49,394 research outputs found
Multidimensional Constrained Global Optimization in Domains with Computable Boundaries
Multidimensional constrained global optimization problem with objective function under Lipschitz condition and constraints generating a feasible domain with computable boundaries is considered. For solving this problem the dimensionality reduction approach on the base of the nested optimization scheme is used. This scheme reduces initial multidimensional problem to a family of one-dimensional subproblems and allows applying univariate methods for the execution of multidimensional optimization. Sequential and parallel modifications of well-known information-statistical methods of Lipschitz optimization are proposed for solving the univariate subproblems arising inside the nested scheme in the case of domains with computable boundaries. A comparison with classical penalty function method being traditional means of taking into account the constraints is carried out. The results of experiments demonstrate a significant advantage of the methods proposed over the penalty function method
A Global Optimisation Toolbox for Massively Parallel Engineering Optimisation
A software platform for global optimisation, called PaGMO, has been developed
within the Advanced Concepts Team (ACT) at the European Space Agency, and was
recently released as an open-source project. PaGMO is built to tackle
high-dimensional global optimisation problems, and it has been successfully
used to find solutions to real-life engineering problems among which the
preliminary design of interplanetary spacecraft trajectories - both chemical
(including multiple flybys and deep-space maneuvers) and low-thrust (limited,
at the moment, to single phase trajectories), the inverse design of
nano-structured radiators and the design of non-reactive controllers for
planetary rovers. Featuring an arsenal of global and local optimisation
algorithms (including genetic algorithms, differential evolution, simulated
annealing, particle swarm optimisation, compass search, improved harmony
search, and various interfaces to libraries for local optimisation such as
SNOPT, IPOPT, GSL and NLopt), PaGMO is at its core a C++ library which employs
an object-oriented architecture providing a clean and easily-extensible
optimisation framework. Adoption of multi-threaded programming ensures the
efficient exploitation of modern multi-core architectures and allows for a
straightforward implementation of the island model paradigm, in which multiple
populations of candidate solutions asynchronously exchange information in order
to speed-up and improve the optimisation process. In addition to the C++
interface, PaGMO's capabilities are exposed to the high-level language Python,
so that it is possible to easily use PaGMO in an interactive session and take
advantage of the numerous scientific Python libraries available.Comment: To be presented at 'ICATT 2010: International Conference on
Astrodynamics Tools and Techniques
On affine scaling inexact dogleg methods for bound-constrained nonlinear systems
Within the framework of affine scaling trust-region methods for bound constrained problems, we discuss the use of a inexact dogleg method as a tool for simultaneously handling the trust-region and the bound constraints while seeking for an approximate minimizer of the model. Focusing on bound-constrained systems of nonlinear equations, an inexact affine scaling method for large scale problems, employing the inexact dogleg procedure, is described. Global convergence results are established without any Lipschitz assumption on the Jacobian matrix, and locally fast convergence is shown under standard assumptions. Convergence analysis is performed without specifying the scaling matrix used to handle the bounds, and a rather general class of scaling matrices is allowed in actual algorithms. Numerical results showing the performance of the method are also given
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