arXiv subjects

Fernando H. C. Dias

Publications and source records attributed to Fernando H. C. Dias.

7 recordsLinked to original sources

arXiv2023

Accelerating ILP solvers for Minimum Flow Decompositions through search space and dimensionality reductions

Given a flow network, the Minimum Flow Decomposition (MFD) problem is finding the smallest possible set of weighted paths whose superposition equals the flow. It is a classical, strongly NP-hard problem that is proven to be useful in RNA transcript assembly and applications outside of Bioinformatics. We improve an existing ILP (Integer Linear Programming) model by Dias et al. [RECOMB 2022] for DAGs by decreasing the solver's search space using solution safety and several other optimizations. This results in a significant speedup compared to the original ILP, of up to 55-90x on average on the hardest instances. Moreover, we show that our optimizations apply also to MFD problem variants, resulting in similar speedups, going up to 123x on the hardest instances. We also developed an ILP model of reduced dimensionality for an MFD variant in which the solution path weights are restricted to a given set. This model can find an optimal MFD solution for most instances, and overall, its accuracy significantly outperforms that of previous greedy algorithms while being up to an order of magnitude faster than our optimized ILP.

q-bio.GN↗

arXiv2023

A Safety Framework for Flow Decomposition Problems via Integer Linear Programming

Many important problems in Bioinformatics (e.g., assembly or multi-assembly) admit multiple solutions, while the final objective is to report only one. A common approach to deal with this uncertainty is finding safe partial solutions (e.g., contigs) which are common to all solutions. Previous research on safety has focused on polynomially-time solvable problems, whereas many successful and natural models are NP-hard to solve, leaving a lack of "safety tools" for such problems. We propose the first method for computing all safe solutions for an NP-hard problem, minimum flow decomposition. We obtain our results by developing a "safety test" for paths based on a general Integer Linear Programming (ILP) formulation. Moreover, we provide implementations with practical optimizations aimed to reduce the total ILP time, the most efficient of these being based on a recursive group-testing procedure. Results: Experimental results on the transcriptome datasets of Shao and Kingsford (TCBB, 2017) show that all safe paths for minimum flow decompositions correctly recover up to 90% of the full RNA transcripts, which is at least 25% more than previously known safe paths, such as (Caceres et al. TCBB, 2021), (Zheng et al., RECOMB 2021), (Khan et al., RECOMB 2022, ESA 2022). Moreover, despite the NP-hardness of the problem, we can report all safe paths for 99.8% of the over 27,000 non-trivial graphs of this dataset in only 1.5 hours. Our results suggest that, on perfect data, there is less ambiguity than thought in the notoriously hard RNA assembly problem. Availability: https://github.com/algbio/mfd-safety

cs.DS↗

arXiv2023

Minimum Flow Decomposition in Graphs with Cycles using Integer Linear Programming

Minimum flow decomposition (MFD) -- the problem of finding a minimum set of weighted source-to-sink paths that perfectly decomposes a flow -- is a classical problem in Computer Science, and variants of it are powerful models in different fields such as Bioinformatics and Transportation. Even on acyclic graphs, the problem is NP-hard, and most practical solutions have been via heuristics or approximations. While there is an extensive body of research on acyclic graphs, currently, there is no \emph{exact} solution on graphs with cycles. In this paper, we present the first ILP formulation for three natural variants of the MFD problem in graphs with cycles, asking for a decomposition consisting only of weighted source-to-sink paths or cycles, trails, and walks, respectively. On three datasets of increasing levels of complexity from both Bioinformatics and Transportation, our approaches solve any instance in under 10 minutes. Our implementations are freely available at github.com/algbio/MFD-ILP.

cs.DS↗

arXiv2022

Fast, Flexible, and Exact Minimum Flow Decompositions via ILP

Minimum flow decomposition (MFD) (the problem of finding a minimum set of paths that perfectly decomposes a flow) is a classical problem in Computer Science, and variants of it are powerful models in multiassembly problems in Bioinformatics (e.g. RNA assembly). However, because this problem and its variants are NP-hard, practical multiassembly tools either use heuristics or solve simpler, polynomial-time solvable versions of the problem, which may yield solutions that are not mini-mal or do not perfectly decompose the flow. Many RNA assemblers also use integer linear programming(ILP) formulations of such practical variants, having the major limitation they need to encode all the potentially exponentially many solution paths. Moreover, the only exact solver for MFD does not scale to large instances and cannot be efficiently generalized to practical MFD variants. In this work, we provide the first practical ILP formulation for MFD (and thus the first fast and exact solver for MFD), based on encoding all of the exponentially many solution paths using only a quadratic number of variables. On both simulated and real flow graphs, our approach solves any instance in under 13 seconds. We also show that our ILP formulation can be easily and efficiently adapted for many practical variants, such as incorporating longer or paired-end reads or minimizing flow errors. We hope that our results can remove the current tradeoff between the complexity of a multi assembly model and its tractability and can lie at the core of future practical RNA assembly tools.

q-bio.GN↗

arXiv2022

Aircraft Conflict Resolution with Trajectory Recovery Using Mixed-Integer Programming

To guarantee the safety of flight operations, decision-support systems for air traffic control must be able to improve the usage of airspace capacity and handle increasing demand. In this study, we address the aircraft conflict avoidance and trajectory recovery problem. The problem of finding least deviation conflict-free aircraft trajectories that guarantee the return to a target waypoint is highly complex due to the nature of the nonlinear trajectories that are sought. We present a two-stage iterative algorithm that first solves initial conflict by manipulating their speed and heading control and then identifying each aircraft's optimal time to recover its trajectory towards their nominal. The avoidance stage extends existing mixed-integer programming formulations, and for the recovery stage, we propose a novel mixed-integer formulation. We assume that speed and heading control are continuous variables for this approach while the recovery time is treated as a discrete variable. In this approach, it is shown that the trajectory recovery costs can be anticipated by inducing avoidance trajectories with higher deviation, therefore obtaining earlier recovery time within few iterations. Numerical results on benchmark conflict resolution problems show that this approach can solve instances with up to 30 aircraft within 10 minutes.

math.OC↗

arXiv2020

Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution

We address the aircraft conflict resolution problem in air traffic control. We introduce new mixed-integer programming formulations for aircraft conflict resolution with speed, heading and altitude control which are based on disjunctive linear separation conditions. We first examine the two-dimensional aircraft conflict resolution problem with speed and heading control represented as continuous decision variables. We show that the proposed disjunctive linear separation conditions are equivalent to the traditional nonlinear conditions for aircraft separation. Further, we characterize conflict-free pairwise aircraft trajectories and propose a simple pre-processing algorithm to identify aircraft pairs which are either always conflict-free, or which cannot be separated using speed and heading control only. We then incorporate altitude control and propose a lexicographic optimization formulation that aims to minimize the number of flight level changes before resolving outstanding conflicts via two-dimensional velocity control. The proposed mixed-integer programming formulations are nonconvex, and we propose convex relaxations, decomposition methods and constraint generation algorithms to solve the two-dimensional and lexicographic optimization formulations to guaranteed optimality. Numerical experiments on four types of conflict resolution benchmarking instances are conducted to test the performance of the proposed mixed-integer formulations. Further, the proposed disjunctive formulations are compared against state-of-the-art formulations based on the so-called shadow separation condition. Our numerical results show that the proposed disjunctive linear separation conditions outperform existing formulations in the literature and can solve significantly more instances to global optimality. For reproducibility purposes, all formulations and instances are made available on a public repository.

math.OC↗

arXiv2020

A two-stage algorithm for aircraft conflict resolution with trajectory recovery

As air traffic volume is continuously increasing, it has become a priority to improve traffic control algorithms to handle future air travel demand and improve airspace capacity. We address the conflict resolution problem in air traffic control using a novel approach for aircraft collision avoidance with trajectory recovery. We present a two-stage algorithm that first solves all initial conflicts by adjusting aircraft headings and speeds, before identifying the optimal time for aircraft to recover towards their target destination. The collision avoidance stage extends an existing mixed-integer programming formulation to heading control. For the trajectory recovery stage, we introduce a novel exact mixed-integer programming formulation as well as a greedy heuristic algorithm. The proposed two-stage approach guarantees that all trajectories during both the collision avoidance and recovery stages are conflict-free. Numerical results on benchmark problems show that the proposed heuristic for trajectory recovery is competitive while also emphasizing the difficulty of this optimization problem. The proposed approach can be used as a decision-support tool for introducing automation in air traffic control.

math.OC↗