arXiv subjects

Eduardo Moreno

Publications and source records attributed to Eduardo Moreno.

14 recordsLinked to original sources

arXiv2026

Exact Hyper-Rectangular Clustering via Adaptive Subset Selection

We study the hyper-rectangular clustering problem (HRCP), where the goal is to partition a set of points into a fixed number of axis-aligned clusters while minimizing the total span. Existing exact approaches, based on mathematical optimization formulations, are limited to relatively small instances due to their strong dependence on the number of data points. We propose an incremental exact algorithm that exploits a key structural property of the problem: optimal cluster boundaries are determined by a subset of points, while interior points do not affect the objective value. The algorithm iteratively solves HRCP on carefully selected subsets of points and expands them only when necessary. A simple optimality condition ensures that, once a solution covers the entire dataset, it is optimal for the original problem. We introduce sampling strategies designed to identify points likely to lie on cluster boundaries, guiding the incremental process toward informative subsets. Computational experiments show that the proposed approach significantly improves scalability, solving instances with up to 10,000 points and substantially outperforming monolithic formulations.

cs.DM↗

arXiv2022

Benders Adaptive-Cuts Method for Two-Stage Stochastic Programs

Benders decomposition is one of the most applied methods to solve two-stage stochastic problems (TSSP) with a large number of scenarios. The main idea behind the Benders decomposition is to solve a large problem by replacing the values of the second-stage subproblems with individual variables, and progressively forcing those variables to reach the optimal value of the subproblems, dynamically inserting additional valid constraints, known as Benders cuts. Most traditional implementations add a cut for each scenario (multi-cut) or a single-cut that includes all scenarios. In this paper we present a novel Benders adaptive-cuts method, where the Benders cuts are aggregated according to a partition of the scenarios, which is dynamically refined using the LP-dual information of the subproblems. This scenario aggregation/disaggregation is based on the Generalized Adaptive Partitioning Method (GAPM), which has been successfully applied to TSSPs. We formalize this hybridization of Benders decomposition and the GAPM, by providing sufficient conditions under which an optimal solution of the deterministic equivalent can be obtained in a finite number of iterations. Our new method can be interpreted as a compromise between the Benders single-cuts and multi-cuts methods, drawing on the advantages of both sides, by rendering the initial iterations faster (as for the single-cuts Benders) and ensuring the overall faster convergence (as for the multi-cuts Benders). Computational experiments on three TSSPs validate these statements, showing that the new method outperforms the other implementations of Benders method, as well as other standard methods for solving TSSPs, in particular when the number of scenarios is very large.

math.OC↗

arXiv2022

Approximation algorithm for resource-constrained project scheduling problems with net present value objective

Resource-constrained project scheduling problems (RCPSP) are at the heart of many production planning problems across a plethora of applications. Although the problem has been studied since the early 1960s, most developments and test instances are limited to problems with less than 300 jobs, far from the thousands present in real-life scenarios. Furthermore, the RCPSP with discounted cost (DC) is critical in many of these settings, which require decision makers to evaluate the net present value of the finished tasks, but the non-linear cost function makes the problem harder to solve or analyze. In this work, we propose a novel approximation algorithm for the RCPSP-DC. Our main contribution is that, through the use of geometrically increasing intervals, we can construct an approximation algorithm, keeping track of precedence constraints, usage of multiple resources, and time requirements. To our knowledge, this is the first approximation algorithm for this problem. Finally, through experimental analysis over real instances, we report the empirical performance of our approach, showing that our technique allows us to solve sizeable underground mining problems within reasonable time frames and gaps much smaller than the theoretically computed ones.

math.OC↗

arXiv2022

FEM modeling and simulation of broadband ultrasonic transducers with randomized inhomogeneous backing material

A FEM application for the accurate design of composite backing of ultrasonic transducers is presented. The idea is to obtain the dependence between the volume ratio of the tungsten powder in an epoxy matrix used as a backing and the final pulsed RF signal emitted by the backed transducer. An inhomogeneous material model for the backing was adopted instead of the classic complex geometrical FEM. The model was developed in Comsol 5.5 using two of its physics interfaces. The first based on classic FEM or continuous Galerkin for ultrasonic propagation in the backing and the second based on a discontinuous Galerkin option for fluid pulsed propagation. In this way it is possible to avoid the use of an impedance-based model. The calculations for the resulting bandwidth are good enough as predicted for Desilets for the 1D case by using the KLM circuital model. We worked in a 2D space, where the transducer face vibration is far away from the assumed piston-like considered by the unidimensional KLM model.

physics.comp-ph↗

arXiv2021

Mass-conservation increases robustness in stochastic reaction-diffusion models of cell crawling

The process of polarization determines the head and tail of single cells. A mechanism of this kind frequently precedes the subsequent cell locomotion and it determines the direction of motion. The process of polarization has frequently been described as a reaction-diffusion mechanism combined with a source of stochastic perturbations. We selected a particular model of amoeboid cell crawling for the motion of Dictyostelium discoideum and studied the interplay between pattern formation and locomotion. Next, we integrated the model in a two-dimensional domain considering the shape deformations of the cells in order to characterize the dynamics. We saw that the condition of pattern formation is finely tuned and we propose a modification based on the use of a mass-conservation constraint to substantially increase the robustness of the mathematical model.

physics.bio-ph↗

arXiv2021

From single to collective motion of social amoebae: a computational study of interacting cells

The coupling of the internal mechanisms of cell polarization to cell shape deformations and subsequent cell crawling poses many interdisciplinary scientific challenges. Several mathematical approaches have been proposed to model the coupling of both processes, where one of the most successful methods relies on a phase field that encodes the morphology of the cell, together with the integration of partial differential equations that account for the polarization mechanism inside the cell domain as defined by the phase field. This approach has been previously employed to model the motion of single cells of the social amoeba Dictyostelium discoideum, a widely used model organism to study actin-driven motility and chemotaxis of eukaryotic cells. Besides single cell motility, Dictyostelium discoideum is also well-known for its collective behavior. Here, we extend the previously introduced model for single cell motility to describe the collective motion of large populations of interacting amoebae by including repulsive interactions between the cells. We performed numerical simulations of this model, first characterizing the motion of single cells in terms of their polarity and velocity vectors. We then systematically studied the collisions between two cells that provided the basic interaction scenarios also observed in larger ensembles of interacting amoebae. Finally, the relevance of the cell density was analyzed, revealing a systematic decrease of the motility with density, associated with the formation of transient cell clusters that emerge in this system. This model is a prototypical active matter system for the investigation of the emergent collective dynamics of deformable, self-driven cells with a highly complex, nonlinear coupling of cell shape deformations, self-propulsion and repulsive cell-cell interactions.

q-bio.CB↗

arXiv2021

Exact reliability optimization for series-parallel graphs using convex envelopes

Given its wide spectrum of applications, the classical problem of all-terminal network reliability evaluation remains a highly relevant problem in network design. The associated optimization problem -- to find a network with the best possible reliability under multiple constraints -- presents an even more complex challenge, which has been addressed in the scientific literature but usually under strong assumptions over failures probabilities and/or the network topology. In this work, we propose a novel reliability optimization framework for network design with failures probabilities that are independent but not necessarily identical. We leverage the linear-time evaluation procedure for network reliability in the series-parallel graphs of Satyanarayana and Wood(1985) to formulate the reliability optimization problem as a mixed-integer nonlinear optimization problem. To solve this nonconvex problem, we use classical convex envelopes of bilinear functions, introduce custom cutting planes, and propose a new family of convex envelopes for expressions that appear in the evaluation of network reliability. Furthermore, we exploit the refinements produced by spatial branch-and-bound to locally strengthen our convex relaxations. Our experiments show that, using our framework, one can efficiently obtain optimal solutions in challenging instances of this problem.

math.OC↗

arXiv2021

Convex envelopes for ray-concave functions

Convexification based on convex envelopes is ubiquitous in the non-linear optimization literature. Thanks to considerable efforts of the optimization community for decades, we are able to compute the convex envelopes of a considerable number of functions that appear in practice, and thus obtain tight and tractable approximations to challenging problems. We contribute to this line of work by considering a family of functions that, to the best of our knowledge, has not been considered before in the literature. We call this family ray-concave functions. We show sufficient conditions that allow us to easily compute closed-form expressions for the convex envelope of ray-concave functions over arbitrary polytopes. With these tools, we are able to provide new perspectives to previously known convex envelopes and derive a previously unknown convex envelope for a function that arises in probability contexts.

math.OC↗

arXiv2020

Generalized Adaptive Partition-based Method for Two-Stage Stochastic Programs with Fixed Recourse

We present a method to solve two-stage stochastic problems with fixed recourse when the uncertainty space can have either discrete or continuous distributions. Given a partition of the uncertainty space, the method is addressed to solve a discrete problem with one scenario for each element of the partition (sub-regions of the uncertainty space). Fixing first stage variables, we formulate a second stage subproblem for each element, and exploiting information from the dual of these problems, we provide conditions that the partition must satisfy to obtain the optimal solution. These conditions provide guidance on how to refine the partition, converging iteratively to the optimal solution. Results from computational experiments show how the method automatically refines the partition of the uncertainty space in the regions of interest for the problem. Our algorithm is a generalization of the adaptive partition-based method presented by Song & Luedtke (2015) for discrete distributions, extending its applicability to more general cases.

math.OC↗

arXiv2017

A study of the Bienstock-Zuckerberg algorithm, Applications in Mining and Resource Constrained Project Scheduling

We study a Lagrangian decomposition algorithm recently proposed by Dan Bienstock and Mark Zuckerberg for solving the LP relaxation of a class of open pit mine project scheduling problems. In this study we show that the Bienstock-Zuckerberg (BZ) algorithm can be used to solve LP relaxations corresponding to a much broader class of scheduling problems, including the well-known Resource Constrained Project Scheduling Problem (RCPSP), and multi-modal variants of the RCPSP that consider batch processing of jobs. We present a new, intuitive proof of correctness for the BZ algorithm that works by casting the BZ algorithm as a column generation algorithm. This analysis allows us to draw parallels with the well-known Dantzig-Wolfe (DW) algorithm. We discuss practical computational techniques for speeding up the performance of the BZ and DW algorithms on project scheduling problems. Finally, we present computational experiments independently testing the effectiveness of the BZ and DW algorithms on different sets of publicly available test instances. Our computational experiments confirm that the BZ algorithm significantly outperforms the DW algorithm for the problems considered. Our computational experiments also show that the proposed speed-up techniques can have a significant impact on solution time. We provide some insights on what might be explaining this significant difference in performance.

math.OC↗

arXiv2016

A decomposition algorithm for computing income taxes with pass-through entities and its application to the Chilean case

Income tax systems with pass-through entities transfer a firm's incomes to the shareholders, which are taxed individually. In 2014, a Chilean tax reform introduced this type of entity and changed to an accrual basis that distributes incomes (but not losses) to shareholders. A crucial step for the Chilean taxation authority is to compute the final income of each individual, given the complex network of corporations and companies, usually including cycles between them. In this paper, we show the mathematical conceptualization and the solution to the problem, proving that there is only one way to distribute incomes to taxpayers. Using the theory of absorbing Markov chains, we define a mathematical model for computing the taxable incomes of each taxpayer, and we propose a decomposition algorithm for this problem. This allows us to compute the solution accurately and with the efficient use of computational resources. Finally, we present some characteristics of the Chilean taxpayers' network and computational results of the algorithm using this network.

q-fin.GN↗

arXiv2012

Blind Deconvolution of Ultrasonic Signals Using High-Order Spectral Analysis and Wavelets

Defect detection by ultrasonic method is limited by the pulse width. Resolution can be improved through a deconvolution process with a priori information of the pulse or by its estimation. In this paper a regularization of the Wiener filter using wavelet shrinkage is presented for the estimation of the reflectivity function. The final result shows an improved signal to noise ratio with better axial resolution.

cs.IT↗

arXiv2007

Minimum de Bruijn Sequence in a Language with Forbidden Substrings

Let be the following strategy to construct a walk in a labeled digraph: at each vertex, we follow the unvisited arc of minimum label. In this work we study for which languages, applying the previous strategy over the corresponding de Bruijn graph, we finish with an Eulerian cycle, in order to obtain the minimal de Bruijn sequence of the language.

math.CO↗

arXiv2005

Minimal Eulerian trail in a labeled digraph

Let $G$ be an Eulerian directed graph with an arc-labeling such that arcs going out from the same vertex have different labels. In this work, we present an algorithm to construct the Eulerian trail starting at an arbitrary vertex $v$ of minimum lexicographical label among labels of all Eulerian trails starting at this vertex. We also show an application of this algorithm to construct the minimal de Bruijn sequence of a language.

cs.DM↗