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Traveling salesman should not be greedy: domination analysis of greedytype heuristics for the TSP
 DISCRETE APPL. MATH
"... Computational experiments show that the greedy algorithm (GR) and the nearest neighbor algorithm (NN), popular choices for tour construction heuristics, work at acceptable level for the Euclidean TSP, but produce very poor results for the general Symmetric and Asymmetric TSP (STSP and ATSP). We p ..."
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Cited by 17 (9 self)
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Computational experiments show that the greedy algorithm (GR) and the nearest neighbor algorithm (NN), popular choices for tour construction heuristics, work at acceptable level for the Euclidean TSP, but produce very poor results for the general Symmetric and Asymmetric TSP (STSP and ATSP). We prove that for every n 2 there is an instance of ATSP (STSP) on n vertices for which GR finds the worst tour. The same result holds for NN. We also analyze the repetitive NN (RNN) that starts NN from every vertex and chooses the best tour obtained. We prove that, for the ATSP, RNN always produces a tour, which is not worse than at least n=2 \Gamma 1 other tours, but for some instance it finds a tour, which is not worse than at most n \Gamma 2 other tours, n 4. We also show that, for some instance of the STSP on n 4 vertices, RNN produces a tour not worse than at most 2 n\Gamma3 tours. These results are in sharp contrast to earlier results by G. Gutin and A. Yeo, and A. Punnen and...
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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Cited by 10 (5 self)
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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
TSP tour domination and Hamilton cycle decompositions of regular digraphs
 Oper. Res. Lett
, 1999
"... In this paper, we solve a problem by Glover and Punnen (1997) from the context of domination analysis, where the performance of a heuristic algorithm is rated by the number of solutions that are not better than the solution found by the algorithm, rather than by the relative performance compared ..."
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Cited by 8 (5 self)
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In this paper, we solve a problem by Glover and Punnen (1997) from the context of domination analysis, where the performance of a heuristic algorithm is rated by the number of solutions that are not better than the solution found by the algorithm, rather than by the relative performance compared to the optimal value. In particular, we show that for the Asymmetric Traveling Salesman Problem (ATSP), there is a deterministic polynomial time algorithm that finds a tour that is at least as good as the median of all tour values. Our algorithm uses an unpublished theorem by Haggkvist on the Hamilton decomposition of regular digraphs. Keywords: ATSP, domination analysis, Hamilton cycle decomposition, regular digraphs 1 Introduction, Terminology and Notation It is well known that most combinatorial optimization problems are NPhard. Due to the lack of polynomial time algorithms to solve NPhard problems to optimality, the following two approaches to deal with such problems have ...
Domination analysis of combinatorial optimization problems
 Discrete Appl. Math
, 2003
"... We use the notion of domination ratio introduced by Glover and Punnen in 1997 to present a new classification of combinatorial optimization (CO) problems: DOMeasy and DOMhard problems. It follows from results proved already in the 1970’s that min TSP (both symmetric and asymmetric versions) is DOM ..."
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Cited by 8 (5 self)
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We use the notion of domination ratio introduced by Glover and Punnen in 1997 to present a new classification of combinatorial optimization (CO) problems: DOMeasy and DOMhard problems. It follows from results proved already in the 1970’s that min TSP (both symmetric and asymmetric versions) is DOMeasy. We prove that several CO problems are DOMeasy including weighted max kSAT and max cut. We show that some other problems, such as max clique and min vertex cover, are DOMhard unless P=NP.
Combinatorial Dominance Guarantees for Heuristic Algorithms (Extended Abstract)
, 2002
"... Daniel Berend* Steven S. Skiena t 1 ..."
A Hybrid Fuzzy Variable Neighborhood Particle Swarm Optimization Algorithm . . .
 JOURNAL OF UNIVERSAL COMPUTER SCIENCE
, 2007
"... Recently, Particle Swarm Optimization (PSO) algorithm has exhibited good performance across a wide range of application problems. A quick review of the literature reveals that research for solving the Quadratic Assignment Problem (QAP) using PSO approach has not much been investigated. In this paper ..."
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Cited by 7 (4 self)
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Recently, Particle Swarm Optimization (PSO) algorithm has exhibited good performance across a wide range of application problems. A quick review of the literature reveals that research for solving the Quadratic Assignment Problem (QAP) using PSO approach has not much been investigated. In this paper, we design a hybrid metaheuristic fuzzy scheme, called as variable neighborhood fuzzy particle swarm algorithm (VNPSO), based on fuzzy particle swarm optimization and variable neighborhood search to solve the QAP. In the hybrid fuzzy scheme, the representations of the position and velocity of the particles in the conventional PSO is extended from the real vectors to fuzzy matrices. A new mapping is introduced between the particles in the swarm and the problem space in an efficient way. We also attempt to theoretically prove that the variable neighborhood particle swarm algorithm converges with a probability of 1 towards the global optimal. The performance of the proposed approach is evaluated and compared with other four different algorithms. Empirical results illustrate that the approach can be applied for solving quadratic assignment problems effectively.
Construction heuristics and domination analysis for the asymmetric TSP
 European J. Oper. Res
, 2001
"... NonEuclidean TSP construction heuristics, and especially asymmetric TSP construction heuristics, have been neglected in the literature by comparison with the extensive eorts devoted to studying Euclidean TSP construction heuristics. Motivation for remedying this gap in the study of construction ..."
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Cited by 7 (2 self)
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NonEuclidean TSP construction heuristics, and especially asymmetric TSP construction heuristics, have been neglected in the literature by comparison with the extensive eorts devoted to studying Euclidean TSP construction heuristics. Motivation for remedying this gap in the study of construction approaches is increased by the fact that such methods are a great deal faster than other TSP heuristics, which can be important for real time problems requiring continuously updated response. The purpose of this paper is to describe two new construction heuristics for the asymmetric TSP and a third heuristic based on combining the other two. Extensive computational experiments are performed for several dierent families of TSP instances, disclosing that our combined heuristic clearly outperforms wellknown TSP construction methods and proves signicantly more robust in obtaining high quality solutions over a wide range of problems. We also provide a short overview of recent results ...
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
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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Cited by 4 (3 self)
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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).