2,246 research outputs found
Mixed integer-linear formulations of cumulative scheduling constraints - A comparative study
This paper introduces two MILP models for the cumulative scheduling constraint and associated pre-processing filters. We compare standard solver performance for these models on three sets of problems and for two of them, where tasks have unitary resource consumption, we also compare them with two models based on a geometric placement constraint. In the experiments, the solver performance of one of the cumulative models, is clearly the best and is also shown to scale very well for a large scale industrial transportation scheduling problem
Global Constraint Catalog, 2nd Edition
This report presents a catalogue of global constraints where
each constraint is explicitly described in terms of graph properties and/or automata and/or first order logical formulae with arithmetic. When available, it also presents some typical usage as well as some pointers to existing
filtering algorithms
Global Constraint Catalog, 2nd Edition (revision a)
This report presents a catalogue of global constraints where
each constraint is explicitly described in terms of graph properties and/or automata and/or first order logical formulae with arithmetic. When available, it also presents some typical usage as well as some pointers to existing
filtering algorithms
Synchronized sweep algorithms for scalable scheduling constraints
This report introduces a family of synchronized sweep based filtering
algorithms for handling scheduling problems involving resource and
precedence constraints. The key idea is to filter all constraints of a
scheduling problem in a synchronized way in order to scale better. In
addition to normal filtering mode, the algorithms can run in greedy
mode, in which case they perform a greedy assignment of start and end
times. The filtering mode achieves a significant speed-up over the
decomposition into independent cumulative and precedence constraints,
while the greedy mode can handle up to 1 million tasks with 64 resources
constraints and 2 million precedences. These algorithms were implemented
in both CHOCO and SICStus
Heuristic Approaches for Generating Local Process Models through Log Projections
Local Process Model (LPM) discovery is focused on the mining of a set of
process models where each model describes the behavior represented in the event
log only partially, i.e. subsets of possible events are taken into account to
create so-called local process models. Often such smaller models provide
valuable insights into the behavior of the process, especially when no adequate
and comprehensible single overall process model exists that is able to describe
the traces of the process from start to end. The practical application of LPM
discovery is however hindered by computational issues in the case of logs with
many activities (problems may already occur when there are more than 17 unique
activities). In this paper, we explore three heuristics to discover subsets of
activities that lead to useful log projections with the goal of speeding up LPM
discovery considerably while still finding high-quality LPMs. We found that a
Markov clustering approach to create projection sets results in the largest
improvement of execution time, with discovered LPMs still being better than
with the use of randomly generated activity sets of the same size. Another
heuristic, based on log entropy, yields a more moderate speedup, but enables
the discovery of higher quality LPMs. The third heuristic, based on the
relative information gain, shows unstable performance: for some data sets the
speedup and LPM quality are higher than with the log entropy based method,
while for other data sets there is no speedup at all.Comment: paper accepted and to appear in the proceedings of the IEEE Symposium
on Computational Intelligence and Data Mining (CIDM), special session on
Process Mining, part of the Symposium Series on Computational Intelligence
(SSCI
Global constraints as graph properties on structured network of elementary constraints of the same type
This report introduces a classification scheme for the global constraints. This classification is based on four basic ingredients from which one can generate almost all existing global constraints and come up with new interesting constraints. Global constraints are defined in a very concise way, in term of graph properties that have to hold, where the graph is a structured network of same elementary constraints. Since this classification is based on the internal structure of the global constraints it is also a strong hint for the pruning algorithms of the global constraints
Linear-time filtering algorithms for the disjunctive constraint and a quadratic filtering algorithm for the cumulative not-first not-last
We present new filtering algorithms for Disjunctive and Cumulative
constraints, each of which improves the complexity of the state-of-theart
algorithms by a factor of log n. We show how to perform TimeTabling
and Detectable Precedences in linear time on the Disjunctive
constraint. Furthermore, we present a linear-time Overload Checking for
the Disjunctive and Cumulative constraints. Finally, we show how
the rule of Not-first/Not-last can be enforced in quadratic time for the
Cumulative constraint. These algorithms rely on the union find data
structure, from which we take advantage to introduce a new data structure
that we call it time line. This data structure provides constant time
operations that were previously implemented in logarithmic time by the
Θ-tree data structure. Experiments show that these new algorithms are
competitive even for a small number of tasks and outperform existing algorithms
as the number of tasks increases. We also show that the time
line can be used to solve specific scheduling problems
A Bayesian approach to constrained single- and multi-objective optimization
This article addresses the problem of derivative-free (single- or
multi-objective) optimization subject to multiple inequality constraints. Both
the objective and constraint functions are assumed to be smooth, non-linear and
expensive to evaluate. As a consequence, the number of evaluations that can be
used to carry out the optimization is very limited, as in complex industrial
design optimization problems. The method we propose to overcome this difficulty
has its roots in both the Bayesian and the multi-objective optimization
literatures. More specifically, an extended domination rule is used to handle
objectives and constraints in a unified way, and a corresponding expected
hyper-volume improvement sampling criterion is proposed. This new criterion is
naturally adapted to the search of a feasible point when none is available, and
reduces to existing Bayesian sampling criteria---the classical Expected
Improvement (EI) criterion and some of its constrained/multi-objective
extensions---as soon as at least one feasible point is available. The
calculation and optimization of the criterion are performed using Sequential
Monte Carlo techniques. In particular, an algorithm similar to the subset
simulation method, which is well known in the field of structural reliability,
is used to estimate the criterion. The method, which we call BMOO (for Bayesian
Multi-Objective Optimization), is compared to state-of-the-art algorithms for
single- and multi-objective constrained optimization
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