Papers by Diego Delle Donne
XI Simposio Argentino de Investigación Operativa (SIO) - JAIIO 42 (2013), 2013
We study a delivery strategy for last-mile deliveries in urban areas which combines freight trans... more We study a delivery strategy for last-mile deliveries in urban areas which combines freight transportation with mass mobility systems with the goal of creating synergies contrasting negative externalities caused by transportation. The idea is to use the residual capacity on public transport means for moving freights within the city. In particular, the system is such that parcels are first transported from origins (central distribution centers) to drop-in stations, which are stop locations on public vehicles itineraries. Then, they are transported through public vehicles to drop-out stations, from where they are delivered to destination by freighters using green vehicles (such as bikes, drones, porters, etc.). The system is known as Freight-On-Transit (FOT). In this paper, we focus on the strategic decisions related to defining the public transportation network that will take part to the delivery system, i.e., which public vehicle lines and stop locations will be included (and thus equipped for the service). We propose different formulations for the problem and effective heuristic solution approaches based on column generation. We perform exhaustive tests aimed at providing managerial insights on the performance and the efficiency of the system.
Electronic Notes in Discrete Mathematics, 2017
Abstract We propose a generalization of the k-coloring problem, namely the minimum chromatic viol... more Abstract We propose a generalization of the k-coloring problem, namely the minimum chromatic violation problem (MCVP). Given a graph G = ( V , E ) , a set of weak edges F ⊂ E and a set of colors C , the MCVP asks for a | C | -coloring of the graph G ′ = ( V , E \ F ) minimizing the number of weak edges with both endpoints receiving the same color. We present an integer programming formulation for this problem and provide an initial polyhedral study of the polytopes arising from this formulation. We give partial characterizations of facet-inducing inequalities and we show how facets from weaker and stronger instances of MCVP (i.e., more/less weak edges) are related. We then introduce a general lifting procedure which generates (sometimes facet-inducing) valid inequalities from generic valid inequalities and we present several facet-inducing families arising from this procedure. Finally, we present another family of facet-inducing inequalities which is not obtained from the prior lifting procedure.
Combinatorial Optimization and Applications, 2018
Dados dos grafos G = (V,EG) y H = (V,EH) definidos sobre el mismo conjunto de vértices y dado un ... more Dados dos grafos G = (V,EG) y H = (V,EH) definidos sobre el mismo conjunto de vértices y dado un conjunto de colores C, el impacto sobre H de un coloreo c : V → C de G, denotado imp(c), es el número de aristas ij ∈ EH tales que c(i) = c(j). En este contexto, el problema de coloreo de máximo impacto consiste en encontrar un coloreo de G que maximice el impacto imp(c) sobre H. Este problema aparece en forma natural en el contexto de asignación de aulas a cursos, situación en la cual es deseable asignar clases del mismo curso a una misma aula. El problema de coloreo de máximo impacto es NP-hard incluso cuando G es un grafo de intervalos (condición habitual en este contexto) y H es la unión de cliques disjuntas y, por este motivo, presentamos en este trabajo un enfoque basado en programación lineal entera para este problema. Continuamos en este trabajo el estudio de una formulación natural del problema de coloreo de máximo impacto por medio de programación lineal entera. Presentamos var...
1 Instituto de Ciencias, Universidad Nacional de General Sarmiento, Argentina 2 Departamento de C... more 1 Instituto de Ciencias, Universidad Nacional de General Sarmiento, Argentina 2 Departamento de Computación, FCEyN, Universidad de Buenos Aires, Argentina 3 Universidad Católica Argentina, Argentina 4 Instituto de Cálculo, FCEyN, Universidad de Buenos Aires, Argentina 5 Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Argentina 6 Departamento de Ingenieŕıa Industrial, FCFM, Universidad de Chile, Chile 7 Instituto de Industria, Universidad Nacional de General Sarmiento, Argentina
ArXiv, 2020
The Sparse Approximation problem asks to find a solution $x$ such that $||y - Hx|| < \alpha$, ... more The Sparse Approximation problem asks to find a solution $x$ such that $||y - Hx|| < \alpha$, for a given norm $||\cdot||$, minimizing the size of the support $||x||_0 := \#\{j \ |\ x_j \neq 0 \}$. We present valid inequalities for Mixed Integer Programming (MIP) formulations for this problem and we show that these families are sufficient to describe the set of feasible supports. This leads to a reformulation of the problem as an Integer Programming (IP) model which in turn represents a Minimum Set Covering formulation, thus yielding many families of valid inequalities which may be used to strengthen the models up. We propose algorithms to solve sparse approximation problems including a branch \& cut for the MIP, a two-stages algorithm to tackle the set covering IP and a heuristic approach based on Local Branching type constraints. These methods are compared in a computational experimentation with the goal of testing their practical potential.
In this work, we study the orientation model for vertex coloring problems with the aim of finding... more In this work, we study the orientation model for vertex coloring problems with the aim of finding partial descriptions of the associated polytopes. We present new families of valid inequalities, most of them supported by paths of the input graph. We develop facet-generating procedures for the associated polytopes, which we denominate path-lifting procedures. Given a path between two vertices and any two valid inequalities, the path-lifting procedure generates an infinite family of valid inequalities. We study conditions ensuring that the obtained inequalities define facets. Finally, we present a large family of valid inequalities, which is obtained by iteratively applying the path-lifting procedure. We conjecture that this family may be sufficient to completely describe the associated polytope when G is a path.
La industria salmonera es uno de los principales sectores de exportación de Chile. En la etapa de... more La industria salmonera es uno de los principales sectores de exportación de Chile. En la etapa de engorda en agua salada, los peces son cultivados en grandes jaulas flotantes agrupadas en centros de cultivo a lo largo de toda la Décima Región del sur de Chile. Al momento de la cosecha, cuando alcanzan un peso y volumen de venta, los peces deben ser transportados en barcos hasta los denominados centros de acopio, ubicados cerca de las plantas de faenado. Llegados al centro de acopio los peces son depositados en grandes jaulas en espera a ser enviados a las plantas de faenado. En estas plantas se realiza la faena y limpieza de los peces que luego son enviados hacia las plantas de proceso mediante transporte terrestre. Uno de los principales desaf́ıos de las empresas salmoneras con este tipo de cadena de proceso es la planificación global de la loǵıstica maŕıtima y terrestre, combinada con la planificación del stock en las jaulas en los centros de acopio y las ĺıneas de producción en l...
El programa “Exactas va a la escuela” (EVE) de la Facultad de Ciencias Exactas y Naturales (FCEyN... more El programa “Exactas va a la escuela” (EVE) de la Facultad de Ciencias Exactas y Naturales (FCEyN) de la Universidad de Buenos Aires ofrece a las escuelas secundarias de la provincia un conjunto de charlas dictadas por oradores de la universidad. Este programa es llevado a cabo por el Equipo de Popularización de la Ciencia, de la FCEyN. Al inicio del año lectivo, cada escuela postula sus preferencias por algunas de las charlas disponibles y el objetivo del programa EVE es asignar al menos una charla a cada escuela en algún momento del año. Cada orador ofrece su actividad durante un peŕıodo limitado dentro del año y en d́ıas y horarios predefinidos, y cada escuela impone también restricciones similares de disponibilidad. Los oradores pueden a su vez imponer restricciones geográficas para los lugares a los que pueden asistir para dictar su charla. Finalmente, cada orador puede definir una frecuencia máxima para el dictado de su charla. Es decir, un orador puede dar su charla más de un...
ArXiv, 2015
Despite the fact that some vertex coloring problems are polynomially solvable on certain graph cl... more Despite the fact that some vertex coloring problems are polynomially solvable on certain graph classes, most of these problems are not "under control" from a polyhedral point of view. The equivalence between \emph{optimization} and \emph{polyhedral separation} suggests that, for these problems, there must exist formulations admitting some elegant characterization for the polytopes associated to them. Therefore, it is interesting to study known formulations for vertex coloring with the goal of finding such characterizations. In this work we study the asymmetric representatives formulation and we show that the corresponding coloring polytope, for a given graph $G$, can be interpreted as the stable set polytope of another graph obtained from $G$. This result allows us to derive complete characterizations for the corresponding coloring polytope for some families of graphs, based on known complete characterizations for the stable set polytope.
Discrete Applied Mathematics, 2021
Waste Management & Research, 2020
A solution strategy based on integer linear programming models has been developed for leaf sweepi... more A solution strategy based on integer linear programming models has been developed for leaf sweeping operations in the Argentine city of Trenque Lauquen. The aim is to achieve efficiency in the assignment of sweepers to city blocks, the identification of leaf bag deposit points and the routes to be followed by collection trucks for leaf bag pickup. Previous to this strategy, sweeper assignments were improvised and inefficient, with blocks often left unswept. Furthermore, no method was available for accurately determining the number of sweepers needed to ensure either full coverage of all city zones within the working day or a balanced work load distribution across all sweepers. Application of the solution strategy by the city has resulted in efficient definitions of sweeper requirements while optimizing sweeper assignments such that all blocks are covered. Once the strategy is fully implemented, the number of bag deposit points under the manual definitions should be reduced by roughl...
Discrete Optimization, 2019
A set of points $X = X_B \cup X_R \subseteq \mathbb{R}^d$ is linearly separable if the convex hul... more A set of points $X = X_B \cup X_R \subseteq \mathbb{R}^d$ is linearly separable if the convex hulls of $X_B$ and $X_R$ are disjoint, hence there exists a hyperplane separating $X_B$ from $X_R$. Such a hyperplane provides a method for classifying new points, according to which side of the hyperplane the new points lie. When such a linear separation is not possible, it may still be possible to partition $X_B$ and $X_R$ into prespecified numbers of groups, in such a way that every group from $X_B$ is linearly separable from every group from $X_R$. We may also discard some points as outliers, and seek to minimize the number of outliers necessary to find such a partition. Based on these ideas, Bertsimas and Shioda proposed the classification and regression by integer optimization (CRIO) method in 2007. In this work we explore the integer programming aspects of the classification part of CRIO, in particular theoretical properties of the associated formulation. We are able to find facet-inducing inequalities coming from the stable set polytope, hence showing that this classification problem has exploitable combinatorial properties.
Discrete Applied Mathematics, 2017
Discrete Optimization, 2016
Despite the fact that many vertex coloring problems are polynomially solvable on certain graph cl... more Despite the fact that many vertex coloring problems are polynomially solvable on certain graph classes, most of these problems are not "under control" from a polyhedral point of view. The equivalence between optimization and separation suggests the existence of integer programming formulations for these problems whose associated polytopes admit elegant characterizations. In this work we address this issue. As a starting point, we focus our attention on the well-known standard formulation for the classical vertex coloring problem. We present some general results about this formulation and we give complete characterizations of the associated polytopes for trees and block graphs. Also, we show that the vertex coloring polytope associated to this formulation for a graph G and a set of colors C corresponds to a face of the stable set polytope of a particular graph S C G and, based on this fact, we derive a new family of valid inequalities generalizing several known families from the literature. We conjecture that this new family of valid inequalities is sufficient to completely describe the vertex coloring polytope associated to cacti graphs. Finally, we study the perfectness of S C G , in particular, we give a characterization of the graphs G for which S C G is perfect and we show that those graphs are exactly block graphs, when |C| > 2.
International Transactions in Operational Research, 2016
Given two graphs G = (V, EG) and H = (V, EH ) over the same set of vertices and given a set of co... more Given two graphs G = (V, EG) and H = (V, EH ) over the same set of vertices and given a set of colors C, the “impact on H” of a coloring c : V → C of G, denoted I(c), is the number of edges i j ∈ EH such that c(i) = c( j). In this setting, the “maximum-impact coloring” problem asks for a proper coloring of G maximizing the impact I(c) on H . This problem naturally arises in the assignment of classrooms to courses, where it is desirable—but not mandatory—to assign lectures from the same course to the same classroom. Since the maximum-impact coloring problem is NP-hard, we propose in this work an integer programming based approach for tackling this problem. To this end, we present an integer programming formulation and study the associated polytope. We provide several families of valid inequalities, and we study under which conditions these inequalities define facets of the associated polytope. Finally, we show computational evidence over real-life instances suggesting that some of these families may be useful in a cutting-plane environment.
Electronic Notes in Discrete Mathematics, 2015
ABSTRACT In a previous work we have presented a procedure for generating rank and non-rank valid ... more ABSTRACT In a previous work we have presented a procedure for generating rank and non-rank valid inequalities for the stable set polytope based on clique projection and lifting operations. In this work we propose to apply another lifting operation and give some sufficient conditions for this new procedure to generate facet defining inequalities. Computational experience shows that the proposed approach allows to obtain tighter upper bounds for the maximum stable set problem. 1 This work has been artially supported by the STIC/AmSud joint program by CAPES (Brazil), CNRS and MAE (France), CONICYT (Chile) and MINCyT (Argentina) and the Pronem program by FUNCAP/CNPq (Brazil).
Journal of the Operational Research Society, 2012
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Papers by Diego Delle Donne