Data rebalancing techniques, including undersampling and oversampling, are common approaches to the problem of classifying imbalanced data. However, indiscriminate oversampling increases the size of the dataset with no regard to "how these additional samples effect the classification in imbalanced datasets." Such behavior often leads to less than desirable accuracy in the presence of noise and introduces underfitting. To prevent these learning obstacles, we developed a bilevel optimization framework where we optimize over samples of majority training data after typical optimization over model parameters takes place. Our framework allows us to dynamically assess a sample’s impact on loss and accepts only those datapoints that improve loss, thereby, finding an optimal subset of majority training data for classification. Experimental results show our proposed technique with F1 scores up to 10% higher than state-of-the-art methods.

Optimizing the controls of quantum systems plays a crucial role in advancing quantum technologies. The time-varying noises in quantum systems and the widespread use of inhomogeneous quantum ensembles raise the need for high-quality quantum controls under uncertainties. In this paper, we consider a stochastic discrete optimization formulation of a discretized binary optimal quantum control problem involving Hamiltonians with predictable uncertainties. We propose a sample-based reformulation that optimizes both risk-neutral and risk-averse measurements of control policies, and solve these with two gradient-based algorithms using sum-up-rounding approaches. Furthermore, we discuss the differentiability of the objective function and prove upper bounds of the gaps between the optimal solutions to binary control problems and their continuous relaxations. We conduct numerical simulations on various sized problem instances based on two applications of quantum pulse optimization; we evaluate different strategies to mitigate the impact of uncertainties in quantum systems. We demonstrate that the controls of our stochastic optimization model achieve significantly higher quality and robustness compared with the controls of a deterministic model. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue. Funding: This work was supported by the US Department of Energy, Advanced Scientific Computing Research [Grants DE-AC02-06CH11357, DE-SC0018018]; Defense Sciences Office, DARPA [Grant IAA-8839-annex-130]; the US National Science Foundation, Division of Civil, Mechanical and Manufacturing Innovation [Grant 2041745]; and the US National Aeronautics and Space Administration (NASA) Ames Research Center [Grant 80ARC020D0010]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0560 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0560 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Quantum optimal control is a technique for controlling the evolution of a quantum system and has been applied to a wide range of problems in quantum physics. We study a binary quantum control optimization problem, where control decisions are binary-valued and the problem is solved in diverse quantum algorithms. In this paper, we utilize classical optimization and computing techniques to develop an algorithmic framework that sequentially optimizes the number of control switches and the duration of each control interval on a continuous time horizon. Specifically, we first solve the continuous relaxation of the binary control problem based on time discretization and then use a heuristic to obtain a controller sequence with a penalty on the number of switches. Then, we formulate a switching time optimization model and apply sequential least-squares programming with accelerated time-evolution simulation to solve the model. We demonstrate that our computational framework can obtain binary controls with high-quality performance and also reduce computational time via solving a family of quantum control instances in various quantum physics applications.

In ACM TOMS Algorithm 1012, the DELAUNAYSPARSE software is given for performing Delaunay interpolation in medium to high dimensions. When extrapolating outside the convex hull of the training set, DELAUNAYSPARSE calls the nonnegative least squares solver DWNNLS to compute projections onto the convex hull. However, DWNNLS and many other available sum-of-squares optimization solvers were not intended for usage with many variable problems, which result from the large training sets that are typical in machine learning applications. Thus, a new PROJECT subroutine is given, based on the highly customizable quadratic program solver BQPD . This solution is shown to be as robust as DELAUNAYSPARSE for projection onto both synthetic and real-world datasets, where other available solvers frequently fail. Although it is intended as an update for DELAUNAYSPARSE , due to the difficulty and prevalence of the problem, this solution is likely to be of external interest as well.

In this paper, we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. Cozad and Sahinidis propose a nonconvex mixed-integer nonlinear program (MINLP), in which binary variables are used to assign operators and nonlinear expressions are used to propagate data values through nonlinear operators, such as square, square root, and exponential. We extend this formulation by adding new cuts that improve the solution of this challenging MINLP. We also propose a heuristic that iteratively builds an expression tree by solving a restricted MINLP. We perform computational experiments and compare our approach with a mixed-integer program–based method and a neural network–based method from the literature. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the Applied Mathematics activity within the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research [Grant DE-AC02-06CH11357]. 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.2022.0050 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0050 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

User-space HPC data services are emerging as an appealing alternative to traditional parallel file systems, because of their ability to be tailored to application needs while eliminating unnecessary overheads incurred by POSIX compliance. The High Energy Physics (HEP) community is progressively turning towards such services to enable high-throughput accesses under heavy concurrency to billions of event data produced by instruments and consumed by subsequent analysis workflows. Such services would benefit from the possibility to be rescaled up and down to adapt to changing workloads, as experimental campaigns progress , in order to optimize resource usage. This paper formalizes rescaling a distributed storage system as a multi objective optimization problem considering three criteria: load balance, data balance, and duration of the rescaling operation. We propose a heuristic for rapidly finding a good approximate solution, while allowing users to weight the criteria as needed. The heuristic is evaluated with Pufferscale, a new rescaling manager for microservice-based distributed storage systems. To validate our approach in a real-world ecosystem, we showcase the use of Pufferscale as a means to enable storage malleability in the HEPnOS storage system for HEP applications.

Modern scientific experimental facilities such as x-ray light sources increasingly require on-demand access to large-scale computing for data analysis, for example to detect experimental errors or to select the next experiment. As the number of such facilities, the number of instruments at each facility, and the scale of computational demands all grow, the question arises as to how to meet these demands most efficiently and cost-effectively. A single computer per instrument is unlikely to be cost-effective because of low utilization and high operating costs. A single national compute facility, on the other hand, introduces a single point of failure and perhaps excessive communication costs. We introduce here methods for evaluating these and other potential design points, such as per-facility computer systems and a distributed multisite "superfacility." We use the U.S. Department of Energy light sources as a use case and build a mixed-integer programming model and a customizable superfacility simulator to enable joint optimization of design choices and associated operational decisions. The methodology and tools provide new insights into design choices for on-demand computing facilities for real-time analysis of scientific experiment data. The simulator can also be used to support facility operations, for example by simulating the impact of events such as outages.

Fluorescence tomographic reconstruction, based on the detection of photons coming from fluorescent emission, can be used for revealing the internal elemental composition of a sample. On the other hand, conventional X-ray transmission tomography can be used for reconstructing the spatial distribution of the absorption coefficient inside a sample. In this work, we integrate both X-ray fluorescence and X-ray transmission data modalities and formulate a nonlinear optimization-based approach for reconstruction of the elemental composition of a given object. This model provides a simultaneous reconstruction of both the quantitative spatial distribution of all elements and the absorption effect in the sample. Mathematically speaking, we show that compared with the single-modality inversion (i.e., the X-ray transmission or fluorescence alone), the joint inversion provides a better-posed problem, which implies a better recovery. Therefore, the challenges in X-ray fluorescence tomography arising mainly from the effects of self-absorption in the sample are partially mitigated. The use of this technique is demonstrated on the reconstruction of several synthetic samples.

Today's leadership computing facilities have enabled the execution of transformative simulations at unprecedented scales. However, analyzing the huge amount of output from these simulations remains a challenge. Most analyses of this output is performed in post-processing mode at the end of the simulation. The time to read the output for the analysis can be significantly high due to poor I/O bandwidth, which increases the end-to-end simulation-analysis time. Simulation-time analysis can reduce this end-to-end time. In this work, we present the scheduling of in-situ analysis as a numerical optimization problem to maximize the number of online analyses subject to resource constraints such as I/O bandwidth, network bandwidth, rate of computation and available memory. We demonstrate the effectiveness of our approach through two application case studies on the IBM Blue Gene/Q system.

This article introduces novel formulations for optimally responding to epidemics and cyber attacks in networks. In our models, at a given time period, network nodes (e.g., users or computing resources) are associated with probabilities of being infected, and each network edge is associated with some probability of propagating the infection. A decision maker would like to maximize the network's utility; keeping as many nodes open as possible, while satisfying given bounds on the probabilities of nodes being infected in the next time period. The model's relation to previous deterministic optimization models and to both probabilistic and deterministic asymptotic models is explored. Initially, maintaining the stochastic independence assumption of previous work, we formulate a nonlinear integer program with high-order multilinear terms. We then propose a quadratic formulation that provides a lower bound and feasible solution to the original problem. Further motivation for the quadratic model is given by showing that it alleviates the assumption of stochastic independence. The quadratic formulation is then linearized in order to be solved by standard integer programming solvers. We develop valid inequalities for the resulting formulations. © 2015 Wiley Periodicals, Inc.NETWORKS, Vol. 66(2), 145–158 2015

This paper proposes a convex relaxation of a sparse support vector machine (SVM) based on the perspective relaxation of mixed-integer nonlinear programs. We seek to minimize the zero-norm of the hyperplane normal vector with a standard SVM hinge-loss penalty and extend our approach to a zero-one loss penalty. The relaxation that we propose is a second-order cone formulation that can be efficiently solved by standard conic optimization solvers. We compare the optimization properties and classification performance of the second-order cone formulation with previous sparse SVM formulations suggested in the literature.

In the era of petascale supercomputing, the importance of load balancing is crucial. Although dynamic load balancing is widespread, it is increasingly difficult to implement effectively with thousands of processors or more, prompting a second look at static load-balancing techniques even though the optimal allocation of tasks to processors is an NP-hard problem. We propose a heuristic static load-balancing algorithm, employing fitted benchmarking data, as an alternative to dynamic load balancing. The problem of allocating CPU cores to tasks is formulated as a mixed-integer nonlinear optimization problem, which is solved by using an optimization solver. On 163,840 cores of Blue Gene/P, we achieved a parallel efficiency of 80% for an execution of the fragment molecular orbital method applied to model protein-ligand complexes quantum-mechanically. The obtained allocation is shown to outperform dynamic load balancing by at least a factor of 2, thus motivating the use of this approach on other coarse-grained applications.

We describe a new solver for convex mixed-integer nonlinear programs (MINLPs) that implements a linearization-based algorithm. The solver is based on an algorithm of Quesada and Grossmann [Quesada, I., I. E. Grossmann. 1992. An LP/NLP based branch-and-bound algorithm for convex MINLP optimization problems. Comput. Chemical Engrg. 16(10–11) 937–947] that avoids the complete re-solution of a master mixed-integer linear program (MILP) by adding new linearizations at open nodes of the branch-and-bound tree whenever an integer solution is found. The new solver, FilMINT, combines the MINTO branch-and-cut framework for MILP with filterSQP to solve the nonlinear programs that arise as subproblems in the algorithm. The MINTO framework allows us to easily employ cutting planes, primal heuristics, and other well-known MILP enhancements for MINLPs. We present detailed computational experiments that show the benefit of such advanced MILP techniques. We offer new suggestions for generating and managing linearizations that are shown to be efficient on a wide range of MINLPs. By carefully incorporating and tuning all these enhancements, an effective solver for convex MINLPs is constructed.

We propose a new approach to convex nonlinear multiobjective optimization that captures the geometry of the Pareto set by generating a discrete set of Pareto points optimally. We show that the problem of finding a maximally uniform representation of the Pareto surface can be formulated as a mathematical program with complementarity constraints. The complementarity constraints arise from modeling the set of Pareto points, and the objective maximizes some quality measure of this discrete set. We present encouraging numerical experience on a range of test problems collected from the literature.