(I) Objective: Design a reinforcement learning (RL) system to optimize bus routes and station placements in a city network. The goal is to minimize costs (bus station construction, bus purchases) while reducing passenger travel times, considering dynamic factors like traffic speeds, one-way streets, military restricted areas, varying passenger volumes/hotspots/destinations by time of day, walking times to stations, and in-bus congestion times.

(II) Problem Modeling and Assumptions:

• City Representation: Model the city as a directed graph (NetworkX). 

  • Nodes are potential bus station locations. 

  • Edges are roads with attributes:

    • Distance.

    • Average speed by time slot (e.g., rush hour vs. off-peak).

    • One-way (directed edges).

    • Restricted areas: Some nodes/edges are military zones (blocked).

• Passengers:  

  • Origins/destinations: Varying by time slots (e.g., morning: more commuters to work hotspots; evening: to residential). 

  • Passenger count: Varying by time slots.

• Time Slots: Divide day into slots with different speeds, demands, hotspots.

• Costs:

  • Station construction: Fixed cost per selected station.

  • Bus purchase: Cost per bus, with multiple buses allowed on same/different routes.

• Passenger Times:

  • Walking time: Distance from passenger origin to nearest station.

  • In-bus time: Travel time on route.

  • Total time: Walking + waiting + in-bus.

• Objectives: Multi-objective reward in RL – minimize passenger time while minimizing costs. 

Reward = - (total passenger time + costs).

(III) RL Environment Design:

• State: Vector representing:

  • Current selected stations (binary mask).

  • Allocated buses per route.

  • Current time slot.

  • Passenger count. 

• Actions: Discrete multi-action space:

  • Select/deselect a station.

  • Add/remove a bus to a route.

  • Choose route path: select start/end nodes, use shortest path avoiding restrictions.

• Reward:

  • Positive for reducing average passenger time.

  • Negative for costs (stations + buses).

  • Penalty for violating restrictions or high times.

• Episode: Starts with empty plan, ends after fixed steps or when budget exhausted. Simulate passenger flows to compute times/costs.