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Alvarez-Miranda, E., & Pereira, J. (2022). A Districting Application with a Quality of Service Objective. Mathematics, 10(1), 13.
Abstract: E-commerce sales have led to a considerable increase in the demand for last-mile delivery companies, revealing several problems in their logistics processes. Among these problems, are not meeting delivery deadlines. For example, in Chile, the national consumer service (SERNAC) indicated that in 2018, late deliveries represented 23% of complaints in retail online sales and were the second most common reason for complaints. Some of the causes are incorrectly designed delivery zones because in many cases, these delivery zones do not account for the demographic growth of cities. The result is an imbalanced workload between different zones, which leads to some resources being idle while others fail to meet their workload in satisfactory conditions. The present work proposes a hybrid method for designing delivery zones with an objective based on improving the quality of express delivery services. The proposed method combines a preprocess based on the grouping of demand in areas according to the structure of the territory, a heuristic that generates multiple candidates for the distribution zones, and a mathematical model that combines the different distribution zones generated to obtain a final territorial design. To verify the applicability of the proposed method, a case study is considered based on the real situation of a Chilean courier company with low service fulfillment in its express deliveries. The results obtained from the computational experiments show the applicability of the method, highlighting the validity of the aggregation procedure and improvements in the results obtained using the hybrid method compared to the initial heuristic. The final solution improves the ability to meet the conditions associated with express deliveries, compared with the current situation, by 12 percentage points. The results also allow an indicative sample of the critical service factors of a company to be obtained, identifying the effects of possible changes in demand or service conditions
Keywords: districtin; glast-mile delivery; hybrid heuristics
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Alvarez-Miranda, E., Campos-Valdes, C., Quiroga, M. M., Moreno-Faguett, M., & Pereira, J. (2020). A Multi-Criteria Pen for Drawing Fair Districts: When Democratic and Demographic Fairness Matter. Mathematics, 8(9), 27 pp.
Abstract: Electoral systems are modified by individuals who have incentives to bias the rules for their political advantage (i.e., gerrymandering). To prevent gerrymandering, legislative institutions can rely on mathematical tools to guarantee democratic fairness and territorial contiguity. These tools have been successfully used in the past; however, there is a need to accommodate additional meanings of the term fairness within the electoral systems of modern democracies. In this paper, we present an optimization framework that considers multiple criteria for drawing districts and assigning the number of representatives. Besides some typical districting criteria (malapportionment and contiguity), we introduce novel criteria for ensuring territorial equilibrium and incentives for candidates to deploy their representation efforts fairly during their campaign and period in office. We test the method, which we denote as Multi-criteria Pen, in a recent and a forthcoming reform of the Chilean electoral system. The results show the potential of our tool to improve the current territorial design and offers insights on the motivations, objectives, and deficiencies of both reform plans.
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Alvarez-Miranda, E., Pereira, J., Torrez-Meruvia H., & Vila, M. (2021). A Hybrid Genetic Algorithm for the Simple Assembly Line Balancing Problem with a Fixed Number of Workstations. Mathematics, 9(17), 2157.
Abstract: The assembly line balancing problem is a classical optimisation problem whose objective is to assign each production task to one of the stations on the assembly line so that the total efficiency of the line is maximized. This study proposes a novel hybrid method to solve the simple version of the problem in which the number of stations is fixed, a problem known as SALBP-2. The hybrid differs from previous approaches by encoding individuals of a genetic algorithm as instances of a modified problem that contains only a subset of the solutions to the original formulation. These individuals are decoded to feasible solutions of the original problem during fitness evaluation in which the resolution of the modified problem is conducted using a dynamic programming based approach that uses new bounds to reduce its state space. Computational experiments show the efficiency of the method as it is able to obtain several new best-known solutions for some of the benchmark instances used in the literature for comparison purposes.
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Campos-Valdes, C., Alvarez-Miranda, E., Quiroga, M. M., Pereira, J., & Duran, F. L. (2021). The Impact of Candidates' Profile and Campaign Decisions in Electoral Results: A Data Analytics Approach. Mathematics, 9(8), 902.
Abstract: In recent years, a wide range of techniques has been developed to predict electoral results and to measure the influence of different factors in these results. In this paper, we analyze the influence of the political profile of candidates (characterized by personal and political features) and their campaign effort (characterized by electoral expenditure and by territorial deployment strategies retrieved from social networks activity) on the electoral results. This analysis is carried out by using three of the most frequent data analyitcs algorithms in the literature. For our analysis, we consider the 2017 Parliamentary elections in Chile, which are the first elections after a major reform of the electoral system, that encompassed a transition from a binomial to a proportional system, a modification of the districts' structure, an increase in the number of seats, and the requirement of gender parity in the lists of the different coalitions. The obtained results reveal that, regardless of the political coalition, the electoral experience of candidates, in particular in the same seat they are running for (even when the corresponding district is modified), is by large the most influential factor to explain the electoral results. However, the attained results show that the influence of other features, such as campaign expenditures, depends on the political coalition. Additionally, by means of a simulation procedure, we show how different levels of territorial deployment efforts might impact on the results of candidates. This procedure could be used by parties and coalitions when planning their campaign strategies.
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Concha-Vega, P., Goles, E., Montealegre, P., & Rios-Wilson, M. (2022). On the Complexity of Stable and Biased Majority. Mathematics, 10(18), 3408.
Abstract: A majority automata is a two-state cellular automata, where each cell updates its state according to the most represented state in its neighborhood. A question that naturally arises in the study of these dynamical systems asks whether there exists an efficient algorithm that can be implemented in order to compute the state configuration reached by the system at a given time-step. This problem is called the prediction problem. In this work, we study the prediction problem for a more general setting in which the local functions can be different according to their behavior in tie cases. We define two types of local rules: the stable majority and biased majority. The first one remains invariant in tie cases, and the second one takes the value 1. We call this class the heterogeneous majority cellular automata (HMCA). For this latter class, we show that in one dimension, the prediction problem for HMCA is in NL as a consequence of the dynamics exhibiting a type of bounded change property, while in two or more dimensions, the problem is P-Complete as a consequence of the capability of the system of simulating Boolean circuits.
Keywords: cellular automata; majority rule; prediction problem
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de la Cruz, R., Meza, C., Narria, N., & Fuentes, C. (2022). A Bayesian Change Point Analysis of the USD/CLP Series in Chile from 2018 to 2020: Understanding the Impact of Social Protests and the COVID-19 Pandemic. Mathematics, 10(18), 3380.
Abstract: Exchange rates are determined by factors such as interest rates, political stability, confidence, the current account on balance of payments, government intervention, economic growth and relative inflation rates, among other variables. In October 2019, an increased climate of citizen discontent with current social policies resulted in a series of massive protests that ignited important political changes in Chile. This event along with the global COVID-19 pandemic were two major factors that affected the value of the US dollar and produced sudden changes in the typically stable USD/CLP (Chilean Peso) exchange rate. In this paper, we use a Bayesian approach to detect and locate change points in the currency exchange rate process in order to identify and relate these points with the important dates related to the events described above. The implemented method can successfully detect the onset of the social protests, the beginning of the COVID-19 pandemic in Chile and the economic reactivation in the US and Europe. In addition, we evaluate the performance of the proposed MCMC algorithms using a simulation study implemented in Python and R.
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de la Cruz, R., Padilla, O., Valle, M. A., & Ruz, G. A. (2021). Modeling Recidivism through Bayesian Regression Models and Deep Neural Networks. Mathematics, 9(6), 639.
Abstract: This study aims to analyze and explore criminal recidivism with different modeling strategies: one based on an explanation of the phenomenon and another based on a prediction task. We compared three common statistical approaches for modeling recidivism: the logistic regression model, the Cox regression model, and the cure rate model. The parameters of these models were estimated from a Bayesian point of view. Additionally, for prediction purposes, we compared the Cox proportional model, a random survival forest, and a deep neural network. To conduct this study, we used a real dataset that corresponds to a cohort of individuals which consisted of men convicted of sexual crimes against women in 1973 in England and Wales. The results show that the logistic regression model tends to give more precise estimations of the probabilities of recidivism both globally and with the subgroups considered, but at the expense of running a model for each moment of the time that is of interest. The cure rate model with a relatively simple distribution, such as Weibull, provides acceptable estimations, and these tend to be better with longer follow-up periods. The Cox regression model can provide the most biased estimations with certain subgroups. The prediction results show the deep neural network's superiority compared to the Cox proportional model and the random survival forest.
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Escobar, C., Vargas, F. J., Peters, A. A., & Carvajal, G. (2023). A Cooperative Control Algorithm for Line and Predecessor Following Platoons Subject to Unreliable Distance Measurements. Mathematics, 11(4), 801.
Abstract: This paper uses a line-following approach to study the longitudinal and lateral problems in vehicle platooning. Under this setup, we assume that inter-vehicle distance sensing is unreliable and propose a cooperative control strategy to render the platoon less vulnerable to these sensing difficulties. The proposed control scheme uses the velocity of the predecessor vehicle, communicated through a Vehicle-to-Vehicle technology, to avoid significant oscillations in the local speed provoked by tracking using unreliable local distance measurements. We implement the proposed control algorithm in the RUPU platform, a low-cost experimental platform with wireless communication interfaces that enable the implementation of cooperative control schemes for mobile agent platooning. The experiments show the effectiveness of the proposed cooperative control scheme in maintaining a suitable performance even when subject to temporal distortions in local measurements, which, in the considered experimental setup, arise from losing the line-of-sight of the local sensors in paths with closed curves.
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Lagos, F., Moreno, S., Yushimito, W. F., & Brstilo, T. (2024). Urban Origin–Destination Travel Time Estimation Using K-Nearest-Neighbor-Based Methods. Mathematics, 12(8), 1255.
Abstract: Improving the estimation of origin�destination (O-D) travel times poses a formidable challenge due to the intricate nature of transportation dynamics. Current deep learning models often require an overwhelming amount of data, both in terms of data points and variables, thereby limiting their applicability. Furthermore, there is a scarcity of models capable of predicting travel times with basic trip information such as origin, destination, and starting time. This paper introduces novel models rooted in the k-nearest neighbor (KNN) algorithm to tackle O-D travel time estimation with limited data. These models represent innovative adaptations of weighted KNN techniques, integrating the haversine distance of neighboring trips and incorporating correction factors to mitigate prediction biases, thereby enhancing the accuracy of travel time estimations for a given trip. Moreover, our models incorporate an adaptive heuristic to partition the time of day, identifying time blocks characterized by similar travel-time observations. These time blocks facilitate a more nuanced understanding of traffic patterns, enabling more precise predictions. To validate the effectiveness of our proposed models, extensive testing was conducted utilizing a comprehensive taxi trip dataset sourced from Santiago, Chile. The results demonstrate substantial improvements over existing state-of-the-art models (e.g., MAPE between 35 to 37% compared to 49 to 60% in other methods), underscoring the efficacy of our approach. Additionally, our models unveil previously unrecognized patterns in city traffic across various time blocks, shedding light on the underlying dynamics of urban mobility.
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Montalva-Medel, M., Ledger, T., Ruz, G. A., & Goles, E. (2021). Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements. Mathematics, 9(6), 600.
Abstract: In Veliz-Cuba and Stigler 2011, Boolean models were proposed for the lac operon in Escherichia coli capable of reproducing the operon being OFF, ON and bistable for three (low, medium and high) and two (low and high) parameters, representing the concentration ranges of lactose and glucose, respectively. Of these 6 possible combinations of parameters, 5 produce results that match with the biological experiments of Ozbudak et al., 2004. In the remaining one, the models predict the operon being OFF while biological experiments show a bistable behavior. In this paper, we first explore the robustness of two such models in the sense of how much its attractors change against any deterministic update schedule. We prove mathematically that, in cases where there is no bistability, all the dynamics in both models lack limit cycles while, when bistability appears, one model presents 30% of its dynamics with limit cycles while the other only 23%. Secondly, we propose two alternative improvements consisting of biologically supported modifications; one in which both models match with Ozbudak et al., 2004 in all 6 combinations of parameters and, the other one, where we increase the number of parameters to 9, matching in all these cases with the biological experiments of Ozbudak et al., 2004.
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Moreno, S., Bórquez-Paredes, D., & Martínez, V. (2023). Analysis of the Characteristics and Speed of Spread of the 'FUNA' on Twitter. Mathematics, 11(7), 1749.
Abstract: The funa is a prevalent concept in Chile that aims to expose a persons bad behavior, punish the aggressor publicly, and warn the community about it. Despite its massive use on the social networks of Chilean society, the real dissemination of funas among communities is unknown. In this paper, we extract, generate, analyze, and compare the Twitter social networks spread of three tweets related to �funas� against three other trending topics, through the analysis of global network characteristics over time (degree distribution, clustering coefficient, hop plot, and betweenness centrality). As observed, funas have a specific behavior, and they disseminate as quickly as a common tweet or more quickly; however, they spread thanks to several network users, generating a cohesive group.
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Munoz-Herrera, S., & Suchan, K. (2022). Local Optima Network Analysis of Multi-Attribute Vehicle Routing Problems. Mathematics, 10(24), 4644.
Abstract: Multi-Attribute Vehicle Routing Problems (MAVRP) are variants of Vehicle Routing Problems (VRP) in which, besides the original constraint on vehicle capacity present in Capacitated Vehicle Routing Problem (CVRP), other attributes that model diverse real-life system characteristics are present. Among the most common attributes studied in the literature are vehicle capacity and route duration constraints. The influence of these restrictions on the overall structure of the problem and the performance of local search algorithms used to solve it has yet to be well known. This paper aims to explain the impact of constraints present in different variants of VRP through the alterations of the structure of the underlying search space that they cause. We focus on Local Optima Network Analysis (LONA) for multiple Traveling Salesman Problem (m-TSP) and VRP with vehicle capacity (CVRP), route duration (DVRP), and both (DCVRP) constraints. We present results that indicate that measures obtained for a sample of local optima provide valuable information on the behavior of the landscape under modifications in the problem's constraints. Additionally, we use the LONA measures to explain the difficulty of VRP instances for solving by local search algorithms.
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Opazo, D., Moreno, S., Alvarez-Miranda, E., & Pereira, J. (2021). Analysis of First-Year University Student Dropout through Machine Learning Models: A Comparison between Universities. Mathematics, 20(9), 2599.
Abstract: Student dropout, defined as the abandonment of a high education program before obtaining the degree without reincorporation, is a problem that affects every higher education institution in the world. This study uses machine learning models over two Chilean universities to predict first-year engineering student dropout over enrolled students, and to analyze the variables that affect the probability of dropout. The results show that instead of combining the datasets into a single dataset, it is better to apply a model per university. Moreover, among the eight machine learning models tested over the datasets, gradient-boosting decision trees reports the best model. Further analyses of the interpretative models show that a higher score in almost any entrance university test decreases the probability of dropout, the most important variable being the mathematical test. One exception is the language test, where a higher score increases the probability of dropout.
Keywords: machine learning; first-year student dropout; universities
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Oviedo, H. (2023). Proximal Point Algorithm with Euclidean Distance on the Stiefel Manifold. Mathematics, 11(11), 2414.
Abstract: In this paper, we consider the problem of minimizing a continuously differentiable function on the Stiefel manifold. To solve this problem, we develop a geodesic-free proximal point algorithm equipped with Euclidean distance that does not require use of the Riemannian metric. The proposed method can be regarded as an iterative fixed-point method that repeatedly applies a proximal operator to an initial point. In addition, we establish the global convergence of the new approach without any restrictive assumption. Numerical experiments on linear eigenvalue problems and the minimization of sums of heterogeneous quadratic functions show that the developed algorithm is competitive with some procedures existing in the literature.
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Ruz, G. A., Henriquez, P. A., & Mascareno, A. (2022). Bayesian Constitutionalization: Twitter Sentiment Analysis of the Chilean Constitutional Process through Bayesian Network Classifiers. Mathematics, 10(2), 166.
Abstract: Constitutional processes are a cornerstone of modern democracies. Whether revolutionary or institutionally organized, they establish the core values of social order and determine the institutional architecture that governs social life. Constitutional processes are themselves evolutionary practices of mutual learning in which actors, regardless of their initial political positions, continuously interact with each other, demonstrating differences and making alliances regarding different topics. In this article, we develop Tree Augmented Naive Bayes (TAN) classifiers to model the behavior of constituent agents. According to the nature of the constituent dynamics, weights are learned by the model from the data using an evolution strategy to obtain a good classification performance. For our analysis, we used the constituent agents' communications on Twitter during the installation period of the Constitutional Convention (July-October 2021). In order to differentiate political positions (left, center, right), we applied the developed algorithm to obtain the scores of 882 ballots cast in the first stage of the convention (4 July to 29 September 2021). Then, we used k-means to identify three clusters containing right-wing, center, and left-wing positions. Experimental results obtained using the three constructed datasets showed that using alternative weight values in the TAN construction procedure, inferred by an evolution strategy, yielded improvements in the classification accuracy measured in the test sets compared to the results of the TAN constructed with conditional mutual information, as well as other Bayesian network classifier construction approaches. Additionally, our results may help us to better understand political behavior in constitutional processes and to improve the accuracy of TAN classifiers applied to social, real-world data.
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Villenas, F. I., Vargas, F. J., & Peters, A. A. (2023). A Kalman-Based Compensation Strategy for Platoons Subject to Data Loss: Numerical and Empirical Study. Mathematics, 11(5), 1228.
Abstract: This article considers a homogeneous platoon with vehicles that communicate through channels prone to data loss. The vehicles use a predecessor-following topology, where each vehicle sends relevant data to the next, and data loss is modeled through a Bernoulli process. To address the lossy communication, we propose a strategy to estimate the missing data based on the Kalman filter with intermittent observations combined with a linear extrapolation stage. This strategy enables the followers to better deal with data dropouts. We compare this approach to one purely based on the linear extrapolation of previous data. The performance of both strategies is analyzed through Monte Carlo simulations and experiments in an ad hoc testbed, considering various data loss and transmission loss probabilities depending on the inter-vehicle distance. The results show that for the considered cases, the proposed strategy outperforms the linear extrapolation approach in terms of tracking and estimation error variances. Our results also show that the proposed strategy can achieve string stability for the mean and variance for both the tracking and estimation errors in scenarios where the basic extrapolation strategy cannot.
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Villenas, F. I., Vargas, F. J., & Peters, A. A. (2023). Exploring the Role of Sampling Time in String Stabilization for Platooning: An Experimental Case Study. Mathematics, 11(13), 2923.
Abstract: In this article, we investigate the behavior of vehicle platoons operating in a predecessor-following configuration, implemented through sampled-data control systems. Our primary focus is to examine the potential influence of the sampling time on the string stability of the platoon. To address this, we begin by designing a string-stable platoon in continuous time. Subsequently, we consider the controller discretization process and proceed to simulate and implement the designed control strategy on an experimental platform at a scaled-down level. Through experimental testing and some theoretical results, we analyze the effects of different sampling times on the string stability performance of the platoon. We observe that an inappropriate selection of the sampling time can lead to a degradation in string stability within the platoon, making the choice of the sampling time crucial in maintaining the desired string stability properties. These findings highlight the importance of carefully considering the sampling time in the implementation of control systems for platooning applications.
Keywords: vehicle platoon; string stability; discrete time; sampled-data systems
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Yuraszeck, F., Mejia, G., Pereira, J., & Vila, M. (2022). A Novel Constraint Programming Decomposition Approach for the Total Flow Time Fixed Group Shop Scheduling Problem. Mathematics, 10(3), 329.
Abstract: This work addresses a particular case of the group shop scheduling problem (GSSP) which will be denoted as the fixed group shop scheduling problem (FGSSP). In a FGSSP, job operations are divided into stages and each stage has a set of machines associated to it which are not shared with the other stages. All jobs go through all the stages in a specific order, where the operations of the job at each stage need to be finished before the job advances to the following stage, but operations within a stage can be performed in any order. This setting is common in companies such as leaf spring manufacturers and other automotive companies. To solve the problem, we propose a novel heuristic procedure that combines a decomposition approach with a constraint programming (CP) solver and a restart mechanism both to avoid local optima and to diversify the search. The performance of our approach was tested on instances derived from other scheduling problems that the FGSSP subsumes, considering both the cases with and without anticipatory sequence-dependent setup times. The results of the proposed algorithm are compared with off-the-shelf CP and mixed integer linear programming (MILP) methods as well as with the lower bounds derived from the study of the problem. The experiments show that the proposed heuristic algorithm outperforms the other methods, specially on large-size instances with improvements of over 10% on average.
Keywords: scheduling; fixed group shop; group shop; constraint programming
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