Airport Pickup

Problem Description

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

Imagine a city composed of locations and possible driveways between these locations. Two of this 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's (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 and refuel/2

Input format

1. 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.

• 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.

Sample #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).}}}

Sample #1 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). }}}

Sample #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_1, 80). }}}

== Sample #2 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). }}}

Author(s)

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