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A Note on Single Alternating Cycle Neighborhoods for the TSP

2005
*
Journal of Heuristics
*

This paper investigates two different local search approaches

doi:10.1007/s10732-005-0713-6
fatcat:67yf6tlutvfndbwvbbihwyscou
*for**the**TSP*. Both approaches are based*on**the*general concept of*single*-*alternating**cycle**neighborhoods*. ...*The*first approach, stems from*the*famous heuristic suggested by Lin and Kernighan and*the*second is based*on**the*notion of stemand-*cycles*developed by Glover in*the*early nineties. ...*Single**Alternating**Cycle**Neighborhoods*In this section we focus*on**the*SACN*neighborhood*and its corresponding moves where*the*added and deleted edges form*a**single**alternating**cycle*. ...##
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A survey of very large-scale neighborhood search techniques

2002
*
Discrete Applied Mathematics
*

*For*this reason,

*a*larger

*neighborhood*does not necessarily produce

*a*more e ective heuristic unless

*one*can search

*the*larger

*neighborhood*in

*a*very e cient manner. ...

*Neighborhood*search algorithms (

*alternatively*called local search algorithms) are

*a*wide class of improvement algorithms where at each iteration an improving solution is found by searching

*the*"

*neighborhood*... Acknowledgements

*The*research of

*the*ÿrst author was supported by

*the*NSF Grant DMI-9900087.

*The*second and third authors were in part supported by

*the*NSF Grants DMI-9810359 and DMI-9820998. ...

##
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Local Search for the Resource Constrained Assignment Problem

2014
*
Algorithmic Approaches for Transportation Modeling, Optimization, and Systems
*

*The*

*alternating*

*cycles*are found by dual arguments from linear programming. ... Our algorithm can be summarized as

*a*k-OPT heuristic, exchanging k arcs of an

*alternating*

*cycle*of

*the*incumbent solution in each improvement step. ... Using

*alternating*

*cycles*as

*neighborhood*structure has been extensively studied in

*the*literature. ...

##
###
The travelling salesman problem: new solvable cases and linkages with the development of approximation algorithms

1997
*
Journal of the Operational Research Society
*

*The*result now follows from

*the*NP- completeness of

*the*Hamiltonian

*cycle*problem

*on*

*a*planar bipartite graph. O It may be

*noted*that

*TSP*

*on*G* is NP-hard

*for*any fixed value of

*the*parameter m. ...

*A*mixed SEE-DEE tour

*on*G*(k) is

*a*tour constructed by

*single*edge ejections

*for*

*the*

*cycles*C(i), i < k, followed by double edge ejections

*for*remaining

*cycles*, where node ¢ and

*a*node of C(k — 1) join ...

##
###
The travelling salesman problem: new solvable cases and linkages with the development of approximation algorithms

1997
*
Journal of the Operational Research Society
*

*The*result now follows from

*the*NP- completeness of

*the*Hamiltonian

*cycle*problem

*on*

*a*planar bipartite graph. O It may be

*noted*that

*TSP*

*on*G* is NP-hard

*for*any fixed value of

*the*parameter m. ...

*A*mixed SEE-DEE tour

*on*G*(k) is

*a*tour constructed by

*single*edge ejections

*for*

*the*

*cycles*C(i), i < k, followed by double edge ejections

*for*remaining

*cycles*, where node ¢ and

*a*node of C(k — 1) join ...

##
###
TSP ejection chains

1997
*
Discrete Applied Mathematics
*

We identify ejection chain methods

doi:10.1016/s0166-218x(96)00123-0
fatcat:d6cvogngpvhrtmpazyoy6a3uba
*for**the*traveling salesman problem based*on**a*special reference structure*for*generating constructions related to*alternating*paths. ... Our approach, which currently has*a*simple tabu search guidance component at*a*local level, also has*the*potential to be combined in more advanced ways with metaheuristics such as genetic algorithms, simulated ... Acknowledgements*The*authors are grateful to*the*two anonymous referees*for*their constructive comments. ...##
###
Traveling salesman problem heuristics: Leading methods, implementations and latest advances

2011
*
European Journal of Operational Research
*

We survey

doi:10.1016/j.ejor.2010.09.010
fatcat:koenh43avzf2vkvhqivvy25equ
*the*leading methods and*the*special components responsible*for*their successful implementations, together with an experimental analysis of computational tests*on**a*challenging and diverse set ... Heuristics*for**the*traveling salesman problem (*TSP*) have made remarkable advances in recent years. ... limiting consideration*for*each of them to examining only*one*possible*alternative**for**the*pair (t 7 , t 8 ). ...##
###
Computing Diverse Sets of High Quality TSP Tours by EAX-Based Evolutionary Diversity Optimisation
[article]

2021
*
arXiv
*
pre-print

Often, it is desirable to compute not just

arXiv:2108.05005v1
fatcat:medyoxs6rbeubh7u23bvvpxlei
*a**single*solution*for**a*given problem, but*a*diverse set of high quality solutions from which*a*decision maker can choose*one**for*implementation. ... Evolutionary algorithms based*on*edge assembly crossover (EAX) constitute some of*the*best performing incomplete solvers*for**the*well-known traveling salesperson problem (*TSP*). ...*Note*that*a*larger*neighborhood*search would be necessary to escape local optima. ...##
###
Doubly-rooted stem-and-cycle ejection chain algorithm for the asymmetric traveling salesman problem

2016
*
Networks
*

Computational experiments

doi:10.1002/net.21676
fatcat:ggq7ii7zczbhdarmfdfsu2xera
*on*an extensive testbed exhibits superior performance*for**the*DR*neighborhood*over its LK counterpart*for**the*ATSP. ... This paper extends our studies*on**the**single*-rooted S&C to examine*the*more advanced doubly-rooted (DR) reference structure. ... Acknowledgements This work was partially supported by FEDER Funds through*the*"Programa Operacional ...##
###
Implementation analysis of efficient heuristic algorithms for the traveling salesman problem

2006
*
Computers & Operations Research
*

*The*state-of-

*the*-art of local search heuristics

*for*

*the*traveling salesman problem (

*TSP*) is chiefly based

*on*algorithms using

*the*classical Lin-Kernighan (LK) procedure and

*the*stem-and-

*cycle*(S&C) ejection ... included in state-of-

*the*-art

*TSP*solution software,

*the*S&C algorithm clearly outperforms all implementations of

*the*LK procedure. ... Special cases also cause extra cuts and merges, such as

*the*case that

*the*

*cycle*occupies

*a*

*single*segment. ...

##
###
ACO-iRBA: A Hybrid Approach to TSPN with Overlapping Neighborhoods
[chapter]

2017
*
Lecture Notes in Computer Science
*

*The*traveling salesman problem with

*neighborhoods*(TSPN) is

*a*generalization of

*TSP*and can be regarded as

*a*combination of

*TSP*and TPP (Touring Polygons Problem). ...

*A*major feature of ACO-iRBA is that it can properly handle situations where

*the*

*neighborhoods*are heavily overlapped. ...

*A*case where

*the*optimal point p 0 i is within

*A*i rather than

*on*

*the*frontier of

*A*i where allowed k ¼ C

*À*tabu k is

*the*collection of

*alternative*cities

*for*ant k (tabu k represents

*the*cities that ant ...

##
###
Cycle Mutation: Evolving Permutations via Cycle Induction

2022
*
Applied Sciences
*

We focus

doi:10.3390/app12115506
fatcat:g5psnz34x5hpvnnbcopa5zohli
*on*evolving permutations*for*ordering problems such as*the*traveling salesperson problem (*TSP*), as well as assignment problems such as*the*quadratic assignment problem (QAP) and largest common ... We experimentally validate these findings showing*cycle*mutation's strengths*on*problems such as QAP and LCS, and its limitations*on*problems such as*the**TSP*, while also showing that it is less prone to ...*Note*that δ 5 (p 1 , p 3 ) = 1 since {0, 2} are fixed points, and there is*a**single**cycle*of*the*elements {1, 3, 5, 4}; and δ 5 (p 3 , p 2 ) = 1, with*a*fixed point*for*element 4, and*a**single**cycle*of ...##
###
Cycle Mutation: Evolving Permutations via Cycle Induction
[article]

2022
*
arXiv
*
pre-print

We focus

arXiv:2205.14125v1
fatcat:6d5osx46pzezdm5w4gbk5ymmry
*on*evolving permutations*for*ordering problems like*the*traveling salesperson problem (*TSP*), as well as assignment problems like*the*quadratic assignment problem (QAP) and largest common subgraph ... We experimentally validate these findings showing*cycle*mutation's strengths*on*problems like QAP and LCS, and its limitations*on*problems like*the**TSP*, while also showing that it is less prone to local ...*Note*that δ 5 (p 1 , p 3 ) = 1 since {0, 2} are fixed points, and there is*a**single**cycle*of*the*elements {1, 3, 5, 4}; and δ 5 (p 3 , p 2 ) = 1, with*a*fixed point*for*element 4, and*a**single**cycle*of ...##
###
Cycle time based multi-goal path optimization for redundant robotic systems

2013
*
2013 IEEE/RSJ International Conference on Intelligent Robots and Systems
*

Finally, experimental tests performed

doi:10.1109/iros.2013.6696591
dblp:conf/iros/GentiliniNS13
fatcat:vcz3mhh5tvbrtnojdzw7ohldvq
*on**a*7-Degree Of Freedom (DOF) industrial vision inspection system show that*the*proposed method is able to drastically reduce*the**cycle*time currently required by ... We instead model it as*a*Traveling Salesman Problem with*Neighborhoods*(TSPN), where each*neighborhood*is defined as*the*set of*the*infinitely many configurations corresponding to*the*same goal placement ... It is worth*noting*that*the*actual formulation of these constraints depends only*on**the*kinematic characteristics of*the*redundant robotic system , not*on**the*edge weighting function or metric used in ...##
###
On solving Travelling Salesman Problem with Vertex Requisitions

2017
*
Yugoslav Journal of Operations Research
*

*The*developed approach also helps in fast enumeration of

*a*

*neighborhood*in

*the*local search and yields an integer programming model with O(n) binary variables

*for*

*the*problem. ...

*The*algorithm, we propose

*for*this problem, has less time complexity compared to

*the*previously known

*one*. ... "good".

*Note*that there are

*a*number of integer linear programming models in

*the*literature

*on*

*the*classical

*TSP*, involving O(n 2 ) Boolean variables. ...

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