Search

In this paper, we propose the continuous variable neighborhood search method for finding all the solutions to a nonlinear system of equations (NSEs). We transform the NSE problem into an equivalent optimization problem, and we use a new objective function that allows us to find all the zeros. Instead of the usual sum-of-squares objective function, our objective function is presented as the sum of absolute values. Theoretical investigation confirms that our objective function provides more accurate solutions regardless of the optimization method used. In addition, we achieve a trade-off (i.e., increased precision at the expense of reduced smoothness). Computational analysis of standard test instances shows that the proposed method is more precise and much faster than two recently developed methods. Similar conclusions are drawn by comparing the proposed method with many other methods in the literature. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0876. [ABSTRACT FROM AUTHOR]

The β-robust machine scheduling has attracted increasing attention as an effective method to hedge against uncertainty. However, existing β-robust scheduling models rely on the normality assumption of uncertain parameters, and existing solution methods are based on branch and bound, which cannot solve problems of 45 jobs within 3,600 seconds. This paper proposes distributionally β-robust scheduling (DRS) models to handle uncertain processing times. The DRS models only require the lower bound, mean, and covariance information of processing times, and have the capability of handling both single and parallel machine problems. Another key contribution of this paper is to devise efficient parametric search (PS) methods for the DRS models. Specifically, we show that there exists a parameterized assignment problem (PAP), such that its optimal solutions are also optimal for the original problem. The proposed methods only need to perform a onedimensional PS and solve a series of PAPs.We further propose a bidirectional PS to reduce the number of PAPs needed to be solved, and we design a speedup shortest augmentation path algorithm for these PAPs. Experimental results on both single and identical parallel machine problems show that the improved PS method outperforms existing algorithms by more than three orders of magnitude improvement in computation time for problems of 45 jobs, and it is able to solve problems of 500 jobs within 0.5 seconds. [ABSTRACT FROM AUTHOR]

This paper makes a contribution to the branch and cut approach to the capacitated vehicle-routing problem (CVRP). In the CVRP, the demands of a set of customers have to be met at minimum total travel cost using vehicles of identical capacity based at a single depot. The potential of maximally violated mod-p cutting-planes (Caprara et al. 2000) for the CVRP is investigated via a computational study. The foundation of the assessment is formed by classes of problem-specific constraints taken from the literature. In several separation algorithms for the CVRP, it is advantageous to shrink inclusionwise maximal minimum-weight cuts in support graphs as preprocessing. It is mentioned how a partition of the set of customers into such mincuts can be computed in a fast and elegant way using the mincut algorithm of Hao and Orlin (1994). Interestingly, maximally violated mod-p cuts, which are general-purpose cuts of Chvátal-Gomory type, stand comparison with problem-specific cuts for the CVRP and they are clearly useful on top of such cuts. The first-time proven optimal solution of the CVRP instance B-n68-k9 is reported. The computation used a branching strategy with far lookahead and relied on maximally violated mod-p cuts. This paper on maximally violated cuts belongs to a set of papers originating from Applegate et al. (1995) where a separation of maximally violated combs for the traveling-salesman problem (TSP) is suggested. [ABSTRACT FROM AUTHOR]

Zero forcing is a graph coloring process based on the following color change rule: all vertices of a graph G are initially colored either blue or white; in each timestep, a white vertex turns blue if it is the only white neighbor of some blue vertex. A zero forcing set of G is a set of blue vertices such that all vertices eventually become blue after iteratively applying the color change rule. The zero forcing number Z (G) is the cardinality of a minimum zero forcing set. In this paper, we propose novel exact algorithms for computing Z (G) based on formulating the zero forcing problem as a two-stage Boolean satisfiability problem. We also propose several heuristics for zero forcing based on iteratively adding blue vertices which color a large part of the remaining white vertices. These heuristics are used to speed up the exact algorithms and can also be of independent interest in approximating Z (G) . Computational results on various types of graphs show that, in many cases, our algorithms offer a significant improvement on the state-of-the-art algorithms for zero forcing. Summary of Contribution: This paper proposes novel algorithms and heuristics for an NP-hard graph coloring problem that has numerous applications. Our exact methods combine Boolean satisfiability modeling with a constraint generation framework commonly used in operations research. The paper also includes an analysis of the facets of the polytope associated with this problem and decomposition techniques which can reduce the size of the problem. Our computational approaches are implemented and tested on a wide variety of graphs and are compared with the state-of-the-art algorithms from the literature. We show that our proposed algorithms based on Boolean satisfiability, in conjunction with the heuristics and order-reduction techniques, yield a significant speedup in some cases. [ABSTRACT FROM AUTHOR]

Recent advances in network representation learning have enabled significant improvement in the link prediction task, which is at the core of many downstream applications. As an increasing amount of mobility data become available because of the development of location-based technologies, we argue that this resourceful mobility data can be used to improve link prediction tasks. In this paper, we propose a novel link prediction framework that utilizes user offline check-in behavior combined with user online social relations. We model user offline location preference via a probabilistic factor model and represent user social relations using neural network representation learning. To capture the interrelationship of these two sources, we develop an anchor link method to align these two different user latent representations. Furthermore, we employ locality-sensitive hashing to project the aggregated user representation into a binary matrix, which not only preserves the data structure but also improves the efficiency of convolutional network learning. By comparing with several baseline methods that solely rely on social networks or mobility data, we show that our unified approach significantly improves the link prediction performance. Summary of Contribution: This paper proposes a novel framework that utilizes both user offline and online behavior for social link prediction by developing several machine learning algorithms, such as probabilistic factor model, neural network embedding, anchor link model, and locality-sensitive hashing. The scope and mission has the following aspects: (1) We develop a data and knowledge modeling approach that demonstrates significant performance improvement. (2) Our method can efficiently manage large-scale data. (3) We conduct rigorous experiments on real-world data sets and empirically show the effectiveness and the efficiency of our proposed method. Overall, our paper can contribute to the advancement of social link prediction, which can spur many downstream applications in information systems and computer science. [ABSTRACT FROM AUTHOR]

When generating multirow intersection cuts for mixed-integer linear optimization problems, an important practical question is deciding which intersection cuts to use. Even when restricted to cuts that are facet defining for the corner relaxation, the number of potential candidates is still very large, especially for instances of large size. In this paper, we introduce a subset of intersection cuts based on the infinity norm that is very small, works for relaxations having arbitrary number of rows and, unlike many subclasses studied in the literature, takes into account the entire data from the simplex tableau. We describe an algorithm for generating these inequalities and run extensive computational experiments in order to evaluate their practical effectiveness in real-world instances. We conclude that this subset of inequalities yields, in terms of gap closure, around 50% of the benefits of using all valid inequalities for the corner relaxation simultaneously, but at a small fraction of the computational cost, and with a very small number of cuts. Summary of Contribution: Cutting planes are one of the most important techniques used by modern mixed-integer linear programming solvers when solving a variety of challenging operations research problems. The paper advances the state of the art on general-purpose multirow intersection cuts by proposing a practical and computationally friendly method to generate them. [ABSTRACT FROM AUTHOR]

Summary of Contribution: Big data analytics has become essential for modern operations research and operations management applications. Statistics methods, such as nonparametric density and function estimation, play important roles in predictive and exploratory data analysis for economics and operations management problems. In this paper, we concentrate on efficiently computing local polynomial regression estimates. We significantly accelerate the computation of such local polynomial estimates by novel applications of multidimensional binary indexed trees (Fenwick 1994) and lazy memory allocation via hashing. Both time and space complexity of our proposed algorithm are nearly linear in the number of inputs. Simulation results confirm the efficiency and effectiveness of our proposed methods. Local polynomial regression is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time complexity which hinders its applicability in large-scale data analysis. In this paper, we significantly accelerate the computation of local polynomial estimates by novel applications of multidimensional binary indexed trees. Both time and space complexity of our proposed algorithm is nearly linear in the number of input data points. Simulation results confirm the efficiency and effectiveness of our proposed approach. Summary of Contribution. Big data analytics has become essential for modern operations research and operations management applications. Statistics methods, such as nonparametric density and function estimation, play important roles in predictive and exploratory data analysis for economics and operations management problems. In this paper, we concentrate on efficiently computing local polynomial regression estimates. We significantly accelerate the computation of such local polynomial estimates by novel applications of multidimensional binary indexed trees and lazy memory allocation via hashing. Both time and space complexity of our proposed algorithm are nearly linear in the number of inputs. Simulation results confirm the efficiency and effectiveness of our proposed methods. [ABSTRACT FROM AUTHOR]

We consider a two-player interdiction problem staged over a graph where the attacker's objective is to minimize the cost of removing edges from the graph so that the defender's objective, that is, the weight of a minimum spanning tree in the residual graph, is increased up to a predefined level r. Standard approaches for graph interdiction frame this type of problems as bilevel formulations, which are commonly solved by replacing the inner problem by its dual to produce a single-level reformulation. In this paper, we study an alternative integer program derived directly from the attacker's solution space and show that this formulation yields a stronger linear relaxation than the bilevel counterpart. Furthermore, we analyze the convex hull of the feasible solutions of the problem and identify several families of facet-defining inequalities that can be used to strengthen this integer program. We then proceed by introducing a different formulation defined by a set of so-called supervalid inequalities that may exclude feasible solutions, albeit solutions whose objective value is not better than that of an edge cut of minimum cost. We discuss several computational aspects required for an efficient implementation of the proposed approaches. Finally, we perform an extensive set of computational experiments to test the quality of these formulations, analyzing and comparing the benefits of each model, as well as identifying further enhancements. Summary of Contribution: Network interdiction has received significant attention over the last couple of decades, with a notable peak of interest in recent years. This paper provides an interesting balance between the theoretical and computational aspects of solving a challenging network interdiction problem via integer programming. We present several technical developments, including a detailed study of the problem's solution space, multiple formulations, and a polyhedral analysis of the convex hull of feasible solutions. We then analyze the results of an extensive set of computational experiments that were used to validate the effectiveness of the different methods we developed in this paper. [ABSTRACT FROM AUTHOR]

We consider the classical convex constrained nonconvex quadratic programming problem where the Hessian matrix of the objective to be minimized has r negative eigenvalues, denoted by (QPr). Based on a biconvex programming reformulation in a slightly higher dimension, we propose a novel branch-and-bound algorithm to solve (QP1) and show that it returns an ɛ -approximate solution of (QP1) in at most O (1 / ɛ ) iterations. We further extend the new algorithm to solve the general (QPr) with r > 1. Computational comparison shows the efficiency of our proposed global optimization method for small r. Finally, we extend the explicit relaxation approach for (QP1) to (QPr) with r > 1. Summary of Contribution: Nonconvex quadratic program (QP) is a classical optimization problem in operations research. This paper aims at globally solving the QP where the Hessian matrix of the objective to be minimized has r negative eigenvalues. It is known to be nondeterministic polynomial-time hard even when r = 1. This paper presents a novel algorithm to globally solve the QP for r = 1 and then extends to general r. Numerical results demonstrate the superiority of the proposed algorithm in comparison with state-of-the-art algorithms/software for small r. [ABSTRACT FROM AUTHOR]

In this paper, we consider the maximum lifetime data gathering tree (MLDT) problem in sensor networks. A data gathering tree is a spanning tree rooted at a specified sink so that every node can send its messages to the sink along the tree. The lifetime of a tree is defined as the minimum lifetime among nodes where each node's lifetime is determined by its initial energy and transmission load. The MLDT problem is NP-hard, and the state-of-the-art solution formulates a decision version of the problem as an integer linear program (ILP) and then solves it by conducting binary search over all possible lifetimes. In this paper, we first give an ILP for the optimization problem rather than its decision version, and then show that using ILP solvers to solve these programs could be highly inefficient. We then propose a branch-and-bound algorithm that incorporates two novel features. First, the bounding method takes into account integer flows, and contains a new set of constraints. Second, a special set of edges are deleted to reduce the number of subproblems generated by the branching process. Numerical simulations on randomly generated networks show that the proposed algorithm outperforms existing algorithms in terms of the number of solved problem instances in a fixed amount of time. Summary of Contribution: We study the maximum lifetime data gathering tree (MLDT) problem in the context of wireless sensor network. MLDT is a fundamental problem in both computer science and operations research. Since sensor nodes are often resource limited, the data gathering tree must be carefully constructed to prolong the network lifetime. In this paper, we first give an integer linear program for the optimization problem rather than its decision version, and then show that using ILP solvers to solve these programs could be highly inefficient. We then propose a branch and bound algorithm that incorporates two novel features. [ABSTRACT FROM AUTHOR]

We study the chance-constrained bin packing problem, with an application to hospital operating room planning. The bin packing problem allocates items of random sizes that follow a discrete distribution to a set of bins with limited capacity, while minimizing the total cost. The bin capacity constraints are satisfied with a given probability. We investigate a big-M and a 0-1 bilinear formulation of this problem. We analyze the bilinear structure of the formulation and use the lifting techniques to identify cover, clique, and projection inequalities to strengthen the formulation. We show that in certain cases these inequalities are facet-defining for a bilinear knapsack constraint that arises in the reformulation. An extensive computational study is conducted for the operating room planning problem that minimizes the number of open operating rooms. The computational tests are performed using problems generated based on real data from a hospital. A lower-bound improvement heuristic is combined with the cuts proposed in this paper in a branch-and-cut framework. The computations illustrate that the techniques developed in this paper can significantly improve the performance of the branch-and-cut method. Problems with up to 1,000 scenarios are solved to optimality in less than an hour. A safe approximation based on conditional value at risk (CVaR) is also solved. The computations show that the CVaR approximation typically leaves a gap of one operating room (e.g., six instead of five) to satisfy the chance constraint. Summary of Contribution: This paper investigates a branch-and-cut algorithm for a chance-constrained bin packing problem with multiple bins. The chance-constrained bin packing provides a modeling framework for applied operations research problems, such as health care, scheduling, and so on. This paper studies alternative computational approaches to solve this problem. Moreover, this paper uses real data from a hospital operating room planning setting as an application to test the algorithmic ideas. This work, therefore, is at the intersection of computing and operations research. Several interesting ideas are developed and studied. These include a strengthened big-M reformulation, analysis of a bilinear reformulation, and identifying certain facet-defining inequalities for this formulation. This paper also gives a lower-bound generation heuristic for a model that minimizes the number of bins. Computational experiments for an operating room planning model that uses data from a hospital demonstrate the computational improvement and importance of the proposed approaches. The techniques proposed in this paper and computational experiments further enhance the interface of computing and operations research. [ABSTRACT FROM AUTHOR]

The exact solution of the NP-hard (nondeterministic polynomial-time hard) maximum cut problem is important in many applications across, for example, physics, chemistry, neuroscience, and circuit layout—which is also due to its equivalence to the unconstrained binary quadratic optimization problem. Leading solution methods are based on linear or semidefinite programming and require the separation of the so-called odd-cycle inequalities. In their groundbreaking research, F. Barahona and A. R. Mahjoub have given an informal description of a polynomial-time algorithm for this problem. As pointed out recently, however, additional effort is necessary to guarantee that the inequalities obtained correspond to facets of the cut polytope. In this paper, we shed more light on a so enhanced separation procedure and investigate experimentally how it performs in comparison with an ideal setting where one could even employ the sparsest, most violated, or geometrically most promising facet-defining odd-cycle inequalities. Summary of Contribution: This paper aims at a better capability to solve binary quadratic optimization or maximum cut problems and their various applications using integer programming techniques. To this end, the paper describes enhancements to a well-known algorithm for the central separation problem arising in this context; it is demonstrated experimentally that these enhancements are worthwhile from a computational point of view. The linear relaxations of the aforementioned problems are typically solved using fewer iterations and cutting planes than with a nonenhanced approach. It is also shown that the enhanced procedure is only slightly inferior to an ideal, enumerative, and, in practice, intractable global cutting-plane selection. [ABSTRACT FROM AUTHOR]

Stochastic programming involves large-scale optimization with exponentially many scenarios. This paper proposes an optimization-based scenario reduction approach to generate high-quality solutions and tight lower bounds by only solving small-scale instances, with a limited number of scenarios. First, we formulate a scenario subset selection model that optimizes the recourse approximation over a pool of solutions. We provide a theoretical justification of our formulation, and a tailored heuristic to solve it. Second, we propose a scenario assortment optimization approach to compute a lower bound—hence, an optimality gap—by relaxing nonanticipativity constraints across scenario "bundles." To solve it, we design a new column-evaluation-and-generation algorithm, which provides a generalizable method for optimization problems featuring many decision variables and hard-to-estimate objective parameters. We test our approach on stochastic programs with continuous and mixed-integer recourse. Results show that (i) our scenario reduction method dominates scenario reduction benchmarks, (ii) our scenario assortment optimization, combined with column-evaluation-and-generation, yields tight lower bounds, and (iii) our overall approach results in stronger solutions, tighter lower bounds, and faster computational times than state-of-the-art stochastic programming algorithms. History: Accepted by Andrea Lodi, Area Editor for Design and Analysis of Algorithms–Discrete. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoc.2023.1295. [ABSTRACT FROM AUTHOR]

We introduce a Python package called RSOME for modeling a wide spectrum of robust and distributionally robust optimization problems. RSOME serves as an open-source framework for modeling various optimization problems subject to distributional ambiguity in a highly readable and mathematically intuitive manner. It is versatile and fits well in the open-source software community in the sense that (i) it is consistent with NumPy arrays in indexing and slicing and; (ii) together with the rich Python libraries for machine learning, data analysis, and visualization, it is easy to implement data-driven models; and (iii) it provides convenient interfaces for users to switch and tune parameters among different solvers. History: Ted Ralphs, Area Editor for Software Tools. Funding: The research of Z. Chen is funded by the Strategic Research Grant [Project 7005792] from the City University of Hong Kong. The research of P. Xiong is supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call [Grant MOE-2019-T3-1-010]. 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.2023.1291) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0146) at (http://dx.doi.org/10.5281/zenodo.7463845). [ABSTRACT FROM AUTHOR]

We propose a preference-learning algorithm for uncovering Decision Makers' (DMs') contingent evaluation strategies in the context of multiple criteria sorting. We assume the preference information in the form of holistic assignment examples derived from the analysis of alternatives' performance vectors and textual descriptions. We characterize the decision policies using a mixture of threshold-based, value-driven preference models and associated latent topics. The latter serve as the stimuli underlying the contingency in decision behavior. Such a probabilistic model is constructed by using a flexible and nonparametric Bayesian framework. The proposed method adopts a hierarchical Dirichlet process as the prior so that a group of DMs can share a countably infinite number of contingent models and topics. For all DMs, it automatically identifies the components representing their evaluation strategies adequately. The posterior is summarized by using the Hamiltonian Monte Carlo sampling method. We demonstrate the method's practical usefulness in a real-world recruitment problem considered by a Chinese IT company. We also compare the approach with counterparts that use a single preference model, implement the parametric framework, or consider each DM's preferences individually. The results indicate that our approach performs favorably in both interpreting DMs' contingent decision behavior and recommending decisions on new alternatives. Furthermore, the approach's performance and robustness are investigated through a computational experiment involving real-world data sets. History: Accepted by Ram Ramesh, Area Editor for Data Science and Machine Learning. Funding: J. Liu received financial support from the National Natural Science Foundation of China [Grants 72071155 and 71701160]. M. Kadziński received financial support from the Polish National Science Center under the SONATA BIS project [Grant DEC-2019/34/E/HS4/00045]. X. Liao received financial support from the National Natural Science Foundation of China [Grant 71872144]. 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.2023.1292) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0328) at (http://dx.doi.org/10.5281/zenodo.7608750). [ABSTRACT FROM AUTHOR]

Constraint programming (CP) has been recently in the spotlight after new CP-based procedures have been incorporated into state-of-the-art solvers, most notably the CP Optimizer from IBM. Classical CP solvers were only capable of guaranteeing the optimality of a solution, but they could not provide bounds for the integer feasible solutions found if interrupted prematurely due to, say, time limits. New versions, however, provide bounds and optimality guarantees, effectively making CP a viable alternative to more traditional mixed-integer programming (MIP) models and solvers. We capitalize on these developments and conduct a computational evaluation of MIP and CP models on 12 select scheduling problems.1 We carefully chose these 12 problems to represent a wide variety of scheduling problems that occur in different service and manufacturing settings. We also consider basic and well-studied simplified problems. These scheduling settings range from pure sequencing (e.g., flow shop and open shop) or joint assignment-sequencing (e.g., distributed flow shop and hybrid flow shop) to pure assignment (i.e., parallel machine) scheduling problems. We present MIP and CP models for each variant of these problems and evaluate their performance over 17 relevant and standard benchmarks that we identified in the literature. The computational campaign encompasses almost 6,623 experiments and evaluates the MIP and CP models along five dimensions of problem characteristics, objective function, decision variables, input parameters, and quality of bounds. We establish the areas in which each one of these models performs well and recognize their conceivable reasons. The obtained results indicate that CP sets new limits concerning the maximum problem size that can be solved using off-the-shelf exact techniques. 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.2023.1287) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0326) at (http://dx.doi.org/10.5281/zenodo.7541223). [ABSTRACT FROM AUTHOR]

Personalized points-of-interest (POI) recommendation is very important for improving the service quality of location-based social network applications. It has become one of the most popular research directions in the industry and academia. However, the realization of high-quality personalized POI recommendation faces three major challenges: (i) the interest drift issue caused by the spatiotemporal dynamics of user check-in behavior, (ii) how to integrate as much heterogeneous information as possible to alleviate data sparseness and cold start issues, and (iii) how to use implicit feedback to model complex high-order nonlinear user-POI interactions. To jointly address all these challenges, we propose the TGVx recommendation framework and establish a dynamic personalized POI deep recommendation model, where T and G respectively represent time and geographic factors, V represents out-of-town visitors, and x represents time slot number. TGVx is composed of x parallel TGV models where the TG module mines high-order nonlinear user-POI interaction relationships and integrates multisource heterogeneous information, and the V module transfers the check-in records of out-of-town visitors in hometowns and generates pseudo check-in records in the target city. Technically, we design a new unsupervised deep learning network T-SemiDAE for the TG module. We built a POI-word heterogeneous network for the V module and used graph embedding technology to match the most similar POIs across cities and transfer check-in records. The experimental results on the actual datasets show that the TGVx model is always better than other advanced models in terms of accuracy and diversity for local and out-of-town recommendation scenarios. Compared with the best baseline model semi-deep auto-encoder with a conditional layer the average improvement rates of accuracy and diversity of TGVx are 17.1% to 58.6% and 2.25% to 28.86%, respectively. In theory, our research effectively uses data science and analysis methods to design a recommender system. In practice, our research is motivated by practical problems, and the research results have high practical promotion value. History: Accepted by Ram Ramesh, Area Editor for Data Science & Machine Learning. Funding: This work was supported by the National Natural Science Foundation of China [Grants 71831003, 72293563, and 72172025], the Dalian Science and Technology Talent Innovation Support Policy Project [The High-level Talent Innovation Team Project 2022RG17], and the Liaoning Provincial Department of Education [Basic Scientific Research Project LJKMZ20221582]. 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.2023.1286) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0010) at (http://dx.doi.org/10.5281/zenodo.7407123). [ABSTRACT FROM AUTHOR]

We address a dynamic covering location problem of an unmanned aerial vehicle base station (UAV-BS), in which the location sequence of a single UAV-BS in a wireless communication network is determined to satisfy data demand arising from ground users. This problem is especially relevant in the context of smart grid and disaster relief. The vertical movement ability of the UAV-BS and nonconvex covering functions in wireless communication restrict utilizing classical planar covering location approaches. Therefore, we develop new formulations to this emerging problem for a finite time horizon to maximize the total coverage. In particular, we develop a mixed-integer nonlinear programming formulation that is nonconvex in nature and propose a Lagrangean decomposition algorithm (LDA) to solve this formulation. Because of the high complexity of the problem, the LDA is still unable to find good local solutions to large-scale problems. Therefore, we develop a continuum approximation (CA) model and show that CA would be a promising approach in terms of both computational time and solution accuracy. Our numerical study also shows that the CA model can be a remedy to build efficient initial solutions for exact solution algorithms. Summary of Contribution: This paper addresses a facet of mixed integer nonlinear programming formulations. Dynamic facility location problems (DFLPs) arise in a wide range of applications. However, classical DFLPs typically focus on the two-dimensional spaces. Emerging technologies in wireless communication and some other promising application areas, such as smart grids, have brought new location problems that cannot be solved with classical approaches. For practical reasons, many research attempts to solve this new problem, especially by researchers whose primary research area is not OR, have seemed far from analyzing the characteristics of the formulations. Rather, solution-oriented greedy heuristics have been proposed. This paper has two main objectives: (i) to close the gap between practical and theoretical sides of this new problem with the help of current knowledge that OR possesses to solve facility location problems and (ii) to support the findings with an exhaustive computational study to show how these findings can be applied to practice. [ABSTRACT FROM AUTHOR]

The separable convex resource allocation problem with nested bound constraints aims to allocate B units of resources to n activities to minimize a separable convex cost function, with lower and upper bounds on the total amount of resources that can be consumed by nested subsets of activities. We develop a new combinatorial algorithm to solve this model exactly. Our algorithm is capable of solving instances with millions of activities in several minutes. The running time of our algorithm is at most 73% of the running time of the current best algorithm for benchmark instances with three classes of convex objectives. The efficiency of our algorithm derives from a combination of constraint relaxation and divide and conquer based on infeasibility information. In particular, nested bound constraints are relaxed first; if the solution obtained violates some bound constraints, we show that the problem can be divided into two subproblems of the same structure and smaller sizes according to the bound constraint with the largest violation. Summary of Contribution. The resource allocation problem is a collection of optimization models with a wide range of applications in production planning, logistics, portfolio management, telecommunications, statistical surveys, and machine learning. This paper studies the resource allocation model with prescribed lower and upper bounds on the total amount of resources consumed by nested subsets of activities. These nested bound constraints are motivated by storage limits, time-window requirements, and budget constraints in various applications. The model also appears as a subproblem in models for green logistics and machine learning, and it has to be solved repeatedly. The model belongs to the class of computationally challenging convex mixed-integer nonlinear programs. We develop a combinatorial algorithm to solve this model exactly. Our algorithm is faster than the algorithm that currently has the best theoretical complexity in the literature on an extensive set of test instances. The efficiency of our algorithm derives from the combination of an infeasibility-guided divide-and-conquer framework and a scaling-based greedy subroutine for resource allocation with submodular constraints. This paper also showcases the prevalent mismatch between the theoretical worst-case time complexity of an algorithm and its practical efficiency. We have offered some explanations of this mismatch through the perspectives of worst-case analysis, specially designed instances, and statistical metrics of numerical experiments. The implementation of our algorithm is available on an online repository. [ABSTRACT FROM AUTHOR]

This paper presents an exact algorithm for the team formation problem, in which the aim is, given a project and its required skills, to construct a capable team that can communicate and collaborate effectively. This combinatorial optimization problem is modeled as a quadratic set covering problem. The study provides a novel branch-and-bound algorithm where a reformulation of the problem is relaxed so that it decomposes into a series of linear set covering problems, and the relaxed constraints are imposed through branching. The algorithm is able to solve instances that are intractable for commercial solvers. The study illustrates an efficient usage of algorithmic methods and modeling techniques for an operations research problem. It contributes to the field of computational optimization by proposing a new application and a new algorithm to solve a quadratic version of a classical combinatorial optimization problem. The team formation problem (TFP) aims to construct a capable team that can communicate and collaborate effectively. The cost of communication is quantified using the proximity of the potential members in a social network. We study a TFP with two measures for communication effectiveness; namely, we minimize the sum of communication costs, and we impose an upper bound on the largest communication cost. This problem can be formulated as a constrained quadratic set covering problem. Our experiments show that a general-purpose solver is capable of solving small and medium-sized instances to optimality. We propose a branch-and-bound algorithm to solve larger sizes: we reformulate the problem and relax it in such a way that it decomposes into a series of linear set covering problems, and we impose the relaxed constraints through branching. Our computational experiments show that the algorithm is capable of solving large-size instances, which are intractable for the solver. Summary of Contribution: This paper presents an exact algorithm for the Team Formation Problem (TFP), in which the aim is, given a project and its required skills, to construct a capable team that can communicate and collaborate effectively. This combinatorial optimization problem is modeled as a quadratic set covering problem. The study provides a novel branch-and-bound algorithm where a reformulation of the problem is relaxed so that it decomposes into a series of linear set covering problems and the relaxed constraints are imposed through branching. The algorithm is able to solve instances that are intractable for commercial solvers. The study illustrates an efficient usage of algorithmic methods and modelling techniques for an operations research problem. It contributes to the field of computational optimization by proposing a new application as well as a new algorithm to solve a quadratic version of a classical combinatorial optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, we study the quadratic assignment problem with a rank-one cost matrix (QAP-R1). Four integer-programming formulations are introduced of which three are assumed to have partial integer data. Unlike the standard quadratic assignment problem, some of our formulations can solve reasonably large instances of QAP-R1 with impressive running times and are faster than some metaheuristics. Pairwise relative strength of the LP relaxations of these formulations are also analyzed from theoretical and experimental points of view. Finally, we present a new metaheuristic algorithm to solve QAP-R1 along with its computational analysis. Our study offers the first systematic experimental analysis of integer-programming models and heuristics for QAP-R1. The benchmark instances with various characteristics generated for our study are made available to the public for future research work. Some new polynomially solvable special cases are also introduced. Summary of Contribution: This paper aims to advance our knowledge and ability in solving an important special case of the quadratic assignment problem. It shows how to exploit inherent properties of an optimization problem to achieve computational advantages, a strategy that was followed by researchers in model building and algorithm developments for decades. Our computational results attest to this time-tested general philosophy. The paper presents the first systematic computational study of the rank one quadratic assignment problem, along with new mathematical programming models and complexity analysis. We believe the theoretical and computational results of this paper will inspire further research on the topic and will be of significant value to practitioners using rank one quadratic assignment models. [ABSTRACT FROM AUTHOR]

This paper studies a multiproduct newsvendor problem with customer-driven demand substitution, where each product, once run out of stock, can be proportionally substituted by the others. This problem has been widely studied in the literature; however, because of nonconvexity and intractability, only limited analytical properties have been reported and no efficient approaches have been proposed. This paper first completely characterizes the optimal order policy when the demand is known and reformulates this nonconvex problem as a binary quadratic program. When the demand is random, we formulate the problem as a two-stage stochastic integer program, derive several necessary optimality conditions, prove the submodularity of the profit function, and also develop polynomial-time approximation algorithms and show their performance guarantees. We further propose a tight upper bound via nonanticipativity dual, which is proven to be very close to the optimal value and can yield a good-quality feasible solution under a mild condition. Our numerical investigation demonstrates effectiveness of the proposed algorithms. Moreover, several useful findings and managerial insights are revealed from a series of sensitivity analyses. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the one-machine scheduling problem with release and delivery times with the minimum makespan objective. Both heuristics and branch-and-bound algorithms have been formulated for the problem. One such branch-and-bound algorithm solves the problem and a variation that requires a delay between the completion of one job and the start of another (delayed precedence constraints). This paper analyzes key components of this branch-and-bound algorithm and proposes an improved heuristic to be used in conjunction with a different search strategy. Computational experiments demonstrate that the modifications lead to substantial improvements in running time and number of iterations on the one-machine problem instances both with and without delayed precedence constraints. [ABSTRACT FROM AUTHOR]

The unit commitment problem with uncertainty is considered one of the most challenging power system scheduling problems. Different stochastic models have been proposed to solve the problem, but such approaches have yet to be applied in industry practice because of computational challenges. In practice, the problem is formulated as a deterministic model with reserve requirements to hedge against uncertainty. However, simply requiring a certain level of reserves cannot ensure power system reliability as the procured reserves may be nondispatchable because of transmission limitations. In this paper, we derive a set of feasibility cuts (constraints) for managing the unit commitment problem with uncertainty. These cuts eliminate unreliable scheduling solutions and reallocate reserves in the power system; they are induced by the extreme rays of a polyhedral dual cone. This paper shows that, with the proposed reformulation, the extreme rays of the dual cone can be characterized by combinatorial selections of transmission lines (arcs) and buses (nodes) of the power system. As a result, the cuts can then be characterized using engineering insights. The unit commitment problem with uncertainty is formulated as a deterministic model with the identified extreme ray feasibility cuts. Test results show that, with the proposed extreme ray feasibility cuts, the problem can be solved more efficiently, and the resulting scheduling decision is also more reliable. [ABSTRACT FROM AUTHOR]

Scope and Mission In the paper, we present an original work related to the modeling and optimization approaches for kidney exchange programs (KEPs). Nowadays, KEPs represent an alternative way for patients suffering from renal failure to find a compatible (living) donor. The problem of determining an assignment of patients to (compatible) donors that maximizes the number of transplants in a KEP can be seen as a vertex-disjoint cycle-packing problem. Thus, KEPs have been extensively studied in the literature of integer programming. In practice, the assignment determined for a KEP might not be implemented due to withdrawals from the program (e.g., a more accurate compatible test shows a new incompatibility or a health condition makes it unable for a patient to participate in a KEP). In our paper, we model the problem of determining a robust solution to the KEP, that is, a solution that minimizes the material and emotional costs of changing an assignment. In this way, we propose and design solution approaches for three recourse policies that anticipate withdrawals. Through computational experiments, we compare the three recourse policies and validate the practical interest of robust solutions. Kidney exchange programs aim at matching end-stage renal disease patients who have a willing but incompatible kidney donor with another donor. The programs comprise a pool of such incompatible patient-donor pairs and, whenever a donor from one pair is compatible with the patient of another pair, and vice versa, the pairs may be matched and exchange kidneys. This is typically a two-step process in which, first, a set of pairs is matched based on preliminary compatibility tests and, second, the matched pairs are notified and more accurate compatibility tests are performed to verify that actual transplantation can take place. These additional tests may reveal incompatibilities not previously detected. When that happens, the planned exchange will not proceed. Furthermore, pairs may drop out before the transplant, and thus the planned exchange is canceled. In this paper, we study the case in which a new set of pairs may be matched if incompatibilities are discovered or a pair withdraws from the program. The new set should be as close as possible to the initial set in order to minimize the material and emotional costs of the changes. Various recourse policies that determine the admissible second-stage actions are investigated. For each recourse policy, we propose a novel adjustable robust integer programming model. We also propose solution approaches to solve this model exactly. The approaches are validated through thorough computational experiments. Summary of Contribution: In the paper, we present an original work related to the modeling and optimization approaches for Kidney Exchange Programs (KEPs). Currently, KEPs represent an alternative way for patients suffering from renal failure to find a compatible (living) donor. The problem of determining an assignment of patients to (compatible) donors that maximizes the number of transplants in a KEP can be seen as a vertex-disjoint cycle packing problem. Thus, KEPs have been extensively studied in the literature of integer programming. In practice, the assignment determined to a KEP might not be implemented due to withdraws from the program (e.g., a more accurate compatible test shows a new incompatibility or a patient health condition unable him/her to participate on the KEP). In our paper, we model the problem of determining a robust solution to the KEP, i.e., a solution that minimizes the material and emotional costs of changing an assignment. In this way, we propose and design solution approaches for three recourse policies that anticipate withdraws. Through computational experiments we compare the three recourse policies and validate the practical interest of robust solutions. [ABSTRACT FROM AUTHOR]

Waiting at the right location at the right time can be critically important in certain variants of time-dependent shortest path problems. We investigate the computational complexity of time-dependent shortest path problems in which there is either a penalty on waiting or a limit on the total time spent waiting at a given subset of the nodes. We show that some cases are nondeterministic polynomial-time hard, and others can be solved in polynomial time, depending on the choice of the subset of nodes, on whether waiting is penalized or constrained, and on the magnitude of the penalty/waiting limit parameter. Summary of Contributions: This paper addresses simple yet relevant extensions of a fundamental problem in Operations Research: the Shortest Path Problem (SPP). It considers time-dependent variants of SPP, which can account for changing traffic and/or weather conditions. The first variant that is tackled allows for waiting at certain nodes but at a cost. The second variant instead places a limit on the total waiting. Both variants have applications in transportation, e.g., when it is possible to wait at certain locations if the benefits outweigh the costs. The paper investigates these problems using complexity analysis and algorithm design, both tools from the field of computing. Different cases are considered depending on which of the nodes contribute to the waiting cost or waiting limit (all nodes, all nodes except the origin, a subset of nodes...). The computational complexity of all cases is determined, providing complexity proofs for the variants that are NP-Hard and polynomial time algorithms for the variants that are in P. [ABSTRACT FROM AUTHOR]

This research proposes and analyzes new models for a stochastic resource allocation problem that arises in a variety of operations contexts. One of the primary contributions of the paper lies in providing a succinct, robust, and general model that can address a range of different risk-based objectives and cost assumptions under uncertainty. Although the model expression is relatively simple, it embeds a reasonably high degree of underlying complexity, as the analysis shows. In addition, in-depth analysis of the model, both in its general form and under various specific risk measures, uncovers some interesting and powerful insights regarding the problem trade-offs. Furthermore, this analysis leads to a highly efficient class of heuristic algorithms for solving the problem, which we demonstrate via numerical experimentation to provide close-to-optimal solutions. This computational benefit is a critical element for solving a class of broadly applicable larger problems for which our problem arises as a subproblem that requires repeated solution. This paper considers a single-resource allocation problem for multiple items with random, independent resource consumption values, known as the static stochastic knapsack problem (SSKP). Whereas the existing SSKP literature generally assumes a risk-neutral objective using an expected value approach, such an approach can maximize expected profit while admitting the possibility of very high losses in some unfavorable scenarios. Because of this, we consider two popular risk measures, conditional value-at-risk (CVaR) and a mean-standard deviation trade-off, in order to address risk within this problem class. Optimizing the trade-offs associated with these risk measures presents significant modeling and computational challenges. To address these challenges, we first provide mixed-integer linear programming models using a scenario-based approach, which can be exploited to provide exact solutions for discrete distributions. For general distributions, a sample average approximation method provides approximate solutions. We then propose a general mixed integer nonlinear optimization modeling approach for the special case of normally distributed resource requirements. This modeling approach incorporates a new class of normalized penalty functions that account for both the expected costs and risks associated with uncertainty, and it can be specialized to a broad class of risk measures, including CVaR and mean-standard deviation. Our results characterize key optimality properties for the associated continuous relaxation of the proposed general model and provide insights on valuable rank-ordering mechanisms for items with uncertain resource needs under different risk measures. For this broadly applicable case, we present a class of efficient and high-performing asymptotically optimal heuristic methods based on these optimality conditions. An extensive numerical study evaluates the efficiency and quality of the proposed solution methods, identifies optimal item selection strategies, and examines the sensitivity of the solution to varying levels of risk, excess weight penalty values, and knapsack capacity values. Summary of Contribution: This research proposes and analyzes new models for a stochastic resource allocation problem that arises in a variety of operations contexts. One of the primary contributions of the paper lies in providing a succinct, robust, and general model that can address a range of different risk-based objectives and cost assumptions under uncertainty. While the model expression is relatively simple, it embeds a reasonably high degree of underlying complexity, as the analysis shows. In addition, in-depth analysis of the model, both in its general form and under various specific risk measures, uncovers some interesting and powerful insights regarding the problem tradeoffs. Furthermore, this analysis leads to a highly efficient class of heuristic algorithms for solving the problem, which we demonstrate via numerical experimentation to provide close-to-optimal solutions. This computational benefit is a critical element for solving a class of broadly applicable larger problems for which our problem arises as a subproblem that requires repeated solution. [ABSTRACT FROM AUTHOR]

Inference-based optimization via simulation, which substitutes Gaussian process (GP) learning for the structural properties exploited in mathematical programming, is a powerful paradigm that has been shown to be remarkably effective in problems of modest feasible-region size and decision-variable dimension. The limitation to "modest" problems is a result of the computational overhead and numerical challenges encountered in computing the GP conditional (posterior) distribution on each iteration. In this paper, we substantially expand the size of discrete-decision-variable optimization-via-simulation problems that can be attacked in this way by exploiting a particular GP—discrete Gaussian Markov random fields—and carefully tailored computational methods. The result is the rapid Gaussian Markov Improvement Algorithm (rGMIA), an algorithm that delivers both a global convergence guarantee and finite-sample optimality-gap inference for significantly larger problems. Between infrequent evaluations of the global conditional distribution, rGMIA applies the full power of GP learning to rapidly search smaller sets of promising feasible solutions that need not be spatially close. We carefully document the computational savings via complexity analysis and an extensive empirical study. Summary of Contribution: The broad topic of the paper is optimization via simulation, which means optimizing some performance measure of a system that may only be estimated by executing a stochastic, discrete-event simulation. Stochastic simulation is a core topic and method of operations research. The focus of this paper is on significantly speeding-up the computations underlying an existing method that is based on Gaussian process learning, where the underlying Gaussian process is a discrete Gaussian Markov Random Field. This speed-up is accomplished by employing smart computational linear algebra, state-of-the-art algorithms, and a careful divide-and-conquer evaluation strategy. Problems of significantly greater size than any other existing algorithm with similar guarantees can solve are solved as illustrations. [ABSTRACT FROM AUTHOR]

Connected dominating set (CDS) problem has been extensively studied in the literature due to its applications in many domains, including computer science and operations research. For example, CDS has been recommended to serve as a virtual backbone in wireless sensor networks (WSNs). Since sensor nodes in WSNs are prone to failures, it is important to build a fault-tolerant virtual backbone that maintains a certain degree of redundancy. A fault-tolerant virtual backbone can be modeled as a k-connected m-fold dominating set (k, m)-CDS. For a connected graph G (V, E) and two fixed integers k and m, a node set C ⊆ V is a (k, m)-CDS of G if every node in V\C has at least m neighbors in C, and the subgraph of G induced by C is k-connected. Previous to this work, approximation algorithms with guaranteed performance ratio in a general graph were known only for k ≤ 3. This paper makes significant progress by presenting a (2k - 1)α0 approximation algorithm for general k and m with m ≥ k, where α0 is the performance ratio for the minimum (1, m)-CDS problem. Using a currently best-known ratio for α0 , our algorithm has performance ratio O(ln∆), where ∆ is the maximum degree of the graph. Simulation results validate the effectiveness of our algorithm. [ABSTRACT FROM AUTHOR]

The generalization of mixed integer program (MIP) techniques to deal with nonlinear, potentially nonconvex, constraints has been a fruitful direction of research for computational mixed integer nonlinear programs (MINLPs) in the last decade. In this paper, we follow that path in order to extend another essential subroutine of modern MIP solvers toward the case of nonlinear optimization: the analysis of infeasible subproblems for learning additional valid constraints. To this end, we derive two different strategies, geared toward two different solution approaches. These are using local dual proofs of infeasibility for LP-based branch-and-bound and the creation of nonlinear dual proofs for NLP-based branch-and-bound, respectively. We discuss implementation details of both approaches and present an extensive computational study, showing that both techniques can significantly enhance performance when solving MINLPs to global optimality. Summary of Contribution: This original article concerns the advancement of exact general-purpose algorithms for solving one of the largest and most prominent problem classes in optimization, mixed integer nonlinear programs (MINLPs). It demonstrates how methods for conflict analysis that learn from infeasible subproblems can be transferred to nonlinear optimization. Further, it develops theory for how nonlinear dual infeasibility proofs can be derived from a nonlinear relaxation. This paper features a thoroughly computational study regarding the impact of conflict analysis techniques on the overall performance of a state-of-the-art MINLP solver when solving MINLPs to global optimality. [ABSTRACT FROM AUTHOR]

Finding sparse solutions to a system of equations and/or inequalities is an important topic in many application areas such as signal processing, statistical regression and nonparametric modeling. Various continuous relaxation models have been proposed and widely studied to deal with the discrete nature of the underlying problem. In this paper, we propose a quadratically constrained ℓ q (0 < q < 1) minimization model for finding sparse solutions to a quadratic system. We prove that solving the proposed model is strongly NP-hard. To tackle the computation difficulty, a first order necessary condition for local minimizers is derived. Various properties of the proposed model are studied for designing an active-set-based descent algorithm to find candidate solutions satisfying the proposed condition. In addition to providing a theoretical convergence proof, we conduct extensive computational experiments using synthetic and real-life data to validate the effectiveness of the proposed algorithm and to show the superior capability in finding sparse solutions of the proposed model compared with other known models in the literature. We also extend our results to a quadratically constrained ℓ q (0 < q < 1) minimization model with multiple convex quadratic constraints for further potential applications. Summary of Contribution: In this paper, we propose and study a quadratically constrained ℓ q minimization (0 < q < 1) model for finding sparse solutions to a quadratic system which has wide applications in sparse signal recovery, image processing and machine learning. The proposed quadratically constrained ℓ q minimization model extends the linearly constrained ℓ q and unconstrained ℓ 2 - ℓ q models. We study various properties of the proposed model in aim of designing an efficient algorithm. Especially, we propose an unrelaxed KKT condition for local/global minimizers. Followed by the properties studied, an active-set based descent algorithm is then proposed with its convergence proof being given. Extensive numerical experiments with synthetic and real-life Sparco datasets are conducted to show that the proposed algorithm works very effectively and efficiently. Its sparse recovery capability is superior to that of other known models in the literature. [ABSTRACT FROM AUTHOR]

The learning of predictive models for data-driven decision support has been a prevalent topic in many fields. However, construction of models that would capture interactions among input variables is a challenging task. In this paper, we present a new preference learning approach for multiple criteria sorting with potentially interacting criteria. It employs an additive piecewise-linear value function as the basic preference model, which is augmented with components for handling the interactions. To construct such a model from a given set of assignment examples concerning reference alternatives, we develop a convex quadratic programming model. Because its complexity does not depend on the number of training samples, the proposed approach is capable for dealing with data-intensive tasks. To improve the generalization of the constructed model on new instances and to overcome the problem of overfitting, we employ the regularization techniques. We also propose a few novel methods for classifying nonreference alternatives in order to enhance the applicability of our approach to different data sets. The practical usefulness of the proposed approach is demonstrated on a problem of parametric evaluation of research units, whereas its predictive performance is studied on several monotone classification problems. The experimental results indicate that our approach compares favourably with the classical UTilités Additives DIScriminantes (UTADIS) method and the Choquet integral-based sorting model. Summary of Contribution. The paper tackles vital challenges at the intersections of multiple criteria decision analysis and machine learning, showing how computationally advanced techniques can be used for faithfully representing human preferences and dealing with complex decision problems. Specifically, we propose a novel preference learning method for multiple criteria sorting problems. The introduced approach incorporates convex quadratic programming to construct a value-based preference model based on large sets of preference statements. In this way, we extend the applicability of decision analysis methods to preferences derived from historical data or observation of users' behavior in addition to the preference judgments explicitly revealed by the decision-makers. The method's practical usefulness is illustrated on a variety of real-world datasets from fields such as higher education, medicine, human resources, and housing market. Its potential for supporting better decision-making is enhanced by both an interpretable form of the assumed model handling interactions between criteria as well as a high predictive performance demonstrated in the extensive computational experiments. [ABSTRACT FROM AUTHOR]

A lower bound for a finite-scenario-based chance-constrained program is the quantile value corresponding to the sorted optimal objective values of scenario subproblems. This quantile bound can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. The quality of the bound depends on how the scenarios are grouped. In this paper, we formulate a mixed-integer bilevel program that optimally groups scenarios to tighten the quantile bounds. For general chance-constrained programs, we propose a branch-and-cut algorithm to optimize the bilevel program, and for chance-constrained linear programs, a mixed-integer linear-programming reformulation is derived. We also propose several heuristics for grouping similar or dissimilar scenarios. Our computational results demonstrate that optimal grouping bounds are much tighter than heuristic bounds, resulting in smaller root-node gaps and better performance of scenario decomposition for solving chance-constrained 0-1 programs. Also, the optimal grouping bounds can be greatly strengthened using larger group size. Summary of Contribution: Chance-constrained programs are in general NP-hard but widely used in practice for lowering the risk of undesirable outcomes during decision making under uncertainty. Assuming finite scenarios of uncertain parameter, chance-constrained programs can be reformulated as mixed-integer linear programs with binary variables representing whether or not the constraints are satisfied in corresponding scenarios. A useful quantile bound for solving chance-constrained programs can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. In this paper, we develop algorithms for optimally and heuristically grouping scenarios to tighten the quantile bounds. We aim to improve both the computation and solution quality of a variety of chance-constrained programs formulated for different Operations Research problems. [ABSTRACT FROM AUTHOR]

Two essential ingredients of modern mixed-integer programming solvers are diving heuristics, which simulate a partial depth-first search in a branch-and-bound tree, and conflict analysis, which learns valid constraints from infeasible subproblems. So far, these techniques have mostly been studied independently: primal heuristics for finding high-quality feasible solutions early during the solving process and conflict analysis for fathoming nodes of the search tree and improving the dual bound. In this paper, we pose the question of whether and how the orthogonal goals of proving infeasibility and generating improving solutions can be pursued in a combined manner such that a state-of-the-art solver can benefit. To do so, we integrate both concepts in two different ways. First, we develop a diving heuristic that simultaneously targets the generation of valid conflict constraints from the Farkas dual and the generation of improving solutions. We show that, in the primal, this is equivalent to the optimistic strategy of diving toward the best bound with respect to the objective function. Second, we use information derived from conflict analysis to enhance the search of a diving heuristic akin to classic coefficient diving. In a detailed computational study, both methods are evaluated on the basis of an implementation in the source-open-solver SCIP. The experimental results underline the potential of combining both diving heuristics and conflict analysis. Summary of Contribution. This original article concerns the advancement of exact general-purpose algorithms for solving one of the largest and most prominent problem classes in optimization, mixed-integer linear programs. It demonstrates how methods for conflict analysis that learn from infeasible subproblems can be combined successfully with diving heuristics that aim at finding primal solutions. For two newly designed diving heuristics, this paper features a thoroughly computational study regarding their impact on the overall performance of a state-of-the-art MIP solver. [ABSTRACT FROM AUTHOR]

Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets. The objective is to minimize the sum of the distances of the chosen set of edges for the worst positions of the vertices in their uncertainty sets. We first prove that these problems are N P -hard even when the feasible sets consist either of all spanning trees or of all s – t paths. Given this hardness, we propose an exact solution algorithm combining integer programming formulations with a cutting plane algorithm, identifying the cases where the separation problem can be solved efficiently. We also propose a conservative approximation and show its equivalence to the affine decision rule approximation in the context of Euclidean distances. We compare our algorithms to three deterministic reformulations on instances inspired by the scientific literature for the Steiner tree problem and a facility location problem. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2023.1276. [ABSTRACT FROM AUTHOR]

Users' contextual engagements can affect their decisions about who to follow on online social networks because engaged (versus disengaged) users tend to seek more information about the interested topic and are more likely to follow relevant accounts successively. However, existing followee recommendation methods neglect to consider contextual engagement by only relying on users' general preferences. In the light of the chronological characteristic of the user's following behavior, we draw on the engagement theory and propose an interpretable algorithm, namely preference-engagement latent Dirichlet allocation (PE-LDA), which integrates users' contextual engagements with their general preferences for followee recommendation. Specifically, we suggest that if engaged in the current interest, a user will be more likely to select a followee relevant to that interest. If not, the user tends to select a followee according to their general preference. To implement this framework, we extend the original LDA by (1) introducing an indicator to represent whether the user is engaged in the current interest or not and (2) allowing a potential dependency between a user's successive interests to describe the condition of contextual engagement. We conduct extensive experiments using a real-world Twitter data set. Results demonstrate the superior performance of PE-LDA compared with several existing methods. History: Accepted by Ram Ramesh, Area Editor for Data Science and Machine Learning. Funding: This work was supported by the National Natural Science Foundation of China [Grants 71702066, 71802192, 71832010, 72172112, and 72272152]. 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.2023.1284) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0172) at (http://dx.doi.org/10.5281/zenodo.7460938). [ABSTRACT FROM AUTHOR]

We propose gradient-based simulation-optimization algorithms to optimize systems that have complicated stochastic structure. The presence of complicated stochastic structure, such as the involvement of infinite-dimensional continuous-time stochastic processes, may cause the exact simulation of the system to be costly or even impossible. On the other hand, for a complicated system, one can sometimes construct a sequence of approximations at different resolutions, where the sequence has finer and finer approximation resolution but higher and higher cost to simulate. With the goal of optimizing the complicated system, we propose algorithms that strategically use the approximations with increasing resolution and higher simulation cost to construct stochastic gradients and perform gradient search in the decision space. To accommodate scenarios where approximations cause discontinuities and lead path-wise gradient estimators to have an uncontrollable bias, stochastic gradients for the proposed algorithms are constructed through finite difference. As a theory support, we prove algorithm convergence, convergence rate, and optimality of algorithm design under the assumption that the objective function for the complicated system is strongly convex, whereas no such assumptions are imposed on the approximations of the complicated system. We then present a multilevel version of the proposed algorithms to further improve convergence rates, when in addition the sequence of approximations can be naturally coupled. History: Accepted by Bruno Tuffin, Area Editor for Simulation. 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.2023.1279) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0289) at (http://dx.doi.org/10.5281/zenodo.7485443). [ABSTRACT FROM AUTHOR]

In the era of big data, people benefit from the existence of tremendous amounts of information. However, availability of said information may pose great challenges. For instance, one big challenge is how to extract useful yet succinct information in an automated fashion. As one of the first few efforts, keyword extraction methods summarize an article by identifying a list of keywords. Many existing keyword extraction methods focus on the unsupervised setting, with all keywords assumed unknown. In reality, a (small) subset of the keywords may be available for a particular article. To use such information, we propose a rigorous probabilistic model based on a semisupervised setup. Our method incorporates the graph-based information of an article into a Bayesian framework via an informative prior so that our model facilitates formal statistical inference, which is often absent from existing methods. To overcome the difficulty arising from high-dimensional posterior sampling, we develop two Markov chain Monte Carlo algorithms based on Gibbs samplers and compare their performance using benchmark data. We use a false discovery rate (FDR)-based approach for selecting the number of keywords, whereas the existing methods use ad hoc threshold values. Our numerical results show that the proposed method compared favorably with state-of-the-art methods for keyword extraction. History: Accepted by Ramaswamy 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.2023.1283) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0234) at (http://dx.doi.org/10.5281/zenodo.7348935). [ABSTRACT FROM AUTHOR]

This article highlights synergies between quantum information science (QIS) and operations research for QIS-curious operations researchers (and vice versa), and the author challenges the community to discover more. History: This "Challenge" paper was invited by the Editor in Chief and based on the topics raised by the author at his plenary address at the 2022 INFORMS Computing Society Conference in Tampa, Florida. Funding: This material is based on work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Accelerated Research in Quantum Computing, Fundamental Algorithmic Research for Quantum Computing. This article has been authored by an employee of National Technology & Engineering Solutions of Sandia, LLC, under Contract DE-NA0003525 with the U.S. Department of Energy (DOE). [ABSTRACT FROM AUTHOR]

We describe PyNumero, an open-source, object-oriented programming framework in Python that supports rapid development of performant parallel algorithms for structured nonlinear programming problems (NLP's) using the Message Passing Interface (MPI). PyNumero provides three fundamental building blocks for developing NLP algorithms: a fast interface for calculating first and second derivatives with the AMPL Solver Library (ASL), a number of interfaces to efficient linear solvers, and block-structured vectors and matrices based on NumPy, SciPy, and MPI that support distributed parallel storage and computation. PyNumero's design enables efficient, parallel algorithm development using high-level Python syntax while keeping expensive numerical calculations in fast, compiled implementations based on languages like C and Fortran. To demonstrate the utility of PyNumero, we also present Parapint, a Python package built on PyNumero for parallel solution of dynamic optimization problems. Parapint includes a parallel interior-point solver based on Schur-Complement decomposition. We illustrate the effectiveness of PyNumero for developing parallel algorithms with both code examples and scalability analyses for parallel matrix-vector dot products, parallel solution of structured systems of linear equations using Schur-Complement decomposition, and the parallel solution of a two-dimensional PDE optimal control problem. Our numerical results show nearly perfect scaling to more than 1,000 cores for large matrix-vector dot products and structured linear systems. Moreover, we obtain more than 354 times speedup for the optimal control example. History: Accepted by Alice Smith, EIC/Ted Ralphs, Area Editor/Software Tools. Funding: This work was funded in part by the Institute for the Design of Advanced Energy Systems (IDAES) with funding from the Office of Fossil Energy, Cross-Cutting Research, U.S. Department of Energy. This work was also funded by Sandia National Laboratories Laboratory Directed Research and Development (LDRD) program. 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.2023.1272) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0285) at (http://dx.doi.org/10.5281/zenodo.7192328). [ABSTRACT FROM AUTHOR]

Simulation optimization involves optimizing some objective function that can only be estimated via stochastic simulation. Many important problems can be profitably viewed within this framework. Whereas many solvers—implementations of simulation-optimization algorithms—exist or are in development, comparisons among solvers are not standardized and are often limited in scope. Such comparisons help advance solver development, clarify the relative performance of solvers, and identify classes of problems that defy efficient solution, among many other uses. We develop performance measures and plots, and estimators thereof, to evaluate and compare solvers and diagnose their strengths and weaknesses on a testbed of simulation-optimization problems. We explain the need for two-level simulation in this context and provide supporting convergence theory. We also describe how to use bootstrapping to obtain error estimates for the estimators. History: Accepted by Bruno Tuffin, area editor for simulation. Funding: This work was supported by the National Science Foundation [Grants CMMI-2035086, CMMI-2206972, and TRIPODS+X DMS-1839346]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplementary Information [https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1261] or is available from the IJOC GitHub software repository (https://github.com/INFORMSJoC) at [http://dx.doi.org/10.5281/zenodo.7329235]. [ABSTRACT FROM AUTHOR]

Intensive care units (ICUs) are crucial resources within hospitals, caring for the most critically ill patients. We propose a novel modeling framework that improves the outflow of ICU patients by anticipating unit interactions and resource sharing within the system. Across an arbitrary bipartite network of units, we consider two types of downstream staffing (baseline and flexible) and a two-stage decision process. In the first stage, we determine the level of flexible bed staffing using existing physical beds at downstream units in anticipation of incoming transfers from the ICUs. In the second stage, we determine the allocation of ICU patients to downstream beds. The goal of the model is to reduce inefficiencies and transfer delays causing ICU bed block due to lack of space in downstream units. We formulate a dynamic multiperiod model and analyze the dual of its (relaxed) stationary counterpart. Decomposing the relaxed stationary model into an ICU and downstream subproblems, we calculate the relative values of downstream beds and derive a practical acuity-based policy for the daily operational decisions. Using a large-scale simulation calibrated with historic hospital data, we demonstrate that our acuity-based policy reduces the number of long-run diverted ICU arrivals, particularly in high-demand scenarios, thus improving ICU throughput, when compared with a deterministic, a generalized randomized-most-idle, and static policies. History: Accepted by J. Paul Brooks, Area Editor for Applications in Biology, Medicine, & Healthcare. Funding: This work was partially supported by National Science Foundation [Grants CMMI-1635301/1635410/1635642]. 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.2022.1267) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0133) at (http://dx.doi.org/10.5281/zenodo.7194693). [ABSTRACT FROM AUTHOR]

Aircraft conflict resolution is one of the major tasks of computer-aided air traffic management and represents a challenging optimization problem. Many models and methods have been proposed to assist trajectory regulation to avoid conflicts. However, the question of testing the different mathematical optimization approaches against each other is still open. Standard benchmarks include unrealistic scenarios in which all the flights move toward a common point or completely random generated instances. There is a lack of a common set of test instances that allows comparison of the available methods under a variety of heterogeneous and representative scenarios. We present a flight deconfliction benchmark generator that allows the user to choose between (i) different predefined scenario inspired by existing benchmarks in the literature; (ii) pseudo-random traffic meeting certain congestion measurements; (iii) and randomly generated traffic. The proposed setting can account for different levels of difficulty in the deconfliction of the aircraft and allows to explore and compare the real limitations of optimization approaches for aircraft conflict resolution. History: Accepted by Ted Ralphs, area editor for Software Tools. Funding: This work was supported by the H2020 Marie Skłodowska-Curie Actions [Grant 764759 ITN "MINOA"]. 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.2022.1265) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0283) at (http://dx.doi.org/10.5281/zenodo.7377734). [ABSTRACT FROM AUTHOR]

The practice of sharing online user information with external third parties has become the focal point of privacy concerns for consumer advocacy groups and policy makers. We explore the decisions by websites regarding the obfuscation that they use to make it difficult for users to discover the extent of information sharing. Using a Bayesian model, we shed light on the websites' incentive to obfuscate user information sharing. We find that as content sensitivity increases, a website reduces its level of obfuscation. Furthermore, more popular websites engage in higher levels of obfuscation than less popular ones. We provide an empirical analysis of obfuscation and user information sharing in News (low content sensitivity) and Health (high content sensitivity) websites and confirm key results from our analytical model. Our analysis illustrates that obfuscation of information sharing is a viable strategy that websites use to improve their profits. History: Ram Ramesh, area editor for Data Science & Machine Learning. Funding: Financial support from the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged. 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.2022.1266) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0070) at http://dx.doi.org/10.5281/zenodo.7336098. [ABSTRACT FROM AUTHOR]

Pareto-optimal sets of multiobjective optimization problems with black-box and computationally expensive objective functions are generally hard to locate within a limited computational budget, and this situation gets even worse when more than three objectives are involved. To this end, we present a novel surrogate-assisted many-objective optimization algorithm RECAS. Unlike most prior studies, the proposed algorithm is a non–evolutionary-based method, and it iteratively determines new points for expensive evaluation via a series of independent reference vector assisted candidate searches. Furthermore, to make the number of surrogates to be maintained independent of the number of objectives, in each candidate search, RECAS constructs a surrogate model in an aggregated manner to approximate the quality assessment indicator of each point rather than a certain objective function. Under some mild assumptions, this study proves that RECAS converges almost surely to the Pareto-optimal front. In the numerical experiments, the effectiveness and reliability of RECAS are examined on both DTLZ and WFG test suites with the number of objectives varying from 2 to 10. Compared with six state-of-the-art many-objective optimization algorithms, RECAS generally performs better in maintaining convergent and well-spread approximation of the Pareto-optimal front. Finally, the good performance of RECAS on two watershed simulation model calibration problems indicates its great potential in handling real-world applications. History: Accepted by Antonio Frangioni, Area Editor for Design and Analysis of Algorithms–Continuous. Funding: This work was supported by the National University of Singapore start-up grant to C.A. Shoemaker [Grant R-266-000-109-133]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplementary Information [https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1260] or is available from the IJOC GitHub software repository (https://github.com/INFORMSJoC) at [http://dx.doi.org/10.5281/zenodo.7243971]. [ABSTRACT FROM AUTHOR]

Apiculture has gained worldwide interest because of its contributions to economic incomes and environmental conservation. In view of these, migratory beekeeping, as a high-yielding technique, is extensively adopted. However, because of the lack of an overall routing plan, beekeepers who follow the experiential migratory routes frequently encounter unexpected detours and suffer losses when faced with problems such as those related to nectar source capacities and the production of bee products. The migratory beekeeping routing problem (MBRP) is proposed based on the practical background of the commercial apiculture industry to optimize the global revenue for beekeepers by comprehensively considering nectar source allocation, migration, production and sales of bee products, and corresponding time decisions. The MBRP is a new variant of the vehicle routing problem but with significantly different production time decisions at the vertices (i.e., nectar sources). That is, only the overlaps between residence durations and flowering periods generate production benefits. Different sales visits cause different gains from the same products; in turn, these lead to different production time decisions at previously visited nectar source locations and even change the visits for production. To overcome the difficulty resulting from the complicated time decisions, we utilize the Dantzig–Wolfe decomposition method and propose a revised labeling algorithm for the pricing subproblems. The tests, performed on instances and a real-world case, demonstrate that the column generation method with the revised labeling algorithm is efficient for solving the MBRP. Compared with traditional routes, a more efficient overall routing schedule for migratory beekeepers is proposed. Summary of Contribution. Based on the practical background of commercial apiculture industry, this paper proposes a new type of routing problem named the migratory beekeeping routing problem (MBRP), which incorporates the selection of productive nodes and sales nodes as well as the production time decision at the productive nodes on a migratory beekeeping network. To overcome the difficulty resulting from the complicated time decisions, we utilize the Dantzig–Wolfe decomposition method and propose a revised labeling algorithm for the pricing subproblems. The tests, performed on instances and a real-world case, demonstrate that the column generation method with the revised labeling algorithm is efficient for solving the MBRP. Compared with traditional routes, a more efficient overall routing schedule for migratory beekeepers is proposed. Therefore, this paper is congruent with, and contributes to, the scope and mission of INFORMS Journal on Computing, especially the area of Network Optimization: Algorithms & Applications. [ABSTRACT FROM AUTHOR]

Bilevel problems are highly challenging optimization problems that appear in many applications of energy market design, critical infrastructure defense, transportation, pricing, and so on. Often these bilevel models are equipped with integer decisions, which makes the problems even harder to solve. Typically, in such a setting in mathematical optimization, one develops primal heuristics in order to obtain feasible points of good quality quickly or to enhance the search process of exact global methods. However, there are comparably few heuristics for bilevel problems. In this paper, we develop such a primal heuristic for bilevel problems with a mixed-integer linear or quadratic upper level and a linear or quadratic lower level. The heuristic is based on a penalty alternating direction method, which allows for a theoretical analysis. We derive a convergence theory stating that the method converges to a stationary point of an equivalent single-level reformulation of the bilevel problem and extensively test the method on a test set of more than 2,800 instances—which is one of the largest computational test sets ever used in bilevel programming. The study illustrates the very good performance of the proposed method in terms of both running times and solution quality. This renders the method a suitable subroutine in global bilevel solvers as well as a reasonable standalone approach.Summary of Contribution: Bilevel optimization problems form a very important class of optimization problems in the field of operations research, which is mainly due to their capability of modeling hierarchical decision processes. However, real-world bilevel problems are usually very hard to solve—especially in the case in which additional mixed-integer aspects are included in the modeling. Hence, the development of fast and reliable primal heuristics for this class of problems is very important. This paper presents such a method. [ABSTRACT FROM AUTHOR]

We provide a comprehensive overview of mixed-integer programming formulations for the unit commitment (UC) problem. UC formulations have been an especially active area of research over the past 12 years due to their practical importance in power grid operations, and this paper serves as a capstone for this line of work. We additionally provide publicly available reference implementations of all formulations examined. We computationally test existing and novel UC formulations on a suite of instances drawn from both academic and real-world data sources. Driven by our computational experience from this and previous work, we contribute some additional formulations for both generator production upper bounds and piecewise linear production costs. By composing new UC formulations using existing components found in the literature and new components introduced in this paper, we demonstrate that performance can be significantly improved—and in the process, we identify a new state-of-the-art UC formulation. [ABSTRACT FROM AUTHOR]

This paper addresses the close-enough traveling salesman problem, a variant of the Euclidean traveling salesman problem, in which the traveler visits a node if it passes through the neighborhood set of that node. We apply an effective strategy to discretize the neighborhoods of the nodes and the carousel greedy algorithm to appropriately select the neighborhoods that, step by step, are added to the partial solution until a feasible solution is generated. Our heuristic, based on these ingredients, is able to compute tight upper and lower bounds on the optimal solution relatively quickly. The computational results, carried out on benchmark instances, show that our heuristic often finds the optimal solution, on the instances where it is known, and in general, the upper bounds are more accurate than those from other algorithms available in the literature. Summary of Contribution: In this paper, we focus on the close-enough traveling salesman problem. This is a problem that has attracted research attention over the last 10 years; it has numerous real-world applications. For instance, consider the task of meter reading for utility companies. Homes and businesses have meters that measure the usage of gas, water, and electricity. Each meter transmits signals that can be read by a meter reader vehicle via radio-frequency identification (RFID) technology if the distance between the meter and the reader is less than r units. Each meter plays the role of a target point and the neighborhood is a disc of radius r centered at each target point. Now, suppose the meter reader vehicle is a drone and the goal is to visit each disc while minimizing the amount of energy expended by the drone. To solve this problem, we develop a metaheuristic approach, called (lb/ub)Alg, which computes both upper and lower bounds on the optimal solution value. This metaheuristic uses an innovative discretization scheme and the Carousel Greedy algorithm to obtain high-quality solutions. On benchmark instances where the optimal solution is known, (lb/ub)Alg obtains this solution 83% of the time. Over the remaining 17% of these instances, the deviation from the optimality is 0.05%, on average. On the instances with the highest overlap ratio, (lb/ub)Alg does especially well. [ABSTRACT FROM AUTHOR]

Distributed generation and remotely controlled switches have emerged as important technologies to improve the resiliency of distribution grids against extreme weather-related disturbances. Therefore it becomes important to study how best to place them on the grid in order to meet a resiliency criteria, while minimizing costs and capturing their dependencies on the associated communication systems that sustain their distributed operations. This paper introduces the Optimal Resilient Design Problem for Distribution and Communication Systems (ORDPDC) to address this need. The ORDPDC is formulated as a two-stage stochastic mixed-integer program that captures the physical laws of distribution systems, the communication connectivity of the smart grid components, and a set of scenarios that specifies which components are affected by potential disasters. The paper proposes an exact branch-and-price algorithm for the ORDPDC that features a strong lower bound and a variety of acceleration schemes to address degeneracy. The ORDPDC model and branch-and-price algorithm were evaluated on a variety of test cases with varying disaster intensities and network topologies. The results demonstrate the significant impact of the network topologies on the expansion plans and costs, as well as the computational benefits of the proposed approach. [ABSTRACT FROM AUTHOR]