Optimization of the Ballistic Guide Design for the SNS FNPB 8.9 A Neutron Line

The optimization of the ballistic guide design for the SNS Fundamental Neutron Physics Beamline 8.9 A line is described. With a careful tuning of the shape of the curve for the tapered section and the width of the straight section, this optimization resulted in more than 75% increase in the neutron flux exiting the 33 m long guide over a straight m=3.5 guide with the same length.Comment: 21 pages, 13 figures; added a paragraph on existing ballistic guides to respond to referee comments; accepted for publication in Nuclear Inst. and Methods in Physics Research,

Counterexample Guided Inductive Optimization Applied to Mobile Robots Path Planning (Extended Version)

We describe and evaluate a novel optimization-based off-line path planning algorithm for mobile robots based on the Counterexample-Guided Inductive Optimization (CEGIO) technique. CEGIO iteratively employs counterexamples generated from Boolean Satisfiability (SAT) and Satisfiability Modulo Theories (SMT) solvers, in order to guide the optimization process and to ensure global optimization. This paper marks the first application of CEGIO for planning mobile robot path. In particular, CEGIO has been successfully applied to obtain optimal two-dimensional paths for autonomous mobile robots using off-the-shelf SAT and SMT solvers.Comment: 7 pages, 14rd Latin American Robotics Symposium (LARS'2017

Optimization of Discrete-parameter Multiprocessor Systems using a Novel Ergodic Interpolation Technique

Modern multi-core systems have a large number of design parameters, most of which are discrete-valued, and this number is likely to keep increasing as chip complexity rises. Further, the accurate evaluation of a potential design choice is computationally expensive because it requires detailed cycle-accurate system simulation. If the discrete parameter space can be embedded into a larger continuous parameter space, then continuous space techniques can, in principle, be applied to the system optimization problem. Such continuous space techniques often scale well with the number of parameters. We propose a novel technique for embedding the discrete parameter space into an extended continuous space so that continuous space techniques can be applied to the embedded problem using cycle accurate simulation for evaluating the objective function. This embedding is implemented using simulation-based ergodic interpolation, which, unlike spatial interpolation, produces the interpolated value within a single simulation run irrespective of the number of parameters. We have implemented this interpolation scheme in a cycle-based system simulator. In a characterization study, we observe that the interpolated performance curves are continuous, piece-wise smooth, and have low statistical error. We use the ergodic interpolation-based approach to solve a large multi-core design optimization problem with 31 design parameters. Our results indicate that continuous space optimization using ergodic interpolation-based embedding can be a viable approach for large multi-core design optimization problems.Comment: A short version of this paper will be published in the proceedings of IEEE MASCOTS 2015 conferenc

On Sound Relative Error Bounds for Floating-Point Arithmetic

State-of-the-art static analysis tools for verifying finite-precision code compute worst-case absolute error bounds on numerical errors. These are, however, often not a good estimate of accuracy as they do not take into account the magnitude of the computed values. Relative errors, which compute errors relative to the value's magnitude, are thus preferable. While today's tools do report relative error bounds, these are merely computed via absolute errors and thus not necessarily tight or more informative. Furthermore, whenever the computed value is close to zero on part of the domain, the tools do not report any relative error estimate at all. Surprisingly, the quality of relative error bounds computed by today's tools has not been systematically studied or reported to date. In this paper, we investigate how state-of-the-art static techniques for computing sound absolute error bounds can be used, extended and combined for the computation of relative errors. Our experiments on a standard benchmark set show that computing relative errors directly, as opposed to via absolute errors, is often beneficial and can provide error estimates up to six orders of magnitude tighter, i.e. more accurate. We also show that interval subdivision, another commonly used technique to reduce over-approximations, has less benefit when computing relative errors directly, but it can help to alleviate the effects of the inherent issue of relative error estimates close to zero

How to Integrate a Polynomial over a Simplex

This paper settles the computational complexity of the problem of integrating a polynomial function f over a rational simplex. We prove that the problem is NP-hard for arbitrary polynomials via a generalization of a theorem of Motzkin and Straus. On the other hand, if the polynomial depends only on a fixed number of variables, while its degree and the dimension of the simplex are allowed to vary, we prove that integration can be done in polynomial time. As a consequence, for polynomials of fixed total degree, there is a polynomial time algorithm as well. We conclude the article with extensions to other polytopes, discussion of other available methods and experimental results.Comment: Tables added with new experimental results. References adde