 1, 0], xi[sm, 0, 1], xi[sm, 1, 1], xi[sm, 0, 2], xi[sm, 1, 2], xi[sm, 0, 3],xi[sm, 1, 3],xi[sm, 0, 4],xi[sm, 1, 4], 1, mu[t+1]])
pai_Nxt_0, pai_Nxt_1 = np.dot(baseNxt, beta[70:83]), np.dot(baseNxt, beta[83:96])
penNxt = pai_Nxt_0 * (p - n + x) + pai_Nxt_1 * .6 * Y
cost = 15*p+30*n+6456*y+100*o
m.setObjective((cost+penNxt+pen)/samples)
m.addConstr(D == .6 * mu[t] * Y + .4 * xi[sm, 1, t]) # random param
m.addConstr(22.4 * y + x - o <= 807)
m.addConstr(538 * y - x >= 0)
m.addConstr(p + x <= 897)
m.setParam('OutputFlag',0)
m.optimize()
if m.status != 2:
print('m.status =',m.status)
exit(3)
valMat[sm,t] = m.ObjVal
grad[48:59] += base * (n.X - p.X - D.X) / samples
grad[59:70] += base * (-Y.X) / samples
grad[70:83] += baseNxt * (p.X - n.X + x.X) / samples
grad[83:96] += baseNxt * (.6 * Y.X) / samples
addTerm += (pai_1 * .4 * xi[sm, 0, t] + pai_Nxt_1 * .4 * xi[sm, 0, t+1])/samples
grad[59:70] += base * .4 * xi[sm, 0, t] / samples
grad[83:96] += baseNxt * .4 * xi[sm, 0, t+1] / samples
t = 5
m = gp.Model('scena')
Y = m.addVar()
p = m.addVar(ub=897)
n = m.addVar()
x = m.addVar()
D = m.addVar()
o = m.addVar(ub=201.75)
y = m.addVar(vtype=GRB.BINARY)
base = np.array([1, xi[sm, 0, 0], xi[sm, 1, 0], xi[sm, 0, 1], xi[sm, 1, 1], xi[sm, 0, 2], xi[sm, 1, 2], xi[sm, 0, 3],xi[sm, 1, 3],xi[sm, 0, 4],xi[sm, 1, 4],xi[sm, 0, 5],xi[sm, 1, 5]])
pai_0, pai_1 = np.dot(base, beta[70:83]), np.dot(base, beta[83:96])
pen = pai_0 * (n - p - D) + pai_1 * -Y
cost = 15*p+150*n+6456*y+100*o
m.setObjective((cost+pen)/samples)
m.addConstr(D == .6 * mu[t] * Y + .4 * xi[sm, 1, t]) # random param
m.addConstr(22.4 * y + x - o <= 807)
m.addConstr(538 * y - x >= 0)
m.addConstr(p + x <= 897)
m.setParam('OutputFlag',0)
m.optimize()
if m.status != 2:
print('m.status =',m.status)
exit(3)
valMat[sm, t] = m.ObjVal
grad[70:83] += base * (n.X - p.X - D.X) / samples
grad[83:96] += base * (-Y.X) / samples
addTerm += (pai_1 * .4 * xi[sm, 0, t]) / samples
grad[83:96] += base * .4 * xi[sm, 0, t] / samples
val = sum(sum(valMat))
print(val)
beta += 1e-12*grad