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An Iterated Local Search Approach for Finding Provably Good Solutions for Very Large TSP Instances [chapter]

Peter Merz, Jutta Huhse
2008 Lecture Notes in Computer Science  
In this paper, we present a highly effective hybrid evolutionary local search algorithm based on the iterated Lin-Kernighan heuristic combined with a lower bound heuristic utilizing 1-trees.  ...  In experiments, we show that the proposed approach is capable of finding short tours with a gap of 0.8% or less for TSP instances up to 10 million cities.  ...  Conclusions We presented a new Iterated Lin-Kernighan heuristic based on the powerful concept of iterated local search.  ... 
doi:10.1007/978-3-540-87700-4_92 fatcat:kxh5bggqhvhjrogwvynip5dkqu

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

César Rego, Dorabela Gamboa, Fred Glover, Colin Osterman
2011 European Journal of Operational Research  
Heuristics for the traveling salesman problem (TSP) have made remarkable advances in recent years.  ...  The foremost algorithms are represented by two families, deriving from the Lin-Kernighan (LK) method and the stem-and-cycle (S&C) method.  ...  time membership test and update, somewhat similar to the sparse set representation described in [5] .) (4) The 2-level tree is a specialized data structure to represent tours in TSP local search algorithms  ... 
doi:10.1016/j.ejor.2010.09.010 fatcat:koenh43avzf2vkvhqivvy25equ

A Parallel and Concurrent Implementation of Lin-Kernighan Heuristic (LKH-2) for Solving Traveling Salesman Problem for Multi-Core Processors using SPC3 Programming Model

Muhammad Ali, Dr. Shahid, Dr. Talat
2011 International Journal of Advanced Computer Science and Applications  
In this paper we have presented a combined parallel and concurrent implementation of Lin-Kernighan Heuristic (LKH-2) for Solving Travelling Salesman Problem (TSP) using a newly developed parallel programming  ...  This study is a part of an on-going research for designing of a new parallel programming model for multi-core processors.  ...  FindTour performs a number of trials, where in each trial it attempts to improve a chosen initial tour using the modified Lin-Kernighan edge exchange heuristics.  ... 
doi:10.14569/ijacsa.2011.020706 fatcat:trnebyhq6bhxrjarcngw55s73q

Survey of Methods of Solving TSP along with its Implementation using Dynamic Programming Approach

Chetan Chauhan, Ravindra Gupta, Kshitij Pathak
2012 International Journal of Computer Applications  
The Traveling salesperson problem is one of the problem in mathematics and computer science which haddrown attention as it is easy to understand and difficult to solve.  ...  An implementation of the traveling salesman problem using dynamic programming is also presented in this paper which generates optimal answer and tested with 25 cities and it executes in reasonable time  ...  In 1990, Bentley developed a new highly efficient variant of the k-d tree [a binary search tree structure extended in k dimensions] data structure, which is used for proximity checking, while he was working  ... 
doi:10.5120/8189-1550 fatcat:5neo2o6eabb6rei356fy47q54i

An effective implementation of the Lin–Kernighan traveling salesman heuristic

Keld Helsgaun
2000 European Journal of Operational Research  
This report describes an implementation of the Lin-Kernighan heuristic, one of the most successful methods for generating optimal or nearoptimal solutions for the symmetric traveling salesman problem.  ...  However, the interest in TSP not only stems from its practical and theoretical importance. The intellectual challenge of solving the problem also plays a role.  ...  In the current implementation of the modified Lin-Kernighan algorithm a tour may be represented in two ways, either by a doubly linked list, or by a twolevel tree [43] .  ... 
doi:10.1016/s0377-2217(99)00284-2 fatcat:ank3v3z2one2djqlk3rfsxttly

IntraClusTSP—An Incremental Intra-Cluster Refinement Heuristic Algorithm for Symmetric Travelling Salesman Problem

László Kovács, László Iantovics, Dimitris Iakovidis
2018 Symmetry  
In this paper we propose a cluster level incremental tour construction method called Intra-cluster Refinement Heuristic (IntraClusTSP).  ...  The proposed method can be used both to extend the tour with a new node and to improve the existing tour.  ...  Conflicts of Interest: The authors declare no conflicts of interest.  ... 
doi:10.3390/sym10120663 fatcat:47vgb26o5ndtvpe44eqroqdwzu

Reducing the Size of Traveling Salesman Problem Instances by Fixing Edges [chapter]

Thomas Fischer, Peter Merz
2007 Lecture Notes in Computer Science  
The Traveling Salesman Problem (TSP) is a well-known NPhard combinatorial optimization problem, for which a large variety of evolutionary algorithms are known.  ...  We argue, that after expanding a reduced tour back to the original instance, the result is nearly as good as applying the used solver to the original problem instance, but requiring significantly less  ...  In the example in Fig. 2 , solid lines represent tour edges and dotted lines represent edges of the minimal spanning tree (MST).  ... 
doi:10.1007/978-3-540-71615-0_7 fatcat:km4wkmh5jrfhrhl4j7a26nleke

Data structures and ejection chains for solving large-scale traveling salesman problems

Dorabela Gamboa, César Rego, Fred Glover
2005 European Journal of Operational Research  
The first implementation uses an Array data structure organized as a doubly linked list to represent TSP tours as well as the S&C reference structure.  ...  The second implementation considers a two-level tree structure.  ...  The first tree structure represents a possible node distribution for the initial reference structure throughout the three tree segments.  ... 
doi:10.1016/j.ejor.2004.04.023 fatcat:ezf63jtqrzb7xh73vvvl5cuzmy

QUANTUM INSPIRED PARTICLE SWARM COMBINED WITH LIN-KERNIGHAN-HELSGAUN METHOD TO THE TRAVELING SALESMAN PROBLEM

Bruno Avila Leal de Meirelles Herrera, Leandro dos Santos Coelho, Maria Teresinha Arns Steiner
2015 Pesquisa Operacional  
As the TSP is a NP (Non-Deterministic Polynomial time)-hard problem, there are several heuristic methods which have been proposed for the past decades in the attempt to solve it the best possible way.  ...  The analyzed approaches were divided into three methods: (i) Lin-Kernighan-Helsgaun (LKH) algorithm; (ii) LKH with initial tour based on uniform distribution; and (iii) an hybrid proposal combining Particle  ...  Lin-Kernighan Heuristic (LK) An important set of heuristics developed for the TSP is made of the k-opt exchanges.  ... 
doi:10.1590/0101-7438.2015.035.03.0465 fatcat:wxted5hy65hfhkdw3wdcgy7d3y

Local Search and the Traveling Salesman Problem: A Feature-Based Characterization of Problem Hardness [chapter]

Olaf Mersmann, Bernd Bischl, Jakob Bossek, Heike Trautmann, Markus Wagner, Frank Neumann
2012 Lecture Notes in Computer Science  
As a measure of problem difficulty for 2-opt we use the approximation ratio that it achieves on a given instance.  ...  With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem (TSP).  ...  Nowadays, variants of these seminal algorithms represent the state-of-the-art in heuristic TSP optimizers.  ... 
doi:10.1007/978-3-642-34413-8_9 fatcat:hdvzgbv3ezahvlcrvugdio77bq

On Randomness and Structure in Euclidean TSP Instances: a Study with Heuristic Methods

Gloria Cerasela Crisan, Elena Nechita, Dana Simian
2021 IEEE Access  
In this article, we study the impact of the structure of a Traveling Salesman Problem instance on the quality of the solution when using two representative heuristics: the population-based Ant Colony Optimization  ...  We classify the instances in structured, semi-structured, and unstructured and perform a between classes and inside-classes analysis.  ...  TSP using two representative heuristics: Ant Colony Optimization (ACO) [1] and Lin-Kernighan method (LK) [2] .  ... 
doi:10.1109/access.2020.3048774 fatcat:bs6cb5djsfgxnke7bwyb3urmta

Solving the Large-Scale TSP Problem in 1 h: Santa Claus Challenge 2020

Radu Mariescu-Istodor, Pasi Fränti
2021 Frontiers in Robotics and AI  
The scalability of traveling salesperson problem (TSP) algorithms for handling large-scale problem instances has been an open problem for a long time.  ...  In this article, we analyze the results and show which design choices are decisive in providing the best solution to the problem with the given constraints.  ...  variant in combination with a variation of the Lin-Kernighan heuristic.  ... 
doi:10.3389/frobt.2021.689908 pmid:34671647 pmcid:PMC8520904 fatcat:7gsikz4oo5blpb7d76gzlcrxhu

Iterative Cartesian Genetic Programming: Creating General Algorithms for Solving Travelling Salesman Problems [chapter]

Patricia Ryser-Welch, Julian F. Miller, Jerry Swan, Martin A. Trefzer
2016 Lecture Notes in Computer Science  
Our experimental results demonstrate that the evolved solvers scale well to much larger TSP instances than those used for training.  ...  In this paper, we introduce a novel extension to Cartesian Genetic Programming that allows it to encode iterative algorithms.  ...  The Centre is co-ordinated by the Universities of Leeds and Manchester.  ... 
doi:10.1007/978-3-319-30668-1_19 fatcat:wzb4sa5zv5ertn2lnfi4eghvri

Informed Heuristics for Guiding Stem-and-Cycle Ejection Chains [article]

Daniel Harabor, Philip Kilby
2011 arXiv   pre-print
The state of the art in local search for the Traveling Salesman Problem is dominated by ejection chain methods utilising the Stem-and-Cycle reference structure.  ...  Though effective such algorithms employ very little information in their successor selection strategy, typically seeking only to minimise the cost of a move.  ...  NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre of Excellence  ... 
arXiv:1103.3904v1 fatcat:zb6agaa2i5ez5n6qap6ehjqk44

Solving the clustered traveling salesman problem via traveling salesman problem methods

Yongliang Lu, Jin-Kao Hao, Qinghua Wu
2022 PeerJ Computer Science  
For this purpose, we first investigate a technique to convert a CTSP instance to a TSP and then apply powerful TSP solvers (including exact and heuristic solvers) to solve the resulting TSP instance.  ...  In this work, we explore a transformation approach that solves the CTSP by converting it to the well-studied TSP.  ...  The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.  ... 
doi:10.7717/peerj-cs.972 pmid:35721414 pmcid:PMC9202618 fatcat:elgqul4f6bfwrhqeyo5xtgdd6e
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