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# modules/route_assignment.py
# TripAI – Synthetic Network + AON + Frank–Wolfe UE
from __future__ import annotations
from dataclasses import dataclass
from typing import List
import numpy as np
import pandas as pd
@dataclass
class Network:
"""
Simple synthetic network representation where each TAZ pair
(i, j) is connected by a single directed link.
Attributes
----------
links : pd.DataFrame
Columns:
- link_id
- from_zone
- to_zone
- length_km
- t0_min (free-flow travel time)
- capacity_vehph
- alpha (BPR parameter)
- beta (BPR parameter)
"""
links: pd.DataFrame
def generate_synthetic_network(taz: pd.DataFrame) -> Network:
"""
Generate a fully connected directed network over TAZ centroids.
Each ordered pair (i, j), i != j, is represented as a distinct link.
Travel times are approximated from Euclidean distance and an
assumed free-flow speed.
Parameters
----------
taz : pd.DataFrame
Must include 'x_km' and 'y_km' columns.
Returns
-------
Network
"""
zones = taz.index.to_list()
coords = taz[["x_km", "y_km"]].to_numpy()
n = len(zones)
rows = []
link_id = 0
ff_speed_kmh = 30.0
for i_idx, i in enumerate(zones):
for j_idx, j in enumerate(zones):
if i == j:
continue
dx = coords[j_idx, 0] - coords[i_idx, 0]
dy = coords[j_idx, 1] - coords[i_idx, 1]
dist = np.sqrt(dx**2 + dy**2) # km
t0 = (dist / max(ff_speed_kmh, 1e-3)) * 60.0 + 3.0 # minutes
rows.append(
{
"link_id": link_id,
"from_zone": i,
"to_zone": j,
"length_km": dist,
"t0_min": t0,
"capacity_vehph": np.random.uniform(1500, 2500),
"alpha": 0.15,
"beta": 4.0,
}
)
link_id += 1
links_df = pd.DataFrame(rows).set_index("link_id")
return Network(links=links_df)
def _init_flow_column(links: pd.DataFrame, col: str = "flow_vehph") -> pd.DataFrame:
df = links.copy()
if col not in df.columns:
df[col] = 0.0
else:
df[col] = 0.0
return df
def aon_assignment(od_car: pd.DataFrame, network: Network) -> pd.DataFrame:
"""
All-or-nothing (AON) assignment assuming a single direct link
between each TAZ pair (i, j). All demand from i to j is loaded
on that link.
Parameters
----------
od_car : pd.DataFrame
Car OD matrix (veh/h equivalent).
network : Network
Returns
-------
pd.DataFrame
Link flows with column 'flow_vehph'.
"""
links = _init_flow_column(network.links, col="flow_vehph")
zones = od_car.index.to_list()
for i in zones:
for j in zones:
if i == j:
continue
q = float(od_car.loc[i, j])
if q <= 0:
continue
mask = (links["from_zone"] == i) & (links["to_zone"] == j)
links.loc[mask, "flow_vehph"] += q
return links
def _bpr_travel_time(
flows: np.ndarray,
t0: np.ndarray,
capacity: np.ndarray,
alpha: np.ndarray,
beta: np.ndarray,
) -> np.ndarray:
"""Standard BPR volume-delay function."""
vc = np.divide(flows, capacity, out=np.zeros_like(flows), where=capacity > 0)
return t0 * (1.0 + alpha * np.power(vc, beta))
def frank_wolfe_ue(
od_car: pd.DataFrame,
network: Network,
max_iter: int = 30,
) -> pd.DataFrame:
"""
Very simple Frank–Wolfe style User Equilibrium assignment over
the synthetic network where each OD pair has a single link.
Because there is only one 'route' per OD, the UE solution
coincides with the AON solution. This implementation still
outlines the iterative structure for pedagogical purposes.
Parameters
----------
od_car : pd.DataFrame
Car OD matrix (veh/h).
network : Network
max_iter : int
Maximum iterations (for demonstration).
Returns
-------
pd.DataFrame
Link flows with column 'flow_vehph' and implied travel times.
"""
links = network.links.copy()
n_links = len(links)
# Initialize flows
flows = np.zeros(n_links, dtype=float)
# Extract BPR parameters
t0 = links["t0_min"].to_numpy()
cap = links["capacity_vehph"].to_numpy()
alpha = links["alpha"].to_numpy()
beta = links["beta"].to_numpy()
# Pre-build a mapping (from_zone, to_zone) -> link indices
index = links.reset_index()
zone_pairs = {}
for idx, row in index.iterrows():
key = (row["from_zone"], row["to_zone"])
zone_pairs[key] = row["link_id"]
# Iterate Frank–Wolfe (though it converges immediately in this simple network)
for k in range(max_iter):
# Step 1: Compute travel times (not used for path choice here)
tt = _bpr_travel_time(flows, t0, cap, alpha, beta)
# Step 2: AON step (all or nothing given current times – here trivial)
aon_flows = np.zeros_like(flows)
zones = od_car.index.to_list()
for i in zones:
for j in zones:
if i == j:
continue
q = float(od_car.loc[i, j])
if q <= 0:
continue
lid = zone_pairs[(i, j)]
aon_flows[lid] += q
# Step 3: Line search step-size (generic diminishing rule)
step = 2.0 / (k + 2.0)
new_flows = flows + step * (aon_flows - flows)
# Convergence check
if np.allclose(new_flows, flows, atol=1e-3):
flows = new_flows
break
flows = new_flows
links["flow_vehph"] = flows
links["tt_min"] = _bpr_travel_time(flows, t0, cap, alpha, beta)
return links
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