684 research outputs found
Evolving test instances of the Hamiltonian completion problem
Predicting and comparing algorithm performance on graph instances is
challenging for multiple reasons. First, there is usually no standard set of
instances to benchmark performance. Second, using existing graph generators
results in a restricted spectrum of difficulty and the resulting graphs are
usually not diverse enough to draw sound conclusions. That is why recent work
proposes a new methodology to generate a diverse set of instances by using an
evolutionary algorithm. We can then analyze the resulting graphs and get key
insights into which attributes are most related to algorithm performance. We
can also fill observed gaps in the instance space in order to generate graphs
with previously unseen combinations of features. This methodology is applied to
the instance space of the Hamiltonian completion problem using two different
solvers, namely the Concorde TSP Solver and a multi-start local search
algorithm.Comment: 12 pages, 12 figures, minor revisions in section
An Analysis of a Recursive and an Iterative Algorithm for Generating Permutations Modified for Travelling Salesman Problem
This paper presents the results of a comparative analysis between a recursive and an iterative algorithm when generating permutation. A number of studies discussing the problem and some methods dealing with its solution are analyzed. Recursion and iteration are approaches used in computer programs to implement different algorithms. An iterative approach is the repeated execution of the same source code until a certain end condition is met. On the other hand, a recursive approach uses a recursive function that repeatedly calls itself. This function contains a source code that must be executed repeatedly. Both algorithms presented in this paper can be used to generate permutations of an n element set. The algorithms are modified so that they can be used to solve the Travelling Salesman Problem (TSP) with a small number of vertices. Several publications that discuss the TSP and some approaches to its solution are also presented. The methodology and the conditions for conducting the experiments are described in details. The obtained results have been analyzed; they show that for the same conditions the iterative algorithm works from of 8 to 16 times faster than the recursive algorithm in all the tested input data. Several approaches to optimize the two algorithms in terms of the number of permutations tested when searching a minimal Hamiltonian cycle are presented
Network Topology Mapping from Partial Virtual Coordinates and Graph Geodesics
For many important network types (e.g., sensor networks in complex harsh
environments and social networks) physical coordinate systems (e.g.,
Cartesian), and physical distances (e.g., Euclidean), are either difficult to
discern or inapplicable. Accordingly, coordinate systems and characterizations
based on hop-distance measurements, such as Topology Preserving Maps (TPMs) and
Virtual-Coordinate (VC) systems are attractive alternatives to Cartesian
coordinates for many network algorithms. Herein, we present an approach to
recover geometric and topological properties of a network with a small set of
distance measurements. In particular, our approach is a combination of shortest
path (often called geodesic) recovery concepts and low-rank matrix completion,
generalized to the case of hop-distances in graphs. Results for sensor networks
embedded in 2-D and 3-D spaces, as well as a social networks, indicates that
the method can accurately capture the network connectivity with a small set of
measurements. TPM generation can now also be based on various context
appropriate measurements or VC systems, as long as they characterize different
nodes by distances to small sets of random nodes (instead of a set of global
anchors). The proposed method is a significant generalization that allows the
topology to be extracted from a random set of graph shortest paths, making it
applicable in contexts such as social networks where VC generation may not be
possible.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with
arXiv:1712.1006
A more robust ant colony learning algorithm : with application to travelling salesman problem
Graph problems model many real life applications, where the quantity of the nodes often changes with time. In such graphs, the evaluation of shortest tour is important as various guiding and navigation systems use this information. Nodes of a graph, in many applications, often change over time, and evaluation of shortest tour is essential whenever a new node is added or deleted. We propose an algorithm that deals with such situations. We have used the Ant System with a different meta-heuristics, to find the shortest tour in a graph. We have analyzed the performance of our proposed algorithm with other algorithms by using the problem instances given in TSPLIB. The proposed modification to the Ant System heuristics will also work for directed and non-fully connected graphs. We show the use of meta-heuristics that make our algorithm free from stagnation, that is, we prevent the ants from taking up the same tour repeatedly which helps to continuously search for better results. Our approach further adopts a method that is a modification to Gallants Technique, to choose the appropriate convergence within the reasonable computation time.\u2
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