Network flow models for intraday personnel scheduling problems

Personnel scheduling problems can be decomposed into two stages. In the first stage for each employee the working days have to be fixed. In the second stage for each day of the planning period an intraday scheduling problem has to be solved. It consists of the assignment of shifts to the employees who have to work on the day and for each working period of an employee a task assignment such that the demand of all tasks for personnel is covered. In Robinson et al. (Burke and Trick (Eds.), Proceedings of the 5th International Conference on the Practice and Theory of Automated Timetabling, 18th August–20th August 2004, Pittsburgh, PA, USA, pp. 561–566, 2005), the intraday problem has been formulated as a maximum flow problem. The assumptions are that, employees are qualified for all tasks, their shifts are given, and they are allowed to change tasks during the day. In this work, we extend the network flow model to cover the case where not all employees are qualified to perform all tasks. The model is further extended to be able to calculate shifts of employees for the given day, assuming that an earliest starting time, a latest finishing time, and a minimal working time are given. Labour cost can be also taken into account by solving a minimum cost network flow problem

Stochastic Dual Coordinate Ascent with Adaptive Probabilities

This paper introduces AdaSDCA: an adaptive variant of stochastic dual coordinate ascent (SDCA) for solving the regularized empirical risk minimization problems. Our modification consists in allowing the method adaptively change the probability distribution over the dual variables throughout the iterative process. AdaSDCA achieves provably better complexity bound than SDCA with the best fixed probability distribution, known as importance sampling. However, it is of a theoretical character as it is expensive to implement. We also propose AdaSDCA+: a practical variant which in our experiments outperforms existing non-adaptive methods

Computable Bounds on Convergence of Markov Chains in Wasserstein Distance

We introduce a unified framework to estimate the convergence of Markov chains to equilibrium using Wasserstein distance. The framework provides convergence bounds with various rates, ranging from polynomial to exponential, all derived from a single contractive drift condition. This approach removes the need for finding a specific set with drift outside and contraction inside. The convergence bounds are explicit, as they can be estimated based on one-step expectations and do not rely on equilibrium-related quantities. To enhance the applicability of the framework, we introduce the large M technique and the boundary removal technique. We illustrate these methods in queueing models and algorithms in stochastic optimization

SDNA: Stochastic Dual Newton Ascent for Empirical Risk Minimization

We propose a new algorithm for minimizing regularized empirical loss: Stochastic Dual Newton Ascent (SDNA). Our method is dual in nature: in each iteration we update a random subset of the dual variables. However, unlike existing methods such as stochastic dual coordinate ascent, SDNA is capable of utilizing all curvature information contained in the examples, which leads to striking improvements in both theory and practice - sometimes by orders of magnitude. In the special case when an L2-regularizer is used in the primal, the dual problem is a concave quadratic maximization problem plus a separable term. In this regime, SDNA in each step solves a proximal subproblem involving a random principal submatrix of the Hessian of the quadratic function; whence the name of the method. If, in addition, the loss functions are quadratic, our method can be interpreted as a novel variant of the recently introduced Iterative Hessian Sketch

Paper Session II-C - High-Resolution Integrated Micro Gyroscope for Space Applications

In this paper, an integrated capacitive gyroscope fabricated by CMOS-MEMS technology is presented. The CMOS-compatibility of the fabrication process enables full integration of the sensor with interface and signal conditioning circuitry on a single chip. The entire microstructure is single-crystal silicon based, resulting in large proof mass and good mechanical behaviors. Thus, high-resolution and high-robustness microgyroscopes can be obtained. With a resolution of about 0.01°/s/Hz112 , the fabricated gyroscope chip is only as small as 1.5mm by 2mm including the sensing elements and integrated electronics. The robustness, light weight and high performance make this type of MEMS gyroscope very suitable for space navigation applications where payload is critical. The on-chip capacitive sensing circuitry employs chopper stabilization technique to minimize the influence of 1/f noise. The on-chip circuits also include a two-stage fully differential amplifier and a DC feedback loop to cancel the DC offset. The CMOS fabrication was performed through MOSIS by using the 4-metal TSMC 0.35 μm CMOS process. The post-CMOS micromachining processing consists of only dry etch steps and uses the interconnect metal layers as etching masks. Single-crystal silicon (SCS) structures are produced by applying a backside etch and forming a 60μm-thick SCS membrane. This work is sponsored by NASA through the UCF/UF Space Research Initiative