267 research outputs found
Filtering Algorithms for the Multiset Ordering Constraint
Constraint programming (CP) has been used with great success to tackle a wide
variety of constraint satisfaction problems which are computationally
intractable in general. Global constraints are one of the important factors
behind the success of CP. In this paper, we study a new global constraint, the
multiset ordering constraint, which is shown to be useful in symmetry breaking
and searching for leximin optimal solutions in CP. We propose efficient and
effective filtering algorithms for propagating this global constraint. We show
that the algorithms are sound and complete and we discuss possible extensions.
We also consider alternative propagation methods based on existing constraints
in CP toolkits. Our experimental results on a number of benchmark problems
demonstrate that propagating the multiset ordering constraint via a dedicated
algorithm can be very beneficial
Learning Hybrid Process Models From Events: Process Discovery Without Faking Confidence
Process discovery techniques return process models that are either formal
(precisely describing the possible behaviors) or informal (merely a "picture"
not allowing for any form of formal reasoning). Formal models are able to
classify traces (i.e., sequences of events) as fitting or non-fitting. Most
process mining approaches described in the literature produce such models. This
is in stark contrast with the over 25 available commercial process mining tools
that only discover informal process models that remain deliberately vague on
the precise set of possible traces. There are two main reasons why vendors
resort to such models: scalability and simplicity. In this paper, we propose to
combine the best of both worlds: discovering hybrid process models that have
formal and informal elements. As a proof of concept we present a discovery
technique based on hybrid Petri nets. These models allow for formal reasoning,
but also reveal information that cannot be captured in mainstream formal
models. A novel discovery algorithm returning hybrid Petri nets has been
implemented in ProM and has been applied to several real-life event logs. The
results clearly demonstrate the advantages of remaining "vague" when there is
not enough "evidence" in the data or standard modeling constructs do not "fit".
Moreover, the approach is scalable enough to be incorporated in
industrial-strength process mining tools.Comment: 25 pages, 12 figure
Sorted-pareto dominance: an extension to pareto dominance and its application in soft constraints
The Pareto dominance relation compares decisions
with each other over multiple aspects, and any decision that
is not dominated by another is called Pareto optimal, which is
a desirable property in decision making. However, the Pareto
dominance relation is not very discerning, and often leads to
a large number of non-dominated or Pareto optimal decisions.
By strengthening the relation, we can narrow down this nondominated
set of decisions to a smaller set, e.g., for presenting
a smaller number of more interesting decisions to a decision
maker. In this paper, we look at a particular strengthening of the
Pareto dominance called Sorted-Pareto dominance, giving some
properties that characterise the relation, and giving a semantics
in the context of decision making under uncertainty. We then
examine the use of the relation in a Soft Constraints setting, and
explore some algorithms for generating Sorted-Pareto optimal
solutions to Soft Constraints problems
Lexicographically-ordered constraint satisfaction problems
We describe a simple CSP formalism for handling multi-attribute preference problems with hard constraints, one that combines hard constraints and preferences so the two are easily distinguished conceptually and for purposes of problem solving. Preferences are represented as a lexicographic order over complete assignments based on variable importance and rankings of values in each domain. Feasibility constraints are treated in the usual manner. Since the preference representation is ordinal in character, these problems can be solved with algorithms that do not require evaluations to be represented explicitly. This includes ordinary CSP algorithms, although these cannot stop searching until all solutions have been checked, with the important exception of heuristics that follow the preference order (lexical variable and value ordering). We describe relations between lexicographic CSPs and more general soft constraint formalisms and show how a full lexicographic ordering can be expressed in the latter. We discuss relations with (T)CP-nets, highlighting the advantages of the present formulation, and we discuss the use of lexicographic ordering in multiobjective optimisation. We also consider strengths and limitations of this form of representation with respect to expressiveness and usability. We then show how the simple structure of lexicographic CSPs can support specialised algorithms: a branch and bound algorithm with an implicit cost function, and an iterative algorithm that obtains optimal values for successive variables in the importance ordering, both of which can be combined with appropriate variable ordering heuristics to improve performance. We show experimentally that with these procedures a variety of problems can be solved efficiently, including some for which the basic lexically ordered search is infeasible in practice
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