Experimental Comparisons of Derivative Free Optimization Algorithms

In this paper, the performances of the quasi-Newton BFGS algorithm, the NEWUOA derivative free optimizer, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), the Differential Evolution (DE) algorithm and Particle Swarm Optimizers (PSO) are compared experimentally on benchmark functions reflecting important challenges encountered in real-world optimization problems. Dependence of the performances in the conditioning of the problem and rotational invariance of the algorithms are in particular investigated.Comment: 8th International Symposium on Experimental Algorithms, Dortmund : Germany (2009

Blaze-DEMGPU: Modular high performance DEM framework for the GPU architecture

AbstractBlaze-DEMGPU is a modular GPU based discrete element method (DEM) framework that supports polyhedral shaped particles. The high level performance is attributed to the light weight and Single Instruction Multiple Data (SIMD) that the GPU architecture offers. Blaze-DEMGPU offers suitable algorithms to conduct DEM simulations on the GPU and these algorithms can be extended and modified. Since a large number of scientific simulations are particle based, many of the algorithms and strategies for GPU implementation present in Blaze-DEMGPU can be applied to other fields. Blaze-DEMGPU will make it easier for new researchers to use high performance GPU computing as well as stimulate wider GPU research efforts by the DEM community

A Novel and Fully Automated Domain Transformation Scheme for Near Optimal Surrogate Construction

Recent developments in surrogate construction predominantly focused on two strategies to improve surrogate accuracy. Firstly, component-wise domain scaling informed by cross-validation. Secondly, regression to construct response surfaces using additional information in the form of additional function-values sampled from multi-fidelity models and gradients. Component-wise domain scaling reliably improves the surrogate quality at low dimensions but has been shown to suffer from high computational costs for higher dimensional problems. The second strategy, adding gradients to train surrogates, typically results in regression surrogates. Counter-intuitively, these gradient-enhanced regression-based surrogates do not exhibit improved accuracy compared to surrogates only interpolating function values. This study empirically establishes three main findings. Firstly, constructing the surrogate in poorly scaled domains is the predominant cause of deteriorating response surfaces when regressing with additional gradient information. Secondly, surrogate accuracy improves if the surrogates are constructed in a fully transformed domain, by scaling and rotating the original domain, not just simply scaling the domain. The domain transformation scheme should be based on the local curvature of the approximation surface and not its global curvature. Thirdly, the main benefit of gradient information is to efficiently determine the (near) optimal domain in which to construct the surrogate. This study proposes a foundational transformation algorithm that performs near-optimal transformations for lower dimensional problems. The algorithm consistently outperforms cross-validation-based component-wise domain scaling for higher dimensional problems. A carefully selected test problem set that varies between 2 and 16-dimensional problems is used to clearly demonstrate the three main findings of this study.Comment: 20 pages, 28 figure

Optimal Design of a Piezoelectric Transducer for Exciting Guided Wave Ultrasound in Rails

An existing Ultrasonic Broken Rail Detection System [1] installed in South Africa on a heavy duty railway line is currently being upgraded to include defect detection and location. To accomplish this, an ultrasonic piezoelectric transducer to strongly excite a guided wave mode with energy concentrated in the web (web mode) of a rail is required. A previous study [2] demonstrated that the recently developed SAFE-3D (Semi-Analytical Finite Element – 3 Dimensional) method can effectively predict the guided waves excited by a resonant piezoelectric transducer. In this study, the SAFE-3D model is used in the design optimization of a rail web transducer. A bound-constrained optimization problem was formulated to maximize the energy transmitted by the transducer in the web mode when driven by a pre-defined excitation signal. Dimensions of the transducer components were selected as the three design variables. A Latin hypercube sampled design of experiments that required a total of 500 SAFE- 3D analyses in the design space was employed in a response surface-based optimization approach. The Nelder-Mead optimization algorithm was then used to find an optimal transducer design on the constructed response surface. The radial basis function response surface was first verified by comparing a number of predicted responses against the computed SAFE-3D responses. The performance of the optimal transducer predicted by the optimization algorithm on the response surface was also verified to be sufficiently accurate using SAFE-3D. The computational advantages of SAFE-3D in transducer design is noteworthy given we needed to conduct more than 500 analyses. The optimal design was then manufactured and experimental measurements were used to validate the predicted performance. The adopted design method has demonstrated the capability to automate the design of transducers for a particular rail cross- section and frequency range

Potential for interactive design simulations in discrete element modelling

This study investigates the potential for combining lower fidelity models with high performance solution strategies such as efficient graphical processing unit (GPU) based discrete element modelling (DEM) to not only do simulations faster but differently. Specifically this study investigates interactive simulation and design for which the simulation environment BlazeDEM-GPU was developed that allows researchers and engineers to interact with simulations. The initial results prove to be promising and warranting extensive research to be conducted in future which may allow for the development of alternative paradigms. In addition to the design cycle, the role that this interactive simulation and design will play in education is invaluable as an in-house corporate training tool for young engineers to actively train and develop understanding for specific industrial processes. This would also allow engineers to conduct just-in-time (JIT) simulation based assessment of processes before commencing on actual site visits, allowing for shorter and more focussed site excursions

Validation of the gpu based blaze-dem framework for hopper discharge

Understanding the dynamical behavior of particulate materials is extremely important to many industrial processes, with typical applications that range from hopper flows in agriculture to tumbling mills in the mining industry. The discrete element method (DEM) has become the defacto standard to simulate particulate materials. The DEM is a compu- tationally intensive numerical approach that is limited to a moderate amount (thousands) of particles when considering fully coupled densely packed systems modeled by realistic par- ticle shape and history dependent constitutive relationships. A large number (millions) of particles can be simulated when the coupling between particles is relaxed to still accurately simulated lesser dense systems. Massively large scale simulations (tens of millions) are possi- ble when particle shapes are simplified, however this may lead to oversimplification when an accurate representation of the particle shape is essential to capture the macroscopic transport of particulates. Polyhedra represent the geometry of most convex particulate materials well and when combined with appropriate contact models predicts realistic mechanical behavior to that of the actual system. Detecting collisions between polyhedra is computationally ex- pensive often limiting simulations to only hundreds of thousands of particles. However, the computational architecture e.g. CPU and GPU plays a significant role on the performance that can be realized. The parallel nature of the GPU allows for a large number of simple independent processes to be executed in parallel. This results in a significant speed up over conventional implementations utilizing the Central Processing Unit (CPU) architecture, when algorithms are well aligned and optimized for the threading model of the GPU. We recently introduced the BLAZE-DEM framework for the GPU architecture that can model millions of pherical and polyhedral particles in a realistic time frame using a single GPU. In this paper we validate BLAZE-DEM for hopper discharge simulations. We firstly compare the flow-rates and patterns of polyhedra and spheres obtained with experiment to that of DEM. We then compare flow-rates between spheres and polyhedra to gauge the effect of particle shape. Finally we perform a large scale DEM simulation using 16 million articles to illustrate the capability of BLAZE-DEM to predict bulk flow in realistic hoppers