161 research outputs found
A geometric constraint over k-dimensional objects and shapes subject to business rules
This report presents a global constraint that enforces rules written
in a language based on arithmetic and first-order logic to hold among a set of objects. In a first step, the rules are rewritten to Quantifier-Free Presburger Arithmetic (QFPA) formulas. Secondly, such
formulas are compiled to generators of k-dimensional forbidden sets. Such generators are a generalization of the indexicals of cc(FD). Finally, the forbidden sets generated by such indexicals are
aggregated by a sweep-based algorithm and used for filtering. The business rules allow to express a great variety of packing and placement constraints, while admitting efficient and effective filtering of the domain variables of the k-dimensional object, without the need to use spatial data structures. The constraint was used to directly encode the packing knowledge of a major car manufacturer and tested on a set of real packing problems under these rules, as well as on a packing-unpacking problem
A Declarative Paradigm for Robust Cumulative Scheduling
International audienceThis paper investigates cumulative scheduling in uncertain environments, using constraint programming. We present a new declarative characterization of robustness, which preserves solution quality.We highlight the significance of our framework on a crane assignment problem with business constraints
Prefix-Projection Global Constraint for Sequential Pattern Mining
Sequential pattern mining under constraints is a challenging data mining
task. Many efficient ad hoc methods have been developed for mining sequential
patterns, but they are all suffering from a lack of genericity. Recent works
have investigated Constraint Programming (CP) methods, but they are not still
effective because of their encoding. In this paper, we propose a global
constraint based on the projected databases principle which remedies to this
drawback. Experiments show that our approach clearly outperforms CP approaches
and competes well with ad hoc methods on large datasets
Parameterised bounds on the sum of variables in time-series constraints
For two families of time-series constraints with the aggregator Sum and features one and width, we provide parameterised sharp lower and upper bounds on the sum of the time-series variables wrt these families of constraints. This is important in many applications, as this sum represents the cost, for example the energy used, or the manpower effort expended. We use these bounds not only to gain a priori knowledge of the overall cost of a problem, we can also use them on increasing prefixes and suffixes of the variables to avoid infeasible partial assignments under a given cost budget. Experiments show that the bounds drastically reduce the effort to find cost limited solutions
Sweep as a Generic Pruning Technique Applied to the Non-Overlapping Rectangles Constraint
We first present a generic pruning technique which aggregates several constraints sharing some variables. The method is derived from an idea called \dfn{sweep} which is extensively used in computational geometry. A first benefit of this technique comes from the fact that it can be applied on several families of global constraints. A second main advantage is that it does not lead to any memory consumption problem since it only requires temporary memory that can be reclaimed after each invocation of the method. We then specialize this technique to the non-overlapping rectangles constraint, describe several optimizations, and give an empirical evaluation based on six sets of test instances of different pattern
Revisiting the tree Constraint
International audienceThis paper revisits the tree constraint introduced in [2] which partitions the nodes of a n-nodes, m-arcs directed graph into a set of node-disjoint anti-arborescences for which only certain nodes can be tree roots. We introduce a new filtering algorithm that enforces generalized arc-consistency in O(n + m) time while the original filtering algorithm reaches O(nm) time. This result allows to tackle larger scale problems involving graph partitioning
The role of the agent's outside options in principal-agent relationships
We consider a principal-agent model of adverse selection where, in order to trade with the principal,
the agent must undertake a relationship-specific investment which affects his outside option to trade,
i.e. the payoff that he can obtain by trading with an alternative principal. This creates a distinction
between the agentâs ex ante (before investment) and ex post (after investment) outside options to trade.
We investigate the consequences of this distinction, and show that whenever an agentâs ex ante and ex
post outside options differ, this may equip the principal with an additional tool for screening among
different agent types, by randomizing over the probability with which trade occurs once the agent
has undertaken the investment. In turn, this may enhance the efficiency of the optimal second-best
contract
On Matrices, Automata, and Double Counting
Matrix models are ubiquitous for constraint problems. Many such problems have a matrix of variables M, with the same constraint defined by a finite-state automaton A on each row of M and a global cardinality constraint gcc on each column of M. We give two methods for deriving, by double counting,
necessary conditions on the cardinality variables of the gcc constraints from the automaton A. The first method yields linear necessary conditions and simple arithmetic constraints. The second method introduces the cardinality automaton, which abstracts the overall behaviour of all the row automata and can be encoded by a set of linear constraints. We evaluate the impact of our methods on a large set of nurse rostering problem instances
Estimating the Number of Solutions of Cardinality Constraints through range and roots Decompositions
International audienceThis paper introduces a systematic approach for estimating the number of solutions of cardinality constraints. A main difficulty of solutions counting on a specific constraint lies in the fact that it is, in general, at least as hard as developing the constraint and its propaga-tors, as it has been shown on alldifferent and gcc constraints. This paper introduces a probabilistic model to systematically estimate the number of solutions on a large family of cardinality constraints including alldifferent, nvalue, atmost, etc. Our approach is based on their decomposition into range and roots, and exhibits a general pattern to derive such estimates based on the edge density of the associated variable-value graph. Our theoretical result is finally implemented within the maxSD search heuristic, that aims at exploring first the area where there are likely more solutions
- âŠ