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Domination analysis of combinatorial optimization algorithms and problems
 In Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications (M.C. Golumbic and I. BenArroyo
, 2005
"... We provide an overview of an emerging area of domination analysis (DA) of combinatorial optimization algorithms and problems. We consider DA theory and its relevance to computational practice. 1 ..."
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We provide an overview of an emerging area of domination analysis (DA) of combinatorial optimization algorithms and problems. We consider DA theory and its relevance to computational practice. 1
A Memetic Algorithm for the Generalized Traveling Salesman Problem ∗
"... The generalized traveling salesman problem (GTSP) is an extension of the wellknown traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The recent studies on this subject ..."
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The generalized traveling salesman problem (GTSP) is an extension of the wellknown traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The recent studies on this subject consider different variations of a memetic algorithm approach to the GTSP. The aim of this paper is to present a new memetic algorithm for GTSP with a powerful local search procedure. The experiments show that the proposed algorithm clearly outperforms all of the known heuristics with respect to both solution quality and running time. While the other memetic algorithms were designed only for the symmetric GTSP, our algorithm can solve both symmetric and asymmetric instances. 1
On the Integrality Ratio for the Asymmetric Traveling Salesman Problem
 Mathematics of Operations Research
, 2006
"... informs ® doi 10.1287/moor.1060.0191 ..."
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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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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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
An Experimental Evaluation of Ejection Chain Algorithms for the Traveling Salesman Problem
"... Ejection chain methods lead the stateoftheart in local search heuristics for the traveling salesman problem (TSP). The most effective local search approaches primarily originate from the StemandCycle ejection chain method and the classical LinKernighan procedure, which can be viewed as an in ..."
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Ejection chain methods lead the stateoftheart in local search heuristics for the traveling salesman problem (TSP). The most effective local search approaches primarily originate from the StemandCycle ejection chain method and the classical LinKernighan procedure, which can be viewed as an instance of an ejection chain method. This paper describes major components of the most effective ejection chain algorithms that are critical for success in solving large scale TSPs. A performance assessment of foremost algorithms is reported based upon an experimental analysis carried out on a standard set of symmetric and asymmetric TSP benchmark problems.
When the greedy algorithm fails
"... We provide a characterization of the cases when the greedy algorithm may produce the unique worst possible solution for the problem of finding a minimum weight base in a uniform independence system when the weights are taken from a finite range. We apply this theorem to TSP and the minimum bisection ..."
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We provide a characterization of the cases when the greedy algorithm may produce the unique worst possible solution for the problem of finding a minimum weight base in a uniform independence system when the weights are taken from a finite range. We apply this theorem to TSP and the minimum bisection problem. The practical message of this paper is that the greedy algorithm should be used with great care, since for many optimization problems its usage seems impractical even for generating a starting solution (that will be improved by a local search or another heuristic).
Improvements to the Oropt Heuristic for the Symmetric Traveling Salesman Problem
, 2005
"... Several variants and generalizations of the Oropt heuristic for the Symmetric Traveling Salesman Problem are developed and compared on random and planar instances. Some of the proposed algorithms are shown to significantly improve upon the standard 2opt and Oropt heuristics. Key words: symmetric ..."
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Several variants and generalizations of the Oropt heuristic for the Symmetric Traveling Salesman Problem are developed and compared on random and planar instances. Some of the proposed algorithms are shown to significantly improve upon the standard 2opt and Oropt heuristics. Key words: symmetric traveling salesman problem, local search heuristics.
PhraseBased Statistical Machine Translation as a Traveling Salesman Problem
"... An efficient decoding algorithm is a crucial element of any statistical machine translation system. Some researchers have noted certain similarities between SMT decoding and the famous Traveling Salesman Problem; in particular (Knight, 1999) has shown that any TSP instance can be mapped to a subcas ..."
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Cited by 3 (1 self)
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An efficient decoding algorithm is a crucial element of any statistical machine translation system. Some researchers have noted certain similarities between SMT decoding and the famous Traveling Salesman Problem; in particular (Knight, 1999) has shown that any TSP instance can be mapped to a subcase of a wordbased SMT model, demonstrating NPhardness of the decoding task. In this paper, we focus on the reverse mapping, showing that any phrasebased SMT decoding problem can be directly reformulated as a TSP. The transformation is very natural, deepens our understanding of the decoding problem, and allows direct use of any of the powerful existing TSP solvers for SMT decoding. We test our approach on three datasets, and compare a TSPbased decoder to the popular beamsearch algorithm. In all cases, our method provides competitive or better performance. 1
Domination analysis for minimum multiprocessor scheduling
"... Let P be a combinatorial optimization problem, and let A be an approximation algorithm for P. The domination ratio domr(A, s) is the maximal real q such that the solution x(I) obtained by A for any instance I of P of size s is not worse than at least the fraction q of the feasible solutions of I. We ..."
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Let P be a combinatorial optimization problem, and let A be an approximation algorithm for P. The domination ratio domr(A, s) is the maximal real q such that the solution x(I) obtained by A for any instance I of P of size s is not worse than at least the fraction q of the feasible solutions of I. We say that P admits an Asymptotic Domination Ratio One (ADRO) algorithm if there is a polynomial time approximation algorithm A for P such that lims→ ∞ domr(A, s) = 1. Alon, Gutin and Krivelevich (J. Algorithms 50 (2004), 118–131) proved that the partition problem admits an ADRO algorithm. We extend their result to the minimum multiprocessor scheduling problem.