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

This chapter is devoted to another important basic scheduling problem: the jobshop problem. This problem is a special case of the RCPSP where only disjunctive resources (machines) and special precedence constraints in form of chains are given. After giving a precise formulation of the job-shop problem in Section 4.1, solution algorithms are discussed. While Section 4.2 deals with heuristic methods, foundations for exact branch-and-bound algorithms are presented in Section 4.3. Afterwards, generalizations and applications of the job-shop problem are considered. In Section 4.4 the concepts of time-lags and blocking are introduced. Then, we consider job-shop problems with flexible machines in Section 4.5, job-shop problems with transport robots in Section 4.6 and job-shop problems with limited buffers in Section 4.7.

Complex Job-Shop Scheduling

A polynomial algorithm is proposed for two scheduling problems for which the complexity status was open. A set of jobs with unit processing times, release dates and outtree precedence relations has to be processed on parallel identical machines such that the total completion time $\sum C_j$ is minimized. It is shown that the problem can be solved in $O(n^2)$ time if no preemption is allowed. Furthermore, it is proved that allowing preemption does not reduce the optimal objective value, which verifies a conjecture of Baptiste and Timkovsky.

/pdf/a-polynomial-algorithm-for-p-p-j-1-r-j-outtree-sigma-c-j-and-2qtyhvi2fn.pdf

A polynomial algorithm for $P | p_j = 1, r_j, outtree | \Sigma C_j$ and $P | p_j = 1,r_j, outtree, pmtn | \Sigma C_j$

We consider the problem of rescheduling trains in the case where one track of a railway section consisting of two tracks in opposing directions is closed due to construction activities. After presenting an appropriate model for this situation we derive a polynomial algorithm for the subproblem of finding an optimal schedule with minimal latenesss if the subsequences of trains for both directions outside the construction site are fixed. Based on this algorithm we propose a local search procedure for the general problem of finding good schedules and report test results for some real world instances.

Scheduling railway traffic at a construction site

Cyclic Scheduling Problems with Linear Precedences and Resource Constraints

In recent years there has been a growing interest in discrete optimization problems satisfying the “Monge”-property or related properties. In this survey some of the recent results on this topic will be presented.

Peter Brucker

Papers

Complex Job-Shop Scheduling

A polynomial algorithm for $P | p_j = 1, r_j, outtree | \Sigma C_j$ and $P | p_j = 1,r_j, outtree, pmtn | \Sigma C_j$

Scheduling railway traffic at a construction site

Cyclic Scheduling Problems with Linear Precedences and Resource Constraints

"Monge"-property and efficient algorithms