Stabilized Benders methods for large-scale combinatorial optimization, with appllication to data privacy

The Cell Suppression Problem (CSP) is a challenging Mixed-Integer Linear Problem arising in statistical tabular data protection. Medium sized instances of CSP involve thousands of binary variables and million of continuous variables and constraints. However, CSP has the typical structure that allows application of the renowned Benders’ decomposition method: once the “complicating” binary variables are fixed, the problem decomposes into a large set of linear subproblems on the “easy” continuous ones. This allows to project away the easy variables, reducing to a master problem in the complicating ones where the value functions of the subproblems are approximated with the standard cutting-plane approach. Hence, Benders’ decomposition suffers from the same drawbacks of the cutting-plane method, i.e., oscillation and slow convergence, compounded with the fact that the master problem is combinatorial. To overcome this drawback we present a stabilized Benders decomposition whose master is restricted to a neighborhood of successful candidates by local branching constraints, which are dynamically adjusted, and even dropped, during the iterations. Our experiments with randomly generated and real-world CSP instances with up to 3600 binary variables, 90M continuous variables and 15M inequality constraints show that our approach is competitive with both the current state-of-the-art (cutting-plane-based) code for cell suppression, and the Benders implementation in CPLEX 12.7. In some instances, stabilized Benders is able to quickly provide a very good solution in less than one minute, while the other approaches were not able to find any feasible solution in one hour.Peer ReviewedPreprin

A fix-and-relax heuristic for controlled tabular adjustment

Controlled tabular adjustment (CTA) is an emerging protect ion technique for tabular data pro- tection. CTA formulates a mixed integer linear programming problem, which is tough for tables of moderate size. Finding a feasible initial solution may ev en be a challenging task for large instances. On the other hand, end users of tabular data prote ction techniques give priority to fast executions and are thus satisfied in practice with suboptima l solutions. In this work the fix-and- relax strategy is applied to large CTA instances. Fix-and-r elax is based on partitioning the set of binary variables into clusters to selectively explore a sma ller branch-and-cut tree. We report ex- tensive computational results on a set of real and random CTA instances. Fix-and-relax is shown to be competitive compared to plain CPLEX branch-and-cut in terms of quickly finding either a feasible solution or a good upper bound in di ffi cult instances.Preprin

Diseño de un modelo de scoring para el otorgamiento de crédito de consumo en una compañía de financiamiento colombiana

Los scoring de crédito son herramientas estadísticas usadas desde los años setenta para asignar una probabilidad de incumplimiento al solicitante de un crédito, al realizar una ponderación de sus variables cualitativas y cuantitativas y, a su vez, con inclusión de las condiciones del crédito solicitado -- El uso de scoring se ha potenciado desde los años noventa con el fin de mitigar el riesgo de crédito de las solicitudes y buscar los clientes que se ajusten al perfil deseado por la entidad, con el fin de dar cumplimiento a lo establecido por el ente regulador en cuanto a la implementación de un sistema de riesgo que disminuya las posibles pérdidas económicas por medio del cuidado de cada uno de las etapas que comprenden el ciclo de crédito, en este caso, de manera específica, el otorgamiento -- El objetivo de este trabajo es diseñar un modelo de scoring basado en la metodología de regresión logística para una entidad financiera del valle de Aburrá, vigilada por la Superintendencia Financiera de Colombia, con base en la información entregada por dicha entidad, que comprende variables cualitativas y cuantitativas de un grupo de clientes en un período establecido -- Para alcanzar el objetivo se llevó a cabo la modelación de una base de datos suministrada por la entidad financiera mencionada en el programa estadístico R, de lo que se obtuvo el diseño de un modelo de scoring de 23 variables cualitativas y cuantitativas capaz de predecir la probabilidad de incumplimiento del deudorCredit scorings are tools used since the 1970s to grant a probability of default to the applicant of a credit, to weigh their qualitative and quantitative variables; and in turn, including the conditions of the requested credit -- The use of scoring has been boosted since the 1990s, in order to mitigate the credit risk of the requests and to find the clients that fit the profile desired by the entity, complying with what was established by the regulator regarding the implementation of a risk system that reduces economic losses taking care of each stage of the credit cycle, in this case specifically, the granting -- Therefore, the objective of this work is to design a scoring model based on the methodology of logistic regression for a financial institution of the valle de Aburrá, supervised by the Superintendencia Financiera de Colombia, based on information provided by the entity, which comprises qualitative and quantitative variables of a group of clients in a set period of tim

The Chebyshev center as an alternative to the analytic center in the feasibility pump

© The Author(s) 2023As a heuristic for obtaining feasible points of mixed integer linear problems, the feasibility pump (FP) generates two sequences of points: one of feasible solutions for the relaxed linear problem; and another of integer points obtained by rounding the linear solutions. In a previous work, the present authors proposed a variant of FP, named analytic center FP, which obtains integer solutions by rounding points in the segment between the linear solution and the analytic center of the polyhedron of the relaxed problem. This work introduces a new FP variant that replaces the analytic center with the Chebyshev center. Two of the benefts of using the Chebyshev center are: (i) it requires the solution of a linear optimization problem (unlike the analytic center, which involves a convex nonlinear optimization problem for its exact solution); and (ii) it is invariant to redundant constraints (unlike the analytic center, which may not be well centered within the polyhedron for problems with highly rank-defcient matrices). The computational results obtained with a set of more than 200 MIPLIB2003 and MIPLIB2010 instances show that the Chebyshev center FP is competitive and can serve as an alternative to other FP variants.This research has been supported by the MCIN/AEI/FEDER project RTI2018-097580-B-I00. Funding Open Access funding provided thanks to the CRUE-CSIC agreement with Springer NaturePeer ReviewedPostprint (published version

Using the analytic center in the feasibility pump

The feasibility pump (FP) [5, 7] has proved to be a successful heuristic for finding feasible solutions if mixed integer linear problems (MILPs). FP was improved in [1] for finding better quality solutions. Briefly, FP alternates between two sequences of points: one of feasible solutions for the relaxed problem (but not integer), and another of integer points (but not feasible for the relaxed problem). Hopefully, the procedure may eventually converge to a feasible and integer solution. Integer points are obtained from the feasible ones by some rounding procedure. This short paper extends FP, such that the integer point is obtained by rounding a point on the (feasible) segment between the computed feasible point and the analytic center for the relaxed linear problem. Since points in the segment are closer (may be even interior) to the convex hull of integer solutions, it may be expected that the rounded point has more chances to become feasible, thus reducing the number of FP iterations. When the selected point to be rounded is the feasible solution of the relaxation (i.e., one of the two end points of the segment), this analytic center FP variant behaves as the standard FP. Computational results show that this variant may be efficient in some MILP instances.Preprin

On using an improved Benders method for cell suppression

The cell suppression problem (CSP) is one of the most widely applied methods for tabular data protection. Given a set of primary cells to be protected, CSP aims at finding a set of secondary cells to be additionally removed to guarantee that estimates of values of primary cells fall out of a predefined protection interval. From a computational point of view, CSP is very challenging even for tables of moderate size and number of primary cells. Currently, the only effective optimal approach for CSP is Benders decomposition (also known as cutting planes). However, the convergence to the optimal solution is often too slow due to well known instability issues of Benders decomposition. This work discusses a recently developed improved Benders method, which focus on finding new solutions in the neighborhood of ”good” points. Some results are reported in the solution of realistic and real-world CSP instances, showing the effectiveness of this approachPeer ReviewedPostprint (author's final draft

Moderate-to-vigorous physical activity levels in physical education, school recess and after-school time. Influence of gender, age, and weight status

Background: Primary and secondary school ages have been considered key moments to address the decrease of moderate-tovigorous physical activity (MVPA). Individual (eg, age, gender, and weight status) and contextual factors (moments of the day) need to be considered for a better explanation of the phenomenon. The quantity and quality of physical activity in Physical Education (PE), school recess (SR), and after school (AS) time need to be taken into account to solve the low levels of MVPA in youth. Methods: A sample of adolescents (N = 231, 14.6 ± 1.2 years old) was studied using accelerometry to determine the objective MVPA level in PE, SR, and AS. Results: Results indicated statistically significant differences on MVPA between contexts (AS > PE > SR, P younger in PE and younger > older in SR time; P girls in all contexts, P nonoverweight in AS, P < .01). Conclusions: Because students did not meet the daily MVPA recommendations, some strategies have been provided in each of the contexts analyzed

Motivación hacia la Educación Física y su relación con la condición física saludable en escolares de Educación Secundaria Obligatoria

Introducción: el aumento de la motivación hacia la Educación Física podría resultar un elemento esencial para propiciar un incremento en la condición física saludable de los escolares. La ausencia de estudios en población española hace necesario el desarrollo de esta línea de investigación. Objetivos: el objetivo del presente estudio fue examinar la asociación entre la motivación hacia la Educación Física y los niveles de condición física saludable en adolescentes de Educación Secundaria Obligatoria. Métodos: un total de 294 escolares (167 varones y 127 mujeres), de 13 a 16 años de edad cumplimentaron la versión española de la Escala de Locus Percibido de Causalidad en Educación Física y realizaron las pruebas de condición física saludable de la Batería ALPHA-Fitness de Alta Prioridad. Resultados: los resultados del estudio mostraron una asociación positiva entre tener una alta motivación hacia la Educación Física y presentar una mayor capacidad cardiorrespiratoria, tanto en niños como en niñas (p < 0,05). En cambio, no se encontró una asociación entre la motivación hacia la Educación Física y el sobrepeso o fuerza muscular. Conclusiones: existe una asociación positiva entre la motivación hacia la Educación Física y la capacidad cardiorrespiratoria. Por tanto, con el objetivo de que los alumnos presenten una capacidad cardiorrespiratoria saludable, los profesores de Educación Física deberían promover la motivación hacia la Educación Física

Disseny, creació i avaluació de material didàctic de pneumàtica i hidràulica a quart d’ESO, i la seva gestió a través d’una intranet.

català: El present TFM tracta de la creació, aportació, gestió (mitjançant un Entorn Virtual d’Aprenentatge, concretament el Moodle) i avaluació de recursos didàctics per a la unitat de pneumàtica i hidràulica al curs de 4t d’ESO. Com que s’ha pogut comprovar a la realitat el desenvolupament d’aquests, s’han pogut treure unes conclusions, algunes verídiques i altres que s’han de considerar des del punt de vista que s’han utilitzat els recursos en període de pràctiques. S’ha utilitzat el moodle com a plataforma per a la gestió, perquè els alumnes que hi ha en l’actualitat hi estan avesat i més encara al quart curs d’ESO, no deixant de banda les aventatges que suposa, poder-hi vincular recursos tic en línia per exemple que, sovint, ajuden molt a la incorporació de nous coneixements i amb una major rapidesa gràcies, sobretot, al món àudiovisual. Pel que fa a l’avaluació s’ha incorporat força aspectes del màster, pel que fa a la creació de rúbriques per a la correcció i avaluació d’activitats. Per últim, s’ha aportat material cercat a la xarxa que s’ha cregut molt dinàmic i amè a l’hora de facilitar l’aprenentatge, així com també dissenyar unes activitats i una pràctica molt contextualitzades i demostracions que acompanyaven les explicacions, basades en la participació de l’alumnat