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TSP  Infrastructure for the Traveling Salesperson Problem
 JOURNAL OF STATISTICAL SOFTWARE
, 2006
"... The traveling salesperson or salesman problem (TSP) is a well known and important combinatorial optimization problem. The goal is to find the shortest tour that visits each city in a given list exactly once and then returns to the starting city. Despite this simple problem statement, solving the TSP ..."
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Cited by 9 (2 self)
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The traveling salesperson or salesman problem (TSP) is a well known and important combinatorial optimization problem. The goal is to find the shortest tour that visits each city in a given list exactly once and then returns to the starting city. Despite this simple problem statement, solving the TSP is difficult since it belongs to the class of NPcomplete problems. The importance of the TSP arises besides from its theoretical appeal from the variety of its applications. In addition to vehicle routing, many other applications, e.g., computer wiring, cutting wallpaper, job sequencing or several data visualization techniques, require the solution of a TSP. In this paper we introduce the R package TSP which provides a basic infrastructure for handling and solving the traveling salesperson problem. The package features S3 classes for specifying a TSP and its (possibly optimal) solution as well as several heuristics to find good solutions. In addition, it provides an interface to Concorde, one of the best exact TSP solvers currently available.
Rearrangement clustering: Pitfalls, remedies, and applications
 Journal of Machine Learning Research
, 2006
"... Given a matrix of values in which the rows correspond to objects and the columns correspond to features of the objects, rearrangement clustering is the problem of rearranging the rows of the matrix such that the sum of the similarities between adjacent rows is maximized. Referred to by various names ..."
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Cited by 6 (0 self)
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Given a matrix of values in which the rows correspond to objects and the columns correspond to features of the objects, rearrangement clustering is the problem of rearranging the rows of the matrix such that the sum of the similarities between adjacent rows is maximized. Referred to by various names and reinvented several times, this clustering technique has been extensively used in many fields over the last three decades. In this paper, we point out two critical pitfalls that have been previously overlooked. The first pitfall is deleterious when rearrangement clustering is applied to objects that form natural clusters. The second concerns a similarity metric that is commonly used. We present an algorithm that overcomes these pitfalls. This algorithm is based on a variation of the Traveling Salesman Problem. It offers an extra benefit as it automatically determines cluster boundaries. Using this algorithm, we optimally solve four benchmark problems and a 2,467gene expression data clustering problem. As expected, our new algorithm identifies better clusters than those found by previous approaches in all five cases. Overall, our results demonstrate the benefits of rectifying the pitfalls and exemplify the usefulness of this clustering technique. Our code is available at our websites.
Worst Case Analysis of MaxRegret, Greedy and Other Heuristics for Multidimensional Assignment and Traveling Salesman Problems
"... Abstract. Optimization heuristics are often compared with each other to determine which one performs best by means of worstcase performance ratio reflecting the quality of returned solution in the worst case. The domination number is a complement parameter indicating the quality of the heuristic in ..."
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Cited by 5 (3 self)
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Abstract. Optimization heuristics are often compared with each other to determine which one performs best by means of worstcase performance ratio reflecting the quality of returned solution in the worst case. The domination number is a complement parameter indicating the quality of the heuristic in hand by determining how many feasible solutions are dominated by the heuristic solution. We prove that the MaxRegret heuristic introduced by Balas and Saltzman finds the unique worst possible solution for some instances of the sdimensional (s ≥ 3) assignment and asymmetric traveling salesman problems of each possible size. We show that the Triple Interchange heuristic (for s = 3) also introduced by Balas and Saltzman and two new heuristics (Part and Recursive Opt Matching) have factorial domination numbers for the sdimensional (s ≥ 3) assignment problem. 1
Continues observation planning for autonomous exploration
, 2004
"... Many applications of autonomous robots depend on the robot being able to navigate in real world environments. In order to navigate or path plan, the robot often needs to consult a map of its surroundings. A truly autonomous robot must, therefore, be able to drive about its environment and use its se ..."
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Cited by 3 (0 self)
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Many applications of autonomous robots depend on the robot being able to navigate in real world environments. In order to navigate or path plan, the robot often needs to consult a map of its surroundings. A truly autonomous robot must, therefore, be able to drive about its environment and use its sensors to build a map before performing any tasks that require this map. Algorithms that control a robot’s motion for the purpose of building a map of an environment are called autonomous exploration algorithms. Because resources such as time and energy are highly constrained in many mobile robot missions, a key requirement of autonomous exploration algorithms is that they cause the robot to explore efficiently. Planning paths to candidate observation points that will lead to efficient exploration is challenging, however, because the set of candidates, and, therefore, the robot’s plan, change frequently as the robot adds information to the map. The main claim of this thesis is that, in situations in which the robot discerns the large scale structure of the environment early on during its exploration, the robot can produce
On Approximating Asymmetric TSP and Related Problems
, 2006
"... In this thesis we study problems related to approximation of asymmetric TSP. First we give worst case examples for the famous algorithm due to Frieze, Gabiati and Maffioli for asymmetric TSP with triangle inequality. Some steps in the algorithm consist of arbitrary choices. To prove lower bounds, th ..."
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In this thesis we study problems related to approximation of asymmetric TSP. First we give worst case examples for the famous algorithm due to Frieze, Gabiati and Maffioli for asymmetric TSP with triangle inequality. Some steps in the algorithm consist of arbitrary choices. To prove lower bounds, these choices need to be specified. We show a worst case performance with some deterministic assumptions on the algorithm and then prove an expected worst case performance for a randomised version of the algorithm. The algorithm by Frieze et al. produces a spanning cactus and makes a TSP tour by shortcuts. We have proven that determining if there is a spanning cactus in a general asymmetric graph is an NPcomplete problem and that finding a minimum spanning cactus in a complete, directed graph with triangle inequality is equivalent to finding the TSP tour and the problems are equally hard to approximate. We also give three other results; we show a connection between asymmetric TSP and TSP in a bipartite graph, we show that it is NPhard to find a cycle cover in a bipartite graph without cycles of length six or less and finally we present some results for a new problem with ordered points on the circle.
Production Lot Sizing and Scheduling with NonTriangular SequenceDependent Setup Times Submitted to International Journal of Production Economics
, 2012
"... This article considers a production lot sizing and scheduling problem with sequencedependent setup times that are not triangular. Consider, for example, a product p that contaminates some other product r unless either a decontamination occurs as part of a substantial setup time stpr or there is a th ..."
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This article considers a production lot sizing and scheduling problem with sequencedependent setup times that are not triangular. Consider, for example, a product p that contaminates some other product r unless either a decontamination occurs as part of a substantial setup time stpr or there is a third product q that can absorb p’s contamination. When setup times are triangular then stpr ≤ stpq + stqr and there is always an optimal lot sequence with at most one lot (AM1L) per product per period. However, product q’s ability to absorb p’s contamination presents a shortcut opportunity and could result in shorter nontriangular setup times such thatstpr> stpq+stqr. This implies that it can sometimes be optimal for a shortcut product such as q to be produced in more than one lot within the same period, breaking the AM1L assumption in much research. This article formulates and explains a new optimal model that not only permits multiple lots (ML) per product per period, but also prohibits subtours using a polynomial number of constraints rather than an exponential number. Computational tests demonstrate the effectiveness of the ML model, even in the presence of just one decontaminating shortcut product, and its fast speed of solution compared to the equivalent AM1L model.