3,416 research outputs found
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
The edge-disjoint path problem on random graphs by message-passing
We present a message-passing algorithm to solve the edge disjoint path
problem (EDP) on graphs incorporating under a unique framework both traffic
optimization and path length minimization. The min-sum equations for this
problem present an exponential computational cost in the number of paths. To
overcome this obstacle we propose an efficient implementation by mapping the
equations onto a weighted combinatorial matching problem over an auxiliary
graph. We perform extensive numerical simulations on random graphs of various
types to test the performance both in terms of path length minimization and
maximization of the number of accommodated paths. In addition, we test the
performance on benchmark instances on various graphs by comparison with
state-of-the-art algorithms and results found in the literature. Our
message-passing algorithm always outperforms the others in terms of the number
of accommodated paths when considering non trivial instances (otherwise it
gives the same trivial results). Remarkably, the largest improvement in
performance with respect to the other methods employed is found in the case of
benchmarks with meshes, where the validity hypothesis behind message-passing is
expected to worsen. In these cases, even though the exact message-passing
equations do not converge, by introducing a reinforcement parameter to force
convergence towards a sub optimal solution, we were able to always outperform
the other algorithms with a peak of 27% performance improvement in terms of
accommodated paths. On random graphs, we numerically observe two separated
regimes: one in which all paths can be accommodated and one in which this is
not possible. We also investigate the behaviour of both the number of paths to
be accommodated and their minimum total length.Comment: 14 pages, 8 figure
Robust Scheduling with GFlowNets
Finding the best way to schedule operations in a computation graph is a
classical NP-hard problem which is central to compiler optimization. However,
evaluating the goodness of a schedule on the target hardware can be very
time-consuming. Traditional approaches as well as previous machine learning
ones typically optimize proxy metrics, which are fast to evaluate but can lead
to bad schedules when tested on the target hardware. In this work, we propose a
new approach to scheduling by sampling proportionally to the proxy metric using
a novel GFlowNet method. We introduce a technique to control the trade-off
between diversity and goodness of the proposed schedules at inference time and
demonstrate empirically that the pure optimization baselines can lead to subpar
performance with respect to our approach when tested on a target model.
Furthermore, we show that conditioning the GFlowNet on the computation graph
enables generalization to unseen scheduling problems for both synthetic and
real-world compiler datasets.Comment: Published at International Conference on Learning Representations
(ICLR) 2023; an earlier version appeared at the NeurIPS 2022 workshop
ML4System
Ant colony optimization for multi-UAV minimum time search in uncertain domains
This paper presents a new approach based on ant colony optimization (ACO) to determine the trajectories of a fleet of unmanned air vehicles (UAVs) looking for a lost target in the minimum possible time. ACO is especially suitable for the complexity and probabilistic nature of the minimum time search (MTS) problem, where a balance between the computational requirements and the quality of solutions is needed. The presented approach includes a new MTS heuristic that exploits the probability and spatial properties of the problem, allowing our ant based algorithm to quickly obtain high-quality high-level straight-segmented UAV trajectories. The potential of the algorithm is tested for different ACO parameterizations, over several search scenarios with different characteristics such as number of UAVs, or target dynamics and location distributions. The statistical comparison against other techniques previously used for MTS (ad hoc heuristics, cross entropy optimization, bayesian optimization algorithm and genetic algorithms) shows that the new approach outperforms the others.This work was supported by Airbus under the SAVIER AER-30459 project
A new sequential covering strategy for inducing classification rules with ant colony algorithms
Ant colony optimization (ACO) algorithms have been successfully applied to discover a list of classification rules. In general, these algorithms follow a sequential covering strategy, where a single rule is discovered at each iteration of the algorithm in order to build a list of rules. The sequential covering strategy has the drawback of not coping with the problem of rule interaction, i.e., the outcome of a rule affects the rules that can be discovered subsequently since the search space is modified due to the removal of examples covered by previous rules. This paper proposes a new sequential covering strategy for ACO classification algorithms to mitigate the problem of rule interaction, where the order of the rules is implicitly encoded as pheromone values and the search is guided by the quality of a candidate list of rules. Our experiments using 18 publicly available data sets show that the predictive accuracy obtained by a new ACO classification algorithm implementing the proposed sequential covering strategy is statistically significantly higher than the predictive accuracy of state-of-the-art rule induction classification algorithms
- …