Design and Analysis of Algorithms

Design and Analysis of Algorithms

COMP 361 Design and Analysis of Algorithms
Assignment 4: Assorted algorithms and problems
12.5% of Final Mark Due: 11:59:00pm Wednesday 16 June 2021
1 Linear programming (20%)
1.1 Use graphical approach to solve linear programming problems (5%)
Consider the following linear programming problem:
max z = 3×1 + 2×2,
s.t. x1 12,
x1 + 3×2 45,
2×1 + x2 30,
x1, x2 0.
Solve the problem above with a graphical method. Identify and report all basic feasible solutions for this problem.
You may find it easier to use pen and paper. If so, please include a clear, high-quality scan in your PDF report.
1.2 Use simplex algorithm to solve linear programming problems (15%)
Use the simplex algorithm to solve the following problem:
min z = x2 x3 2×1,
s.t. 3×1 + x2 + x3 50,
2×1 + x2 + 2×3 20,
2×1 + 2×2 + x3 20,
x1, x2, x3 0.
For each step, calculate the table in the canonical form, the pivot row, the new Basic Variable (BV) and the new
Non-Basic Variable (NBV). Make sure you show your working clearly. You may find it easier to use pen and paper.
If so, please include a clear, high-quality scan in your PDF report.
2 Travelling salesman problem solved in different ways
The travelling salesman problem (TSP) is a well known problem. Consider a salesperson who is tasked with visiting
n cities labelled v1, v2, …, vn. The salesperson starts in their home city, v1, and wants to find a tour which visits
every city exactly once and returns home in as short distance as possible. This can be intuitively represented by a
graph, where vertices are cities and edges are the distance between two cities. In this assignment, we focus on the
symmetric TSP: the graph is undirected and so the distances along both directions of an edge are the same.
2.1 Dataset
To explore this problem, we will use a dataset provided by the TSPLib website1
, which contains a lot of discrete and
combinatorial optimisation problem datasets and solutions.
A variety of problem instances for the symmetric TSP can be downloaded from the following link:

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