Benchmarking RCGAu on the Noiseless BBOB Testbed

RCGAu is a hybrid real-coded genetic algorithm with “uniform random direction” search mechanism. The uniform random direction search mechanism enhances the local search capability of RCGA. In this paper, RCGAu was tested on the BBOB-2013 noiseless testbed using restarts till a maximum number of function evaluations (#FEs) of 105 × D are reached, where D is the dimension of the function search space. RCGAu was able to solve several test functions in the low search dimensions of 2 and 3 to the desired accuracy of 108. Although RCGAu found it difficult in getting a solution with the desired accuracy 108 for high conditioning and multimodal functions within the specified maximum #FEs, it was able to solve most of the test functions with dimensions up to 40 with lower precisions

An investigation of K-means clustering to high and multi-dimensional biological data

PURPOSE – The K-means clustering algorithm has been intensely researched owing to its simplicity of implementation and usefulness in the clustering task. However, there have also been criticisms on its performance, in particular, for demanding the value of K before the actual clustering task. It is evident from previous researches that providing the number of clusters a priori does not in any way assist in the production of good quality clusters. The authors' investigations in this paper also confirm this finding. The purpose of this paper is to investigate further, the usefulness of the K-means clustering in the clustering of high and multi-dimensional data by applying it to biological sequence data. DESIGN/METHODOLOGY/APPROACH – The authors suggest a scheme which maps the high dimensional data into low dimensions, then show that the K-means algorithm with pre-processor produces good quality, compact and well-separated clusters of the biological data mapped in low dimensions. For the purpose of clustering, a character-to-numeric conversion was conducted to transform the nucleic/amino acids symbols to numeric values.1 pdf file.Barileé B. Baridam, M. M. Alihttp://www.emeraldsight.com/journalshtm?/issn=0368-492Xhb201

A Tabu Search-Based Memetic Algorithm for Hardware/Software Partitioning

Hardware/software (HW/SW) partitioning is to determine which components of a system are implemented on hardware and which ones on software. It is one of the most important steps in the design of embedded systems. The HW/SW partitioning problem is an NP-hard constrained binary optimization problem. In this paper, we propose a tabu search-based memetic algorithm to solve the HW/SW partitioning problem. First, we convert the constrained binary HW/SW problem into an unconstrained binary problem using an adaptive penalty function that has no parameters in it. A memetic algorithm is then suggested for solving this unconstrained problem. The algorithm uses a tabu search as its local search procedure. This tabu search has a special feature with respect to solution generation, and it uses a feedback mechanism for updating the tabu tenure. In addition, the algorithm integrates a path relinking procedure for exploitation of newly found solutions. Computational results are presented using a number of test instances from the literature. The algorithm proves its robustness when its results are compared with those of two other algorithms. The effectiveness of the proposed parameter-free adaptive penalty function is also shown

Mathematical Modeling and Optimal Blank Generation in Glass Manufacturing

This paper discusses the stock size selection problem (Chambers and Dyson, 1976), which is of relevance in the float glass industry. Given a fixed integer N, generally between 2 and 6 (but potentially larger), we find the N best sizes for intermediate stock from which to cut a roster of orders. An objective function is formulated with the purpose of minimizing wastage, and the problem is phrased as a combinatorial optimization problem involving the selection of columns of a cost matrix. Some bounds and heuristics are developed, and two exact algorithms (depth-first search and branch-and-bound) are applied to the problem, as well as one approximate algorithm (NOMAD). It is found that wastage reduces dramatically as N increases, but this trend becomes less pronounced for larger values of N (beyond 6 or 7). For typical values of N, branch-and-bound is able to find the exact solution within a reasonable amount of time

Certification of Bounds of Non-linear Functions: the Templates Method

The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture yields thousands of inequalities. We introduce an approximation algorithm, which combines ideas of the max-plus basis method (in optimal control) and of the linear templates method developed by Manna et al. (in static analysis). This algorithm consists in bounding some of the constituents of the function by suprema of quadratic forms with a well chosen curvature. This leads to semialgebraic optimization problems, solved by sum-of-squares relaxations. Templates limit the blow up of these relaxations at the price of coarsening the approximation. We illustrate the efficiency of our framework with various examples from the literature and discuss the interfacing with Coq.Comment: 16 pages, 3 figures, 2 table

Observability Estimate for the Fractional Order Parabolic Equations on Measurable Sets

We establish an observability estimate for the fractional order parabolic equations evolved in a bounded domain Ω of R . The observation region is × , where and are measurable subsets of Ω and (0, ), respectively, with positive measure. This inequality is equivalent to the null controllable property for a linear controlled fractional order parabolic equation. The building of this estimate is based on the Lebeau-Robbiano strategy and a delicate result in measure theory provided i