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This manuscript explores novel complexity results for the feasibility problem over $p$-order cones, extending the foundational work of Porkolab and Khachiyan. By leveraging the intrinsic structure of $p$-order cones, we derive refined complexity bounds that surpass those obtained via standard semidefinite programming reformulations. Our analysis not only improves theoretical bounds but also provides practical insights into the computational efficiency of solving such problems. In addition to establishing complexity results, we derive explicit bounds for solutions when the feasibility problem admits one. For infeasible instances, we analyze their discrepancy quantifying the degree of infeasibility. Finally, we examine specific cases of interest, highlighting scenarios where the geometry of $p$-order cones or problem structure yields further computational simplifications. These findings contribute to both the theoretical understanding and practical tractability of optimization problems involving $p$-order cones., Comment: 21 pages, 2 tables

This paper studies a practical regional demand continuous multifacility location problems whose main goal is to locate a given number of services and entry points in each region to distribute certain products to the users at minimum transportation cost. Additionally, a minimum satisfaction level is required for the customers in each region. This satisfaction is measured through continuous preference functions that reflect the satisfaction degree of each location in the region. We provide a mathematical optimization-based framework for the problem and derive suitable Mixed Integer Second Order Cone optimization models for some interesting situations: norm-based transportation costs for the services to the entry points, and different families of preference functions. Among these preference functions, we highlight those derived from economic production models and distance-based preferences. We conduct an extensive computational study along two main lines: a computational approach, where we provide optimal solutions for up to 500 demand regions in the single-facility case and up to $50$ for the p-facility case; and a qualitative approach, where we analyze whether the incorporation of preferences is statistically significant compared to the case without preferences.

Chemical reaction networks (CRNs) are essential for modeling and analyzing complex systems across fields, from biochemistry to economics. Autocatalytic reaction network -- networks where certain species catalyze their own production -- are particularly significant for understanding self-replication dynamics in biological systems and serve as foundational elements in formalizing the concept of a circular economy. In a previous study, we developed a mixed-integer linear optimization-based procedure to enumerate all minimal autocatalytic subnetworks within a network. In this work, we define the maximum growth factor (MGF) of an autocatalytic subnetwork, develop mathematical optimization approaches to compute this metric, and explore its implications in the field of economics and dynamical systems. We develop exact approaches to determine the MGF of any subnetwork based on an iterative procedure with guaranteed convergence, which allows for identifying autocatalytic subnetworks with the highest MGF. We report the results of computational experiments on synthetic CRNs and two well-known datasets, namely the Formose and E. coli reaction networks, identifying their autocatalytic subnetworks and exploring their scientific ramifications. Using advanced optimization techniques and interdisciplinary applications, our framework adds an essential resource to analyze complex systems modeled as reaction networks.

In this paper we provide a novel mathematical optimization based methodology to perturb the features of a given observation to be re-classified, by a tree ensemble classification rule, to a certain desired class. The method is based on these facts: the most viable changes for an observation to reach the desired class do not always coincide with the closest distance point (in the feature space) of the target class; individuals put effort on a few number of features to reach the desired class; and each individual is endowed with a probability to change each of its features to a given value, which determines the overall probability of changing to the target class. Putting all together, we provide different methods to find the features where the individuals must exert effort to maximize the probability to reach the target class. Our method also allows us to rank the most important features in the tree-ensemble. The proposed methodology is tested on a real dataset, validating the proposal., Comment: 30 pages, 4 Figures, 4 Tables

In this review, automatic defect inspection algorithms that analyze Electron Microscope (EM) images of Semiconductor Manufacturing (SM) products are identified, categorized, and discussed. This is a topic of critical importance for the SM industry as the continuous shrinking of device patterns has led to increasing defectivity and a greater prevalence of higher-resolution imaging tools such as EM. These aspects among others threaten to increase costs as a result of increased inspection time-to-solution and decreased yield, respectively. Relevant research papers were systematically identified in four popular publication databases in January 2024. A total of 103 papers were selected after screening for novel contributions relating to automatic EM image analysis algorithms for semiconductor defect inspection. These papers were then categorized based on the inspection tasks they addressed, their evaluation metrics, and the type of algorithms used. A notable finding from this categorization is that reference-based defect detection algorithms were the most popular algorithm type until 2020 when deep learning-based inspection algorithms became more popular, especially for defect classification. Furthermore, four broader research questions were discussed to come to the following conclusions: (i) the key components of inspection algorithms are set up, pre-processing, feature extraction, and final prediction; (ii) the maturity of the manufacturing process affects the data availability and required sensitivity of inspection algorithms; (iii) key challenges for these algorithms relate to the desiderata of minimizing time-to-solution which pushes for high imaging throughput, reducing manual input during algorithm setup, and higher processing throughput; and (iv) three promising directions for future work are suggested based on gaps in the reviewed literature that address key remaining limitations.

In this research, we introduce a unified end-to-end Automated Defect Classification-Detection-Segmentation (ADCDS) framework for classifying, detecting, and segmenting multiple instances of semiconductor defects for advanced nodes. This framework consists of two modules: (a) a defect detection module, followed by (b) a defect segmentation module. The defect detection module employs Deformable DETR to aid in the classification and detection of nano-scale defects, while the segmentation module utilizes BoxSnake. BoxSnake facilitates box-supervised instance segmentation of nano-scale defects, supported by the former module. This simplifies the process by eliminating the laborious requirement for ground-truth pixel-wise mask annotation by human experts, which is typically associated with training conventional segmentation models. We have evaluated the performance of our ADCDS framework using two distinct process datasets from real wafers, as ADI and AEI, specifically focusing on Line-space patterns. We have demonstrated the applicability and significance of our proposed methodology, particularly in the nano-scale segmentation and generation of binary defect masks, using the challenging ADI SEM dataset where ground-truth pixelwise segmentation annotations were unavailable. Furthermore, we have presented a comparative analysis of our proposed framework against previous approaches to demonstrate its effectiveness. Our proposed framework achieved an overall mAP@IoU0.5 of 72.19 for detection and 78.86 for segmentation on the ADI dataset. Similarly, for the AEI dataset, these metrics were 90.38 for detection and 95.48 for segmentation. Thus, our proposed framework effectively fulfils the requirements of advanced defect analysis while addressing significant constraints., Comment: Accepted in ECCV 2024 2nd workshop on Vision-based InduStrial InspectiON (VISION)

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., Comment: 18 pages, 10 figures

Deep learning-based semiconductor defect inspection has gained traction in recent years, offering a powerful and versatile approach that provides high accuracy, adaptability, and efficiency in detecting and classifying nano-scale defects. However, semiconductor manufacturing processes are continually evolving, leading to the emergence of new types of defects over time. This presents a significant challenge for conventional supervised defect detectors, as they may suffer from catastrophic forgetting when trained on new defect datasets, potentially compromising performance on previously learned tasks. An alternative approach involves the constant storage of previously trained datasets alongside pre-trained model versions, which can be utilized for (re-)training from scratch or fine-tuning whenever encountering a new defect dataset. However, adhering to such a storage template is impractical in terms of size, particularly when considering High-Volume Manufacturing (HVM). Additionally, semiconductor defect datasets, especially those encompassing stochastic defects, are often limited and expensive to obtain, thus lacking sufficient representation of the entire universal set of defectivity. This work introduces a task-agnostic, meta-learning approach aimed at addressing this challenge, which enables the incremental addition of new defect classes and scales to create a more robust and generalized model for semiconductor defect inspection. We have benchmarked our approach using real resist-wafer SEM (Scanning Electron Microscopy) datasets for two process steps, ADI and AEI, demonstrating its superior performance compared to conventional supervised training methods., Comment: Accepted for presentation at the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases 2024 Industry Track

Precision in identifying nanometer-scale device-killer defects is crucial in both semiconductor research and development as well as in production processes. The effectiveness of existing ML-based approaches in this context is largely limited by the scarcity of data, as the production of real semiconductor wafer data for training these models involves high financial and time costs. Moreover, the existing simulation methods fall short of replicating images with identical noise characteristics, surface roughness and stochastic variations at advanced nodes. We propose a method for generating synthetic semiconductor SEM images using a diffusion model within a limited data regime. In contrast to images generated through conventional simulation methods, SEM images generated through our proposed DL method closely resemble real SEM images, replicating their noise characteristics and surface roughness adaptively. Our main contributions, which are validated on three different real semiconductor datasets, are: i) proposing a patch-based generative framework utilizing DDPM to create SEM images with intended defect classes, addressing challenges related to class-imbalance and data insufficiency, ii) demonstrating generated synthetic images closely resemble real SEM images acquired from the tool, preserving all imaging conditions and metrology characteristics without any metadata supervision, iii) demonstrating a defect detector trained on generated defect dataset, either independently or combined with a limited real dataset, can achieve similar or improved performance on real wafer SEM images during validation/testing compared to exclusive training on a real defect dataset, iv) demonstrating the ability of the proposed approach to transfer defect types, critical dimensions, and imaging conditions from one specified CD/Pitch and metrology specifications to another, thereby highlighting its versatility., Comment: 8 pages, 11 figures, to be presented at 2024 International Symposium ELMAR, and published by IEEE in the conference proceedings

Due to potential pitch reduction, the semiconductor industry is adopting High-NA EUVL technology. However, its low depth of focus presents challenges for High Volume Manufacturing. To address this, suppliers are exploring thinner photoresists and new underlayers/hardmasks. These may suffer from poor SNR, complicating defect detection. Vision-based ML algorithms offer a promising solution for semiconductor defect inspection. However, developing a robust ML model across various image resolutions without explicit training remains a challenge for nano-scale defect inspection. This research's goal is to propose a scale-invariant ADCD framework capable to upscale images, addressing this issue. We propose an improvised ADCD framework as SEMI-SuperYOLO-NAS, which builds upon the baseline YOLO-NAS architecture. This framework integrates a SR assisted branch to aid in learning HR features by the defect detection backbone, particularly for detecting nano-scale defect instances from LR images. Additionally, the SR-assisted branch can recursively generate upscaled images from their corresponding downscaled counterparts, enabling defect detection inference across various image resolutions without requiring explicit training. Moreover, we investigate improved data augmentation strategy aimed at generating diverse and realistic training datasets to enhance model performance. We have evaluated our proposed approach using two original FAB datasets obtained from two distinct processes and captured using two different imaging tools. Finally, we demonstrate zero-shot inference for our model on a new, originating from a process condition distinct from the training dataset and possessing different Pitch characteristics. Experimental validation demonstrates that our proposed ADCD framework aids in increasing the throughput of imaging tools for defect inspection by reducing the required image pixel resolutions.

In this paper, we propose a new mathematical optimization approach to make decisions on the optimal design of a logistic system to produce biogas from waste. We provide an integrated model that allows decision makers to optimally determine the locations of different types of plants and pipelines involved in the logistic process, as well as the most efficient distribution of the products (from waste to biomethane) along the supply chain. We analyze the mathematical model and reduce its size, being able to solve realistic instances in reasonable CPU times. The results of our computational experiments, both in synthetic and in a case study instance, prove the validity of our proposal in practical applications., Comment: 25 pages, 7 figures, 3 tables

Moore Law states that transistor density will double every two years, which is sustained until today due to continuous multi-directional innovations, such as extreme ultraviolet lithography, novel patterning techniques etc., leading the semiconductor industry towards 3nm node and beyond. For any patterning scheme, the most important metric to evaluate the quality of printed patterns is EPE, with overlay being its largest contribution. Overlay errors can lead to fatal failures of IC devices such as short circuits or broken connections in terms of P2P electrical contacts. Therefore, it is essential to develop effective overlay analysis and control techniques to ensure good functionality of fabricated semiconductor devices. In this work we have used an imec N14 BEOL process flow using LELE patterning technique to print metal layers with minimum pitch of 48nm with 193i lithography. FF structures are decomposed into two mask layers (M1A and M1B) and then the LELE flow is carried out to make the final patterns. Since a single M1 layer is decomposed into two masks, control of overlay between the two masks is critical. The goal of this work is of two-fold as, (a) to quantify the impact of overlay on capacitance and (b) to see if we can predict the final capacitance measurements with selected machine learning models at an early stage. To do so, scatterometry spectra are collected on these electrical test structures at (a)post litho, (b)post TiN hardmask etch, and (c)post Cu plating and CMP. Critical Dimension and overlay measurements for line-space pattern are done with SEM post litho, post etch and post Cu CMP. Various machine learning models are applied to do the capacitance prediction with multiple metrology inputs at different steps of wafer processing. Finally, we demonstrate that by using appropriate machine learning models we are able to do better prediction of electrical results.

In semiconductor manufacturing, lithography has often been the manufacturing step defining the smallest possible pattern dimensions. In recent years, progress has been made towards high-NA (Numerical Aperture) EUVL (Extreme-Ultraviolet-Lithography) paradigm, which promises to advance pattern shrinking (2 nm node and beyond). However, a significant increase in stochastic defects and the complexity of defect detection becomes more pronounced with high-NA. Present defect inspection techniques (both non-machine learning and machine learning based), fail to achieve satisfactory performance at high-NA dimensions. In this work, we investigate the use of the Slicing Aided Hyper Inference (SAHI) framework for improving upon current techniques. Using SAHI, inference is performed on size-increased slices of the SEM images. This leads to the object detector's receptive field being more effective in capturing small defect instances. First, the performance on previously investigated semiconductor datasets is benchmarked across various configurations, and the SAHI approach is demonstrated to substantially enhance the detection of small defects, by approx. 2x. Afterwards, we also demonstrated application of SAHI leads to flawless detection rates on a new test dataset, with scenarios not encountered during training, whereas previous trained models failed. Finally, we formulate an extension of SAHI that does not significantly reduce true-positive predictions while eliminating false-positive predictions., Comment: 12 pages, 9 figures, to be presented at International Conference on Machine Intelligence with Applications (ICMIA), and to be published in conference proceedings by AIP

In this paper, we analyze minimal representations of $(p,\boldsymbol{\alpha})$-power cones as simpler cones. We derive some new results on the complexity of the representations, and we provide a procedure to construct a minimal representation by means of second order cones in case $\boldsymbol{\alpha}$ and $p$ are rational. The construction is based on the identification of the cones with a graph, the mediated graph. Then, we develop a mixed integer linear optimization formulation to obtain the optimal mediated graph, and then, the minimal representation. We present the results of a series of computational experiments in order to analyze the computational performance of the approach, both to obtain the representation and its incorporation into a practical conic optimization model that arises in facility location., Comment: 23 pages, 8 figures, 4 tables

The International Workshop on Locational Analysis and Related Problems will take place during September 7-8, 2023 in Edinburgh (United Kingdom). It is organized by the Spanish Location Network and the Location Group GELOCA from the Spanish Society of Statistics and Operations Research (SEIO). The Spanish Location Network is a group of more than 140 researchers from several Spanish universities organized into 7 thematic groups. The Network has been funded by the Spanish Government since 2003. The current project is RED2022-134149-T. One of the main activities of the Network is a yearly meeting aimed at promoting the communication among its members and between them and other researchers, and to contribute to the development of the location field and related problems. As a proof of the internationalization of this research group, this will be the first time that the meeting is held out of Spain. The topics of interest are location analysis and related problems. This includes location models, networks, transportation, logistics, exact and heuristic solution methods, and computational geometry, among others., Comment: The proceedings book of the previous editions can be found at arXiv:2002.08287 arXiv:2002.08293 arXiv:2002.08300 arXiv:2002.01702 arXiv:2202.13878

A growing need exists for efficient and accurate methods for detecting defects in semiconductor materials and devices. These defects can have a detrimental impact on the efficiency of the manufacturing process, because they cause critical failures and wafer-yield limitations. As nodes and patterns get smaller, even high-resolution imaging techniques such as Scanning Electron Microscopy (SEM) produce noisy images due to operating close to sensitivity levels and due to varying physical properties of different underlayers or resist materials. This inherent noise is one of the main challenges for defect inspection. One promising approach is the use of machine learning algorithms, which can be trained to accurately classify and locate defects in semiconductor samples. Recently, convolutional neural networks have proved to be particularly useful in this regard. This systematic review provides a comprehensive overview of the state of automated semiconductor defect inspection on SEM images, including the most recent innovations and developments. 38 publications were selected on this topic, indexed in IEEE Xplore and SPIE databases. For each of these, the application, methodology, dataset, results, limitations and future work were summarized. A comprehensive overview and analysis of their methods is provided. Finally, promising avenues for future work in the field of SEM-based defect inspection are suggested., Comment: 16 pages, 12 figures, 3 tables

Developing a mathematical understanding of autocatalysis in reaction networks has both theoretical and practical implications. We review definitions of autocatalytic networks and prove some properties for minimal autocatalytic subnetworks (MASs). We show that it is possible to classify MASs in equivalence classes, and develop mathematical results about their behavior. We also provide linear-programming algorithms to exhaustively enumerate them and a scheme to visualize their polyhedral geometry and combinatorics. We then define cluster chemical reaction networks, a framework for coarse-graining real chemical reactions with positive integer conservation laws. We find that the size of the list of minimal autocatalytic subnetworks in a maximally connected cluster chemical reaction network with one conservation law grows exponentially in the number of species. We end our discussion with open questions concerning an ecosystem of autocatalytic subnetworks and multidisciplinary opportunities for future investigation., Comment: 36 pages, 17 figures, 7 tables

In this paper, we provide a mathematical optimization-based framework to determine the location of leak detection devices along a network. Assuming that the devices are endowed with a known coverage area, we analyze two different models. The first model aims to minimize the number of devices to be located in order to (fully or partially) cover the volume of the network. In the second model, the number of devices is given, and the goal is to locate them to provide a coverage volume as broad as possible. Unlike other approaches in the literature, in our models, it is not assumed that the devices are located on the network (nodes or edges) but in the whole space and that the different segments in the networks may be partially covered, which allows for more flexible coverage. We also derive a method to construct initial solutions as well as a math-heuristic approach for solving the problem for larger instances. We report the results of a series of experiments on real-world water supply pipeline networks, supporting the validity of our models., Comment: 31 pages, 13 Figures, 3 Tables

We consider facility location problems with a new form of equity criterion. Demand points have preference order on the sites where the plants can be located. The goal is to find the location of the facilities minimizing the envy felt by the demand points with respect to the rest of demand points allocated to the same plant. After defining this new envy criterion and the general framework based on it, we provide formulations that model this approach in both the discrete and the continuous framework. The problems are illustrated with examples and the computational tests reported show the potential and limits of each formulation on several types of instances. Although this article is mainly focused on the introduction, modelling and formulation of this new concept of envy, some improvements for all the formulations presented are developed, obtaining in some cases better solution times., Comment: 23 pages, 8 figures

This paper introduces Weighted Optimal Classification Forests (WOCFs), a new family of classifiers that takes advantage of an optimal ensemble of decision trees to derive accurate and interpretable classifiers. We propose a novel mathematical optimization-based methodology which simultaneously constructs a given number of trees, each of them providing a predicted class for the observations in the feature space. The classification rule is derived by assigning to each observation its most frequently predicted class among the trees. We provide a mixed integer linear programming formulation (MIP) for the problem and several novel MIP strengthening / scaling techniques. We report the results of our computational experiments, from which we conclude that our method has equal or superior performance compared with state-of-the-art tree-based classification methods for small to medium-sized instances. We also present three real-world case studies showing that our methodology has very interesting implications in terms of interpretability. Overall, WOCFs complement existing methods such as CART, Optimal Classification Trees, Random Forests and XGBoost. In addition to its Pareto improvement on accuracy and interpretability, we also see unique properties emerging in terms of different trees focusing on different feature variables. This provides nontrivial improvement in interpretability and usability of the trained model in terms of counterfactual explanation. Thus, despite the apparent computational challenge of WOCFs that limit the size of the problems that can be efficiently solved with current MIP, this is an important research direction that can lead to qualitatively different insights for researchers and complement the toolbox of practitioners for high stakes problems., Comment: 30 pages, 9 figures, 2 table

This paper provides a general mathematical optimization based framework to incorporate fairness measures from the facilities' perspective to Discrete and Continuous Maximal Covering Location Problems. The main ingredients to construct a function measuring fairness in this problem are the use of: (1) ordered weighted averaging operators, a family of aggregation criteria very popular to solve multiobjective combinatorial optimization problems; and (2) $\alpha$-fairness operators which allow to generalize most of the equity measures. A general mathematical optimization model is derived which captures the notion of fairness in maximal covering location problems. The models are firstly formulated as mixed integer non-linear optimization problems for both the discrete and the continuous location spaces. Suitable mixed integer second order cone optimization reformulations are derived using geometric properties of the problem. Finally, the paper concludes with the results obtained on an extensive battery of computational experiments on real datasets. The obtained results support the convenience of the proposed approach., Comment: 31 pages, 15 figures, 2 tables

This paper introduces the Hub Location Problem under Link Failures, a hub location problem in which activated inter-hub links may fail with a given probability. Two different optimization models are studied, which construct hub backbone networks protected under hub links disruptions by imposing that for each commodity an additional routing path exists besides its original routing path. Both models consider the minimization of the set-up costs of the activated hubs and inter-hub links plus the expected value of the routing costs of the original and alternative paths. The first model builds explicitly the alternative routing paths, while the second model guarantees that for each commodity at least one alternative path exists using a large set of connectivity constraints, although the alternative paths are not built explicitly. The results of extensive computational testing allow to analyze the performance of the two proposed models and to evaluate the extra cost required to design a robust backbone network under hub links failures. The obtained results support the validity of the proposal., Comment: 31 pages, 10 figures, 6 tables

This paper introduces a general modeling framework for a multi-type maximal covering location problem in which the position of facilities in different metric spaces are simultaneously decided to maximize the demand generated by a set of points. From the need of intertwining location decisions in discrete and in continuous sets, a general hybridized problem is considered in which some types of facilities are to be located in finite sets and the others in continuous metric spaces. A natural non-linear model is proposed for which an integer linear programming reformulation is derived. A branch-and-cut algorithm is developed for better tackling the problem. The study proceeds considering the particular case in which the continuous facilities are to be located in the Euclidean plane. In this case, taking advantage from some geometrical properties it is possible to propose an alternative integer linear programming model. The results of an extensive battery of computational experiments performed to assess the methodological contribution of this work is reported on. The data consists of up to 920 demand nodes using real geographical and demographic data., Comment: 19 pages, 5 figures, 2 tables

In this paper we present a novel mathematical optimization-based methodology to construct tree-shaped classification rules for multiclass instances. Our approach consists of building Classification Trees in which, except for the leaf nodes, the labels are temporarily left out and grouped into two classes by means of a SVM separating hyperplane. We provide a Mixed Integer Non Linear Programming formulation for the problem and report the results of an extended battery of computational experiments to assess the performance of our proposal with respect to other benchmarking classification methods., Comment: 26 pages, 8 Figures, 3 tables

In this paper, we address the Continuous Multifacility Monotone Ordered Median Problem. This problem minimizes a monotone ordered weighted median function of the distances between given demand points in $\mathbb{R}^d$ and its closest facility among the $p$ selected, also in a continuous space. We propose a new branch-and-price procedure for this problem, and two mathehuristics. One of them is a decomposition-based procedure and the other an aggregation-based heuristic. We give detailed discussions of the validity of the exact formulations and also specify the implementation details of all the solution procedures. Besides, we assess their performance in an extensive computational experience that shows the superiority of the branch-and-price approach over the compact formulation in medium-sized instances. To handle larger instances it is advisable to resort to the matheuristics that also report rather good results., Comment: 28 pages, 8 tables, 1 figure, 1 appendix

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., Comment: 23 p\'aginas, 10 figures, 4 Algorithms, 3 Tables

A model of opinion formation on a Small World type topology is studied to observe qualitatively its difference with one is own conviction versus the opinion of others. It is possible to observe that the relation between conviction to copy the agent with whom it interacts and this agent is an undecided agent who leaves decisions to chance becomes outstanding since the probability of undecided agents is greater than 0.1 and is maintained until 0.7 so that in the border regions, it is only a transition towards this predictive., Comment: 6 pages, 3 figures

The effect of undecided agents is studied within populations in an opinion-forming dynamic, varying the number of undecided agents for different proportions of populations in a complete opinion-exchange network. The result is that the dynamic depends on the number of undecided agents, with 10\% of the undecided population potentially affecting the change in consensus and then becoming linear with a negative slope., Comment: 9 pages, 8 figures

In this paper we propose a novel methodology to construct Optimal Classification Trees that takes into account that noisy labels may occur in the training sample. Our approach rests on two main elements: (1) the splitting rules for the classification trees are designed to maximize the separation margin between classes applying the paradigm of SVM; and (2) some of the labels of the training sample are allowed to be changed during the construction of the tree trying to detect the label noise. Both features are considered and integrated together to design the resulting Optimal Classification Tree. We present a Mixed Integer Non Linear Programming formulation for the problem, suitable to be solved using any of the available off-the-shelf solvers. The model is analyzed and tested on a battery of standard datasets taken from UCI Machine Learning repository, showing the effectiveness of our approach., Comment: 18 Pages, 2 Figures, 1 Table

In this paper we provide a mathematical programming based decision tool to optimally reallocate and share equipments between different units in emergency situations under lack of resources. The approach is motivated by the COVID-19 pandemic in which many Heath National Systems were not able to satisfy the demand of ventilators, sanitary individual protection equipments or different human resources. Our tool is based in two main principles: (1) Part of the stock of equipments at a unit that is not needed (in near future) could be shared to other units; and (2) extra stock to be shared among the units in a region can be efficiently distributed taking into account the demand of the units. The decisions are taken with the aim of minimizing certain measures of the non-covered demand in a region where a given network structured set of units is given. The mathematical programming models that we provide are stochastic and multiperiod and we provide different robust objective functions. Since the proposed models are computationally hard to solve, we provide a divide-et-conquer math-heuristic approach. We report the results of applying our approach to the data of the COVID-19 case in different regions of Spain, highlighting some interesting conclusions of our analysis, such as the great increase of treated patients if the proposed redistribution tool is applied., Comment: 28 pages, 14 Figures, list of 18 resources

In this paper we analyze a continuous version of the maximal covering location problem, in which the facilities are required to be interconnected by means of a graph structure in which two facilities are allowed to be linked if a given distance is not exceed. We provide a mathematical programming framework for the problem and different resolution strategies. First, we propose a Mixed Integer Non Linear Programming formulation, and derive properties of the problem that allow us to project the continuous variables out avoiding the nonlinear constraints, resulting in an equivalent pure integer programming formulation. Since the number of constraints in the integer programming formulation is large and the constraints are, in general, difficult to handle, we propose two branch-&-cut approaches that avoid the complete enumeration of the constraints resulting in more efficient procedures. We report the results of an extensive battery of computational experiments comparing the performance of the different approaches., Comment: 32 pages, 8 Figures, 6 Tables

In this paper we propose novel methodologies to construct Support Vector Machine -based classifiers that takes into account that label noises occur in the training sample. We propose different alternatives based on solving Mixed Integer Linear and Non Linear models by incorporating decisions on relabeling some of the observations in the training dataset. The first method incorporates relabeling directly in the SVM model while a second family of methods combines clustering with classification at the same time, giving rise to a model that applies simultaneously similarity measures and SVM. Extensive computational experiments are reported based on a battery of standard datasets taken from UCI Machine Learning repository, showing the effectiveness of the proposed approaches., Comment: 17 pages, 5 figures, 2 tables

In this paper we study the problem of locating a given number of hyperplanes minimizing an objective function of the closest distances from a set of points. We propose a general framework for the problem in which norm-based distances between points and hyperplanes are aggregated by means of ordered median functions. A compact Mixed Integer Linear (or Non Linear) programming formulation is presented for the problem and also an extended set partitioning formulation with an exponential number of variables is derived. We develop a column generation procedure embedded within a branch-and-price algorithm for solving the problem by adequately performing its preprocessing, pricing and branching. We also analyze geometrically the optimal solutions of the problem, deriving properties which are exploited to generate initial solutions for the proposed algorithms. Finally, the results of an extensive computational experience are reported. The issue of scalability is also addressed showing theoretical upper bounds on the errors assumed by replacing the original datasets by aggregated versions., Comment: 30 pages, 5 Tables, 3 Figures

In this paper we propose an extension of the Uncapacitated Hub Location Problem where the potential positions of the hubs are not fixed in advance. Instead, they are allowed to belong to a region around an initial discrete set of nodes. We give a general framework in which the collection, transportation and distribution costs are based on norm-based distances and the hub-activation set-up costs depend, not only on the the location of the hub that are opened but also on the size of the region where they are placed. Two alternative mathematical programming formulations are proposed. The first one is a compact formulation while the second one involves a family of constraints of exponential size that we separate efficiently giving rise to a branch-and-cut algorithm. The results of an extensive computational experience are reported showing the advantages of each of the approaches., Comment: 19 pages, 4 tables, 3 figures

In this paper we analyze the extension of the classical smallest enclosing disk problem to the case of the location of a polyellipsoid to fully cover a set of demand points in $\mathbb{R}^d$. We prove that the problem is polynomially solvable in fixed dimension and analyze mathematical programming formulations for it. We also consider some geometric approaches for the problem in case the foci of the polyellipsoids are known. Extensions of the classical algorithm by Elzinga-Hearn are also derived for this new problem. Moreover, we address several extensions of the problem, as the case where the foci of the enclosing polyellipsoid are not given and have to be determined among a potential set of points or the induced covering problems when instead of polyellipsoids, one uses ordered median polyellipsoids. For these problems we also present Mixed Integer (Non) Linear Programming strategies that lead to efficient ways to solve it., Comment: 26 pages, 5 Figures, 4 Tables

In this paper studies the maximal covering location problem, assuming imprecise knowledge of all data involved. The considered problem is modeled from a fuzzy perspective producing suitable fuzzy Pareto solutions. Some properties of the fuzzy model are studied, which validate the equivalent mixed-binary linear multiobjective formulation proposed. A solution algorithm is developed, based on the augmented weighted Tchebycheff method, which produces solutions of guaranteed Pareto optimality. The effectiveness of the algorithm has been tested with a series of computational experiments, whose numerical results are presented and analyzed, Comment: 24 pages, 3 figures, 4 tables

In this paper we present a Mixed Integer Nonlinear Programming model that we developed as part of a pilot study requested by the R&D company Metrolab in order to design tools for finding solutions for line planning and timetable situations in automated urban metro subway networks. Our model incorporates important factors in public transportation systems from both, a cost-oriented and a passenger-oriented perspective, as time-dependent demands, interchange stations, short-turns and technical features of the trains in use. The incoming flows of passengers are modeled by means of piecewise linear demand functions which are parameterized in terms of arrival rates and bulk arrivals. Decisions about frequencies, train capacities, short-turning and timetables for a given planning horizon are jointly integrated to be optimized in our model. Finally, a novel Math-Heuristic approach is proposed to solve the problem. The results of extensive computational experiments are reported to show its applicability and effectiveness to handle real-world subway networks, Comment: 30 pages, 6 figures, 9 tables

In this paper, we present a novel approach to construct multiclass classifiers by means of arrangements of hyperplanes. We propose different mixed integer (linear and non linear) programming formulations for the problem using extensions of widely used measures for misclassifying observations where the \textit{kernel trick} can be adapted to be applicable. Some dimensionality reductions and variable fixing strategies are also developed for these models. An extensive battery of experiments has been run which reveal the powerfulness of our proposal as compared with other previously proposed methodologies., Comment: 8 Figures, 2 Tables

In this paper, we present an improved methodology to compute $\omega$-invariant of numerical semigroup. The approach is based on adapting a recent resolution method for optimizing a linear function over the set of efficient solutions of a multiple objective integer linear programming problem. The numerical experiments show the efficiency of the proposed technique compared to the existing methods., Comment: 11 pages