In recent years, there has been an increasing need to understand the complex interdependencies between critical infrastructure systems, for example, electric power, natural gas, and potable water. Whereas open-source and commercial tools for the independent simulation of these systems are well established, frameworks for cosimulation with other systems are nascent and tools for co-optimization are scarce—the major challenge being the hidden combinatorics that arise when connecting multiple-infrastructure system models. Building toward a comprehensive solution for modeling interdependent infrastructure systems, this work presents InfrastructureModels, an extensible, open-source mathematical programming framework for co-optimizing multiple interdependent infrastructures. This work provides new insights into methods and programming abstractions that make state-of-the-art independent infrastructure models composable with minimal additional effort. To that end, this paper presents the design of the InfrastructureModels framework, documents key components of the software’s implementation, and demonstrates its effectiveness with three case studies on canonical co-optimization tasks arising in interdependent infrastructure systems. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: The work was funded by Los Alamos National Laboratory’s Directed Research and Development project “The Optimization of Machine Learning: Imposing Requirements on Artificial Intelligence” and the U.S. Department of Energy’s Office of Electricity Advanced Grid Modeling projects “Joint Power System and Natural Gas Pipeline Optimal Expansion Planning” and “Coordinated Planning and Operation of Water and Power Infrastructures for Increased Resilience and Reliability.” This work was carried out under the U.S. DOE contract no. [DE-AC52-06NA25396]. 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.2022.0118 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0118 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Funding: This work was supported by the U.S. Department of Energy (DOE) Advanced Grid Modeling project, Coordinated Planning and Operation of Water and Power Infrastructures for Increased Resilience and Reliability. Incorporation of the PolyhedralRelaxations Julia package was supported by Los Alamos National Laboratory’s Directed Research and Development program under the project Fast, Linear Programming-Based Algorithms with Solution Quality Guarantees for Nonlinear Optimal Control Problems [Grant 20220006ER]. All work at Los Alamos National Laboratory was conducted under the auspices of the National Nuclear Security Administration of the U.S. DOE, Contract No. 89233218CNA000001. This work was also authored in part by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the U.S. DOE, Contract No. DE-AC36-08GO28308. 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.2022.0233 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0233 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm and Quantum Annealing can potentially demonstrate significant run-time performance benefits over current state-of-the-art solutions. Inspired by existing methods to characterize classical optimization algorithms, we analyze the solution quality obtained by solving Max-cut problems using gate-model quantum devices and a quantum annealing device. This is used to guide the development of an advanced benchmarking framework for quantum computers designed to evaluate the trade-off between run-time execution performance and the solution quality for iterative hybrid quantum-classical applications. The framework generates performance profiles through compelling visualizations that show performance progression as a function of time for various problem sizes and illustrates algorithm limitations uncovered by the benchmarking approach. As an illustration, we explore the factors that influence quantum computing system throughput, using results obtained through execution on various quantum simulators and quantum hardware systems.

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims at explaining the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM’s quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations.

This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the convex quadratic relaxation of the optimal transmission switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. We then introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the optimal transmission switching problem in power systems. Using the proposed improvements, along with bound propagation, on 23 medium-sized test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on five instances. The tightened model has promising computational results when compared with state-of-the-art formulations.

This article considers a probabilistic generalization of the N‐k failure‐identification problem in power transmission networks, where the probability of failure of each component in the network is known a priori and the goal of the problem is to find a set of k components that maximizes disruption to the system loads weighted by the probability of simultaneous failure of the k components. The resulting problem is formulated as a bilevel mixed‐integer nonlinear program. Convex relaxations, linear approximations, and heuristics are developed to obtain feasible solutions that are close to the optimum. A general cutting‐plane algorithm is proposed to solve the convex relaxation and linear approximations of the N‐k problem. Extensive numerical results corroborate the effectiveness of the proposed algorithms on small‐, medium‐, and large‐scale test instances; the test instances include the IEEE 14‐bus system, the IEEE single‐area and three‐area RTS96 systems, the IEEE 118‐bus system, the WECC 240‐bus test system, the 1354‐bus PEGASE system, and the 2383‐bus Polish winter‐peak test system.

While MOOCs have taken the world by storm, questions remain about their pedagogical value and high rates of attrition. In this paper we argue that MOOCs which have open entry and open curriculum structures, place pressure on learners to not only have the requisite knowledge and skills to complete the course, but also the skills to traverse the course in adaptive ways that lead to success. The empirical study presented in the paper investigated the degree to which students' prior knowledge and skills, and their engagement with the MOOC as measured through learning analytics, predict end-of-MOOC performance. The findings indicate that prior knowledge is the most significant predictor of MOOC success followed by students' ability to revise and revisit their previous work.

In the last five years, the world has seen a remarkable level of interest in Massive Open Online Courses, or MOOCs. A consistent message from universities participating in MOOC delivery is their eagerness to understand students' online learning processes. This paper reports on an exploratory investigation of students' learning processes in two MOOCs which have different curriculum and assessment designs. When viewed through the lens of common MOOC learning analytics, the high level of initial student interest and, ultimately, the high level of attrition, makes these two courses appear very similar to each other, and to MOOCs in general. With the goal of developing a greater understanding of students' patterns of learning behavior in these courses, we investigated alternative learning analytic approaches and visual representations of the output of these analyses. Using these approaches we were able to meaningfully classify student types and visualize patterns of student engagement which were previously unclear. The findings from this research contribute to the educational community's understanding of students' engagement and performance in MOOCs, and also provide the broader learning analytics community with suggestions of new ways to approach learning analytic data analysis and visualization.

The practice of discrete optimization involves modeling and solving complex combinatorial problems which have never been encountered before and for which no universal computational paradigm exists. Teaching such skills is challenging: Students must learn, not only the core technical skills, but also an ability to think creatively in order to select and adapt a paradigm to solve the problem at hand. This paper explores the question of whether the teaching of such creative skills translates to massive open online courses (MOOCs). It first describes a methodology for teaching discrete optimization that has been successful on campus over fifteen years. It then discusses how to adapt the campus format to a MOOC version. The success of the approach is evaluated through extensive data analytics enabled by the wealth of information produced by MOOCs.

Linear active-power-only power flow approximations are pervasive in the planning and control of power systems. However, AC power systems are governed by a system of nonlinear nonconvex power flow equations. Existing linear approximations fail to capture key power flow variables, including reactive power and voltage magnitudes, both of which are necessary in many applications that require voltage management and AC power flow feasibility. This paper proposes novel linear-programming models (the LPAC models) that incorporate reactive power and voltage magnitudes in a linear power flow approximation. The LPAC models are built on a polyhedral relaxation of the cosine terms in the AC equations as well as Taylor approximations of the remaining nonlinear terms. Experimental comparisons with AC solutions on a variety of standard IEEE and Matpower benchmarks show that the LPAC models produce accurate values for active and reactive power, phase angles, and voltage magnitudes. The potential benefits of the LPAC models are illustrated on two “proof-of-concept” studies in power restoration and capacitor placement.

This paper considers the restoration of multiple interdependent infrastructures after a man-made or natural disaster. Modern infrastructures feature complex cyclic interdependencies and require a holistic restoration process. This paper presents the first scalable approach for the last-mile restoration of the joint electrical power and gas infrastructures. It builds on an earlier three-stage decomposition for restoring the power network that decouples the restoration ordering and the routing aspects. The key contributions of the paper are (1) mixed-integer programming models for finding a minimal restoration set and a restoration ordering and (2) a randomized adaptive decomposition to obtain high-quality solutions within the required time constraints. The approach is validated on a large selection of benchmarks based on the United States infrastructures and state-of-the-art weather and fragility simulation tools. The results show significant improvements over current field practices.

Many database applications deploy hundreds or thousands of indexes to speed up query execution. Despite a plethora of prior work on index selection, designing and deploying indexes remains a difficult task for database administrators. First, real-world businesses often require online index deployment, and the traditional off-line approach to index selection ignores intermediate workload performance during index deployment. Second, recent work on on-line index selection does not address effects of complex interactions that manifest during index deployment.