arXiv subjects

Gabriel González

Publications and source records attributed to Gabriel González.

10 recordsLinked to original sources

arXiv2026

Dimensional Decomposition and Column Generation for Bin Dimensioning in E-Commerce Fulfillment Centers

A fulfillment center (FC) is a specialized logistics facility where e-commerce inventory is received, stored, and processed. Its internal organization directly impacts space utilization and the performance of put-away and picking operations. Items are stored in bins following strict operational guidelines to ensure productivity in both activities, so bin dimensions must be tailored to the product profile of each facility to maximize space utilization. % We address the bin dimensioning problem arising in e-commerce fulfillment centers: given a set of candidate bin types and a large, heterogeneous inventory, determine the number of bins of each type and assign all items so as to minimize total bin volume, subject to operational constraints governing how products may be combined within a single bin. We develop a dimensional decomposition that exploits these constraints to reduce the three-dimensional packing problem to a one-dimensional block-positioning problem. Building on this decomposition, we formulate the problem as a mixed-integer linear program and propose two solution methods: a Best-Fit-Decreasing (BFD) heuristic and a column generation scheme that produces tight LP lower bounds. Computational experiments on four synthetic datasets, calibrated on proprietary data from an American e-commerce fintech and ranging from 1.5 thousand to 1.5 million SKUs, show that the BFD heuristic scales to instances with up to 1.7 million blocks, and that column generation certifies a BFD--LP gap of 2.26\% on the smallest dataset. The experiments further reveal a structural divide in solution quality across datasets, driven by the interaction between operational constraints and each facility's product profile.

math.OC↗

arXiv2026

Optimization of Kinetic--Stoichiometric Growth Bounds over Autocatalytic Subnetworks

Autocatalytic subnetworks govern sustained production and balanced growth in chemical reaction systems and can be naturally represented as directed multihypergraphs that jointly encode stoichiometric structure and reaction kinetics. Existing optimization approaches identify such subnetworks by maximizing their structural amplification, typically measured through the Maximum Amplification Factor (MAF). However, structural amplification alone does not determine growth potential, since highly amplifying subnetworks may be kinetically inefficient. Motivated by recent kinetic--stoichiometric bounds on balanced growth under scalable dynamics, we study the problem of selecting the autocatalytic subnetwork maximizing the growth bound $(α^*-1)\|\mathbb{S}|_{\mathcal A'}\|_κ$, where $α^*$ is the MAF and $\|\mathbb{S}|_{\mathcal A'}\|_κ$ is a kinetic consumption norm. We formulate the problem as a mixed-integer bilinear optimization model combining hypergraph selection with generalized fractional amplification constraints. Exploiting the discrete structure of the kinetic norm, we develop an exact parametric algorithm in which each subproblem reduces to MAF maximization and is solved through a Dinkelbach-type generalized fractional programming method. Finite convergence and global optimality are established. Applications to the Oregonator, the formose reaction, carbon-fixation cycles, and synthetic benchmark networks show when maximizing the kinetic--stoichiometric bound differs from maximizing the MAF alone, revealing the interplay between stoichiometric amplification, reaction kinetics, and balanced growth. The proposed framework provides an exact optimization methodology for identifying reaction subnetworks with the highest theoretical growth potential.

math.OC↗

arXiv2026

Optimal Embedding of Wiring Diagrams in Constrained Three-Dimensional Spaces

This paper investigates the \emph{Wiring Diagram Problem} (WDP), a three-dimensional layout design problem arising in industrial applications such as cable harness design and pipeline routing in constrained environments. In these settings, hierarchical tree-like systems composed of supply units, intermediate devices (e.g., valves or junctions), and terminal components must be spatially arranged and interconnected while satisfying stringent engineering requirements, including safety separation distances, obstacle avoidance, geometric feasibility, and constructibility constraints. We develop an optimization-based framework that formulates the WDP as a mixed-integer linear programming model capturing both topological and spatial design requirements within a unified formulation. To address the combinatorial and geometric complexity of three-dimensional routing, the feasible design space is discretized into structured network graphs that preserve engineering constraints while reducing dimensionality. The resulting model minimizes total cable or pipeline length while ensuring compliance with all technical specifications. Computational experiments on representative industrial instances demonstrate the robustness and practical applicability of the proposed approach for automated layout generation.

math.OC↗

arXiv2025

A Standardized Benchmark for Multilabel Antimicrobial Peptide Classification

Antimicrobial peptides have emerged as promising molecules to combat antimicrobial resistance. However, fragmented datasets, inconsistent annotations, and the lack of standardized benchmarks hinder computational approaches and slow down the discovery of new candidates. To address these challenges, we present the Expanded Standardized Collection for Antimicrobial Peptide Evaluation (ESCAPE), an experimental framework integrating over 80.000 peptides from 27 validated repositories. Our dataset separates antimicrobial peptides from negative sequences and incorporates their functional annotations into a biologically coherent multilabel hierarchy, capturing activities across antibacterial, antifungal, antiviral, and antiparasitic classes. Building on ESCAPE, we propose a transformer-based model that leverages sequence and structural information to predict multiple functional activities of peptides. Our method achieves up to a 2.56% relative average improvement in mean Average Precision over the second-best method adapted for this task, establishing a new state-of-the-art multilabel peptide classification. ESCAPE provides a comprehensive and reproducible evaluation framework to advance AI-driven antimicrobial peptide research.

cs.LG↗

arXiv2025

Identifying Self-Amplifying Hypergraph Structures through Mathematical Optimization

In this paper, we introduce the concept of self-amplifying structures for hypergraphs, positioning it as a key element for understanding propagation and internal reinforcement in complex systems. To quantify this phenomenon, we define the maximal amplification factor, a metric that captures how effectively a subhypergraph contributes to its own amplification. We then develop an optimization-based methodology to compute this measure. Building on this foundation, we tackle the problem of identifying the subhypergraph maximizing the amplification factor, formulating it as a mixed-integer nonlinear programming (MINLP) problem. To solve it efficiently, we propose an exact iterative algorithm with proven convergence guarantees. In addition, we report the results of extensive computational experiments on realistic synthetic instances, demonstrating both the relevance and effectiveness of the proposed approach. Finally, we present a case study on chemical reaction networks, including the Formose reaction and E. coli core metabolism, where our framework successfully identifies known and novel autocatalytic subnetworks, highlighting its practical relevance to systems chemistry and biology.

math.OC↗

arXiv2024

Fixed Topology Minimum-Length Trees with Neighborhoods

In this paper, we introduce the Fixed Topology Minimum-Length Tree with Neighborhood Problem, which aims to embed a rooted tree-shaped graph into a $d$-dimensional metric space while minimizing its total length provided that the nodes must be embedded to some restricted areas. This problem has significant applications in efficiently routing cables or pipelines in engineering designs. We propose novel mathematical optimization-based approaches to solve different versions of the problem based on the domain for the embedding. In cases where the embedding maps to a continuous space, we provide several Mixed Integer Nonlinear Optimization formulations. If the embedding is to a network, we derive a mixed integer linear programming formulation as well as a dimensionality reduction methodology that allows for solving larger problems in less CPU time. A data-driven methodology is also proposed to construct a proper network based on the instance of the problem. We report the results of a battery of computational experiments that validate our proposal.

math.OC↗

arXiv2022

Comment on "Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficientes"

Z.E. Musielak has reported in 2008 J. Phys. A: Math. Theor. {\bf 41} 055205 methods to obtain standard and non-standard Lagrangians and identify classes of equations of motion that admit a Lagrangian description. In this comment we show how to obtain new non-standard Lagrangians using the non-standard Lagrangians previously found. In particular, it is demonstrated that for every non-standard Lagrangian one can generate a new non-standard Lagrangian associated to a new equation of motion.

physics.class-ph↗

arXiv2021

Network Flow based approaches for the Pipelines Routing Problem in Naval Design

In this paper we propose a general methodology for the optimal automatic routing of spatial pipelines motivated by a recent collaboration with Ghenova, a leading Naval Engineering company. We provide a minimum cost multicommodity network flow based model for the problem incorporating all the technical requirements for a feasible pipeline routing. A branch-and-cut approach is designed and different matheuristic algorithms are derived for solving efficiently the problem. We report the results of a battery of computational experiments to assess the problem performance as well as a case study of a real-world naval instance provided by our partner company.

math.OC↗

arXiv2019

Topography effect on the seismogenic deformation of the earth's surface

A comparison of the displacements of the earth's surface after an earthquake was made, calculating with the analytical expressions coming from an infinite flat slab approximation and compared with these numerically considering the topography of the Earth. One conclusion of this work is that the flat Earth approximation, has a greater error in the lateral displacement than in the vertical one. It can also be noted that the error in the magnitude of the displacement is less or of the order of ten percent of the maximum displacement of the earth's surface.

physics.geo-ph↗

arXiv2009

Optical $Λ$ transitions and quantum computing in the $^{15}$N-V$^{-}$ Center in Diamond

We present a thorough derivation of the excited state energy levels of the negatively charged $^{15}$N-V$^{-}$ center in diamond for the strong applied electric field case. We show that in the $^{15}$N-V$^{-}$ center a spin non-conserving two-photon $Λ$ transition exists that is mediated by the hyperfine interaction, which provides the possibility to write quantum information. Using second order perturbation theory we obtain a $Λ$ transition rate of the order of 10 MHz at room temperature, which allows for approximately $10^4$ quantum logic operations within the spin coherence time $τ_d(T=300 K)\approx 1m$s of the $^{15}$N-V$^{-}$ center.

cond-mat.mes-hall↗