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Stability Analysis for the Modification Method under the A Priori Strategy of the PTSP

2020
*
IEEE Access
*

An exact

doi:10.1109/access.2020.3001278
fatcat:6romtev2gjfhlmjsnq5qsbyrbu
*Branch**and**Bound*is used*for*recognizing*the**TSPs*that are not stable. ... We propose in this paper*a*new formulation*for**the*stability of*the*Traveling Salesman Problem (*TSP*) compared with its*probabilistic*version,*the**Probabilistic*Traveling Salesman Problem (PTSP). ... So we present here,*the*different*TSP*detected unstable.*A*.*PROBABILISTIC**BRANCH**AND**BOUND**ALGORITHM**The**Branch**and**Bound**algorithm*that we use here was proposed by Amar et al. [3] . ...##
###
In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation

2016
*
Notices of the American Mathematical Society
*

*The*

*TSP*is

*a*case in point. In fact, many of

*the*concepts

*and*techniques of combinatorial optimization were originally conceived

*for*

*the*

*TSP*. ... notices of

*the*AMs 635 BOOK REVIEW

*The*traveling salesman problem, or

*TSP*

*for*short, poses both

*a*complexity question

*and*

*a*computational challenge. ... It should be noted that

*TSP*history runs

*parallel*to

*the*development of

*algorithms*

*for*general integer linear ity constraints. ...

##
###
Page 7483 of Mathematical Reviews Vol. , Issue 2004i
[page]

2004
*
Mathematical Reviews
*

We then review

*the*implementation of SYMPHONY*and*COIN/BCP, two existing frameworks*for*im- plementing*parallel**branch*, cut,*and*price. ... Summary: “In discrete optimization, most exact solution ap- proaches are based on*branch**and**bound*, which is conceptually easy to*parallelize*in its simplest forms. ...##
###
Page 2241 of Mathematical Reviews Vol. , Issue 2003C
[page]

2003
*
Mathematical Reviews
*

Summary: “

*Branch*, cut,*and*price (BCP) is an LP-based*branch**and**bound*technique*for*solving large-scale discrete optimiza- tion problems (DOPs). ... , Ted K. (1-LEHI-MFS; Bethlehem, PA); Trotter, Leslie E., Jr. (1-CRNL-ENO; Ithaca, NY)*Branch*, cut,*and*price: sequential*and**parallel*. ...##
###
Ant Colony Optimization: Overview and Recent Advances
[chapter]

2010
*
International Series in Operations Research and Management Science
*

*For*example, when stopping exact methods, like

*Branch*&

*Bound*, before completion [10, 95] (

*for*example, after some given time

*bound*, or when some guarantee on

*the*solution quality is obtained through

*the*... use of lower

*and*upper

*bounds*), we can convert exact

*algorithms*into approximate ones. ... Hybridizations of ACO with

*branch*-

*and*-

*bound*techniques

*The*integration of tree search techniques into constructive

*algorithms*is an appealing possibility of hybridization since

*the*

*probabilistic*solution ...

##
###
The mystical power of twoness: in memoriam Eugene L. Lawler

1998
*
Journal of Scheduling
*

This paper reviews

doi:10.1002/(sici)1099-1425(199806)1:1<3::aid-jos1>3.0.co;2-b
fatcat:dbbwgjjgdzgarpbmvxgmpq3qvy
*the*work of Eugene 1. Lawler, one of*the*early investigators of combinatorial optimization*and**the*architect of deterministic machine scheduling theory. ... After sketching his research career*and*examining*the*development of his interests, I describe some of his seminal results in scheduling theory*and*recall one of his contributions to scientific journalism ... I wish to thank Karen Aardal, Francesco Maffioli*and*David Shmoys*for*their help in taking care of Gene's scientific legacy,*and**for*their comments on*a*draft of this paper. ...##
###
Computational Complexity for Physicists
[article]

2002
*
arXiv
*
pre-print

These lecture notes are an informal introduction to

arXiv:cond-mat/0012185v2
fatcat:z6egxrzirvfzpchemisqnzmfai
*the*theory of computational complexity*and*its links to quantum computing*and*statistical mechanics. ...*The*textbook formula is*a*particular*algorithm*,*and**the*time complexity of an*algorithm*is only an upper*bound**for**the*inherent complexity of*a*problem. ... In fact we will see in section 2.3.1 that there exists*a*polynomial*algorithm**for**TSP*(D) if*and*only if there exists*a*polynomial*algorithm**for**TSP*. ...##
###
The mystical power of twoness: in memoriam Eugene L. Lawler

1998
*
Journal of Scheduling
*

This paper reviews

doi:10.1002/(sici)1099-1425(199806)1:1<3::aid-jos1>3.3.co;2-2
fatcat:kauex7gxxnanrfknclrgztddu4
*the*work of Eugene 1. Lawler, one of*the*early investigators of combinatorial optimization*and**the*architect of deterministic machine scheduling theory. ... After sketching his research career*and*examining*the*development of his interests, I describe some of his seminal results in scheduling theory*and*recall one of his contributions to scientific journalism ... I wish to thank Karen Aardal, Francesco Maffioli*and*David Shmoys*for*their help in taking care of Gene's scientific legacy,*and**for*their comments on*a*draft of this paper. ...##
###
Computational complexity for physicists

2002
*
Computing in science & engineering (Print)
*

In fact, we see later that

doi:10.1109/5992.998639
fatcat:4olgee7t7bhmzml6bsuji6gskq
*a*polynomial*algorithm*exists*for**the**TSP*(D) if*and*only if there exists*a*polynomial*algorithm**for**the**TSP*. ... This quantum*parallelism*resembles*a*nondeterministic*algorithm*with its goto both instruction*and*its exponentially*branching*execution tree. ...##
###
Parallelized solution to the asymmetric travelling salesman problem using central processing unit acceleration

2022
*
Indonesian Journal of Electrical Engineering and Computer Science
*

In order to find

doi:10.11591/ijeecs.v25.i3.pp1795-1802
fatcat:ub37ig2ytvebxelyr5njyhr3wa
*the*exact optimal solution, we have used*the*held-karp*algorithm*involving dynamic programming*and*to reduce*the*time taken to find*the*optimal path, we have used*a*multi-threaded approach ... This method is an extension of*a*well researched solution to*the**TSP*; however, this method shows that solutions to computationally intensive problems involving sub-problems such as*the*asymmetic travelling ... Li et al. have provided an improved multicore based*parallel**branch**and**bound**algorithm*to solve classic*TSP*with its shortcomings in [24] . ...##
###
Ant Colony Optimization: A Component-Wise Overview
[chapter]

2018
*
Handbook of Heuristics
*

*The*indirect communication

*and*foraging behavior of certain species of ants has inspired

*a*number of optimization

*algorithms*

*for*NP-hard problems. ... In addition,

*the*chapter introduces

*a*software framework that unifies

*the*implementation of these ACO

*algorithms*

*for*two example problems,

*the*traveling salesman problem

*and*

*the*quadratic assignment problem ... Thus,

*a*natural extension of ACO is to make use of tree search techniques such as

*branch*-

*and*-

*bound*. ...

##
###
Parallel Implementation of the Max_Min Ant System for the Travelling Salesman Problem on GPU

2014
*
International Journal of Computer Applications
*

ACO is

doi:10.5120/17455-7406
fatcat:iimclv7hyfalvine66fv7rwdka
*a*nature based inspired*algorithm*based on heuristics to find*the*solution*for*combinatorial optimization problems such as*TSP*. ... Thus with this implementation we are able to gain*a*speedup of 4.01x in CPU*parallel**and*up to 11.29x speedup in GPU*parallel*. ... Classical approach to solve*TSP*are dynamic programming,*branch**and**bound*which uses heuristic*and*exact method*and*results into exact solution. ...##
###
Some recent contributions to routing and location problems

2003
*
Networks
*

It summarizes theoretical insights, modeling approaches,

doi:10.1002/net.10086
fatcat:egctmowa2bhgfa5d5e5abmhop4
*and*heuristic*and*exact*algorithms**for*routing*and*location presented at*the*CORAL 2003 Workshop held in Tenerife (Spain). ... This report is more than just*a*summary of some results of*the*present state of*the*art in routing*and*location problems. ...*The*work in progress aims at designing*a**branch*-*and*-*bound*scheme to exactly solve this problem. Joaquı ´n Pacheco [19] talked about "Two Scatter Search*Algorithms**for*Two Location Problems." ...##
###
A Survey of Ant Colony Optimization with Social Network

2014
*
International Journal of Computer Applications
*

growing discipline .Ant take decision with

doi:10.5120/18779-0098
fatcat:hmjnxnn5vnha3fc7vpdipl5wmu
*the*help of special type of chemical "pheromone'. ... Base on this concept ACO meta-heuristic which helps to solve combinational problems such as*TSP*, Graph color, job shop Network routing, machine learning etc. ... Advantage of ACO solution is placement of ants on node in*parallel*, which start constructing solution from every node Although ACO*for**TSP*not generates optimal universal solution but it is better*for*...##
###
How traveling salespersons prove their identity
[chapter]

1995
*
Lecture Notes in Computer Science
*

*The*XTSP is

*a*close relative of

*the*famous

*TSP*

*and*consists of nding

*a*Hamiltonian circuit of

*a*given length, given

*a*complete directed graph

*and*

*the*distances between all vertices. ... Thus,

*the*set of tools

*for*use in public-key cryptography is enlarged. ... Acknowledgements I am grateful to an anonymous referee of 5]

*for*pointing me towards identi cation schemes

*and*to Stefan Thienel

*for*providing

*the*empiric results. ...

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