290,776 research outputs found
Objective Improvement in Information-Geometric Optimization
Information-Geometric Optimization (IGO) is a unified framework of stochastic
algorithms for optimization problems. Given a family of probability
distributions, IGO turns the original optimization problem into a new
maximization problem on the parameter space of the probability distributions.
IGO updates the parameter of the probability distribution along the natural
gradient, taken with respect to the Fisher metric on the parameter manifold,
aiming at maximizing an adaptive transform of the objective function. IGO
recovers several known algorithms as particular instances: for the family of
Bernoulli distributions IGO recovers PBIL, for the family of Gaussian
distributions the pure rank-mu CMA-ES update is recovered, and for exponential
families in expectation parametrization the cross-entropy/ML method is
recovered. This article provides a theoretical justification for the IGO
framework, by proving that any step size not greater than 1 guarantees monotone
improvement over the course of optimization, in terms of q-quantile values of
the objective function f. The range of admissible step sizes is independent of
f and its domain. We extend the result to cover the case of different step
sizes for blocks of the parameters in the IGO algorithm. Moreover, we prove
that expected fitness improves over time when fitness-proportional selection is
applied, in which case the RPP algorithm is recovered
Geometric Duality for Convex Vector Optimization Problems
Geometric duality theory for multiple objective linear programming problems
turned out to be very useful for the development of efficient algorithms to
generate or approximate the whole set of nondominated points in the outcome
space. This article extends the geometric duality theory to convex vector
optimization problems.Comment: 21 page
An Octree-Based Approach towards Efficient Variational Range Data Fusion
Volume-based reconstruction is usually expensive both in terms of memory
consumption and runtime. Especially for sparse geometric structures, volumetric
representations produce a huge computational overhead. We present an efficient
way to fuse range data via a variational Octree-based minimization approach by
taking the actual range data geometry into account. We transform the data into
Octree-based truncated signed distance fields and show how the optimization can
be conducted on the newly created structures. The main challenge is to uphold
speed and a low memory footprint without sacrificing the solutions' accuracy
during optimization. We explain how to dynamically adjust the optimizer's
geometric structure via joining/splitting of Octree nodes and how to define the
operators. We evaluate on various datasets and outline the suitability in terms
of performance and geometric accuracy.Comment: BMVC 201
Interactive design exploration for constrained meshes
In architectural design, surface shapes are commonly subject to geometric constraints imposed by material, fabrication or assembly. Rationalization algorithms can convert a freeform design into a form feasible for production, but often require design modifications that might not comply with the design intent. In addition, they only offer limited support for exploring alternative feasible shapes, due to the high complexity of the optimization algorithm. We address these shortcomings and present a computational framework for interactive shape exploration of discrete geometric structures in the context of freeform architectural design. Our method is formulated as a mesh optimization subject to shape constraints. Our formulation can enforce soft constraints and hard constraints at the same time, and handles equality constraints and inequality constraints in a unified way. We propose a novel numerical solver that splits the optimization into a sequence of simple subproblems that can be solved efficiently and accurately. Based on this algorithm, we develop a system that allows the user to explore designs satisfying geometric constraints. Our system offers full control over the exploration process, by providing direct access to the specification of the design space. At the same time, the complexity of the underlying optimization is hidden from the user, who communicates with the system through intuitive interfaces
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