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11
Tabu Search: A Tutorial
 Interfaces
, 1990
"... Tabu search is a "higher level " heuristic procedure for solving optimization problems, designed to guide other methods (or their component processes) to escape the trap of local optimality. Tabu search has obtained optimal and near optimal solutions to a wide variety of classical and practical prob ..."
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Cited by 91 (2 self)
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Tabu search is a "higher level " heuristic procedure for solving optimization problems, designed to guide other methods (or their component processes) to escape the trap of local optimality. Tabu search has obtained optimal and near optimal solutions to a wide variety of classical and practical problems in applications ranging from scheduling to telecommunications and from character recognition to neural networks. It uses flexible structures memory (to permit search information to be exploited more thoroughly than by rigid memory systems or memoryless systems), conditions for strategically constraining and freeing the search process (embodied in tabu restrictions and aspiration criteria), and memory functions of varying time spans for intensifying and diversifying the search (reinforcing attributes historically found good and driving the search into new regions). Tabu search can be integrated with branchandbound and cutting plane procedures, and it has the ability to start with a simple implementation that can be upgraded over time to incorporate more advanced or specialized elements. T abu search is a metaheuristic that can to prevent them from becoming trapped at be superimposed on other procedures locally optimal solutions. The method can
Probabilistic Deduction with Conditional Constraints over Basic Events
 J. Artif. Intell. Res
, 1999
"... We study the problem of probabilistic deduction with conditional constraints over basic events. We show that globally complete probabilistic deduction with conditional constraints over basic events is NPhard. We then concentrate on the special case of probabilistic deduction in conditional constrai ..."
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Cited by 44 (30 self)
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We study the problem of probabilistic deduction with conditional constraints over basic events. We show that globally complete probabilistic deduction with conditional constraints over basic events is NPhard. We then concentrate on the special case of probabilistic deduction in conditional constraint trees. We elaborate very efficient techniques for globally complete probabilistic deduction. In detail, for conditional constraint trees with point probabilities, we present a local approach to globally complete probabilistic deduction, which runs in linear time in the size of the conditional constraint trees. For conditional constraint trees with interval probabilities, we show that globally complete probabilistic deduction can be done in a global approach by solving nonlinear programs. We show how these nonlinear programs can be transformed into equivalent linear programs, which are solvable in polynomial time in the size of the conditional constraint trees. 1. Introduction Dealing wit...
Probabilistic Default Reasoning with Conditional Constraints
 ANN. MATH. ARTIF. INTELL
, 2000
"... We present an approach to reasoning from statistical and subjective knowledge, which is based on a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. More precisely, we introduce the notions of , lexicographic, ..."
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Cited by 35 (20 self)
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We present an approach to reasoning from statistical and subjective knowledge, which is based on a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. More precisely, we introduce the notions of , lexicographic, and conditional entailment for conditional constraints, which are probabilistic generalizations of Pearl's entailment in system , Lehmann's lexicographic entailment, and Geffner's conditional entailment, respectively. We show that the new formalisms have nice properties. In particular, they show a similar behavior as referenceclass reasoning in a number of uncontroversial examples. The new formalisms, however, also avoid many drawbacks of referenceclass reasoning. More precisely, they can handle complex scenarios and even purely probabilistic subjective knowledge as input. Moreover, conclusions are drawn in a global way from all the available knowledge as a whole. We then show that the new formalisms also have nice general nonmonotonic properties. In detail, the new notions of , lexicographic, and conditional entailment have similar properties as their classical counterparts. In particular, they all satisfy the rationality postulates proposed by Kraus, Lehmann, and Magidor, and they have some general irrelevance and direct inference properties. Moreover, the new notions of  and lexicographic entailment satisfy the property of rational monotonicity. Furthermore, the new notions of , lexicographic, and conditional entailment are proper generalizations of both their classical counterparts and the classical notion of logical entailment for conditional constraints. Finally, we provide algorithms for reasoning under the new formalisms, and we analyze its computational com...
Aggregating disparate estimates of chance
, 2004
"... We consider a panel of experts asked to assign probabilities to events, both logically simple and complex. The events evaluated by different experts are based on overlapping sets of variables but may otherwise be distinct. The union of all the judgments will likely be probabilistic incoherent. We ad ..."
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Cited by 19 (4 self)
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We consider a panel of experts asked to assign probabilities to events, both logically simple and complex. The events evaluated by different experts are based on overlapping sets of variables but may otherwise be distinct. The union of all the judgments will likely be probabilistic incoherent. We address the problem of revising the probability estimates of the panel so as to produce a coherent set that best represents the group’s expertise.
Resolution and the Integrality of Satisfiability Problems
 Mathematical Programming
, 1995
"... A satisfiability problem can be regarded as a nondisjoint union of set covering problems. We show that if the resolution method of theorem proving is applied to the satisfiability problem, its constraint set defines an integral polytope if and only if the constraint sets of the set covering problems ..."
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Cited by 8 (0 self)
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A satisfiability problem can be regarded as a nondisjoint union of set covering problems. We show that if the resolution method of theorem proving is applied to the satisfiability problem, its constraint set defines an integral polytope if and only if the constraint sets of the set covering problems do. In this sense, resolution reduces the integrality question for the satisfiability problem to that for the set covering problem. 1 Introduction The satisfiability problem of propositional logic asks whether a set of logical clauses can be true simultaneously. The clauses can be represented as linear inequalities that have a 01 solution if and only if the clauses are satisfiable. In many cases one is not only interested in the 01 solubility of this constraint set but in solving a 01 optimization problem subject to it. Such a problem is implicit, for instance, in the maximum satisfiability problem [13, 15], which assigns weights to the constraints and seeks the maximum weight feasible ...
New Methods for Computing Inferences in First Order Logic
 Annals of Operations Research
, 1991
"... Recent improvements in satisfiability algorithms for propositional logic have made partial instantiation methods for first order predicate logic computationally more attractive. Two such methods have been proposed, one by R. Jeroslow and a hypergraph method for datalog formulas by G. Gallo and G. Ra ..."
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Cited by 6 (2 self)
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Recent improvements in satisfiability algorithms for propositional logic have made partial instantiation methods for first order predicate logic computationally more attractive. Two such methods have been proposed, one by R. Jeroslow and a hypergraph method for datalog formulas by G. Gallo and G. Rago. We show that they are instances of two general approaches to partial instantiation, and we develop these approaches for a large decidable fragment of first order logic (the 98 fragment). 1 Introduction The last few years have seen a surge of interest in applying the computational methods of combinatorial optimization to logical inference problems. Most of this effort has been directed toward propositional logic [2, 3, 4, 5, 10, 14, 15, 16, 17, 18, 19, 22] [23, 26] and probabilistic logic [1, 7, 12, 13, 20, 24, 25]. Less work in this area has focused on predicate logic, but it is nonetheless reaching a stage at which it can make a significant contribution to computational methods...
A Linear Programming Framework for Logics of Uncertainty
 in HICSS93 Proceedings (26th Hawaii International Conference on Systems Sciences
, 1992
"... Several logics for reasoning under uncertainty distribute "probability mass" over sets in some sense. These include probabilistic logic, DempsterShafer theory, other logics based on belief functions, and secondorder probabilistic logic. We show that these logics are instances of a certain type of ..."
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Cited by 6 (1 self)
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Several logics for reasoning under uncertainty distribute "probability mass" over sets in some sense. These include probabilistic logic, DempsterShafer theory, other logics based on belief functions, and secondorder probabilistic logic. We show that these logics are instances of a certain type of linear programming model, typically with exponentially many variables. We also show how a single linear program package can implement these logics computationally if one "plugs in" a different column generation subroutine for each logic. 1 Introduction Several logics for reasoning under uncertainty are variations on a theme. Numbers, perhaps probabilities, are assigned to propositions to indicate degrees of confidence. The object is to determine the degree of confidence one can have in a conclusion inferred from the propositions. Dependencies among the propositions require that some of the "probability mass" assigned to one proposition be distributed to others. Solution of this distributio...
Logical Inference and Polyhedral Projection
 Proceeedings, Computer Science Logic Workshop (CSL'91), Lecture Notes in Computer Science 626
, 1992
"... We explore connections between polyhedral projection and inference in propositional logic. We formulate the problem of drawing all inferences that contain a restricted set of atoms (i.e., all inferences that pertain to a given question) as a logical projection problem. We show that polyhedral pro ..."
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Cited by 6 (1 self)
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We explore connections between polyhedral projection and inference in propositional logic. We formulate the problem of drawing all inferences that contain a restricted set of atoms (i.e., all inferences that pertain to a given question) as a logical projection problem. We show that polyhedral projection partially solves this problem and in particular derives precisely those inferences that can be obtained by a certain form of unit resolution. We prove that this unit resolution algorithm is exponential in the number of atoms in the restricted set but is polynomial in the problem size when this number of fixed. We also survey a number of new satisfiability algorithms that have been suggested by the polyhedral interpretation of propositional logic. 1 Introduction The inference problem in propositional logic is closely connected with polyhedral theory. In the last few years this connection has suggested a number of new inference algorithms that have substantially advanced the st...
Probabilistic default reasoning with strict and defeasible conditional constraints
 Institut für Informationssysteme
, 2000
"... z, lexicographic, and conditional entailment have similar propertiesas their classical counterparts. In particular, they all satisfy the rationality postulates proposed by Kraus, Lehmann, and Magidor, and they have some general irrelevance and direct inference properties. Moreover, the new notions ..."
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Cited by 3 (3 self)
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z, lexicographic, and conditional entailment have similar propertiesas their classical counterparts. In particular, they all satisfy the rationality postulates proposed by Kraus, Lehmann, and Magidor, and they have some general irrelevance and direct inference properties. Moreover, the new notions of z and lexicographic entailment satisfy the property of rationalmonotonicity. Furthermore, the new notions of
Some Results on Generalized Coherence of Conditional Probability Bounds
 Proc. of The Third International Symposium on Imprecise Probabilities and their Applications (ISIPTA ’03
, 2003
"... Based on the coherence principle of de Finetti and a related notion of generalized coherence (gcoherence), we adopt a probabilistic approach to uncertainty based on conditional probability bounds. Our notion of gcoherence is equivalent to the "avoiding uniform loss" property for lower and upper pr ..."
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Cited by 1 (0 self)
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Based on the coherence principle of de Finetti and a related notion of generalized coherence (gcoherence), we adopt a probabilistic approach to uncertainty based on conditional probability bounds. Our notion of gcoherence is equivalent to the "avoiding uniform loss" property for lower and upper probabilities (a la Walley). Moreover, given a gcoherent imprecise assessment by our algorithms we can correct it obtaining the associated coherent assessment (in the sense of Walley and Williams). As is well known, the problems of checking gcoherence and propagating tight gcoherent intervals are NP and FP NP complete, respectively, and thus NPhard. Two notions which may be helpful to reduce computational effort are those of non relevant gain and basic set. Exploiting them, our algorithms can use linear systems with reduced sets of variables and/or linear constraints. In this paper we give some insights on the notions of non relevant gain and basic set. We consider several families with three conditional events, obtaining some results characterizing gcoherence in such cases. We also give some more general results.