COCO: The Experimental Procedure

We present a budget-free experimental setup and procedure for benchmarking numericaloptimization algorithms in a black-box scenario. This procedure can be applied with the COCO benchmarking platform. We describe initialization of and input to the algorithm and touch upon therelevance of termination and restarts.Comment: ArXiv e-prints, arXiv:1603.0877

A collocation method for the solution of the first boundary value problem of elasticity in R^2

We present a spline collocation method for the numerical solution of a system of integral equations on a polygon in ĝ2. This integral equation arises if one solves the first boundary value problem for the Lam'e equation with a double layer potential. The derivation and the analysis of the integral equation is given in detail. The optimal order of the spline collocation method is proved for sufficiently graded meshes

COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting

We introduce COCO, an open source platform for Comparing Continuous Optimizers in a black-box setting. COCO aims at automatizing the tedious and repetitive task of benchmarking numerical optimization algorithms to the greatest possible extent. The platform and the underlying methodology allow to benchmark in the same framework deterministic and stochastic solvers for both single and multiobjective optimization. We present the rationales behind the (decade-long) development of the platform as a general proposition for guidelines towards better benchmarking. We detail underlying fundamental concepts of COCO such as the definition of a problem as a function instance, the underlying idea of instances, the use of target values, and runtime defined by the number of function calls as the central performance measure. Finally, we give a quick overview of the basic code structure and the currently available test suites.Comment: Optimization Methods and Software, Taylor & Francis, In press, pp.1-3

Local Equation of State and Velocity Distributions of a Driven Granular Gas

We present event-driven simulations of a granular gas of inelastic hard disks with incomplete normal restitution in two dimensions between vibrating walls (without gravity). We measure hydrodynamic quantities such as the stress tensor, density and temperature profiles, as well as velocity distributions. Relating the local pressure to the local temperature and local density, we construct a local constitutive equation. For strong inelasticities the local constitutive relation depends on global system parameters, like the volume fraction and the aspect ratio. For moderate inelasticities the constitutive relation is approximately independent of the system parameters and can hence be regarded as a local equation of state, even though the system is highly inhomogeneous with heterogeneous temperature and density profiles arising as a consequence of the energy injection. Concerning the local velocity distributions we find that they do not scale with the square root of the local granular temperature. Moreover the high-velocity tails are different for the distribution of the x- and the y-component of the velocity, and even depend on the position in the sample, the global volume fraction, and the coefficient of restitution.Comment: 14 pages, 14 figures of which Figs. 13a-f and Fig. 14 are archived as separate .gif files due to upload-size limitations. A version of the paper including all figures in better quality can be downloaded at http://www.theorie.physik.uni-goettingen.de/~herbst/download/LocEqSt.ps.gz (3.8 MB, ps.gz) or at http://www.theorie.physik.uni-goettingen.de/~herbst/download/LocEqSt.pdf (4.9 MB, pdf