We present a new family of subgradient methods that dynamically incorporate knowledge of the geometry of the data observed in earlier iterations to perform more informative gradient-based learning. Metaphorically, the adaptation allows us to find needles in haystacks in the form of very predictive but rarely seen features. Our paradigm stems from recent advances in stochastic optimization and online learning which employ proximal functions to control the gradient steps of the algorithm. We describe and analyze an apparatus for adaptively modifying the proximal function, which significantly simplifies setting a learning rate and results in regret guarantees that are provably as good as the best proximal function that can be chosen in hindsight. We give several efficient algorithms for empirical risk minimization problems with common and important regularization functions and domain constraints. We experimentally study our theoretical analysis and show that adaptive subgradient methods outperform state-of-the-art, yet non-adaptive, subgradient algorithms.

Adaptive Subgradient Methods for Online Learning and Stochastic Optimization.

/pdf/adaptive-subgradient-methods-for-online-learning-and-1nnwnbmnxy.pdf

Adaptive Subgradient Methods for Online Learning and Stochastic Optimization

https://sci2s.ugr.es/sites/default/files/files/Teaching/GraduatesCourses/Metaheuristicas/Bibliography/VNS.pdf

Variable neighborhood search

Variable Neighborhood Search.

Network function virtualization (NFV) has drawn significant attention from both industry and academia as an important shift in telecommunication service provisioning. By decoupling network functions (NFs) from the physical devices on which they run, NFV has the potential to lead to significant reductions in operating expenses (OPEX) and capital expenses (CAPEX) and facilitate the deployment of new services with increased agility and faster time-to-value. The NFV paradigm is still in its infancy and there is a large spectrum of opportunities for the research community to develop new architectures, systems and applications, and to evaluate alternatives and trade-offs in developing technologies for its successful deployment. In this paper, after discussing NFV and its relationship with complementary fields of software defined networking (SDN) and cloud computing, we survey the state-of-the-art in NFV, and identify promising research directions in this area. We also overview key NFV projects, standardization efforts, early implementations, use cases, and commercial products.

/pdf/network-function-virtualization-state-of-the-art-and-29gg3feprt.pdf

Network Function Virtualization: State-of-the-Art and Research Challenges

Resource-constrained project scheduling: Notation, classification, models, and methods

Consider the following generalization of the classical job-shop scheduling problem in which a set of machines is associated with each operation of a job. The operation can be processed on any of the machines in this set. For each assignment μ of operations to machines letP(μ) be the corresponding job-shop problem andf(μ) be the minimum makespan ofP(μ). How to find an assignment which minimizesf(μ)? For problems with two jobs a polynomial algorithm is derived.

Job-shop scheduling with multi-purpose machines

http://www.dia.uniroma3.it/~pacciare/CORSI/MSP/Brucker1994.pdf

A branch and bound algorithm for the job-shop scheduling problem

We address the problem of scheduling n jobs on a batching machine to minimize regular scheduling criteria that are non-decreasing in the job completion times A batching machine is a machine that can handle up to b jobs simultaneously The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time The processing time of a batch is equal to the largest processing time of any job in the batch We analyse two variants: the unbounded model, where b⩾n; and the bounded model, where b<n



For the unbounded model, we give a characterization of a class of optimal schedules, which leads to a generic dynamic programming algorithm that solves the problem of minimizing an arbitrary regular cost function in pseudopolynomial time The characterization leads to more efficient dynamic programming algorithms for specific cost functions: a polynomial algorithm for minimizing the maximum cost, an O(n3) time algorithm for minimizing the number of tardy jobs, an O(n2) time algorithm for minimizing the maximum lateness, and an O(n log n) time algorithm for minimizing the total weighted completion time Furthermore, we prove that minimizing the weighted number of tardy jobs and the total weighted tardiness are NP-hard problems



For the bounded model, we derive an O(nb(b−1)) time dynamic programming algorithm for minimizing total completion time when b>1; for the case with m different processing times, we give a dynamic programming algorithm that requires O(b2m22m) time Moreover, we prove that due date based scheduling criteria give rise to NP-hard problems Finally, we show that an arbitrary regular cost function can be minimized in polynomial time for a fixed number of batches © 1998 John Wiley & Sons, Ltd

/pdf/scheduling-a-batching-machine-dfh4lgbz76.pdf

Peter Brucker

Papers

Resource-constrained project scheduling: Notation, classification, models, and methods

Job-shop scheduling with multi-purpose machines

A branch and bound algorithm for the job-shop scheduling problem

Scheduling a batching machine

A branch and bound algorithm for the resource-constrained project scheduling problem