Set Of Necessary Constraints Research Articles

MINLP formulations for continuous piecewise linear function fitting

We consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. https://doi.org/10.1007/s10589-014-9647-y) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise linear curve that is not the graph of a function, because it misses a set of necessary constraints. We provide two counterexamples to illustrate this effect, and propose three alternative models that correct this behavior. We investigate the theoretical relationship between these models and evaluate their computational performance.

Checkpointing Strategies for Shared High-Performance Computing Platforms

Input/output (I/O) from various sources often contend for scarcely available bandwidth. For example, checkpoint/restart (CR) protocols can help to ensure application progress in failure-prone environments. However, CR I/O alongside an application's normal, requisite I/O can increase I/O contention and might negatively impact performance. In this work, we consider different aspects (system-level scheduling policies and hardware) that optimize the overall performance of concurrently executing CR-based applications that share I/O resources. We provide a theoretical model and derive a set of necessary constraints to minimize the global waste on a given platform. Our results demonstrate that Young/Daly's optimal checkpoint interval, despite providing a sensible metric for a single, undisturbed application, is not sufficient to optimally address resource contention at scale. We show that by combining optimal checkpointing periods with contention-aware system-level I/O scheduling strategies, we can significantly improve overall application performance and maximize the platform throughput. Finally, we evaluate how specialized hardware, namely burst buffers, may help to mitigate the I/O contention problem. Overall, these results provide critical analysis and direct guidance on how to design efficient, CR ready, large -scale platforms without a large investment in the I/O subsystem.

Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function.

We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index N-representability P-, Q-, and G-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly occupied many-electron wave function, i.e., a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index N-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, N2, and CN(-)). This work is motivated by the fact that a doubly occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as L(3), where L is the number of spatial orbitals. Since the doubly occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly occupied framework.

A note on “event-based MILP models for resource-constrained project scheduling problems”

Recently, new mixed integer linear programming formulations for the resource-constrained project scheduling problem were proposed by Koné et al. [3]. Unfortunately, the presentation of the first new model (called start/end-based formulation SEE) was not correct. More precisely, a set of necessary constraints representing the relative positioning of start and end events of activities was unintentionally omitted in the paper although it was present in the integer program used for the computational experiments. After presenting a counterexample showing the incorrectness, we provide a disaggregated and an aggregated variant of the set of necessary constraints, the disaggregated formulation yielding in theory a better linear programming relaxation. We present computational results showing that although the linear programming relaxations of both formulations yield equivalently poor lower bounds, the disaggregated formulation shows in average a better performance for integer solving of a well-known set of 30-activity instances.

MAV-BASED REAL-TIME LOCALIZATION OF TERRESTRIAL TARGETS WITH CM-LEVEL ACCURACY: FEASIBILITY STUDY

Abstract. We carry out a comprehensive feasibility study for a real-time cm-level localization of a predefined terrestrial target from a MAV-based autonomous platform. Specifically, we conduct an error propagation analysis which quantifies all potential error sources, and accounts for their respective contribution to the final result. Furthermore, we provide a description of a practical MAV system using the available technology and of-the-shelf components. We demonstrate that, indeed, the desired localization precision of a few centimeters may be realistically achieved under a set of necessary constraints.