SlideShare a Scribd company logo
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)
0
5
10
15
20
25
30
RelativeError(%)
Greedy
LS(HC)
Greedy+HC
0
1
2
3
4
5
6
Time(Sec)
Greedy
LS(HC)
Greedy+HC

More Related Content

What's hot

(Icca 2014) shortest path analysis in social graphs
(Icca 2014) shortest path analysis in social graphs(Icca 2014) shortest path analysis in social graphs
(Icca 2014) shortest path analysis in social graphs
Waqas Nawaz
 
Master of Computer Application (MCA) – Semester 4 MC0080
Master of Computer Application (MCA) – Semester 4  MC0080Master of Computer Application (MCA) – Semester 4  MC0080
Master of Computer Application (MCA) – Semester 4 MC0080
Aravind NC
 
Chord Algorithm
Chord AlgorithmChord Algorithm
Chord Algorithm
Sijia Lyu
 
A Study of RSA Algorithm in Cryptography
A Study of RSA Algorithm in CryptographyA Study of RSA Algorithm in Cryptography
A Study of RSA Algorithm in Cryptography
ijtsrd
 
ICDE-2015 Shortest Path Traversal Optimization and Analysis for Large Graph C...
ICDE-2015 Shortest Path Traversal Optimization and Analysis for Large Graph C...ICDE-2015 Shortest Path Traversal Optimization and Analysis for Large Graph C...
ICDE-2015 Shortest Path Traversal Optimization and Analysis for Large Graph C...
Waqas Nawaz
 
Content addressable network(can)
Content addressable network(can)Content addressable network(can)
Content addressable network(can)
Amit Dahal
 
Shell Sort and Selection Sort Algorithm
Shell Sort and Selection Sort AlgorithmShell Sort and Selection Sort Algorithm
Shell Sort and Selection Sort Algorithm
Romeo Carinugan
 
Insertion sort and shell sort
Insertion sort and shell sortInsertion sort and shell sort
Insertion sort and shell sort
Praveen Kumar
 
Chord- A Scalable Peer-to-Peer Lookup Service for Internet Applications
Chord- A Scalable Peer-to-Peer Lookup Service for Internet ApplicationsChord- A Scalable Peer-to-Peer Lookup Service for Internet Applications
Chord- A Scalable Peer-to-Peer Lookup Service for Internet Applications
Chandan Thakur
 
Labreport
LabreportLabreport
Labreport
AMR koura
 
Doubly Linked List || Operations || Algorithms
Doubly Linked List || Operations || AlgorithmsDoubly Linked List || Operations || Algorithms
Doubly Linked List || Operations || Algorithms
Shubham Sharma
 
Enhance The K Means Algorithm On Spatial Dataset
Enhance The K Means Algorithm On Spatial DatasetEnhance The K Means Algorithm On Spatial Dataset
Enhance The K Means Algorithm On Spatial Dataset
AlaaZ
 
3.4 density and grid methods
3.4 density and grid methods3.4 density and grid methods
3.4 density and grid methods
Krish_ver2
 
Hierachical clustering
Hierachical clusteringHierachical clustering
Data miningpresentation
Data miningpresentationData miningpresentation
Data miningpresentation
Manoj Krishna Yadavalli
 
K means clustering algorithm
K means clustering algorithmK means clustering algorithm
K means clustering algorithm
Darshak Mehta
 
Clique and sting
Clique and stingClique and sting
Clique and sting
Subramanyam Natarajan
 
Shell sort in Data Structure Using C
Shell sort in Data Structure Using CShell sort in Data Structure Using C
Shell sort in Data Structure Using C
Ashish Gaurkhede
 
Shell sort
Shell sortShell sort
Shell sort
Nauman Ali
 
SCHEDULING DAGs WITHOUT CONSIDERING COMMUNICATION
SCHEDULING DAGs WITHOUT CONSIDERING COMMUNICATIONSCHEDULING DAGs WITHOUT CONSIDERING COMMUNICATION
SCHEDULING DAGs WITHOUT CONSIDERING COMMUNICATION
University of Technology - Iraq
 

What's hot (20)

(Icca 2014) shortest path analysis in social graphs
(Icca 2014) shortest path analysis in social graphs(Icca 2014) shortest path analysis in social graphs
(Icca 2014) shortest path analysis in social graphs
 
Master of Computer Application (MCA) – Semester 4 MC0080
Master of Computer Application (MCA) – Semester 4  MC0080Master of Computer Application (MCA) – Semester 4  MC0080
Master of Computer Application (MCA) – Semester 4 MC0080
 
Chord Algorithm
Chord AlgorithmChord Algorithm
Chord Algorithm
 
A Study of RSA Algorithm in Cryptography
A Study of RSA Algorithm in CryptographyA Study of RSA Algorithm in Cryptography
A Study of RSA Algorithm in Cryptography
 
ICDE-2015 Shortest Path Traversal Optimization and Analysis for Large Graph C...
ICDE-2015 Shortest Path Traversal Optimization and Analysis for Large Graph C...ICDE-2015 Shortest Path Traversal Optimization and Analysis for Large Graph C...
ICDE-2015 Shortest Path Traversal Optimization and Analysis for Large Graph C...
 
Content addressable network(can)
Content addressable network(can)Content addressable network(can)
Content addressable network(can)
 
Shell Sort and Selection Sort Algorithm
Shell Sort and Selection Sort AlgorithmShell Sort and Selection Sort Algorithm
Shell Sort and Selection Sort Algorithm
 
Insertion sort and shell sort
Insertion sort and shell sortInsertion sort and shell sort
Insertion sort and shell sort
 
Chord- A Scalable Peer-to-Peer Lookup Service for Internet Applications
Chord- A Scalable Peer-to-Peer Lookup Service for Internet ApplicationsChord- A Scalable Peer-to-Peer Lookup Service for Internet Applications
Chord- A Scalable Peer-to-Peer Lookup Service for Internet Applications
 
Labreport
LabreportLabreport
Labreport
 
Doubly Linked List || Operations || Algorithms
Doubly Linked List || Operations || AlgorithmsDoubly Linked List || Operations || Algorithms
Doubly Linked List || Operations || Algorithms
 
Enhance The K Means Algorithm On Spatial Dataset
Enhance The K Means Algorithm On Spatial DatasetEnhance The K Means Algorithm On Spatial Dataset
Enhance The K Means Algorithm On Spatial Dataset
 
3.4 density and grid methods
3.4 density and grid methods3.4 density and grid methods
3.4 density and grid methods
 
Hierachical clustering
Hierachical clusteringHierachical clustering
Hierachical clustering
 
Data miningpresentation
Data miningpresentationData miningpresentation
Data miningpresentation
 
K means clustering algorithm
K means clustering algorithmK means clustering algorithm
K means clustering algorithm
 
Clique and sting
Clique and stingClique and sting
Clique and sting
 
Shell sort in Data Structure Using C
Shell sort in Data Structure Using CShell sort in Data Structure Using C
Shell sort in Data Structure Using C
 
Shell sort
Shell sortShell sort
Shell sort
 
SCHEDULING DAGs WITHOUT CONSIDERING COMMUNICATION
SCHEDULING DAGs WITHOUT CONSIDERING COMMUNICATIONSCHEDULING DAGs WITHOUT CONSIDERING COMMUNICATION
SCHEDULING DAGs WITHOUT CONSIDERING COMMUNICATION
 

Recently uploaded

The Ipsos - AI - Monitor 2024 Report.pdf
The  Ipsos - AI - Monitor 2024 Report.pdfThe  Ipsos - AI - Monitor 2024 Report.pdf
The Ipsos - AI - Monitor 2024 Report.pdf
Social Samosa
 
06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM
06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM
06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM
Timothy Spann
 
一比一原版(UO毕业证)渥太华大学毕业证如何办理
一比一原版(UO毕业证)渥太华大学毕业证如何办理一比一原版(UO毕业证)渥太华大学毕业证如何办理
一比一原版(UO毕业证)渥太华大学毕业证如何办理
aqzctr7x
 
一比一原版卡尔加里大学毕业证(uc毕业证)如何办理
一比一原版卡尔加里大学毕业证(uc毕业证)如何办理一比一原版卡尔加里大学毕业证(uc毕业证)如何办理
一比一原版卡尔加里大学毕业证(uc毕业证)如何办理
oaxefes
 
Experts live - Improving user adoption with AI
Experts live - Improving user adoption with AIExperts live - Improving user adoption with AI
Experts live - Improving user adoption with AI
jitskeb
 
Predictably Improve Your B2B Tech Company's Performance by Leveraging Data
Predictably Improve Your B2B Tech Company's Performance by Leveraging DataPredictably Improve Your B2B Tech Company's Performance by Leveraging Data
Predictably Improve Your B2B Tech Company's Performance by Leveraging Data
Kiwi Creative
 
Palo Alto Cortex XDR presentation .......
Palo Alto Cortex XDR presentation .......Palo Alto Cortex XDR presentation .......
Palo Alto Cortex XDR presentation .......
Sachin Paul
 
一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理
一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理
一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理
hyfjgavov
 
社内勉強会資料_Hallucination of LLMs               .
社内勉強会資料_Hallucination of LLMs               .社内勉強会資料_Hallucination of LLMs               .
社内勉強会資料_Hallucination of LLMs               .
NABLAS株式会社
 
一比一原版(lbs毕业证书)伦敦商学院毕业证如何办理
一比一原版(lbs毕业证书)伦敦商学院毕业证如何办理一比一原版(lbs毕业证书)伦敦商学院毕业证如何办理
一比一原版(lbs毕业证书)伦敦商学院毕业证如何办理
ywqeos
 
UofT毕业证如何办理
UofT毕业证如何办理UofT毕业证如何办理
UofT毕业证如何办理
exukyp
 
一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理
一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理
一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理
aguty
 
Sample Devops SRE Product Companies .pdf
Sample Devops SRE  Product Companies .pdfSample Devops SRE  Product Companies .pdf
Sample Devops SRE Product Companies .pdf
Vineet
 
一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理
一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理
一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理
nyvan3
 
Jio cinema Retention & Engagement Strategy.pdf
Jio cinema Retention & Engagement Strategy.pdfJio cinema Retention & Engagement Strategy.pdf
Jio cinema Retention & Engagement Strategy.pdf
inaya7568
 
一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理
一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理
一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理
1tyxnjpia
 
University of New South Wales degree offer diploma Transcript
University of New South Wales degree offer diploma TranscriptUniversity of New South Wales degree offer diploma Transcript
University of New South Wales degree offer diploma Transcript
soxrziqu
 
DSSML24_tspann_CodelessGenerativeAIPipelines
DSSML24_tspann_CodelessGenerativeAIPipelinesDSSML24_tspann_CodelessGenerativeAIPipelines
DSSML24_tspann_CodelessGenerativeAIPipelines
Timothy Spann
 
Cell The Unit of Life for NEET Multiple Choice Questions.docx
Cell The Unit of Life for NEET Multiple Choice Questions.docxCell The Unit of Life for NEET Multiple Choice Questions.docx
Cell The Unit of Life for NEET Multiple Choice Questions.docx
vasanthatpuram
 
一比一原版(Unimelb毕业证书)墨尔本大学毕业证如何办理
一比一原版(Unimelb毕业证书)墨尔本大学毕业证如何办理一比一原版(Unimelb毕业证书)墨尔本大学毕业证如何办理
一比一原版(Unimelb毕业证书)墨尔本大学毕业证如何办理
xclpvhuk
 

Recently uploaded (20)

The Ipsos - AI - Monitor 2024 Report.pdf
The  Ipsos - AI - Monitor 2024 Report.pdfThe  Ipsos - AI - Monitor 2024 Report.pdf
The Ipsos - AI - Monitor 2024 Report.pdf
 
06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM
06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM
06-12-2024-BudapestDataForum-BuildingReal-timePipelineswithFLaNK AIM
 
一比一原版(UO毕业证)渥太华大学毕业证如何办理
一比一原版(UO毕业证)渥太华大学毕业证如何办理一比一原版(UO毕业证)渥太华大学毕业证如何办理
一比一原版(UO毕业证)渥太华大学毕业证如何办理
 
一比一原版卡尔加里大学毕业证(uc毕业证)如何办理
一比一原版卡尔加里大学毕业证(uc毕业证)如何办理一比一原版卡尔加里大学毕业证(uc毕业证)如何办理
一比一原版卡尔加里大学毕业证(uc毕业证)如何办理
 
Experts live - Improving user adoption with AI
Experts live - Improving user adoption with AIExperts live - Improving user adoption with AI
Experts live - Improving user adoption with AI
 
Predictably Improve Your B2B Tech Company's Performance by Leveraging Data
Predictably Improve Your B2B Tech Company's Performance by Leveraging DataPredictably Improve Your B2B Tech Company's Performance by Leveraging Data
Predictably Improve Your B2B Tech Company's Performance by Leveraging Data
 
Palo Alto Cortex XDR presentation .......
Palo Alto Cortex XDR presentation .......Palo Alto Cortex XDR presentation .......
Palo Alto Cortex XDR presentation .......
 
一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理
一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理
一比一原版兰加拉学院毕业证(Langara毕业证书)学历如何办理
 
社内勉強会資料_Hallucination of LLMs               .
社内勉強会資料_Hallucination of LLMs               .社内勉強会資料_Hallucination of LLMs               .
社内勉強会資料_Hallucination of LLMs               .
 
一比一原版(lbs毕业证书)伦敦商学院毕业证如何办理
一比一原版(lbs毕业证书)伦敦商学院毕业证如何办理一比一原版(lbs毕业证书)伦敦商学院毕业证如何办理
一比一原版(lbs毕业证书)伦敦商学院毕业证如何办理
 
UofT毕业证如何办理
UofT毕业证如何办理UofT毕业证如何办理
UofT毕业证如何办理
 
一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理
一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理
一比一原版澳洲西澳大学毕业证(uwa毕业证书)如何办理
 
Sample Devops SRE Product Companies .pdf
Sample Devops SRE  Product Companies .pdfSample Devops SRE  Product Companies .pdf
Sample Devops SRE Product Companies .pdf
 
一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理
一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理
一比一原版英国赫特福德大学毕业证(hertfordshire毕业证书)如何办理
 
Jio cinema Retention & Engagement Strategy.pdf
Jio cinema Retention & Engagement Strategy.pdfJio cinema Retention & Engagement Strategy.pdf
Jio cinema Retention & Engagement Strategy.pdf
 
一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理
一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理
一比一原版(Sheffield毕业证书)谢菲尔德大学毕业证如何办理
 
University of New South Wales degree offer diploma Transcript
University of New South Wales degree offer diploma TranscriptUniversity of New South Wales degree offer diploma Transcript
University of New South Wales degree offer diploma Transcript
 
DSSML24_tspann_CodelessGenerativeAIPipelines
DSSML24_tspann_CodelessGenerativeAIPipelinesDSSML24_tspann_CodelessGenerativeAIPipelines
DSSML24_tspann_CodelessGenerativeAIPipelines
 
Cell The Unit of Life for NEET Multiple Choice Questions.docx
Cell The Unit of Life for NEET Multiple Choice Questions.docxCell The Unit of Life for NEET Multiple Choice Questions.docx
Cell The Unit of Life for NEET Multiple Choice Questions.docx
 
一比一原版(Unimelb毕业证书)墨尔本大学毕业证如何办理
一比一原版(Unimelb毕业证书)墨尔本大学毕业证如何办理一比一原版(Unimelb毕业证书)墨尔本大学毕业证如何办理
一比一原版(Unimelb毕业证书)墨尔本大学毕业证如何办理
 

Group y algorithm 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