@article{yoo_escobedo_kemmer_chiou_2024, title={Elicitation and aggregation of multimodal estimates improve wisdom of crowd effects on ordering tasks}, volume={14}, ISSN={["2045-2322"]}, DOI={10.1038/s41598-024-52176-3}, abstractNote={Abstract}, number={1}, journal={SCIENTIFIC REPORTS}, author={Yoo, Yeawon and Escobedo, Adolfo R. and Kemmer, Ryan and Chiou, Erin}, year={2024}, month={Feb} }
 @article{akbari_escobedo_2023, title={Approximate Condorcet Partitioning: Solving large-scale rank aggregation problems}, url={https://doi.org/10.1016/j.cor.2023.106164}, DOI={10.1016/j.cor.2023.106164}, abstractNote={Rank aggregation has ubiquitous applications in computer science, operations research, and various other fields. Most attention on this problem has focused on an NP-hard variant known as Kemeny aggregation, for which solution approaches with provable guarantees that can handle difficult high-dimensional instances remain elusive. This work introduces exact and approximate methodologies inspired by the social choice foundations of the problem, namely the Condorcet Criterion. We formalize the concept of the finest-Condorcet partition for rankings that may contain ties and specify its required conditions. We prove that this partition is unique and devise an efficient algorithm to obtain it. To deal with instances where it does not yield many subsets, we propose Approximate Condorcet Partitioning (ACP), with which larger subsets can be further broken down and more easily solved. ACP is a scalable solution technique capable of handling large instances while still providing provable guarantees. Although ACP approximation factors are instance-specific, their values were lower than those offered by all known constant-factor approximation schemes — inexact algorithms whose resulting objective values are guaranteed to be within a specified fixed percent of the optimal objective value — for all 113 instances tested herein (containing up to 2,820 items). What is more, ACP obtained solutions that deviated by at most two percent from the optimal objective function values for a large majority of these instances.}, journal={Computers & Operations Research}, author={Akbari, Sina and Escobedo, Adolfo R.}, year={2023}, month={May} }
 @inbook{bhogaraju_jain_jaiswal_escobedo_2023, title={Assessing the Effects of Expanded Input Elicitation and Machine Learning-Based Priming on Crowd Stock Prediction}, url={https://doi.org/10.1007/978-3-031-41774-0_1}, DOI={10.1007/978-3-031-41774-0_1}, abstractNote={The stock market is affected by a seemingly infinite number of factors, making it highly uncertain yet impactful. A large determinant of stock performance is public sentiment, which can often be volatile. To integrate human inputs in a more structured and effective manner, this study explores a combination of the wisdom of crowds concept and machine learning (ML) for stock price prediction. A crowdsourcing study is developed to test three ways to elicit stock predictions from the crowd. The study also assesses the impact of priming participants with estimates provided by an Long Short Term Model (LSTM) model herein developed for this context.}, author={Bhogaraju, Harika and Jain, Arushi and Jaiswal, Jyotika and Escobedo, Adolfo R.}, year={2023} }
 @article{akbari_escobedo_2023, title={Beyond kemeny rank aggregation: A parameterizable-penalty framework for robust ranking aggregation with ties}, url={https://doi.org/10.1016/j.omega.2023.102893}, DOI={10.1016/j.omega.2023.102893}, abstractNote={Rank Aggregation has ubiquitous applications in operations research, artificial intelligence, computational social choice, and various other fields. Interest in this problem has increased due in part to the need to consolidate lists of rankings and scores output by different decision-making processes and algorithms. Although most attention has focused on the variant of this problem induced by the Kemeny-Snell distance, other robust rank aggregation problems have been proposed. This work delves into the rank aggregation problem under the generalized Kendall-tau distance —a parameterizable-penalty distance measure for comparing rankings with ties— which contains Kemeny aggregation as a special case. First, it derives exact and heuristic solution methods. Second, it introduces a social choice property (GXCC) that encloses existing variations of the Condorcet criterion as special cases, thereby expanding this seminal social choice concept beyond Kemeny aggregation for the first time. GXCC offers both computational and theoretical advantages. In particular, GXCC may help to divide the original problem into smaller subproblems, while still ensuring that solving them independently yields the optimal solution to the original problem. Experiments on two benchmark datasets conducted herein show that the featured exact and heuristic solution methods can benefit from GXCC. Finally, this work derives new theoretical insights into the effects of the generalized Kendall-tau distance penalty parameter on the optimal ranking and on the proposed social choice property.}, journal={Omega}, author={Akbari, Sina and Escobedo, Adolfo R.}, year={2023}, month={Sep} }
 @article{escobedo_yasmin_2023, title={Derivations of large classes of facet defining inequalities of the weak order polytope using ranking structures}, volume={46}, ISSN={["1573-2886"]}, DOI={10.1007/s10878-023-01075-w}, number={3}, journal={JOURNAL OF COMBINATORIAL OPTIMIZATION}, author={Escobedo, Adolfo R. and Yasmin, Romena}, year={2023}, month={Oct} }
 @article{escobedo_2023, title={Exact Matrix Factorization Updates for Nonlinear Programming}, volume={9}, ISSN={["1526-5528"]}, url={https://doi.org/10.1287/ijoc.2021.0331}, DOI={10.1287/ijoc.2021.0331}, abstractNote={ LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered when solving an optimization problem. Standard floating-point algorithms are highly efficient but remain susceptible to the accumulation of round-off errors, which can lead solvers to return feasibility and optimality claims that are actually invalid. This paper introduces a novel direct solution approach for solving sequences of closely related SLEs encountered in nonlinear programming efficiently and without round-off errors. Specifically, it introduces rank-one update algorithms for the round-off error–free factorization framework, a tool set built on integer-preserving arithmetic that has led to the development and implementation of extremely reliable subroutines for solving SLEs occurring in linear programming. The formal guarantees of the presented algorithms are established through the derivation of theoretical insights. Their advantages are supported with computational experiments, which demonstrate upward of 75× improvements over exact factorization runtimes on fully dense matrices with more than one million entries. A significant advantage of the featured integer-preserving framework is that the length of any matrix coefficient produced by its algorithms is bounded polynomially in the size of the inputs without having to resort to greatest common divisor operations, which are required by and thereby hinder an efficient implementation of exact rational arithmetic approaches. }, journal={INFORMS JOURNAL ON COMPUTING}, author={Escobedo, Adolfo R.}, year={2023}, month={Sep} }
 @article{escobedo_2023, title={Software for "Exact Matrix Factorization Updates for Nonlinear Programming"}, url={https://doi.org/10.1287/ijoc.2021.0331.cd}, DOI={10.1287/ijoc.2021.0331.cd}, abstractNote={LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered when solving an optimization prob-lem. Standard floating-point algorithms are highly efficient but remain susceptible to the accumulation of round-off errors, which can lead solvers to return feasibility and optimal-ity claims that are actually invalid. This paper introduces a novel direct solution approach for solving sequences of closely related SLEs encountered in nonlinear programming effi-ciently and without round-off errors. Specifically, it introduces rank-one update algorithms for the round-off error–free factorization framework, a tool set built on integer-preserving arithmetic that has led to the development and implementation of extremely reliable sub-routines for solving SLEs occurring in linear programming. The formal guarantees of the presented algorithms are established through the derivation of theoretical insights. Their advantages are supported with computational experiments, which demonstrate upward of 75×improvements over exact factorization runtimes on fully dense matrices with more than one million entries. A significant advantage of the featured integer-preserving frame-work is that the length of any matrix coefficient produced by its algorithms is bounded polynomially in the size of the inputs without having to resort to greatest common divisor operations, which are required by and thereby hinder an efficient implementation of exact rational arithmetic approaches.}, journal={INFORMS Journal on Computing}, author={Escobedo, Adolfo}, year={2023}, month={Sep} }
 @article{an axiomatic distance methodology for aggregating multimodal evaluations_2022, journal={To appear in Information Sciences}, year={2022} }
 @article{yoo_escobedo_2021, title={A New Binary Programming Formulation and Social Choice Property for Kemeny Rank Aggregation}, volume={18}, url={https://doi.org/10.1287/deca.2021.0433}, DOI={10.1287/deca.2021.0433}, abstractNote={Rank aggregation is widely used in group decision making and many other applications, where it is of interest to consolidate heterogeneous ordered lists. Oftentimes, these rankings may involve a large number of alternatives, contain ties, and/or be incomplete, all of which complicate the use of robust aggregation methods. In particular, these characteristics have limited the applicability of the aggregation framework based on the Kemeny-Snell distance, which satisfies key social choice properties that have been shown to engender improved decisions. This work introduces a binary programming formulation for the generalized Kemeny rank aggregation problem—whose ranking inputs may be complete and incomplete, with and without ties. Moreover, it leverages the equivalence of two ranking aggregation problems, namely, that of minimizing the Kemeny-Snell distance and of maximizing the Kendall-τ correlation, to compare the newly introduced binary programming formulation to a modified version of an existing integer programming formulation associated with the Kendall-τ distance. The new formulation has fewer variables and constraints, which leads to faster solution times. Moreover, we develop a new social choice property, the nonstrict extended Condorcet criterion, which can be regarded as a natural extension of the well-known Condorcet criterion and the Extended Condorcet criterion. Unlike its parent properties, the new property is adequate for handling complete rankings with ties. The property is leveraged to develop a structural decomposition algorithm, through which certain large instances of the NP-hard Kemeny rank aggregation problem can be solved exactly in a practical amount of time. To test the practical implications of the new formulation and social choice property, we work with instances constructed from a probabilistic distribution and with benchmark instances from PrefLib, a library of preference data.}, number={4}, journal={Decision Analysis}, author={Yoo, Yeawon and Escobedo, Adolfo R.}, year={2021}, month={Dec}, pages={296–320} }
 @inproceedings{kassem_gudivada_escobedo_campbell_2021, title={A decision support tool for calculating waste collection needs}, url={https://www.proquest.com/openview/0fb7ed2195ee0bdaa5e4ed7bb1b35a70/1?pq-origsite=gscholar&cbl=51908}, booktitle={Institute of Industrial and Systems Engineers (IISE) Annual Conference}, author={Kassem, Zeyad and Gudivada, Venkata Saisrikar and Escobedo, Adolfo R. and Campbell, William F.}, year={2021}, pages={944–949} }
 @inproceedings{enhancing image classification capabilities of crowdsourcing-based methods through expanded input elicitation_2021, url={https://ojs.aaai.org/index.php/HCOMP/article/view/18949}, booktitle={AAAI Conference on Human Computation and Crowdsourcing (HCOMP)}, year={2021}, month={Nov} }
 @inproceedings{lower bounds on kemeny rank aggregation with non-strict rankings_2021, booktitle={IEEE Symposium Series on Computational Intelligence (SSCI)}, year={2021}, month={Dec} }
 @article{skolfield_escobedo_2021, title={Operations research in optimal power flow: A guide to recent and emerging methodologies and applications}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85118535029&partnerID=MN8TOARS}, DOI={10.1016/j.ejor.2021.10.003}, abstractNote={The fields of power system engineering and operations research are growing rapidly and becoming increasingly entwined. This survey aims to strengthen the connections between the two communities by introducing specific power systems problems and the theoretical operations research approaches implemented to address them in recent years. It discusses a number of optimal power flow applications including expansion planning, regular operation, markets, network resiliency, and unit commitment.}, journal={European Journal of Operational Research}, author={Skolfield, J.K. and Escobedo, A.R.}, year={2021} }
 @article{skolfield_escobedo_ramirez-vergara_2021, title={Transmission and capacity expansion planning against rising temperatures: A case study in Arizona}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85109516110&partnerID=MN8TOARS}, journal={arXiv}, author={Skolfield, J.K. and Escobedo, A.R. and Ramirez-Vergara, J.}, year={2021} }
 @inproceedings{skolfield_escobedo_ramirez-vergara_2021, title={Transmission and capacity expansion planning against rising temperatures: A case study in Arizona}, url={https://www.proquest.com/openview/ec45bb33740ee0a46302982da4e89313/1?pq-origsite=gscholar&cbl=51908}, booktitle={Institute of Industrial and Systems Engineers (IISE) Annual Conference}, author={Skolfield, J.Kyle and Escobedo, Adolfo R. and Ramirez-Vergara, Jose}, year={2021}, pages={872–877} }
 @inproceedings{kyle skolfield_yasmin_escobedo_huie_2020, title={A Comparison of Axiomatic Distance-Based Collective Intelligence Methods for Wireless Sensor Network State Estimation in the Presence of Information Injection}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85095606822&partnerID=MN8TOARS}, DOI={10.1109/WF-IoT48130.2020.9221131}, abstractNote={Wireless sensor networks are a cost-effective means of data collection, especially in areas which may not have significant infrastructure. There are significant challenges associated with the reliability of measurements, in particular due to their distributed nature. As such, it is important to develop methods that can extract reliable state estimation results in the presence of errors. This work proposes and compares methods based on collective intelligence ideas, namely consensus ranking and rating models, which are founded on axiomatic distances and intuitive social choice properties. The efficacy of these methods to assess a transmitted signal’s strength with varying quantity and quality of incompleteness in the network’s readings is tested.}, booktitle={IEEE World Forum on Internet of Things, WF-IoT 2020 - Symposium Proceedings}, publisher={IEEE}, author={Kyle Skolfield, J. and Yasmin, R. and Escobedo, A.R. and Huie, L.M.}, year={2020} }
 @article{yoo_escobedo_skolfield_2020, title={A new correlation coefficient for comparing and aggregating non-strict and incomplete rankings}, volume={285}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85082474817&partnerID=MN8TOARS}, DOI={10.1016/j.ejor.2020.02.027}, abstractNote={We introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non-strict (i.e., with-ties) and incomplete (i.e., unknown) preferences. The correlation coefficient is designed to enforce a neutral treatment of incompleteness whereby no assumptions are made about individual preferences involving unranked objects. The new measure, which can be regarded as a generalization of the seminal Kendall tau correlation coefficient, is proven to satisfy a set of metric-like axioms and to be equivalent to a recently developed ranking distance function associated with Kemeny aggregation. In an effort to further unify and enhance both robust ranking methodologies, this work proves the equivalence of an additional distance and correlation-coefficient pairing in the space of non-strict incomplete rankings. These connections induce new exact optimization methodologies: a specialized branch and bound algorithm and an exact integer programming formulation. Moreover, the bridging of these complementary theories reinforces the singular suitability of the featured correlation coefficient to solve the general consensus ranking problem. The latter premise is bolstered by an accompanying set of experiments on random instances, which are generated via a herein developed sampling technique connected with the classic Mallows distribution of ranking data. Associated experiments with the branch and bound algorithm demonstrate that, as data becomes noisier, the featured correlation coefficient yields relatively fewer alternative optimal solutions and that the aggregate rankings tend to be closer to an underlying ground truth shared by a majority.}, number={3}, journal={European Journal of Operational Research}, publisher={Elsevier BV}, author={Yoo, Y. and Escobedo, A.R. and Skolfield, J.K.}, year={2020}, pages={1025–1041} }
 @article{escobedo_yasmin_2020, title={Derivations of large classes of facet defining inequalities of the weak order polytope using ranking structures}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85104428542&partnerID=MN8TOARS}, journal={arXiv}, author={Escobedo, A.R. and Yasmin, R.}, year={2020} }
 @inproceedings{enhancing collective estimates by aggregating cardinal and ordinal inputs_2020, url={https://ojs.aaai.org//index.php/HCOMP/article/view/7465}, booktitle={AAAI Conference on Human Computation and Crowdsourcing (HCOMP)}, year={2020}, month={Nov} }
 @article{zhang_bansal_escobedo_2020, title={Risk-neutral and risk-averse transmission switching for load shed recovery with uncertain renewable generation and demand}, volume={14}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85092554377&partnerID=MN8TOARS}, DOI={10.1049/iet-gtd.2020.0964}, abstractNote={One of the main desired capabilities of the smart grid is ‘self-healing’, which is the ability to quickly restore power after a disturbance. Due to critical outage events, customer demand or load is at times disconnected or shed temporarily. While deterministic optimisation models have been devised to help operators expedite load shed recovery by harnessing the flexibility of the grid's topology (i.e. transmission line switching), an important issue that remains unaddressed is how to cope with the uncertainty in generation and demand encountered during the recovery process. This study introduces two-stage stochastic models to deal with these uncertain parameters, and one of them incorporates conditional value-at-risk to measure the risk level of unrecovered load shed. The models are implemented using a scenario-based approach where the objective is to maximise load shed recovery in the bulk transmission network by switching transmission lines and performing other corrective actions (e.g. generator re-dispatch) after the topology is modified. The benefits of the proposed stochastic models are compared with a deterministic mean-value model, using the IEEE 118- and 14-bus test cases. Experiments highlight how the proposed approach can serve as an offline contingency analysis tool, and how this method aids self-healing by recovering more load shedding.}, number={21}, journal={IET Generation, Transmission and Distribution}, publisher={Institution of Engineering and Technology (IET)}, author={Zhang, Y. and Bansal, M. and Escobedo, A.R.}, year={2020}, pages={4936–4945} }
 @article{kyle skolfield_escobar_escobedo_2019, title={Derivation and generation of path-based valid inequalities for transmission expansion planning}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093423715&partnerID=MN8TOARS}, journal={arXiv}, author={Kyle Skolfield, J. and Escobar, L.M. and Escobedo, A.R.}, year={2019} }
 @article{lourenco_escobedo_moreno-centeno_davis_2019, title={Exact solution of sparse linear systems via left-looking roundoff-error-free LU factorization in time proportional to arithmetic work}, volume={40}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85070855826&partnerID=MN8TOARS}, DOI={10.1137/18M1202499}, abstractNote={The roundoff-error-free (REF) LU factorization, along with the REF forward and backward substitution algorithms, allows a rational system of linear equations to be solved exactly and efficiently. T...}, number={2}, journal={SIAM Journal on Matrix Analysis and Applications}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Lourenco, C. and Escobedo, A.R. and Moreno-Centeno, E. and Davis, T.A.}, year={2019}, pages={609–638} }
 @inproceedings{escobar_escobedo_escobar_romero_2018, title={Bus-Angle Difference Structural Cuts for Transmission System Expansion Planning with L-l Reliability}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85061935375&partnerID=MN8TOARS}, DOI={10.1109/EPEC.2018.8598449}, abstractNote={This paper presents a methodology to solve the long-term transmission network expansion planning problem considering L-l reliability. The methodology supplements an underlying mixed-integer linear programming formulation with cutting planes derived from structural insights of bus-angle differences involving buses connected by paths of existing and/or expansion lines. The addition of these cutting planes expedites the solution process by yielding tighter relaxation bounds within a branch-and-cut framework, thereby reducing computational times and memory requirements. In order to solve the resulting problems, this work uses the AMPL modeling language interfaced with the CPLEX mathematical programming solver. The practicality of the methodology is tested via the Southern Brazilian System, yielding very promising results.}, booktitle={2018 IEEE Electrical Power and Energy Conference, EPEC 2018}, publisher={IEEE}, author={Escobar, L.M. and Escobedo, A.R. and Escobar, D. and Romero, R.}, year={2018} }
 @article{escobedo_moreno-centeno_lourenco_2018, title={Solution of dense linear systems via roundoff-error-free factorization algorithms: Theoretical connections and computational comparisons}, volume={44}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85060552334&partnerID=MN8TOARS}, DOI={10.1145/3199571}, abstractNote={
            Exact solving of systems of linear equations (SLEs) is a fundamental subroutine within number theory, formal verification of mathematical proofs, and exact-precision mathematical programming. Moreover, efficient exact SLE solution methods could be valuable for a growing body of science and engineering applications where current fixed-precision standards have been deemed inadequate. This article contains key derivations relating, and computational tests comparing, two exact direct solution frameworks: roundoff-error-free (REF) LU factorization and rational arithmetic LU factorization. Specifically, both approaches solve the linear system
            Ax
            =
            b
            by factoring the matrix A into the product of a lower triangular (L) and upper triangular (U) matrix,
            A
            =
            LU
            . Most significantly, the featured findings reveal that the integer-preserving REF factorization framework solves dense SLEs one order of magnitude faster than the exact rational arithmetic approach while requiring half the memory. Since rational LU is utilized for basic solution validation in exact linear and mixed-integer programming, these results offer preliminary evidence of the potential of the REF factorization framework to be utilized within this specific context. Additionally, this article develops and analyzes an efficient streamlined version of Edmonds’s Q-matrix approach that can be implemented as another basic solution validation approach. Further experiments demonstrate that the REF factorization framework also outperforms this alternative integer-preserving approach in terms of memory requirements and computational effort. General purpose codes to solve dense SLEs exactly via any of the aforementioned methods have been made available to the research and academic communities.
          }, number={4}, journal={ACM Transactions on Mathematical Software}, publisher={Association for Computing Machinery (ACM)}, author={Escobedo, A.R. and Moreno-Centeno, E. and Lourenco, C.}, year={2018}, pages={1–24} }
 @article{escobedo_moreno-centeno_2017, title={Roundoff-error-free basis updates of lu factorizations for the efficient validation of optimality certificates}, volume={38}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85031804952&partnerID=MN8TOARS}, DOI={10.1137/16M1089630}, abstractNote={The roundoff-error-free (REF) LU and Cholesky factorizations, combined with the REF substitution algorithms, allow rational systems of linear equations to be solved exactly and efficiently by worki...}, number={3}, journal={SIAM Journal on Matrix Analysis and Applications}, publisher={Society for Industrial & Applied Mathematics (SIAM)}, author={Escobedo, Adolfo R. and Moreno-Centeno, Erick}, year={2017}, pages={829–853} }
 @article{moreno-centeno_escobedo_2016, title={Axiomatic aggregation of incomplete rankings}, volume={48}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84958759167&partnerID=MN8TOARS}, DOI={10.1080/0740817X.2015.1109737}, abstractNote={ABSTRACT In many different applications of group decision-making, individual ranking agents or judges are able to rank only a small subset of all available candidates. However, as we argue in this article, the aggregation of these incomplete ordinal rankings into a group consensus has not been adequately addressed. We propose an axiomatic method to aggregate a set of incomplete rankings into a consensus ranking; the method is a generalization of an existing approach to aggregate complete rankings. More specifically, we introduce a set of natural axioms that must be satisfied by a distance between two incomplete rankings; prove the uniqueness and existence of a distance satisfying such axioms; formulate the aggregation of incomplete rankings as an optimization problem; propose and test a specific algorithm to solve a variation of this problem where the consensus ranking does not contain ties; and show that the consensus ranking obtained by our axiomatic approach is more intuitive than the consensus ranking obtained by other approaches.}, number={6}, journal={IIE Transactions (Institute of Industrial Engineers)}, publisher={Informa UK Limited}, author={Moreno-Centeno, Erick and Escobedo, Adolfo R.}, year={2016}, pages={475–488} }
 @article{escobedo_moreno-centeno_2015, title={Roundoff-error-free algorithms for solving linear systems via cholesky and LU factorizations}, volume={27}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84948667630&partnerID=MN8TOARS}, DOI={10.1287/ijoc.2015.0653}, abstractNote={ LU and Cholesky factorizations are computational tools for efficiently solving linear systems that play a central role in solving linear programs and several other classes of mathematical programs. In many documented cases, however, the roundoff errors accrued during the construction and implementation of these factorizations lead to the misclassification of feasible problems as infeasible and vice versa. Hence, reducing these roundoff errors or eliminating them altogether is imperative to guarantee the correctness of the solutions provided by optimization solvers. To achieve this goal without having to use rational arithmetic, we introduce two roundoff-error-free factorizations that require storing the same number of individual elements and performing a similar number of operations as the traditional LU and Cholesky factorizations. Additionally, we present supplementary roundoff-error-free forward and backward substitution algorithms, thereby providing a complete tool set for solving systems of linear equations exactly and efficiently. An important property shared by the featured factorizations and substitution algorithms is that their individual coefficients’ maximum word length—i.e., the maximum number of digits required for expression—is bounded polynomially. Unlike the rational arithmetic methods used in practice to solve linear systems exactly, however, the algorithms herein presented do not require any gcd calculations to bound the entries’ word length. We also derive various other related theoretical results, including the total computational complexity of all the roundoff-error-free processes herein presented. }, number={4}, journal={INFORMS Journal on Computing}, publisher={Institute for Operations Research and the Management Sciences (INFORMS)}, author={Escobedo, Adolfo R. and Moreno-Centeno, Erick}, year={2015}, pages={677–689} }
 @article{escobedo_moreno-centeno_hedman_2014, title={Topology control for load shed recovery}, volume={29}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84897607427&partnerID=MN8TOARS}, DOI={10.1109/TPWRS.2013.2286009}, abstractNote={This paper introduces load shed recovery actions for transmission networks by presenting the dc optimal load shed recovery with transmission switching model (DCOLSR-TS). The model seeks to reduce the amount of load shed, which may result due to transmission line and/or generator contingencies, by modifying the bulk power system topology. Since solving DCOLSR-TS is computationally difficult, the current work also develops a heuristic (MIP-H), which improves the system topology while specifying the required sequence of switching operations. Experimental results on a list of N-1 and N-2 critical contingencies of the IEEE 118-bus test case demonstrate the advantages of utilizing MIP-H for both online load shed recovery and recurring contingency-response analysis. This is reinforced by the introduction of a parallelized version of the heuristic (Par-MIP-H), which solves the list of critical contingencies close to 5x faster than MIP-H with 8 cores and up to 14x faster with increased computational resources. The current work also tests MIP-H on a real-life, large-scale network in order to measure the computational performance of this tool on a real-world implementation.}, number={2}, journal={IEEE Transactions on Power Systems}, publisher={Institute of Electrical & Electronics Engineers (IEEE)}, author={Escobedo, A.R. and Moreno-Centeno, E. and Hedman, K.W.}, year={2014}, pages={908–916} }