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141
Revising Hull and Box Consistency
 INT. CONF. ON LOGIC PROGRAMMING
, 1999
"... Most intervalbased solvers in the constraint logic programming framework are based on either hull consistency or box consistency (or a variation of these ones) to narrow domains of variables involved in continuous constraint systems. This paper rst presents HC4, an algorithm to enforce hull consist ..."
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Cited by 107 (14 self)
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Most intervalbased solvers in the constraint logic programming framework are based on either hull consistency or box consistency (or a variation of these ones) to narrow domains of variables involved in continuous constraint systems. This paper rst presents HC4, an algorithm to enforce hull consistency without decomposing complex constraints into primitives. Next, an extended denition for box consistency is given and the resulting consistency is shown to subsume hull consistency. Finally, BC4, a new algorithm to eciently enforce box consistency is described, that replaces BC3the original solely Newtonbased algorithm to achieve box consistencyby an algorithm based on HC4 and BC3 taking care of the number of occurrences of each variable in a constraint. BC4 is then shown to signicantly outperform both HC3 (the original algorithm enforcing hull consistency by decomposing constraints) and BC3. 1 Introduction Finite representation of numbers precludes computers from exactly solv...
Problem Structure in the Presence of Perturbations
 In Proceedings of the 14th National Conference on AI
, 1997
"... Recent progress on search and reasoning procedures has been driven by experimentation on computationally hard problem instances. Hard random problem distributions are an important source of such instances. Challenge problems from the area of finite algebra have also stimulated research on searc ..."
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Cited by 81 (21 self)
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Recent progress on search and reasoning procedures has been driven by experimentation on computationally hard problem instances. Hard random problem distributions are an important source of such instances. Challenge problems from the area of finite algebra have also stimulated research on search and reasoning procedures. Nevertheless, the relation of such problems to practical applications is somewhat unclear. Realistic problem instances clearly have more structure than the random problem instances, but, on the other hand, they are not as regular as the structured mathematical problems. We propose a new benchmark domain that bridges the gap between the purely random instances and the highly structured problems, by introducing perturbations into a structured domain. We will show how to obtain interesting search problems in this manner, and how such problems can be used to study the robustness of search control mechanisms. Our experiments demonstrate that the performan...
HeavyTailed Distributions in Combinatorial Search
, 1997
"... Combinatorial search methods often exhibit a large variability in performance. We study the cost profiles of combinatorial search procedures. Our study reveals some intriguing properties of such cost profiles. The distributions are often characterized by very long tails or "heavy tails". W ..."
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Cited by 75 (14 self)
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Combinatorial search methods often exhibit a large variability in performance. We study the cost profiles of combinatorial search procedures. Our study reveals some intriguing properties of such cost profiles. The distributions are often characterized by very long tails or "heavy tails". We will show that these distributions are best characterized by a general class of distributions that have no moments (i.e., an infinite mean, variance, etc.). Such nonstandard distributions have recently been observed in areas as diverse as economics, statistical physics, and geophysics. They are closely related to fractal phenomena, whose study was introduced by Mandelbrot. We believe this is the first finding of these distributions in a purely computational setting. We also show how random restarts can effectively eliminate heavytailed behavior, thereby dramatically improving the overall performance of a search procedure.
Alma0: An Imperative Language that Supports Declarative Programming
, 1998
"... Architecture The Alma Abstract Architecture (AAA) is the virtual architecture used during the intermediate code generation phase of the Alma0 compiler. The AAA combines the features of the abstract machines for imperative languages and for logic programming languages. The compiler compiles the Al ..."
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Cited by 56 (11 self)
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Architecture The Alma Abstract Architecture (AAA) is the virtual architecture used during the intermediate code generation phase of the Alma0 compiler. The AAA combines the features of the abstract machines for imperative languages and for logic programming languages. The compiler compiles the Alma0 programs into AAA programs. In a second phase the AAA instructions are translated into C statements. As the Alma0 language itself, the AAA aims to combine the best of both worlds; elements were taken from virtual machines used to compile imperative languages (in particular the RISC architecture described in Wirth [1996, pp. 5559], and from the WAM machine used to compile a logical language (see AitKaci [1991]). Still, the AAA resembles most the virtual machines used in the compilation of imperative languages. The additions made to provide for the extensions of the Alma0 language are the failure handling instructions ONFAIL, FAIL, 40 \Delta Krzysztof R. Apt et al the log ...
Universally Quantified Interval Constraints
 PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING
, 2000
"... Nonlinear real constraint systems with universally and/or existentially quantified variables often need be solved in such contexts as control design or sensor planning. To date, these systems are mostly handled by computing a quantifierfree equivalent form by means of Cylindrical Algebraic Decompo ..."
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Cited by 54 (0 self)
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Nonlinear real constraint systems with universally and/or existentially quantified variables often need be solved in such contexts as control design or sensor planning. To date, these systems are mostly handled by computing a quantifierfree equivalent form by means of Cylindrical Algebraic Decomposition (CAD). However, CAD restricts its input to be conjunctions and disjunctions of polynomial constraints with rational coefficients, while some applications such as camera control involve systems with arbitrary forms where time is the only universally quantified variable. In this paper, the handling of universally quantified variables is first related to the computation of innerapproximation of real relations.
Yet Another Local Search Method for Constraint Solving
 In AAAI Fall Symposium on Using Uncertainty within Computation, Cape Cod
, 2001
"... We propose a generic, domainindependent local search method called adaptive search for solving Constraint Satisfaction Problems (CSP). We design a new heuristics that takes advantage of the structure of the problem in terms of constraints and variables and can guide the search more precisely th ..."
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Cited by 53 (19 self)
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We propose a generic, domainindependent local search method called adaptive search for solving Constraint Satisfaction Problems (CSP). We design a new heuristics that takes advantage of the structure of the problem in terms of constraints and variables and can guide the search more precisely than a global cost function to optimize (such as for instance the number of violated constraints). We also use an adaptive memory in the spirit of Tabu Search in order to prevent stagnation in local minima and loops. This method is generic, can apply to a large class of constraints (e.g. linear and nonlinear arithmetic constraints, symbolic constraints, etc) and naturally copes with overconstrained problems. Preliminary results on some classical CSP problems show very encouraging performances. 1
A Computational Study of Constraint Satisfaction for Multiple Capacitated Job Shop Scheduling
 European Journal of Operational Research
, 1996
"... Weintroduce the multiple capacitated job shop scheduling problem as a generalization of the job shop scheduling problem. In this problem machines may process several operations simultaneously.We presentan algorithm based on constraint satisfaction techniques to handle the problem e#ectively. The ..."
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Cited by 45 (3 self)
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Weintroduce the multiple capacitated job shop scheduling problem as a generalization of the job shop scheduling problem. In this problem machines may process several operations simultaneously.We presentan algorithm based on constraint satisfaction techniques to handle the problem e#ectively. The most importantnovel feature of our algorithm is the consistency checking. An empirical performance analysis is performed using a wellknown set of instances of the job shop scheduling problem and a newly constructed set of instances of the multiple capacitated job shop scheduling problem. We show that our algorithm performs well for both sets of instances.
Mixed Logical/Linear Programming
 Discrete Applied Mathematics
, 1996
"... Mixed logical/linear programming (MLLP) is an extension of mixed integer/linear programming (MILP). It represents the discrete elements of a problem with logical propositions and provides a more natural modeling framework than MILP. It can also have computational advantages, partly because it elimin ..."
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Cited by 42 (11 self)
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Mixed logical/linear programming (MLLP) is an extension of mixed integer/linear programming (MILP). It represents the discrete elements of a problem with logical propositions and provides a more natural modeling framework than MILP. It can also have computational advantages, partly because it eliminates integer variables when they serve no purpose, provides alternatives to the traditional continuous relaxation, and applies logic processing algorithms. This paper surveys previous work and attempts to organize ideas associated with MLLP, some old and some new, into a coherent framework. It articulates potential advantages and disadvantages of MLLP and illustrates some of them with computational experiments. 1 Introduction Mixed logical/linear programming (MLLP) is a general approach to formulating and solving optimization problems that have both discrete and continuous elements. Mixed integer/linear programming (MILP), the traditional approach, is effective in many instances. But it unn...
Scheduling a Major College Basketball Conference  Revisited
 Operations Research
, 2002
"... Nemhauser and Trick presented the problem of nding a timetable for the 1997/98 Atlantic Coast Conference (ACC) in basketball. Their solution, found with a combination of integer programming and exhaustive enumeration, was accepted by the ACC. ..."
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Cited by 38 (6 self)
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Nemhauser and Trick presented the problem of nding a timetable for the 1997/98 Atlantic Coast Conference (ACC) in basketball. Their solution, found with a combination of integer programming and exhaustive enumeration, was accepted by the ACC.
A Unifying Framework for Integer and Finite Domain Constraint Programming
, 1997
"... We present a unifying framework for integer linear programming and finite domain constraint programming, which is based on a distinction of primitive and nonprimitive constraints and a general notion of branchandinfer. We compare the two approaches with respect to their modeling and solving capab ..."
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Cited by 35 (2 self)
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We present a unifying framework for integer linear programming and finite domain constraint programming, which is based on a distinction of primitive and nonprimitive constraints and a general notion of branchandinfer. We compare the two approaches with respect to their modeling and solving capabilities. We introduce symbolic constraint abstractions into integer programming. Finally, we discuss possible combinations of the two approaches.