UWL CS452/552 Arti?cial Intelligence

Posted 2020-11-15 clga

Homework 1 — Using A* Search
UWL CS452/552 Arti?cial Intelligence
Fall 2019
For your ?rst homework, please write a Java[1] class which implements A* search to ?nd the
best travel path betwee two cities, given cost information between a subset of pairs of those cities.
In the resources for this homework linked from Canvas, you will ?nd two Java source ?les.
One of these classes, FoundPath, just bundles up the details of an A* search. The other class,
Pathfinder, is an abstract class which you will extend. The core of your work is the method
getPathInfo[2]:
public abstract FoundPath getPathInfo(String startCity, String endCity);
Your class AStar should extend Pathfinder, implementing an A* search to ?nd the shortest path
between the named start- and endpoints. Its result bundles up certain information which your
search should gather:
• The sequence of cities in the best path between cities, or an empty list if no such path is
possible. The ?rst element of this list should be startCity, and the last element of this list
should be endCity.
• The total cost of following the above path, or the empty instance if there no such path is
possible[3]
.
• The number of nodes which A* generated in the search (i.e. nodes ever placed into the
frontier).
• The number of nodes le? in the frontier at the end of the search (i.e. nodes in the frontier
but never expanded).
The FoundPath interface describes methods for these values, and your implementation of getPathInfo
should return an object implementing this interface.
Your class AStar should provide (among any other constructors which you might use for your
own development and testing purposes) a one-argument constructor, where the argument is a
String naming a ?le containing information about the cities known to your algorithm. Such a ?le
will have the format shown in Figure 1. That is, the ?le describes a set of N cities, with ?xed
(latitude, longitude) locations, de?ned on the ?rst N + 1 lines of the ?le. 1 The next set of lines
describes distances between pairs of named cities (lines starting with ‘#’ are comments). Each pair
of cities appears at most once in this list. If some pair of cities is in the list, then the distance
between them is the same in both directions. If some pair of cities is not in the list, then there
is no direct connection between those two cities, and any path between those cities must pass
# name latitude longitude
<CITY NAME 1> <LAT 1> <LON 1>
...
<CITY NAME N> <LAT N><LON N>
# distances
<CITY NAME X1>, <CITY NAME Y1>: <MILES BETWEEN CITY X1 AND CITY Y1>
...
<CITY NAME XM>, <CITY NAME YM>: <MILES BETWEEN CITY XM AND CITY YM>
Figure 1: The cities speci?cation ?le.
# name latitude longitude
La Crosse 43.8 -91.24
La Crescent 43.83 -91.3
Winona 44.06 -91.67
Minneapolis 44.98 -93.27
# distances
La Crosse, La Crescent: 5.0
La Crosse, Winona: 31.6
La Crescent, Winona: 27.5
La Crescent, Minneapolis: 142.0
Winona, Minneapolis: 116.0
Figure 2: A small example of a cities speci?cation.
through some other city ?rst (if any such path exists). Figure 2 shows a small example with four
local cities. This small ?le will be included in the examples to be made available on Canvas.
For your A* heuristic, you should use the length of the shortest possible arc on the surface of
the Earth between a city C and the goal G.
[4] If calculated correctly, this arc length is guaranteed
to be an admissible and consistent heuristic for the data sets given.
Your code should be e?cient enough that it can handle the larger example ?le which you will
receive, which contains data for several hundred cities. However, small examples are typically
easier for debugging. You are of course encouraged to make additional examples for your own
purposes.
You should assume that the getPathInfo will be called more than once per instance. It should
return consistent results for the same information from call to call.
We will see in class that the most basic speci?cation of A* allows a single city to appear multiple
times during a search path. The algorithm will not output these non-optimal paths as solutions,
but it will still explore them as it tries to ?nd the optimal path. For domains with non-decreasing
path costs (like this one), generating these paths is ine?cient, and we will want to avoid it. There
will be two submission points for your code:
• Your ?rst implementation should leave this ine?ciency in, so repeated nodes are allowed
during search.
• Your second submission should remove this ine?ciency, so that repeated nodes are ignored
2
along a single path.
Your code should be well-formatted, and documented with both Javadoc and inline comments.
The inline comments should focus on the explanation of the AI ideas implemented.
There are a number of other abstract methods de?ned in Pathfinder.java, and a number of
additional requirements mentioned in the Javadoc comments of that ?le, which I expect you to
implement.
The two implementations for this assignment are due on Thursday, September 26, at the
usual deadline time of 11:59pm (La Crosse local time). Do not resubmit the FoundPath.java
and Pathfinder.java ?les, which you must not alter. Details of the exact form and mechanics of
the submission are to follow.
Notes
1. I prefer that you code the solution in Java, but I am open to discussing other languages.
Come speak with me before you start, so we can discuss feasibility and agree on a protocol.
Two points related to choosing an alternative language:
• Do not wait to discuss this: because we may need time to think about the format of
your work, and because I can manage only so many other languages.
• I have not yet written all of the homeworks for this class, and I cannot guarantee that
every homework will support alternative languages.
2. The full ?le also contains Javadoc comments, additional declarations, and helper/administrative
methods — see the full source for details.
3. The java.util.Optional class represents a value which could be present, or which might
not exist at all. See its Javadoc API documentation for more information, and for the static
methods used to create an Optional instance.
4. Details of how to calculate this distance using the Haversine formula can be found at
http://andrew.hedges.name/experiments/haversine . Note that for this formula to work:
• The inputs to any of the trigonometry functions must be in the form of radians, not
degrees. Since the data given in the input ?le has latitude and longitude in degrees, you
will need to convert.
• Since distances in the input are given in miles, you should also use miles for the radius
of the Earth.
Do not worry about possible errors in the heuristic arising from the fact that our Earth is
not a perfect sphere.

 

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