Discrete Optimization With Interval Data

Kasperski, Adam

Editore: Springer Verlag, 2008
ISBN 10: 3540784837 / ISBN 13: 9783540784838
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Riassunto: Operations research often solves deterministic optimization problems based on elegantand conciserepresentationswhereall parametersarepreciselyknown. In the face of uncertainty, probability theory is the traditional tool to be appealed for, and stochastic optimization is actually a signi?cant sub-area in operations research. However, the systematic use of prescribed probability distributions so as to cope with imperfect data is partially unsatisfactory. First, going from a deterministic to a stochastic formulation, a problem may becomeintractable. Agoodexampleiswhengoingfromdeterministictostoch- tic scheduling problems like PERT. From the inception of the PERT method in the 1950’s, it was acknowledged that data concerning activity duration times is generally not perfectly known and the study of stochastic PERT was launched quite early. Even if the power of today’s computers enables the stochastic PERT to be addressed to a large extent, still its solutions often require simplifying assumptions of some kind. Another di?culty is that stochastic optimization problems produce solutions in the average. For instance, the criterion to be maximized is more often than not expected utility. This is not always a meaningful strategy. In the case when the underlying process is not repeated a lot of times, let alone being one-shot, it is not clear if this criterion is realistic, in particular if probability distributions are subjective. Expected utility was proposed as a rational criterion from ?rst principles by Savage. In his view, the subjective probability distribution was - sically an artefact useful to implement a certain ordering of solutions.

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In operations research applications we are often faced with the problem of incomplete or uncertain data. This book considers solving combinatorial optimization problems with imprecise data modeled by intervals and fuzzy intervals. It focuses on some basic and traditional problems, such as minimum spanning tree, shortest path, minimum assignment, minimum cut and various sequencing problems. The interval based approach has become very popular in the recent decade. Decision makers are often interested in hedging against the risk of poor (worst case) system performance. This is particularly important for decisions that are encountered only once. In order to compute a solution that behaves reasonably under any likely input data, the maximal regret criterion is widely used. Under this criterion we seek a solution that minimizes the largest deviation from optimum over all possible realizations of the input data.

The minmax regret approach to discrete optimization with interval data has attracted considerable attention in the recent decade. This book summarizes the state of the art in the area and addresses some open problems. Furthermore, it contains a chapter devoted to the extension of the framework to the case when fuzzy intervals are applied to model uncertain data. The fuzzy intervals allow a more sophisticated uncertainty evaluation in the setting of possibility theory.

This book is a valuable source of information for all operations research practitioners who are interested in modern approaches to problem solving. Apart from the description of the theoretical framework, it also presents some algorithms that can be applied to solve problems that arise in practice.

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Titolo: Discrete Optimization With Interval Data
Casa editrice: Springer Verlag
Data di pubblicazione: 2008
Legatura: Hardcover
Condizione libro: New

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Descrizione libro Springer-Verlag Gmbh Jun 2008, 2008. Buch. Condizione libro: Neu. Neuware - Operations research often solves deterministic optimization problems based on elegantand conciserepresentationswhereall parametersarepreciselyknown. In the face of uncertainty, probability theory is the traditional tool to be appealed for, and stochastic optimization is actually a signi cant sub-area in operations research. However, the systematic use of prescribed probability distributions so as to cope with imperfect data is partially unsatisfactory. First, going from a deterministic to a stochastic formulation, a problem may becomeintractable. Agoodexampleiswhengoingfromdeterministictostoch- tic scheduling problems like PERT. From the inception of the PERT method in the 1950's, it was acknowledged that data concerning activity duration times is generally not perfectly known and the study of stochastic PERT was launched quite early. Even if the power of today's computers enables the stochastic PERT to be addressed to a large extent, still its solutions often require simplifying assumptions of some kind. Another di culty is that stochastic optimization problems produce solutions in the average. For instance, the criterion to be maximized is more often than not expected utility. This is not always a meaningful strategy. In the case when the underlying process is not repeated a lot of times, let alone being one-shot, it is not clear if this criterion is realistic, in particular if probability distributions are subjective. Expected utility was proposed as a rational criterion from rst principles by Savage. In his view, the subjective probability distribution was - sically an artefact useful to implement a certain ordering of solutions. 220 pp. Englisch. Codice libro della libreria 9783540784838

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Descrizione libro Springer-Verlag Gmbh Jun 2008, 2008. Buch. Condizione libro: Neu. Neuware - Operations research often solves deterministic optimization problems based on elegantand conciserepresentationswhereall parametersarepreciselyknown. In the face of uncertainty, probability theory is the traditional tool to be appealed for, and stochastic optimization is actually a signi cant sub-area in operations research. However, the systematic use of prescribed probability distributions so as to cope with imperfect data is partially unsatisfactory. First, going from a deterministic to a stochastic formulation, a problem may becomeintractable. Agoodexampleiswhengoingfromdeterministictostoch- tic scheduling problems like PERT. From the inception of the PERT method in the 1950's, it was acknowledged that data concerning activity duration times is generally not perfectly known and the study of stochastic PERT was launched quite early. Even if the power of today's computers enables the stochastic PERT to be addressed to a large extent, still its solutions often require simplifying assumptions of some kind. Another di culty is that stochastic optimization problems produce solutions in the average. For instance, the criterion to be maximized is more often than not expected utility. This is not always a meaningful strategy. In the case when the underlying process is not repeated a lot of times, let alone being one-shot, it is not clear if this criterion is realistic, in particular if probability distributions are subjective. Expected utility was proposed as a rational criterion from rst principles by Savage. In his view, the subjective probability distribution was - sically an artefact useful to implement a certain ordering of solutions. 220 pp. Englisch. Codice libro della libreria 9783540784838

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Descrizione libro Springer-Verlag Gmbh Jun 2008, 2008. Buch. Condizione libro: Neu. Neuware - Operations research often solves deterministic optimization problems based on elegantand conciserepresentationswhereall parametersarepreciselyknown. In the face of uncertainty, probability theory is the traditional tool to be appealed for, and stochastic optimization is actually a signi cant sub-area in operations research. However, the systematic use of prescribed probability distributions so as to cope with imperfect data is partially unsatisfactory. First, going from a deterministic to a stochastic formulation, a problem may becomeintractable. Agoodexampleiswhengoingfromdeterministictostoch- tic scheduling problems like PERT. From the inception of the PERT method in the 1950's, it was acknowledged that data concerning activity duration times is generally not perfectly known and the study of stochastic PERT was launched quite early. Even if the power of today's computers enables the stochastic PERT to be addressed to a large extent, still its solutions often require simplifying assumptions of some kind. Another di culty is that stochastic optimization problems produce solutions in the average. For instance, the criterion to be maximized is more often than not expected utility. This is not always a meaningful strategy. In the case when the underlying process is not repeated a lot of times, let alone being one-shot, it is not clear if this criterion is realistic, in particular if probability distributions are subjective. Expected utility was proposed as a rational criterion from rst principles by Savage. In his view, the subjective probability distribution was - sically an artefact useful to implement a certain ordering of solutions. 220 pp. Englisch. Codice libro della libreria 9783540784838

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Descrizione libro Springer-Verlag Gmbh Jun 2008, 2008. Buch. Condizione libro: Neu. - In operations research applications we are often faced with the problem of incomplete or uncertain data. This book considers solving combinatorial optimization problems with imprecise data modeled by intervals and fuzzy intervals. It focuses on some basic and traditional problems, such as minimum spanning tree, shortest path, minimum assignment, minimum cut and various sequencing problems. The interval based approach has become very popular in the recent decade. Decision makers are often interested in hedging against the risk of poor (worst case) system performance. This is particularly important for decisions that are encountered only once. In order to compute a solution that behaves reasonably under any likely input data, the maximal regret criterion is widely used. Under this criterion we seek a solution that minimizes the largest deviation from optimum over all possible realizations of the input data.The minmax regret approach to discrete optimization with interval data has attracted considerable attention in the recent decade. This book summarizes the state of the art in the area and addresses some open problems. Furthermore, it contains a chapter devoted to the extension of the framework to the case when fuzzy intervals are applied to model uncertain data. The fuzzy intervals allow a more sophisticated uncertainty evaluation in the setting of possibility theory. This book is a valuable source of information for all operations research practitioners who are interested in modern approaches to problem solving. Apart from the description of the theoretical framework, it also presents some algorithms that can be applied to solve problems that arise in practice. 220 pp. Englisch. Codice libro della libreria 9783540784838

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