A Column Generation Algorithm with Dynamic Constraint Aggregation for Minimum Sum-of-Squares Clustering

An exact approach for maximizing the lifetime of sensor networks with adjustable sensing ranges

Column generation is a fundamental technique for solving large-scale combinatorial optimization problems such as unit commitment and vehicle routing, yet its performance is often limited by dual oscillation. This study explores the intrinsic cause of this phenomenon from the perspective of shadow price theory and demonstrates that dual oscillation arises from the lack of marginal interpretability of Lagrange multipliers when multiple dual solutions coexist. To address this issue, an improved column generation framework is proposed in which traditional multipliers are replaced with minimum-norm multipliers that possess clear economic meaning and act as directional shadow prices. A generalized pricing subproblem is formulated, and partial minimum-norm multipliers are obtained through convex quadratic optimization to guide column generation. Numerical experiments on a simplified single-period unit commitment case and large-scale cutting stock problems showed that the proposed approach eliminated invalid column generation and achieved speedy convergence to the optimal solution within only two iterations for the unit commitment case, and the classical column generation exhibited slow convergence with dual oscillation in large-scale scenarios while the improved algorithm achieved fast and stable convergence. The results indicate that the stabilization method enhances the consistency of dual variables and provides a more robust foundation for the theoretical and practical development of column generation algorithms.

Column generation is an increasingly popular basic tool for the solution of large-scale mathematical programming problems. As problems being solved grow bigger, column generation may however become less efficient in its present form, where columns typically are not optimizing, and finding an optimal solution instead entails finding an optimal convex combination of a huge number of them. We present a class of column generation algorithms in which the columns defining the restricted master problem may be chosen to be optimizing in the limit, thereby reducing the total number of columns needed. This first article is devoted to the convergence properties of the algorithm class, and includes global (asymptotic) convergence results for differentiable minimization, finite convergence results with respect to the optimal face and the optimal solution, and extensions of these results to variational inequality problems. An illustration of its possibilities is made on a nonlinear network flow model, contrasting its convergence characteristics to that of the restricted simplicial decomposition (RSD) algorithm.

This paper develops a cost-effective sequential route recommender system to provide real-time routing recommendations for vacant taxis searching for the next passenger. We propose a prediction-and-optimization framework to recommend the searching route that maximizes the expected profit of the next successful passenger pickup based on the dynamic taxi demand-supply distribution. Specifically, this system features a deep learning-based predictor that dynamically predicts the passenger pickup probability on a road segment and a recursive searching algorithm that recommends the optimal searching route. The predictor integrates a graph convolution network (GCN) to capture the spatial distribution and a long short-term memory (LSTM) to capture the temporal dynamics of taxi demand and supply. The GCN-LSTM model can accurately predict the pickup probability on a road segment with the consideration of potential taxi oversupply. Then, the dynamic distribution of pickup probability is fed into the route optimization algorithm to recommend the optimal searching routes sequentially as route inquiries emerge in the system. The recursion tree-based route optimization algorithm can significantly reduce the computational time and provide the optimal routes within seconds for real-time implementation. Finally, extensive experiments using Beijing Taxi GPS data demonstrate the effectiveness and efficiency of the proposed recommender system. History: Accepted by Ram Ramesh, Area Editor for Data Science and Machine Learning. Funding: This work was partially supported by the Hong Kong Research Grants Council [Grants CityU 21500220, CityU 11504322] and the National Natural Science Foundation of China [Grant 72201222]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2021.0112 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0112 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

We present a new difference of convex functions algorithm (DCA) for solving linear and nonlinear mixed complementarity problems (MCPs). The approach is based on the reformulation of bilinear complementarity constraints as difference of convex (DC) functions, more specifically, the difference of scalar, convex quadratic terms. This reformulation gives rise to a DC program, which is solved via sequential linear approximations of the concave term using standard DCA techniques. The reformulation is based on a generalization of earlier results on recasting bilinearities and leads to a novel algorithmic framework for MCPs. Through extensive numerical experimentation, the proposed approach, referred to as DCA-BL, proves to be an efficient heuristic for complementarity problems. For linear complementarity problems (LCPs), we test the approach on a number of randomly generated instances by varying the size, the density, and the eigenvalue distribution of the LCP matrix, providing insights into the numerical properties of DCA-BL. In addition, we apply the framework to a market equilibrium problem and find that DCA-BL scales well on realistic LCP instances. Also, through experimentation, we find that that DCA-BL performs particularly well compared with other DC-based complementarity approaches in the literature if the LCP is highly dense, asymmetric, or indefinite. Lastly, the method is successfully applied to a set of equilibrium problems with second-order cone constraints, which give rise to nonlinear complementarity problems, with applications to stochastic equilibrium problems in water infrastructure and finance. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Funding: This work was supported by the Division of Civil, Mechanical and Manufacturing Innovation [Grant 2113891], the Division of Electrical, Communications and Cyber Systems [Grant 2114100], the Office of Naval Research Global [Grant 00014-22-1-2649], Petrobras [Grant 4324713], the Division of Mathematical Sciences [Grant 2318519], and the Danmarks Frie Forskningsfond [Grant 0217-00009B]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0822 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0822 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Mobile technologies and AI enable health data collection from devices, allowing effective monitoring. Traditional methods often compromise privacy, but federated learning (FL) offers a potential solution. However, current FL approaches face two issues: they don’t identify key health features for clinical intervention, and their aggregation overlooks patient multidimensional heterogeneity. This study seeks to develop a new FL method to tackle these challenges and enhance privacy in mobile health monitoring. This study proposes a novel FL method combining (1) a spatial and temporal attention-based prediction model (STA-Pred) that uses attention to identify key spatial and temporal features, and (2) a multidimensional heterogeneity-based aggregation protocol (MDH-Aggr), which aggregates components based on their heterogeneity to handle multidimensional differences. Experiments on three data sets show that our method outperforms existing methods in several patient-monitoring contexts. This study enhances understanding of how to leverage mobile technologies and AI to enable privacy-preserving health monitoring that promotes the social good. Additionally, it advances FL research through two innovative designs (STA-Pred and MDH-Aggr). History: This paper has been accepted by Kaushik Dutta for the Special Issue on Responsible AI and Data Science for Social Good. Funding: Y. Chai, H. Liu, and Y. Liu are supported by the National Natural Science Foundation of China [Grants 72342011, 72322019, 72188101, and 72402001]. Dr. L. Wang’s work was in part supported by the National Natural Science Foundation of China [Grant 72271027], Hainan Provincial Natural Science Foundation of China [Grant 726MS0458], and Beijing Institute of Technology Research Fund Program for Young Scholars [Grant XSQD-202216004]. X. Liu is not supported by any funds or associated with any of the abovementioned funds. Supplemental Materials: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0521 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0521 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/.

Infodemic is a significant concern for society, and numerous studies have explored artificial intelligence (AI)-based solutions to manage it. However, existing methods fail to make sense of the complex situation of infodemic and fail to manage infodemic in a proactive manner. To tackle this challenge, we formalize infodemic topic prediction (ITP) as a distinct research problem. ITP aims to identify emerging topics to provide a global view of the situation, as well as to predict the probability of a topic becoming an infodemic to enable proactive management. Although some relevant methods exist, they are insufficient in modeling the intertopic relationships where each topic is closely connected to all others in a group of topics (called multilateral intertopic relationships). This study proposes a new hypergraph-based ITP framework that models the multilateral intertopic relationship with a novel hypergraph. Specifically, we introduce a novel temporal topic hypergraph (TTH) where topics are treated as nodes, and the multilateral intertopic relationships in both semantic and temporal perspectives are modeled by hyperedges. The main novelties are twofold. First, our TTH is a novel hypergraph that can cope with newly emerged topics through the proposed directed and undirected hyperedges. Second, we propose a novel similarity-based transformation method (STM) that reduces the complexity of hypergraph transformation from [Formula: see text] to [Formula: see text], making it scalable for social media data. Evaluations on infodemics during the COVID-19 and the Mpox pandemic demonstrate the effectiveness of our framework. This study contributes to responsible infodemic management by formalizing the task of ITP and introducing a novel framework for it, which enables public health organizations, social media platforms, and policymakers to proactively make sense of and effectively respond to infodemic. History: This paper has been accepted by Kaushik Dutta for the Special Issue on the Responsible AI and Data Science for Social Good. Funding: L. Zhao, S. Ding, Y. Chai and S. Yang are supported by the National Natural Science Foundation of China [Grants 72293581, 72188101, 72342011, and 72322019]. J. Xie and X. Fang are not supported by any funds and are not associated with any of the above mentioned funds. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0660 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0660 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

There is a recent proliferation of research on the integration of machine learning and optimization. One expansive area within this research stream is optimization over pre-trained predictive models, which proposes the use of pre-trained predictive models as surrogates for uncertain or highly complex objective functions. In this setting, features of the predictive models become decision variables in the optimization problem. Despite a recent surge in publications in this area, only a few papers note the importance of incorporating trust-region considerations in this decision-making pipeline, that is, enforcing solutions to be similar to the data used to train the predictive models. Without such constraints, the evaluation of the predictive model at solutions obtained from optimization cannot be trusted and the practicality of the solutions may be unreasonable. In this paper, we provide an overview of the approaches appearing in the literature to construct a trust region and propose three alternative approaches. Our numerical evaluation highlights that trust-region constraints learned through our newly proposed approaches compare favorably with previously suggested approaches, both in terms of solution quality and computational time. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0312 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0312 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Kidney exchange problems with immunosuppressants extend the classical kidney exchange problem by allowing a limited number of arcs that do not belong to the compatibility graph to be included in the solution. Among these, the kidney exchange problem with reserve arcs (KEP-RA) assumes that any arc can be made compatible, whereas the kidney exchange problem with half-compatible arcs (KEP-HCA) assumes that this is the case only for a subset of arcs. Starting with KEP-RA, we first show that existing integer linear programming formulations for the kidney exchange problem can easily be extended to include reserve arcs. We then demonstrate that there always exists an optimal KEP-RA solution in which every cyclic set of exchanges contains at most one reserve arc, and we use this property to develop effective variable reduction procedures and new ad hoc modeling structures. We also extend these findings to the case where nondirected donors are included. Experiments show that trivial model extensions are not able to cope with medium-sized instances, whereas our enhanced models can solve instances with up to a thousand recipient-donor pairs. We also evaluate the number of transplants enabled by each reserve arc in various settings, demonstrating that although reserve arcs tend to have a diminishing return, there are instances for which this is not the case. Finally, we demonstrate how our techniques can be integrated into a variable and constraint generation algorithm to solve KEP-HCA and show that its performance complements that of a trivial model extension. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: D. Manlove was supported by the Engineering and Physical Sciences Research Council [Grant EP/X013618/1]. This work used the Dutch national e-infrastructure with the support of the SURF Cooperative [Grants EINF-8220 and EINF-12272]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.1071 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.1071 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

We present a new flow-based formulation for identical parallel machine scheduling with a regular objective function and without idle time. The formulation is constructed with the help of a decision diagram that represents all job sequences that respect specific ordering rules. These rules rely on a partition of the planning horizon into, generally nonuniform, periods and do not exclude all optimal solutions, but they constrain solutions to adhere to a canonical form. The new formulation has numerous variables and constraints, and hence we apply a Dantzig-Wolfe decomposition to compute the linear programming relaxation in reasonable time; the resulting lower bound is stronger than the bound from the classical time-indexed formulation. We develop a branch-and-price framework that solves three instances from the literature for the first time. We compare the new formulation with the time-indexed and arc time–indexed formulation by means of a series of computational experiments. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work was partially funded by the European Union’s Horizon 2020 research and innovation program under [Marie Skłodowska-Curie Grant 754462]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0301 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0301 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

We study a robust auction design problem with a minimax regret objective, in which a seller seeks a mechanism for selling multiple items to multiple bidders with additive values. The seller knows that the bidders’ values range over a box uncertainty set but has no information on their probability distribution. The robust auction design model we study requires no distributional information except for upper bounds on the bidders’ values for each item. This model is relevant if there is no trustworthy distributional information or if any distributional information is costly or time-consuming to acquire. We propose a mechanism that sells each item separately via a second price auction with a random reserve price and prove that this mechanism is optimal using duality techniques from robust optimization. We then interpret the auction design problem as a zero-sum game between the seller, who chooses a mechanism, and a fictitious adversary or “nature,” who chooses the bidders’ values from within the uncertainty set with the aim to maximize the seller’s regret. We characterize the Nash equilibrium of this game analytically when the bidders are symmetric. The Nash strategy of the seller coincides with the optimal separable second price auction, whereas the Nash strategy of nature is mixed and constitutes a probability distribution on the uncertainty set under which each bidder’s values for the items are comonotonic. We also study a restricted auction design problem over deterministic mechanisms. In this setting, we characterize the suboptimality of a separable second price auction with deterministic reserve prices and show that this auction becomes optimal if the bidders are symmetric. The optimal mechanism is derived in closed form and can easily be implemented by practitioners. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This research was funded by the Swiss National Science Foundation [Grant BSCGI0_157733] and by the Ministry of Education, Singapore, under its Academic Research Fund Tier 2 [Grant MOE-T2EP20222-0003]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0275 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0275 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

This study introduces a new optimization model and a branch-and-cut approach for synthesizing optimal quantum circuits for reversible Boolean functions, which are pivotal components in quantum algorithms. Although heuristic algorithms have been extensively explored for quantum circuit synthesis, research on exact counterparts remains relatively limited. However, the need to design quantum circuits with guaranteed optimality is increasing, especially for improving computational fidelity on noisy intermediate-scale quantum devices. This study presents mathematical optimization as a viable option for optimal synthesis, with the potential to accommodate practical considerations arising in fast-evolving quantum technologies. We set a demonstrative problem to implement reversible Boolean functions using high-level gates known as multiple control Toffoli gates while minimizing a technology-based proxy called quantum cost—the number of low-level gates used to realize each high-level gate. To address this problem, we propose a discrete optimization model based on a multicommodity network and discuss potential future variations at an abstract level to incorporate technical considerations. A customized branch and cut is then developed upon different aspects of our model, including polyhedron integrality, surrogate constraints, and variable prioritization. Our experiments demonstrate the robustness of the proposed approach in finding cost-optimal circuits for all benchmark instances within a two-hour time frame. Furthermore, we present interesting intuitions from these experiments and compare our computational results with relevant studies, highlighting newly discovered circuits with the lowest quantum costs reported in this paper. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing. This paper has been accepted for the INFORMS Journal on Computing Special Issue on Quantum Computing. Funding: This research was supported by the Ministry of Science and Information and Communication Technology, South Korea [Grants 2017R1E1A1A0307098814 and 2020R1A4A307986411]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0562 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0562 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Ranking problems are commonly encountered in practical applications, including order priority ranking, wine quality ranking, and piston slap noise performance ranking. The responses of these ranking applications are often considered as continuous responses, and there is uncertainty on which scoring function is used to model the responses. In this paper, we address the scoring function uncertainty of continuous response ranking problems by proposing a ranking model averaging (RMA) method. With a set of candidate models varied by scoring functions, RMA assigns weights for each model determined by a K-fold crossvalidation criterion based on pairwise loss. We provide two main theoretical properties for RMA. First, we prove that the averaging ranking predictions of RMA are asymptotically optimal in achieving the lowest possible ranking risk. Second, we provide a bound on the difference between the empirical RMA weights and theoretical optimal ones, and we show that RMA weights are consistent. Simulation results validate RMA superiority over competing methods in reducing ranking risk. Moreover, when applied to empirical examples—order priority, wine quality, and piston slap noise—RMA shows its effectiveness in building accurate ranking systems. History: Accepted by Ram Ramesh, Area Editor for Data Science & Machine Learning. Funding: This research was supported by the Beijing Municipal Natural Science Foundation [Grant 1222002], the National Natural Science Foundation of China [Grants 12071457, 12201018, 12301364, 71925007, 72091212, and 72273120], National Quality Infrastructure [Grant 2022YFF0609903], the Chinese Academy of Sciences Project for Young Scientists in Basic Research [Grant YSBR-008], and the Natural Science Foundation of Anhui Province [Grant 2308085QA09]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0257 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0257 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

We study a stochastic perishable inventory control problem with endogenous (decision-dependent) uncertainty in shelf life of units. Our primary motivation is determining ordering policies for blood platelets. Hospitals typically order their required platelets from a central supplier, and as such, the shelf life of units at the time of delivery can be subject to significant variability. Determining optimal ordering quantities is a challenging task because of the short maximum shelf life of platelets (three to five days after testing) and high uncertainty in daily demand. We formulate the problem as an infinite-horizon discounted Markov decision process (MDP). The model captures salient features observed in our data from a network of Canadian hospitals and allows for fixed ordering costs. We show that with uncertainty in shelf life, the value function of the MDP is nonconvex and key structural properties valid under deterministic shelf life no longer hold. Hence, we propose an approximate dynamic programming (ADP) algorithm to find approximate policies. We approximate the value function using a linear combination of basis functions and tune the parameters using a simulation-based policy iteration algorithm. We evaluate the performance of the proposed policy using extensive numerical experiments in parameter regimes relevant to the platelet inventory management problem. We further leverage the ADP algorithm to evaluate the impact of ignoring shelf-life uncertainty. Finally, we evaluate the out-of-sample performance of the ADP algorithm in a case study using real data and compare it with the historical hospital performance and other benchmarks. After tuning the parameters, the ADP policy can be computed online in a few seconds and results in more than 50% lower expiration and shortage rates compared with the historical rates. In addition, it performs better or as well as other benchmarks, including an exact policy that ignores uncertainty in shelf life and becomes hard to compute for larger instances of the problem. History: Accepted by Paul Brooks, Area Editor for Applications in Biology, Medicine, & Healthcare. Funding: V. Sarhangian was supported by the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2018-04518]. H. Abouee-Mehrizi was supported by the Natural Sciences and Engineering Council of Canada [Grant RGPIN-2019-05625]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0245 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0245 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Forecasting the market risk for publicly traded companies is a critical task for market participants. Financial economics research demonstrates that the textual information contained in corporate disclosures, such as earnings conference call transcripts, can effectively predict a firm’s future risk. This finding has inspired a growing body of research focused specifically on transcript-based approaches to risk forecasting. However, earnings transcripts are typically long documents with thousands of words. Prior transcript-based risk forecasting studies that represent the entire transcript as one text sequence often fail to capture risk-relevant information and fall short in risk forecasting. In this work, we propose a novel divide-and-contrast machine learning method for predicting risks from earnings conference call transcripts. We exploit the semistructured nature of an earnings transcript and decompose it into several semantically coherent conversation units, ranging from the finest grained question–answer pair level to the coarsest grained transcript level. We then propose contrastive learning objectives as an auxiliary task to the risk forecasting objective, facilitating the learning of risk-relevant information from the earnings transcripts. We conduct experiments on a data set of U.S. market earnings call transcripts. The experimental results show that our proposed divide-and-contrast method substantially outperforms state-of-the-art methods by significantly reducing errors in risk forecasting. This paper sheds light on extracting informative insights from lengthy financial documents to support informed decision making. History: Accepted by Ram Ramesh, Area Editor for Data Science and Machine Learning. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0195 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0195 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .