Convex relaxation of mixture regression with efficient algorithms

We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data.

Improved bounds for subband-adaptive iterative shrinkage/thresholding algorithms.

This paper presents new methods for computing the step sizes of the subband-adaptive iterative shrinkage-thresholding algorithms proposed by Bayram & Selesnick and Vonesch & Unser. The method yields tighter wavelet-domain bounds of the system matrix, thus leading to improved convergence speeds. It is directly applicable to non-redundant wavelet bases, and we also adapt it for cases of redundant frames. It turns out that the simplest and most intuitive setting for the step sizes that ignores subband aliasing is often satisfactory in practice. We show that our methods can be used to advantage with reweighted least squares penalty functions as well as L1 penalties. We emphasize that the algorithms presented here are suitable for performing inverse filtering on very large datasets, including 3D data, since inversions are applied only to diagonal matrices and fast transforms are used to achieve all matrix-vector products.

Single-sensor maximum power point tracking algorithms

Single-sensor maximum power point tracking algorithms for photovoltaic systems are presented. The algorithms have the features, characteristics and advantages of the widely used incremental conductance (INC) algorithm. However; unlike the INC algorithm which requires two sensors (the voltage sensor and the current sensor), the single-sensor algorithms are more desirable because they require only one sensor: the voltage sensor. The algorithms operate by maximising power at the DC-DC converter output, instead of the input. © 2013 The Institution of Engineering and Technology.

A PDE viewpoint on basic properties of coordination algorithms with symmetries

Several recent control applications consider the coordination of subsystems through local interaction. Often the interaction has a symmetry in state space, e.g. invariance with respect to a uniform translation of all subsystem values. The present paper shows that in presence of such symmetry, fundamental properties can be highlighted by viewing the distributed system as the discrete approximation of a partial differential equation. An important fact is that the symmetry on the state space differs from the popular spatial invariance property, which is not necessary for the present results. The relevance of the viewpoint is illustrated on two examples: (i) ill-conditioning of interaction matrices in coordination/consensus problems and (ii) the string instability issue. ©2009 IEEE.

Optimization Algorithms on Matrix Manifolds

This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms.

Enhancing and developing the practical optimisation capabilities and intelligence of automatic design software

In the modern engineering design cycle the use of computational tools becomes a neces- sity. The complexity of the engineering systems under consideration for design increases dramatically as the demands for advanced and innovative design concepts and engineering products is expanding. At the same time the advancements in the available technology in terms of computational resources and power, as well as the intelligence of the design software, accommodate these demands and make them a viable approach towards the chal- lenge of real-world engineering problems. This class of design optimisation problems is by nature multi-disciplinary. In the present work we establish enhanced optimisation capabil- ities within the Nimrod/O tool for massively distributed execution of computational tasks through cluster and computational grid resources, and develop the potential to combine and benefit from all the possible available technological advancements, both software and hardware. We develop the interface between a Free Form Deformation geometry manage- ment in-house code with the 2D airfoil aerodynamic efficiency evaluation tool XFoil, and the well established multi-objective heuristic optimisation algorithm NSGA-II. A simple airfoil design problem has been defined to demonstrate the functionality of the design sys- tem, but also to accommodate a framework for future developments and testing with other state-of-the-art optimisation algorithms such as the Multi-Objective Genetic Algorithm (MOGA) and the Multi-Objective Tabu Search (MOTS) techniques. Ultimately, heav- ily computationally expensive industrial design cases can be realised within the presented framework that could not be investigated before. © 2012 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc.

Enhancing and developing the practical optimisation capabilities and intelligence of automatic design software

In the modern engineering design cycle the use of computational tools becomes a necessity. The complexity of the engineering systems under consideration for design increases dramatically as the demands for advanced and innovative design concepts and engineering products is expanding. At the same time the advancements in the available technology in terms of computational resources and power, as well as the intelligence of the design software, accommodate these demands and make them a viable approach towards the challenge of real-world engineering problems. This class of design optimisation problems is by nature multi-disciplinary. In the present work we establish enhanced optimisation capabilities within the Nimrod/O tool for massively distributed execution of computational tasks through cluster and computational grid resources, and develop the potential to combine and benefit from all the possible available technological advancements, both software and hardware. We develop the interface between a Free Form Deformation geometry management in-house code with the 2D airfoil aerodynamic efficiency evaluation tool XFoil, and the well established multi-objective heuristic optimisation algorithm NSGA-II. A simple airfoil design problem has been defined to demonstrate the functionality of the design system, but also to accommodate a framework for future developments and testing with other state-of-the-art optimisation algorithms such as the Multi-Objective Genetic Algorithm (MOGA) and the Multi-Objective Tabu Search (MOTS) techniques. Ultimately, heavily computationally expensive industrial design cases can be realised within the presented framework that could not be investigated before. ©2012 AIAA.

A self-adaptive genetic algorithm applied to multi-objective optimization of an airfoil

Genetic algorithms (GAs) have been used to tackle non-linear multi-objective optimization (MOO) problems successfully, but their success is governed by key parameters which have been shown to be sensitive to the nature of the particular problem, incorporating concerns such as the numbers of objectives and variables, and the size and topology of the search space, making it hard to determine the best settings in advance. This work describes a real-encoded multi-objective optimizing GA (MOGA) that uses self-adaptive mutation and crossover, and which is applied to optimization of an airfoil, for minimization of drag and maximization of lift coefficients. The MOGA is integrated with a Free-Form Deformation tool to manage the section geometry, and XFoil which evaluates each airfoil in terms of its aerodynamic efficiency. The performance is compared with those of the heuristic MOO algorithms, the Multi-Objective Tabu Search (MOTS) and NSGA-II, showing that this GA achieves better convergence.

Designing and testing an advanced pneumatic braking system for heavy vehicles

Heavy goods vehicles exhibit poor braking performance in emergency situations when compared to other vehicles. Part of the problem is caused by sluggish pneumatic brake actuators, which limit the control bandwidth of their antilock braking systems. In addition, heuristic control algorithms are used that do not achieve the maximum braking force throughout the stop. In this article, a novel braking system is introduced for pneumatically braked heavy goods vehicles. The conventional brake actuators are improved by placing high-bandwidth, binary-actuated valves directly on the brake chambers. A made-for-purpose valve is described. It achieves a switching delay of 3-4 ms in tests, which is an order of magnitude faster than solenoids in conventional anti-lock braking systems. The heuristic braking control algorithms are replaced with a wheel slip regulator based on sliding mode control. The combined actuator and slip controller are shown to reduce stopping distances on smooth and rough, high friction (μ = 0.9) surfaces by 10% and 27% respectively in hardware-in-the-loop tests compared with conventional ABS. On smooth and rough, low friction (μ = 0.2) surfaces, stopping distances are reduced by 23% and 25%, respectively. Moreover, the overall air reservoir size required on a heavy goods vehicle is governed by its air usage during an anti-lock braking stop on a low friction, smooth surface. The 37% reduction in air usage observed in hardware-in-the-loop tests on this surface therefore represents the potential reduction in reservoir size that could be achieved by the new system. © 2012 IMechE.

Optimization algorithms and ODE's in MDO

There is a need for a stronger theoretical understanding of Multidisciplinary Design Optimization (MDO) within the field. Having developed a differential geometry framework in response to this need, we consider how standard optimization algorithms can be modeled using systems of ordinary differential equations (ODEs) while also reviewing optimization algorithms which have been derived from ODE solution methods. We then use some of the framework's tools to show how our resultant systems of ODEs can be analyzed and their behaviour quantitatively evaluated. In doing so, we demonstrate the power and scope of our differential geometry framework, we provide new tools for analyzing MDO systems and their behaviour, and we suggest hitherto neglected optimization methods which may prove particularly useful within the MDO context. Copyright © 2013 by ASME.