Airport Pickup

Problem Description

A planning problem that involves moving objects around a weighted graph.

Imagine a city composed of locations and possible driveways between these locations. Two of these locations are Airports and some are Gas Stations. A set of passengers are waiting in Airport #1 and Airport #2. Passengers from Airport #1 need to reach Airport #2 and vice versa.

A set of vehicles are located around the city. Each of these vehicles can pick and transport one passenger at a time.

Driving a vehicle between two city locations costs the vehicle certain amount of gasoline. Initially, all vehicles have certain amount of gasoline already in them. If a vehicle runs out of gasoline, it cannot be driven anymore. Vehicles can re-fill gasoline at a Gas Station.

Find a plan to drive the vehicles and move all the passengers to their respective destinations.

A problem instance consists of a description of a city (a weighted undirected graph), information about which locations in the city are Airports and Gas Stations, and statements about the location and status of vehicles and passengers.

Predicates

• Input: location/1, driveway/3, airport/1, gasstation/1, passenger/1, init_at/2, vehicle/2, init_at/2, init_gas/2

• Output: drive/3, pick/2, drop/2, refuel/2

Input format

A. Atoms to describe the city:

1. location(L) listing the names of locations.

2. driveway(L1, L2, D) where L1 and L2 are locations, indicating that it is possible to drive from L1 to L2 ( and from L2 to L1 ) and that the gasoline cost from L1 to L2 is D. 0 < D <= 100.

3. airport(L) indicating that location L is an airport. (there will be exactly 2 locations listed as airports)

4. gasstation(L) indicating that location L is a gas station.

B. Atoms to describe the passengers:

1. passenger(P) listing the names of passengers

2. init_at(P,L) stating that passenger P is initially at location L, where L is an airport.

C. Atoms to describe the vehicles:

1. vehicle(V, M) stating that V is a vehicle and its maximum gasoline capacity is M, 100 < M <= 500.

2. init_at(V, L) stating that vehicle V is initially at location L.

3. init_gas(V, G) indicating that initially, vehicle V has G units of gasoline. 0<= G <= M. where M is the maximum gasoline capacity of the vehicle.

Output format

The output format is a sequence of instructions to drive the cars and move the passengers. This sequence is formed with the atoms drive(V,L,S), pick(V,P), drop(V,P) and refuel(V,S) where:

A. drive(V,L,S) indicates vehicle V drives to location L at step S of the instruction sequence. This action is possible only if V is in a location adjacent to L at step S. It is not possible for a vehicle V to be driven at the same time it is being refueled or is picking or dropping a passenger. In other words, for a vehicle x it is not possible for drive(x,L,S) to appear with pick(x,P,S), drop(x,P,S) or refuel(x,S) in the same step in the output sequence.

B. pick(V,P,S) indicates vehicle V picks passenger P at step S. This action is possible only if V and P are at the same location at step S.

C. drop(V,P,S) indicates vehicle V drops passenger P at step S. This action is possible only if V is carrying P at step S.

D. refuel(V,S) indicated vehicle V fills up its gas tank at step S of the sequence.

This action is only possible if V is at a gas station.

Time steps are given as integers starting from 0.

Example(s)

Example #1

Input:

location(1). location(2). location(3). location(4).
airport(1). airport(4).
gasstation(3).
driveway(1,2,10).
driveway(2,3,20).
driveway(3,4,15). 

passenger(a).
init_at(a,1).

vehicle(taxi_1, 100).
init_at(taxi_1, 2).  init_gas(taxi_1, 50).

Output:

drive(taxi_1, 1, 0).   
pick(taxi_1, a, 1). 
drive(taxi_1, 2, 2).   
drive(taxi_1, 3, 3).   
refuel(taxi_1, 4)      
drive(taxi_1, 4, 5).   
drop(taxi_1, a, 6). 

Example #2

Input:

location(1). location(2). location(3). location(4).
airport(1). airport(4).
gasstation(3).
driveway(1,2,10).
driveway(2,3,20).
driveway(3,4,15). 

passenger(a).  init_at(a,1).
passenger(b).  init_at(b,4).

vehicle(taxi_1, 100). init_at(taxi_1, 1).  init_gas(taxi_1, 50).
vehicle(taxi_2, 80).  init_at(taxi_2, 4).  init_gas(taxi_2, 80). 

Output:

pick(taxi_1, a, 0).    pick(taxi_2, b, 0).
drive(taxi_1, 2, 1).   drive(taxi_2, 3, 1).   
drive(taxi_1, 3, 2).   drive(taxi_2, 2, 2).         
drive(taxi_1, 4, 3).   drive(taxi_2, 1, 3).   
drop(taxi_1, a, 4).    drop(taxi_2, b, 4). 

Notes and Updates

• Fixed typo on example 2 on 19/03/2011;
• Training Instances: updated on date 03/02/2011;
• Specification: updated on date 28/01/2011;

Author(s)

• Author: A. Ricardo Morales
  • Affiliation: Texas Tech University, United States