Scale Optimization Problems Research Articles

Overlap Removal by Stochastic Gradient Descent With(out) Shape Awareness.

In many 2D visualizations, data points are projected without considering their surface area, although they are often represented as shapes in visualization tools. These shapes support the display of information such as labels or encode data with size or color. However, inappropriate shape and size selections can lead to overlaps that obscure information and hinder the visualization's exploration. Overlap Removal (OR) algorithms have been developed as a layout post-processing solution to ensure that the visible graphical elements accurately represent the underlying data. As the original data layout contains vital information about its topology, it is essential for OR algorithms to preserve it as much as possible. This article presents an extension of the previously published FORBID algorithm by introducing a new approach that models OR as a joint stress and scaling optimization problem, utilizing efficient stochastic gradient descent. The goal is to produce an overlap-free layout that proposes a compromise between compactness (to ensure the encoded data is still readable) and preservation of the original layout (to preserve the structures that convey information about the data). Additionally, this article proposes SORDID, a shape-aware adaptation of FORBID that can handle the OR task on data points having any polygonal shape. Our approaches are compared against state-of-the-art algorithms, and several quality metrics demonstrate their effectiveness in removing overlaps while retaining the compactness and structures of the input layouts.

Energy performance of heuristics and meta-heuristics for real-time joint resource scaling and consolidation in virtualized networked data centers

In this paper, we explore on a comparative basis the performance suitability of meta-heuristic, sometime denoted as random search algorithms, and greedy-type heuristics for the energy-saving joint dynamic scaling and consolidation of the network-plus-computing resources hosted by networked virtualized data centers when the target is the support of real-time streaming-type applications. For this purpose, the energy and delay performances of Tabu Search (TS), Simulated Annealing (SA) and Evolutionary Strategy (ES) meta-heuristics are tested and compared with the corresponding ones of Best-Fit Decreasing-type heuristics, in order to give insight on the resulting performance-versus-implementation complexity trade-offs. In principle, the considered meta-heuristics and heuristics are general formal approaches that can be applied to large classes of (typically, non-convex and mixed integer) optimization problems. However, specially for the meta-heuristics, a main challenge is to design them to properly address the real-time joint computing-plus-networking resource consolidation and scaling optimization problem. To this purpose, the aim of this paper is: (i) introduce a novel Virtual Machine Allocation (VMA) scheme that aims at choosing a suitable set of possible Virtual Machine placements among the (possibly, non-homogeneous) set of available servers; (ii) propose a new class of random search algorithms (RSAs) denoted as consolidation meta-heuristic, considering the VMA problem in RSAs. In particular, the design of novel variants of meta-heuristics, namely TS-RSC, SA-RSC and ES-RSC, is particularized to the resource scaling and consolidation (RSC) problem; (iii) compare the results of the obtained new RSAs class against some state-of-the-art heuristic approaches. A set of experimental results, both simulated and real-world ones, support the effectiveness of the proposed approaches against the traditional ones.

A decomposition approach for a very large scale optimal diversity management problem

This paper focuses on the solution of the optimal diversity management problem formulated as a p-Median problem. The problem is solved for very large scale real instances arising in the car industry and defined on a graph with several tens of thousands of nodes and with several millions of arcs. The particularity is that the graph can consist of several non connected components. This property is used to decompose the problem into a series of p-Median subproblems of a smaller dimension. We use a greedy heuristic and a Lagrangian heuristic for each subproblem. The solution of the whole problem is obtained by solving a suitable assignment problem using a Branch-and-Bound algorithm.