-
Notifications
You must be signed in to change notification settings - Fork 2
/
cocp_supply_chain.py
365 lines (275 loc) · 9.07 KB
/
cocp_supply_chain.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
#!/usr/bin/env python
# coding: utf-8
# In[1]:
import torch
import cvxpy as cp
import numpy as np
import scipy.sparse as spa
from cvxpylayers.torch import CvxpyLayer
import networkx as nx
import matplotlib.pyplot as plt
import pandas as pd
from tqdm import tqdm
import argparse
# In[2]:
parser = argparse.ArgumentParser()
parser.add_argument("--seed", type=int, default=0, help="random seed")
parser.add_argument(
"--mismatch", type=float, default=0.0, help="parameter mismatch percent"
)
args = parser.parse_args()
SEED = args.seed
print("SEED:", SEED)
np.random.seed(SEED)
torch.manual_seed(SEED)
# generate problem data
n = 4 # nodes
k = 2 # suppliers (with prices p)
c = 2 # retail (with demand d)
m = 8 # links
supply_links = [0, 1]
retail_links = [6, 7]
internode_links = [2, 3, 4, 5]
# Incidence matrices (nodes x links)
A_in = np.array(
[
[1, 0, 0, 0, 0, 0, 0, 0], # 1 (supply)
[0, 1, 0, 0, 0, 0, 0, 0], # 2 (supply)
[0, 0, 1, 0, 0, 1, 0, 0], # 3 (retail)
[0, 0, 0, 1, 1, 0, 0, 0], # 4 (retail)
]
)
A_out = np.array(
[
[0, 0, 1, 1, 0, 0, 0, 0], # 1 (supply)
[0, 0, 0, 0, 1, 0, 0, 0], # 2 (supply)
[0, 0, 0, 0, 0, 0, 1, 0], # 3 (retail)
[0, 0, 0, 0, 0, 1, 0, 1], # 4 (retail)
]
)
# Prices
mu_p = torch.tensor([0, 0.1]).double()
sigma_p = torch.tensor([0.2, 0.2]).double()
mean_p = torch.exp(mu_p + sigma_p ** 2 / 2).double().view(k, 1)
var_p = (torch.exp(sigma_p ** 2) - 1) * torch.exp(2 * mean_p + sigma_p ** 2)
# Demands
mu_d = torch.tensor([0.0, 0.4]).double()
sigma_d = torch.tensor([0.2, 0.2]).double()
mean_d = torch.exp(mu_d + sigma_d ** 2 / 2).double().view(c, 1)
var_d = (torch.exp(sigma_d ** 2) - 1) * torch.exp(2 * mean_d + sigma_d ** 2)
# Uncertainty distribution (prices and demands)
w_dist = torch.distributions.log_normal.LogNormal(
torch.cat([mu_p, mu_d], 0), torch.cat([sigma_p, sigma_d], 0)
)
# Capacities
h_max = 3.0 # Maximum capacity in every node
u_max = 2.0 # Link flow capacity
# Storage cost parameters, W(x) = alpha'x + beta'x^2 + gamma
alpha = 0.01
beta = 0.01
# Transportation cost parameters
tau = 0.05 * np.ones((m - k - c, 1))
tau_th = torch.tensor(tau, dtype=torch.double)
r = 1.3 * np.ones((k, 1))
r_th = torch.tensor(r, dtype=torch.double)
# In[3]:
print(w_dist.sample())
print(mean_p)
print(var_p)
print(mean_d)
print(var_d)
# In[4]:
# Define linear dynamics
# x = (h, p^{wh}, d)
# u = u
# w = (p^{wh}, d)
# x_{t+1} = Ax_{t} + Bu_{t} + w
A_d = np.bmat(
[
[np.eye(n), np.zeros((n, k + c))],
[np.zeros((k + c, n)), np.zeros((k + c, k + c))],
]
)
A_d_th = torch.tensor(A_d, dtype=torch.double)
B_d = np.vstack([A_in - A_out, np.zeros((k + c, m))])
B_d_th = torch.tensor(B_d, dtype=torch.double)
n_x, n_u = B_d.shape
# In[5]:
# Setup policy
# Parameters
P_sqrt = cp.Parameter((n, n)) # 4x4
q = cp.Parameter((n, 1)) # 4x1
x = cp.Parameter((n_x, 1)) # 8x1
h, p, d = x[:n], x[n : n + k], x[n + k :]
# Variables
u = cp.Variable((n_u, 1))
h_next = cp.Variable((n, 1))
# Cvxpy Layer
stage_cost = cp.vstack([p, tau, -r]).T @ u
next_stage_cost = cp.sum_squares(P_sqrt @ h_next) + q.T @ h_next
constraints = [
h_next == h + (A_in - A_out) @ u,
h_next <= h_max,
0 <= u,
u <= u_max,
A_out @ u <= h,
u[retail_links] <= d,
]
prob = cp.Problem(cp.Minimize(stage_cost + next_stage_cost), constraints)
policy = CvxpyLayer(prob, [x, P_sqrt, q], [u])
# In[6]:
def stage_cost(x, u):
assert x.shape[0] == u.shape[0]
batch_size = x.shape[0]
r_batch = r_th.repeat(batch_size, 1, 1)
tau_batch = tau_th.repeat(batch_size, 1, 1)
h, p, dh = x[:, :n], x[:, n : n + k], x[:, n + k :]
m = len(u)
# Selling + buying + shipping cost
s_vec = torch.cat([p, tau_batch, -r_batch], 1).double()
S = torch.bmm(s_vec.transpose(1, 2), u)
H = alpha * h + beta * (h ** 2) # Storage cost
return torch.sum(S, 1) + torch.sum(H, 1)
def simulate(x, u):
assert x.shape[0] == u.shape[0]
batch_size = x.shape[0]
A_batch = A_d_th.repeat(batch_size, 1, 1)
B_batch = B_d_th.repeat(batch_size, 1, 1)
zer = torch.zeros(batch_size, n, 1).double()
w = w_dist.sample((batch_size,)).double().view((batch_size, k + c, 1))
w_batch = torch.cat([zer, w], 1).double()
return torch.bmm(A_batch, x) + torch.bmm(B_batch, u) + w_batch
def loss(policy, params, time_horizon, batch_size=1, seed=None, is_eval=True):
mismatch = args.mismatch # mismatch parameter
noise = (
lambda input_tensor, mismatch: input_tensor
if is_eval
else input_tensor + mismatch * torch.randn_like(input_tensor)
)
P_sqrt, q = noise(params[0], mismatch), noise(params[1], mismatch)
if seed is not None:
torch.manual_seed(seed)
# Batchify input
x_b_0 = h_max * torch.rand(batch_size, n, 1).double()
w_0 = w_dist.sample((batch_size,)).double().view((batch_size, k + c, 1))
x_batch = torch.cat([x_b_0, w_0], 1).double()
# Repeat parameter values
P_sqrt_batch = P_sqrt.repeat(batch_size, 1, 1)
q_batch = q.repeat(batch_size, 1, 1)
cost = 0.0
x_t = x_batch
x_hist = [x_batch]
u_hist = []
for t in range(time_horizon):
u_t = policy(
x_t, P_sqrt_batch, q_batch, solver_args={"acceleration_lookback": 0}
)[0]
x_t = simulate(x_t, u_t)
cost += stage_cost(x_t, u_t).mean() / time_horizon
x_hist.append(x_t)
u_hist.append(u_t)
return cost, x_hist, u_hist
def monte_carlo(policy, params, time_horizon, batch_size=1, trials=10, seed=None):
if seed is not None:
torch.manual_seed(seed)
results = []
x = []
u = []
for i in range(trials):
cost, x_hist, u_hist = loss(
policy, params, time_horizon, batch_size=batch_size, seed=seed
)
results.append(cost.item())
x.append(x_hist)
u.append(u_hist)
return results, x, u
# In[7]:
def train(policy, params, time_horizon, lr, epochs, batch_size):
opt = torch.optim.SGD(params, lr=lr)
val_costs = []
best_params = []
# updating without gradient
with tqdm(total=epochs) as pbar:
for epoch in range(epochs):
with torch.no_grad():
val_cost_mc, x_behav, u_behav = monte_carlo(
policy, params, time_horizon, 1, trials=10, seed=SEED
)
val_cost = np.mean(val_cost_mc)
val_costs.append(val_cost)
torch.manual_seed(epoch)
opt.zero_grad()
(
cost,
_,
_,
) = loss(policy, params, time_horizon, batch_size, seed=None, is_eval=False)
cost.backward()
pbar.set_description("epoch %d, valid %.4f" % (epoch, val_cost))
# TODO: Print gradient norm (possibly clip it)
# torch.nn.utils.clip_grad_norm_(params, 1)
# for p in params:
# print(p.grad.data.norm(2).item())
opt.step()
# scheduler.step(val_cost)
pbar.update(1)
return val_costs, [np.array(p.detach().numpy()) for p in params], x_behav, u_behav
# In[8]:
def loss_aggregate(policy, param_set, time_horizon, batch_size=1, seed=None):
costs = []
for param in param_set:
costs.append(loss(policy, params, time_horizon, batch_size=1, seed=None)[0])
best_zetas = np.argsort(costs) # update to return parameters
return best_zetas
# In[9]:
# Perform training
time_horizon = 10
epochs = 200
batch_size = 1
lr = 0.05
# Initialize value function V(x) = x'Px + q'x
# centered at h_max/2 (between 0 and h_max) of each node
P_sqrt = torch.eye(n, requires_grad=True, dtype=torch.double)
q = -h_max * torch.ones(n, 1, dtype=torch.double)
# P_sqrt = torch.zeros(n, n).double()
# q = torch.zeros((n, 1)).double()
q.requires_grad_(True)
params = [P_sqrt, q]
# Baseline
P_sqrt_baseline = torch.eye(n, dtype=torch.double)
q_baseline = -h_max * torch.ones(n, 1, dtype=torch.double)
# P_sqrt_baseline = torch.zeros(n, n).double()
# q_baseline = torch.zeros((n, 1)).double()
baseline_params = [P_sqrt_baseline, q_baseline]
baseline_costs, x_behav_bl, u_behav_bl = monte_carlo(
policy, baseline_params, time_horizon, batch_size=1, trials=10, seed=SEED
)
baseline_cost = np.mean(baseline_costs)
print("Baseline cost: ", baseline_cost)
print("Perform training")
val_cost, params, x_behav, u_behav = train(
policy, params, time_horizon, lr, epochs, batch_size
)
print("Final cost: ", val_cost[-1])
improvement = 100 * np.abs(baseline_cost - val_cost[-1]) / np.abs(baseline_cost)
print("Performance improvement: %.2f %% over baseline cost" % improvement)
# Store final values
P_sqrt_train = P_sqrt.detach().numpy()
q_train = q.detach().numpy()
# In[ ]:
# plt.plot(val_cost, c="k", label="Loss")
# plt.xlabel("iteration")
# plt.ylabel("cost")
# plt.tight_layout()
# plt.savefig("supply_chain_training.pdf")
# plt.show()
# In[ ]:
path = f"experiments/COCP_mismatch_{args.mismatch}.csv"
try:
df = pd.read_csv(path)
df.insert(SEED, SEED, val_cost)
except:
df = pd.DataFrame(val_cost)
df.to_csv(path, index=False)
# In[ ]:
len(df.columns)