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A Note on Single Alternating Cycle Neighborhoods for the TSP

Birger Funke, Tore Grünert, Stefan Irnich
2005 Journal of Heuristics  
This paper investigates two different local search approaches 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.  ... 
doi:10.1007/s10732-005-0713-6 fatcat:67yf6tlutvfndbwvbbihwyscou

A survey of very large-scale neighborhood search techniques

Ravindra K. Ahuja, Özlem Ergun, James B. Orlin, Abraham P. Punnen
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.  ... 
doi:10.1016/s0166-218x(01)00338-9 fatcat:q75y577kdbcdffh46dafrb47uq

Local Search for the Resource Constrained Assignment Problem

Markus Reuther, Marc Herbstritt
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.  ... 
doi:10.4230/oasics.atmos.2014.62 dblp:conf/atmos/Reuther14 fatcat:aa5zkcizx5cglfb32n7t3rr5te

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

F Glover, A P Punnen
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  ... 
doi:10.1038/sj.jors.2600392 fatcat:zs3hwmhevjb57afyprrh3rlgbm

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

F Glover, A P Punnen
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  ... 
doi:10.1057/palgrave.jors.2600392 fatcat:nax3kr6o5rdybbj3dbyhrs27gm

TSP ejection chains

Erwin Pesch, Fred Glover
1997 Discrete Applied Mathematics  
We identify ejection chain methods 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.  ... 
doi:10.1016/s0166-218x(96)00123-0 fatcat:d6cvogngpvhrtmpazyoy6a3uba

Traveling salesman problem heuristics: Leading methods, implementations and latest advances

César Rego, Dorabela Gamboa, Fred Glover, Colin Osterman
2011 European Journal of Operational Research  
We survey 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 ).  ... 
doi:10.1016/j.ejor.2010.09.010 fatcat:koenh43avzf2vkvhqivvy25equ

Computing Diverse Sets of High Quality TSP Tours by EAX-Based Evolutionary Diversity Optimisation [article]

Adel Nikfarjam, Jakob Bossek, Aneta Neumann, Frank Neumann
2021 arXiv   pre-print
Often, it is desirable to compute not just 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.  ... 
arXiv:2108.05005v1 fatcat:medyoxs6rbeubh7u23bvvpxlei

Doubly-rooted stem-and-cycle ejection chain algorithm for the asymmetric traveling salesman problem

César Rego, Dorabela Gamboa, Fred Glover
2016 Networks  
Computational experiments 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  ... 
doi:10.1002/net.21676 fatcat:ggq7ii7zczbhdarmfdfsu2xera

Implementation analysis of efficient heuristic algorithms for the traveling salesman problem

Dorabela Gamboa, César Rego, Fred Glover
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.  ... 
doi:10.1016/j.cor.2005.06.014 fatcat:g5iof6dn7favppwwx7turhdlxu

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

Yuanlong Qin, Bo Yuan
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  ... 
doi:10.1007/978-3-319-68759-9_8 fatcat:hscxb62ifzehhpmylpzl62s6zi

Cycle Mutation: Evolving Permutations via Cycle Induction

Vincent A. Cicirello
2022 Applied Sciences  
We focus 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  ... 
doi:10.3390/app12115506 fatcat:g5psnz34x5hpvnnbcopa5zohli

Cycle Mutation: Evolving Permutations via Cycle Induction [article]

Vincent A. Cicirello
2022 arXiv   pre-print
We focus 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  ... 
arXiv:2205.14125v1 fatcat:6d5osx46pzezdm5w4gbk5ymmry

Cycle time based multi-goal path optimization for redundant robotic systems

Iacopo Gentilini, Kenji Nagamatsu, Kenji Shimada
2013 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems  
Finally, experimental tests performed 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  ... 
doi:10.1109/iros.2013.6696591 dblp:conf/iros/GentiliniNS13 fatcat:vcz3mhh5tvbrtnojdzw7ohldvq

On solving Travelling Salesman Problem with Vertex Requisitions

Anton Eremeev, Yulia Kovalenko
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.  ... 
doi:10.2298/yjor161012003e fatcat:hjl4opairzcyfmgeh7xubilrei
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