Clustering search

This paper presents the Clustering Search (CS) as a new hybrid metaheuristic, which works in conjunction with other metaheuristics, managing the implementation of local search algorithms for optimization problems. Usually the local search is costly and should be used only in promising regions of the search space. The CS assists in the discovery of these regions by dividing the search space into clusters. The CS and its applications are reviewed and a case study for a problem of capacitated clustering is presented.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Universidade Federal do MaranhãoUniversidade Federal de São Paulo (UNIFESP)Instituto Nacional de Pesquisas EspaciaisUNIFESPSciEL

Hybrid quantum annealing for larger-than-QPU lattice-structured problems

Quantum processing units (QPUs) executing annealing algorithms have shown promise in optimization and simulation applications. Hybrid algorithms are a natural bridge to additional applications of larger scale. We present a straightforward and effective method for solving larger-than-QPU lattice-structured Ising optimization problems. Performance is compared against simulated annealing with promising results, and improvement is shown as a function of the generation of D-Wave QPU used.Comment: 21 pages, 15 figures, supplementary code attachmen

Computational Methods for Computer Vision : Minimal Solvers and Convex Relaxations

Robust fitting of geometric models is a core problem in computer vision. The most common approach is to use a hypothesize-and-test framework, such as RANSAC. In these frameworks the model is estimated from as few measurements as possible, which minimizes the risk of selecting corrupted measurements. These estimation problems are called minimal problems, and they can often be formulated as systems of polynomial equations. In this thesis we present new methods for building so-called minimal solvers or polynomial solvers, which are specialized code for solving such systems. On several minimal problems we improve on the state-of-the-art both with respect to numerical stability and execution time.In many computer vision problems low rank matrices naturally occur. The rank can serve as a measure of model complexity and typically a low rank is desired. Optimization problems containing rank penalties or constraints are in general difficult. Recently convex relaxations, such as the nuclear norm, have been used to make these problems tractable. In this thesis we present new convex relaxations for rank-based optimization which avoid drawbacks of previous approaches and provide tighter relaxations. We evaluate our methods on a number of real and synthetic datasets and show state-of-the-art results

Robust subspace clustering via joint weighted Schatten-p norm and Lq norm minimization

© 2017 SPIE. Low-rank representation (LRR) has been successfully applied to subspace clustering. However, the nuclear norm in the standard LRR is not optimal for approximating the rank function in many real-world applications. Meanwhile, the L21 norm in LRR also fails to characterize various noises properly. To address the above issues, we propose an improved LRR method, which achieves low rank property via the new formulation with weighted Schatten-p norm and Lq norm (WSPQ). Specifically, the nuclear norm is generalized to be the Schatten-p norm and different weights are assigned to the singular values, and thus it can approximate the rank function more accurately. In addition, Lq norm is further incorporated into WSPQ to model different noises and improve the robustness. An efficient algorithm based on the inexact augmented Lagrange multiplier method is designed for the formulated problem. Extensive experiments on face clustering and motion segmentation clearly demonstrate the superiority of the proposed WSPQ over several state-of-the-art methods

Multidisciplinary Design Optimization for Space Applications

Multidisciplinary Design Optimization (MDO) has been increasingly studied in aerospace engineering with the main purpose of reducing monetary and schedule costs. The traditional design approach of optimizing each discipline separately and manually iterating to achieve good solutions is substituted by exploiting the interactions between the disciplines and concurrently optimizing every subsystem. The target of the research was the development of a flexible software suite capable of concurrently optimizing the design of a rocket propellant launch vehicle for multiple objectives. The possibility of combining the advantages of global and local searches have been exploited in both the MDO architecture and in the selected and self developed optimization methodologies. Those have been compared according to computational efficiency and performance criteria. Results have been critically analyzed to identify the most suitable optimization approach for the targeted MDO problem