traveling salesman problem.ppt
TRANSCRIPT
-
7/27/2019 Traveling Salesman Problem.ppt
1/24
Traveling Salesman Problem
-
7/27/2019 Traveling Salesman Problem.ppt
2/24
TSP
The goal is, to find the most economical way for a
select number of cities with the following
restrictions:
- Must visit each city once and only once
- Must return to the original starting point
-
7/27/2019 Traveling Salesman Problem.ppt
3/24
BASICS
Complete Graph vertices joined by a single edge
Weighted Graph edges carry a value
Hamiltonian Circuit - connects all points on a graph, passes
through each point only once, returns to origin
Hamiltonian Path - A route not returning to the beginning
-
7/27/2019 Traveling Salesman Problem.ppt
4/24
Finding an Approximate Solution
Cheapest Link Algorithm
Edge with smallest weight is drawn first
Edge with second smallest weight is drawn in
Continue unless it closes a smaller circuit or three
edges come out of one vertex
Finished once a complete Hamilton Circuit is drawn
-
7/27/2019 Traveling Salesman Problem.ppt
5/24
Cheapest Link Algorithm
-
7/27/2019 Traveling Salesman Problem.ppt
6/24
Cheapest Link Algorithm
-
7/27/2019 Traveling Salesman Problem.ppt
7/24
Cheapest Link Algorithm
-
7/27/2019 Traveling Salesman Problem.ppt
8/24
Cheapest Link Algorithm
-
7/27/2019 Traveling Salesman Problem.ppt
9/24
Cheapest Link Algorithm
-
7/27/2019 Traveling Salesman Problem.ppt
10/24
Finding an Approximate Solution
Nearest Neighbor Algorithm
Start at any given vertex
Travel to edge that yields smallest weight and has not
been traveled through yet
Continue until we have a complete Hamilton circuit
-
7/27/2019 Traveling Salesman Problem.ppt
11/24
Nearest Neighbor Algorithm
-
7/27/2019 Traveling Salesman Problem.ppt
12/24
Nearest Neighbor Algorithm
-
7/27/2019 Traveling Salesman Problem.ppt
13/24
Nearest Neighbor Algorithm
-
7/27/2019 Traveling Salesman Problem.ppt
14/24
Nearest Neighbor Algorithm
-
7/27/2019 Traveling Salesman Problem.ppt
15/24
Nearest Neighbor Algorithm
-
7/27/2019 Traveling Salesman Problem.ppt
16/24
Comparing Approximating Methods
Cheapest Link Nearest Neighbor
Total weight for
Cheapest Link 31
Nearest Neighbor 33
-
7/27/2019 Traveling Salesman Problem.ppt
17/24
17
A 42-City Problem (The Nearest Neighbour Method)
(Starting at City 1)
1
21
20
19
29
7
30
28
3137
3236
11
9
34
10
39
38
35
12
33
8
2726
624
25
14
1523
22
213
16
3
17 4
18
42
40
41
5
-
7/27/2019 Traveling Salesman Problem.ppt
18/24
18
The Nearest Neighbour Method (Starting at City 1)
1
21
20
19
29
7
30
28
3137
3236
11
9
34
10
39
38
35
12
33
8
2726
624
25
14
1523
22
213
16
3
17 4
18
42
40
41
5
-
7/27/2019 Traveling Salesman Problem.ppt
19/24
19
The Nearest Neighbour Method (Starting at City 1)
Length 1498
1
21
20
19
29
7
30
28
3137
3236
11
9
34
10
39
38
35
12
33
8
2726
624
25
14
1523
22
213
16
3
17 4
18
42
40
41
5
-
7/27/2019 Traveling Salesman Problem.ppt
20/24
20
29
Remove Crossovers
1
21
20
19
7
30
28
31 37
32 36
11
9
34
10
39
38
35
12
33
8
2726
624
25
14
15 23
22
213
16
317 4
18
42
40
41
5
-
7/27/2019 Traveling Salesman Problem.ppt
21/24
21
Remove Crossovers
1
21
20
19
29
7
30
28
31 37
32 36
11
9
34
10
39
38
35
12
33
8
2726
624
25
14
15 23
22
213
16
317 4
18
42
40
41
5
-
7/27/2019 Traveling Salesman Problem.ppt
22/24
22
Remove Crossovers Length 1453
1
21
20
19
29
7
30
28
31 37
32 36
11
9
34
10
39
38
35
12
33
8
2726
624
25
14
15 23
22
213
16
317 4
18
42
40
41
5
-
7/27/2019 Traveling Salesman Problem.ppt
23/24
Applications of the TSP
Computer Wiring - connecting together computer
components using minimum
wire length
Archaeological Seriation - ordering sites in time
Genome Sequencing - arranging DNA fragments in
sequence
Planning, logistics, and the manufacture of microchips
-
7/27/2019 Traveling Salesman Problem.ppt
24/24
THANK YOU