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12
On the Solution of Traveling Salesman Problems
 DOC. MATH. J. DMV
, 1998
"... Following the theoretical studies of J.B. Robinson and H.W. Kuhn in the late 1940s and the early 1950s, G.B. Dantzig, R. Fulkerson, and S.M. Johnson demonstrated in 1954 that large instances of the TSP could be solved by linear programming. Their approach remains the only known tool for solving TS ..."
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Cited by 164 (7 self)
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Following the theoretical studies of J.B. Robinson and H.W. Kuhn in the late 1940s and the early 1950s, G.B. Dantzig, R. Fulkerson, and S.M. Johnson demonstrated in 1954 that large instances of the TSP could be solved by linear programming. Their approach remains the only known tool for solving TSP instances with more than several hundred cities; over the years, it has evolved further through the work of M. Grötschel , S. Hong , M. Jünger , P. Miliotis , D. Naddef , M. Padberg
On the History of Combinatorial Optimization (till 1960)
"... Introduction As a coherent mathematical discipline, combinatorial optimization is relatively young. When studying the history of the field, one observes a number of independent lines of research, separately considering problems like optimum assignment, shortest spanning tree, transportation, and the ..."
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Cited by 9 (0 self)
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Introduction As a coherent mathematical discipline, combinatorial optimization is relatively young. When studying the history of the field, one observes a number of independent lines of research, separately considering problems like optimum assignment, shortest spanning tree, transportation, and the traveling salesman problem. Only in the 1950's, when the unifying tool of linear and integer programming became available and the area of operations research got intensive attention, these problems were put into one framework, and relations between them were laid. Indeed, linear programming forms the hinge in the history of combinatorial optimization. Its initial conception by Kantorovich and Koopmans was motivated by combinatorial applications, in particular in transportation and transshipment. After the formulation of linear programming as generic problem, and the development in 1947 by Dantzig of the simplex method as a tool, one has tried to attack about all combinatorial opti
Modelassisted Estimation of Forest Resources With Generalized Additive Models
, 2003
"... Multiphase surveys are often conducted in forest inventory, with the goal of estimating forested area and tree characteristics over large regions. This article describes how designbased estimation of such quantities, based on information gathered during ground visits of sampled plots, can be ma ..."
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Cited by 5 (0 self)
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Multiphase surveys are often conducted in forest inventory, with the goal of estimating forested area and tree characteristics over large regions. This article describes how designbased estimation of such quantities, based on information gathered during ground visits of sampled plots, can be made more precise by incorporating auxiliary information available from remote sensing. The relationship between the ground visit measurements and the remote sensing variables is modelled using generalized additive models. Nonparametric estimators for these models are discussed and applied to forest data collected in the mountains of northern Utah in the United States. Modelassisted estimators that utilize the nonparametric regression fits are proposed for these data. The design
Overview PREFACE
, 2006
"... This course provides a solid grounding in modern surveysampling theory and methods. The lesson plan includes the first 9 chapters of the assigned text (probability sampling, stratification, allocation, multistage sampling, ratio and regression estimation, domain estimation, variance estimation in ..."
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This course provides a solid grounding in modern surveysampling theory and methods. The lesson plan includes the first 9 chapters of the assigned text (probability sampling, stratification, allocation, multistage sampling, ratio and regression estimation, domain estimation, variance estimation in complex surveys, and methods for handling nonresponse) and Chapter 12 (twophase sampling, smalldomain estimation, multiple frames, capture/recapture). This is augmented by the instructor’s comments on the text plus supplemental notes on topics like Wilson confidence intervals for small proportions, unequal probability sampling, and the largesample properties of common estimation strategies. A final lesson covers the multipleregression estimator.
MultiStage Sampling on Successive Occasions where FirstStage Units are Drawn with Unequal Probabilities and with Replacement
, 1966
"... A multistage sampling design, particularly intended for large scale sample surveys on successive (or repeated) occasions is developed. The sampling design is general in the sense that the probabilities of selecting units (for the preliminary firststage sa~le) are arbitrary. Each of these firststa ..."
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A multistage sampling design, particularly intended for large scale sample surveys on successive (or repeated) occasions is developed. The sampling design is general in the sense that the probabilities of selecting units (for the preliminary firststage sa~le) are arbitrary. Each of these firststage units is drawn with replacement. The technique of partial replacement of firststage sa~ling units is based on the order of occurrence of these units. The partial replacement technique is developed to meet two basic objectives: (i) To spread the burden of reporting among respondents which may be expected to help in maintaining a high rate of response. (ii) To enable the sampler to take advantage of the saItij?ling design in the reduction of sampling variance of several estimators proposed. Several ways of utilizing the past as well as the present information from the sampling design to estimate the total, and the change in total of a population characteristic of interest, are presented. The nature of the gain in efficiency from using the four different forms of estimators in estimati~g the total, and the change in total, is explored. The comparisons of efficiency among the estimators wherever possible, are given under certain assumptions simiiar to the assumption of Second Order or Weak Sense Stationarity · used in conventional time series analysis. • The estimation theory is covered in detail for twostage sampling on two successive occasions. The extension to higher stage sampling on more than two successive occasions is sufficiently indicated, In all, the reduction in the variance of an estimator whenever achieved, is in the total variance namely, the between firststage units variance plus the within firststage units variance, and so on if there are more than two stages of sampling.
Rotation Designs and Composite Estimation in Sample Surveys  Part 1. Motivating Their Use
, 2008
"... One can think of a rotation design as a compromise between a complete sample overlap and taking independent samples. Each extreme has advantages and disadvantages. By using a rotation design, one hopes to realize some of the variance reduction of the complete sample overlap, while reducing its exces ..."
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One can think of a rotation design as a compromise between a complete sample overlap and taking independent samples. Each extreme has advantages and disadvantages. By using a rotation design, one hopes to realize some of the variance reduction of the complete sample overlap, while reducing its excess burden. In this paper, we start by motivating the use of a rotation design and composite estimation to improve the estimator of current level of a parameter, θt, then look at compositing to improve the estimator of change, θt! θt1. Some consideration is then given to doing both: estimating level and change simultaneously. Finally, we briefly discuss other practical issues that influence the choice of designs and estimators, including generalizing the estimators, panel conditioning, cost, the mode of data collection, and respondent burden.
USE OF A NONLINEAR MODEL FOR IMPROVED ESTIMATION IN CLUSTER SAMPLING
"... Several researchers have attempted to develop a general law to predict a general relationship between variance within cluster S and size of the cluster M for purposes like 2 w determination of optimum cluster size etc. In the present study a nonlinear model has been S and M which has shown improvem ..."
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Several researchers have attempted to develop a general law to predict a general relationship between variance within cluster S and size of the cluster M for purposes like 2 w determination of optimum cluster size etc. In the present study a nonlinear model has been S and M which has shown improvement suggested for describing the relationship between 2 w over existing models and results have also been verified with the help of an example.
Improvement on the Nonresponse in the Population Ratio of Mean for Current Occasion in Sampling on Two Occasions
"... In this article, we attempt the problem of estimation of the population ratio of mean in mail surveys. This problem is conducted for current occasion in the context of sampling on two occasions when there is nonresponse (i) on both occasions, (ii) only on the first occasion and (iii) only on the sec ..."
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In this article, we attempt the problem of estimation of the population ratio of mean in mail surveys. This problem is conducted for current occasion in the context of sampling on two occasions when there is nonresponse (i) on both occasions, (ii) only on the first occasion and (iii) only on the second occasion. We obtain the gain in efficiency of all the estimators over the direct estimate using no information gathered on the first occasion. We derive the sample sizes and the saving in cost for all the estimators, which have the same precision than the direct estimate using no information gathered on the first occasion. An empirical study that allows us to investigate the performance of the proposed strategy is carried out.