173 research outputs found
Solving the Bottleneck Traveling Salesman Problem Using the Lin-Kernighan-Helsgaun Algorithm
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POPMUSIC for the Travelling Salesman Problem
POPMUSIC— Partial OPtimization Metaheuristic Under Special Intensification Conditions — is a template for tackling large problem instances. This metaheuristic has been shown to be very efficient for various hard combinatorial problems such as p-median, sum of squares clustering, vehicle routing, map labelling and location routing. A key point for treating large Travelling Salesman Problem (TSP) instances is to consider only a subset of edges connecting the cities. The main goal of this article is to present how to build a list of good candidate edges with a complexity lower than quadratic in the context of TSP instances given by a general function. The candidate edges are found with a technique exploiting tour merging and the POPMUSIC metaheuristic. When these candidate edges are provided to a good local search engine, high quality solutions can be found quite efficiently. The method is tested on TSP instances of up to several million cities with different structures (Euclidean uniform, clustered, 2D to 5D, grids, toroidal distances). Numerical results show that solutions of excellent quality can be obtained with an empirical complexity lower than quadratic without exploiting the geometrical properties of the instances
Lin-Kernighan Heuristic Adaptations for the Generalized Traveling Salesman Problem
The Lin-Kernighan heuristic is known to be one of the most successful
heuristics for the Traveling Salesman Problem (TSP). It has also proven its
efficiency in application to some other problems. In this paper we discuss
possible adaptations of TSP heuristics for the Generalized Traveling Salesman
Problem (GTSP) and focus on the case of the Lin-Kernighan algorithm. At first,
we provide an easy-to-understand description of the original Lin-Kernighan
heuristic. Then we propose several adaptations, both trivial and complicated.
Finally, we conduct a fair competition between all the variations of the
Lin-Kernighan adaptation and some other GTSP heuristics. It appears that our
adaptation of the Lin-Kernighan algorithm for the GTSP reproduces the success
of the original heuristic. Different variations of our adaptation outperform
all other heuristics in a wide range of trade-offs between solution quality and
running time, making Lin-Kernighan the state-of-the-art GTSP local search.Comment: 25 page
Edge Elimination in TSP Instances
The Traveling Salesman Problem is one of the best studied NP-hard problems in
combinatorial optimization. Powerful methods have been developed over the last
60 years to find optimum solutions to large TSP instances. The largest TSP
instance so far that has been solved optimally has 85,900 vertices. Its
solution required more than 136 years of total CPU time using the
branch-and-cut based Concorde TSP code [1]. In this paper we present graph
theoretic results that allow to prove that some edges of a TSP instance cannot
occur in any optimum TSP tour. Based on these results we propose a
combinatorial algorithm to identify such edges. The runtime of the main part of
our algorithm is for an n-vertex TSP instance. By combining our
approach with the Concorde TSP solver we are able to solve a large TSPLIB
instance more than 11 times faster than Concorde alone
Constrained Local Search for Last-Mile Routing
Last-mile routing refers to the final step in a supply chain, delivering
packages from a depot station to the homes of customers. At the level of a
single van driver, the task is a traveling salesman problem. But the choice of
route may be constrained by warehouse sorting operations, van-loading
processes, driver preferences, and other considerations, rather than a
straightforward minimization of tour length. We propose a simple and efficient
penalty-based local-search algorithm for route optimization in the presence of
such constraints, adopting a technique developed by Helsgaun to extend the LKH
traveling salesman problem code to general vehicle-routing models. We apply his
technique to handle combinations of constraints obtained from an analysis of
historical routing data, enforcing properties that are desired in high-quality
solutions. Our code is available under the open-source MIT license. An earlier
version of the code received the $100,000 top prize in the Amazon Last Mile
Routing Research Challenge organized in 2021
Tunnelling Crossover Networks for the Asymmetric TSP
Local optima networks are a compact representation of fitness landscapes that can be used for analysis and visualisation. This paper provides the first analysis of the Asymmetric Travelling Salesman Problem using local optima networks. These are generated by sampling the search space by recording the progress of an existing evolutionary algorithm based on the Generalised Asymmetric Partition Crossover. They are compared to networks sampled through the Chained Lin-Kernighan heuristic across 25 instances. Structural differences and similarities are identified, as well as examples where crossover smooths the landscape
EARL: Joint Entity and Relation Linking for Question Answering over Knowledge Graphs
Many question answering systems over knowledge graphs rely on entity and
relation linking components in order to connect the natural language input to
the underlying knowledge graph. Traditionally, entity linking and relation
linking have been performed either as dependent sequential tasks or as
independent parallel tasks. In this paper, we propose a framework called EARL,
which performs entity linking and relation linking as a joint task. EARL
implements two different solution strategies for which we provide a comparative
analysis in this paper: The first strategy is a formalisation of the joint
entity and relation linking tasks as an instance of the Generalised Travelling
Salesman Problem (GTSP). In order to be computationally feasible, we employ
approximate GTSP solvers. The second strategy uses machine learning in order to
exploit the connection density between nodes in the knowledge graph. It relies
on three base features and re-ranking steps in order to predict entities and
relations. We compare the strategies and evaluate them on a dataset with 5000
questions. Both strategies significantly outperform the current
state-of-the-art approaches for entity and relation linking.Comment: International Semantic Web Conference 201
The effect of the asymmetry of road transportation networks on the traveling salesman problem
The routing of vehicles on road transportation networks is an area of great importance to transportation planners within scientific literature. This field includes well known and studied problems like traveling salesman problems or TSP or the more realistic asymmetric variant or ATSP, whose applications extend to other areas of transport and operations research. This work studies the effect that the asymmetry of road transportation networks, geographical location and territory have over TSP and ATSP methods. We conduct comprehensive experiments in order to assess the effects that these factors have on some of the best known algorithms for the TSP/ATSP. We demonstrate that all these factors have a significant influence in solution time and quality. Furthermore, we show that the solutions obtained with Euclidean matrices and those obtained with real distance matrices differ significantly. © 2011 Elsevier Ltd. All rights reserved.The authors would like to warmly thank Prof. Keld Helsgaun, Prof. Yuichi Nagata, Profs. Boris Goldengorin and Gerold Jager, and especially Prof. Matteo Fischetti, for facilitating the code of their great algorithms. This work is partially funded by the Spanish Ministry of Science and Innovation, under the project "SMPA Advanced Parallel Multiobjective Sequencing: Practical and Theoretical Advances" with reference DPI2008-03511/DPI. The authors should also thank the IMPIVA-Institute for the Small and Medium Valencian Enterprise, for the project OSC with references IMIDIC/2008/137, IMIDIC/2009/198 and 175 and the Polytechnic University of Valencia, for the project PPAR with reference 3147.Rodríguez Villalobos, A.; Ruiz García, R. (2012). The effect of the asymmetry of road transportation networks on the traveling salesman problem. Computers and Operations Research. 39(7):1566-1576. https://doi.org/10.1016/j.cor.2011.09.005S1566157639
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