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An Energy Budget 21S1 CZ3005

创建日期：2024-04-17 16:23:28

所属分类：计算机computer science

标签： CZ3005

An Energy Budget

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Finding a Shortest Path with An Energy Budget

21S1 CZ3005 Assignment 1

1. Problem description

We are given a problem of finding a shortest traverse path between two locations within a certain
energy budget. This scenario often happens in the transportation where a shorter path is not
necessarily more energy efficient (e.g., the road may be very bumpy or has heavy traffic). We illustrate
our problem with the following example:

Figure 1: A small example.
Suppose we are given a graph with a predefined source node () and a target node (). Each edge in
the graph is associated with a pair of values (,) where denotes the distance and denotes the
energy cost. Also see Figure 1 for an illustration. The job is to find the shortest path between and
such that the accumulated energy cost along the path does not exceed an energy budget. Specifically,
we want to find the shortest path from Jurong East to Changi Airport not exceeding an energy budget
11. We can observe that although the path S->2->T has the shortest travel distance 10, its accumulated
energy cost 12 exceeds the energy budget 11. Thus, this path is infeasible. In this example, the path
S->1->T is the shortest feasible path.

1.1 Problem instance

You will be given a problem instance of New York city (NYC) road network of the United State. This
instance is taken and modified from the 9th DIMACS implementation challenge. This instance has
264346 nodes and 730100 edges. You will be given four python dictionary files:

1.1.1 Graph dictionary G
The graph is given as an adjacency list where the neighbor list of node ‘v’ can be accessed with G[‘v’].

1.1.2 Node coordination dictionary Coord
The coordination of a node ‘v’ is a pair (X, Y) which can be accessed with Coord[‘v’]

1.1.3 Edge distance dictionary Dist
The distance between a pair of node (v, w) can be accessed with Dist[‘v,w’].

1.1.4 Edge cost dictionary Cost
The energy cost between a pair of node (v, w) can be accessed with Cost[‘v,w’.]

2. Requirements and guidelines

2.1 Tasks and marking criteria

You will need to solve three tasks that are listed as follow:

Task 1: You will need to solve a relaxed version of the NYC instance where we do not have the energy
constraint. You can use any algorithm we discussed in the lectures. Note that this is equivalent to
solving the shortest path problem.
(30 marks)

Task 2: You will need to implement an uninformed search algorithm (e.g., the DFS, BFS, UCS) to solve
the NYC instance.
(30 marks)

Task 3: You will need to develop an A* search algorithm to solve the NYC instance. The key is to
develop a suitable heuristic function for the A* search algorithm in this setting.
(40 marks)

For tasks 2 and 3, the energy budget is set to be 287932. For all the 3 tasks, the starting and ending
nodes are set to be ‘1’ and ‘50’, respectively.

(Please note that the NYC instance is provided separately as formatted in section 1.1)

2.2 Output format

The output of your algorithm should be formatted as the following (using Figure 1 as an example):

Shortest path: S->1->T.
Shortest distance: 12.
Total energy cost: 10.

2.3 Programming language

For the sake of running your codes, you are required to use Python or Java. Please name your program
file “main.py” or “main.java” and put the file under the main folder named with your team’s name. You
should also put the instance files into your main folder. You must make sure your codes are runnable.
The TAs may run your codes by simply executing the command “python main.py” or “java main”. All
the algorithms must be implemented by you.

3. Teaming Formation

You are required to form a team of up to 3 people to complete this project. A team with only a single
person is also allowed. For team size that is larger than one, you need to clearly state the contribution
of each team member.

4. Honor Code

If you use any existing code, libraries, etc. and consult any papers, books, online references, etc. for
your project, you must cite your sources in your report and clearly indicate which parts of the
project are your contributions and which parts were implemented by others. Using others’
code/ideas without acknowledgement will lead to failure of your project.

5. Deliverables

You are required to produce:
(1) A final report of no more than 5 pages. Name your report as -final-report.pdf.
(2) Source codes for your project. Your source codes are to be submitted in .zip format. Name
the zip file as -final-code.zip.

The following is a suggested structure for the report:
(1) Title, team members.
(2) For each task, explain your approach, output, etc.
(3) Contribution: Please clearly state the contribution of each team member if you have more than
one member in your team.
(4) Conclusion: What have you learned?
(5) References: Please cite the sources you consulted in the report.

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