Algorithm Project to Solve Travel Salesman Problem

CSE 6140

GROUP Y

BO WANG, MAYANK GUPTA, XING XIN, MAHDI ROOZBAHANI

IMPLEMENTED ALGORITHMS

1. Branch and Bound

2. Greedy Heuristic

3. MST Approximation

4. Local Search

* We implemented algorithms in Python Programming Language

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.

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

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

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

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

OUR INTERESTING RESULT

Creating a hybrid method by combing greedy heuristic and local search

(Using rough Greedy Solution as the Hill Climbing input path)

burm

a14

ulys

ses1

6

berlin

52

kroA

100

ch15

0

gr20

20

5

10

15

20

25

30

Greedy

LS(HC)

Greedy+HC

Rel

ativ

e E

rror

(%

)

burm

a14

ulys

ses1

6

berlin5

2

kroA

100

ch15

0

gr20

20

1

2

3

4

5

6

Greedy

LS(HC)

Greedy+HC

Tim

e (S

ec)