CSE Algorithm Project Presentation

1. Algorithm Project to Solve
Travel Salesman Problem
CSE 6140
GROUP Y
BO WANG, MAYANK GUPTA, XING XIN, MAHDI
ROOZBAHANI

2. IMPLEMENTED ALGORITHMS
1. Branch and Bound
2. Greedy Heuristic
3. MST Approximation
4. Local Search
* We implemented algorithms in Python Programming Language

3. BRANCH AND BOUND
1. We used adjacency matrix to create the state space tree
(Priority Queue)
2. Lower Bound was computed based on the mean of two
minimum shortest edges
3. A partial solution is obtained when we reach to an upper
level of a leaf node
4. Branch and Bound final solution is obtained when the
queue is empty.

4. GREEDY HEURISTIC (FURTHEST POINT INSERTION ALGORITHM)
1. Start with a random node
2. Add a new node whose minimal distance to a tour
node is maximal

5. MST APPROXIMATION
1. Find Minimum Spanning Tree based on Prim or
Kruskal algorithm
2. Choose a random vertex as root and implementing
DFS in the tree.
3. Output each node the first met

6. LOCAL SEARCH (SIMULATED ANNEALING)
1. Generate a random path
2. Randomly pick two vertices and switch vertices between
them
3. New path (lower weight or higher weight with decreasing
probability)
4. Iteration on steps 2 and 3, until we reach to the minimum
temperature

7. LOCAL SEARCH (HILL CLIMBING)
1. Generate a random path
2. Randomly pick two vertices and switch vertices
between them (repeat it for better solution)
3. We might get stuck in local minima
4. Iteration on steps 2 through 3 (new path for step 3 
if it has lower weight

8. OUR INTERESTING RESULT
Creating a hybrid method by combing greedy heuristic and local
search (Using rough Greedy Solution as the Hill Climbing input path)
0
5
10
15
20
25
30
RelativeError(%)
Greedy
LS(HC)
Greedy+HC

9. 0
1
2
3
4
5
6
Time(Sec)
Greedy
LS(HC)
Greedy+HC