Index Information Algorithm with Local Tuning for Solving Multidimensional Global Optimization Problems with Multiextremal Constraints

Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust nonconvex subregions are considered. Both the objective function and the constraints may be partially defined. To solve such problems an algorithm is proposed, that uses Peano space-filling curves and the index scheme to reduce the original problem to a H\"{o}lder one-dimensional one. Local tuning on the behaviour of the objective function and constraints is used during the work of the global optimization procedure in order to accelerate the search. The method neither uses penalty coefficients nor additional variables. Convergence conditions are established. Numerical experiments confirm the good performance of the technique.Comment: 29 pages, 5 figure

Towards recovery of complex shapes in meshes using digital images for reverse engineering applications

When an object owns complex shapes, or when its outer surfaces are simply inaccessible, some of its parts may not be captured during its reverse engineering. These deficiencies in the point cloud result in a set of holes in the reconstructed mesh. This paper deals with the use of information extracted from digital images to recover missing areas of a physical object. The proposed algorithm fills in these holes by solving an optimization problem that combines two kinds of information: (1) the geometric information available on the surrounding of the holes, (2) the information contained in an image of the real object. The constraints come from the image irradiance equation, a first-order non-linear partial differential equation that links the position of the mesh vertices to the light intensity of the image pixels. The blending conditions are satisfied by using an objective function based on a mechanical model of bar network that simulates the curvature evolution over the mesh. The inherent shortcomings both to the current holefilling algorithms and the resolution of the image irradiance equations are overcom

Integrated Dynamic Facade Control with an Agent-based Architecture for Commercial Buildings

Dynamic façades have significant technical potential to minimize heating, cooling, and lighting energy use and peak electric demand in the perimeter zone of commercial buildings, but the performance of these systems is reliant on being able to balance complex trade-offs between solar control, daylight admission, comfort, and view over the life of the installation. As the context for controllable energy-efficiency technologies grows more complex with the increased use of intermittent renewable energy resources on the grid, it has become increasingly important to look ahead towards more advanced approaches to integrated systems control in order to achieve optimum life-cycle performance at a lower cost. This study examines the feasibility of a model predictive control system for low-cost autonomous dynamic façades. A system architecture designed around lightweight, simple agents is proposed. The architecture accommodates whole building and grid level demands through its modular, hierarchical approach. Automatically-generated models for computing window heat gains, daylight illuminance, and discomfort glare are described. The open source Modelica and JModelica software tools were used to determine the optimum state of control given inputs of window heat gains and lighting loads for a 24-hour optimization horizon. Penalty functions for glare and view/ daylight quality were implemented as constraints. The control system was tested on a low-power controller (1.4 GHz single core with 2 GB of RAM) to evaluate feasibility. The target platform is a low-cost ($35/unit) embedded controller with 1.2 GHz dual-core cpu and 1 GB of RAM. Configuration and commissioning of the curtainwall unit was designed to be largely plug and play with minimal inputs required by the manufacturer through a web-based user interface. An example application was used to demonstrate optimal control of a three-zone electrochromic window for a south-facing zone. The overall approach was deemed to be promising. Further engineering is required to enable scalable, turnkey solutions

Lecture 02: Tile Low-rank Methods and Applications (w/review)

As simulation and analytics enter the exascale era, numerical algorithms, particularly implicit solvers that couple vast numbers of degrees of freedom, must span a widening gap between ambitious applications and austere architectures to support them. We present fifteen universals for researchers in scalable solvers: imperatives from computer architecture that scalable solvers must respect, strategies towards achieving them that are currently well established, and additional strategies currently being developed for an effective and efficient exascale software ecosystem. We consider recent generalizations of what it means to “solve” a computational problem, which suggest that we have often been “oversolving” them at the smaller scales of the past because we could afford to do so. We present innovations that allow to approach lin-log complexity in storage and operation count in many important algorithmic kernels and thus create an opportunity for full applications with optimal scalability

An inflationary differential evolution algorithm for space trajectory optimization

In this paper we define a discrete dynamical system that governs the evolution of a population of agents. From the dynamical system, a variant of Differential Evolution is derived. It is then demonstrated that, under some assumptions on the differential mutation strategy and on the local structure of the objective function, the proposed dynamical system has fixed points towards which it converges with probability one for an infinite number of generations. This property is used to derive an algorithm that performs better than standard Differential Evolution on some space trajectory optimization problems. The novel algorithm is then extended with a guided restart procedure that further increases the performance, reducing the probability of stagnation in deceptive local minima.Comment: IEEE Transactions on Evolutionary Computation 2011. ISSN 1089-778