DECMO2: a robust hybrid and adaptive multi-objective evolutionary algorithm.

We describe a hybrid and adaptive coevolutionary optimization method that can efficiently solve a wide range of multi-objective optimization problems (MOOPs) as it successfully combines positive traits from three main classes of multi-objective evolutionary algorithms (MOEAs): classical approaches that use Pareto-based selection for survival criteria, approaches that rely on differential evolution, and decomposition-based strategies. A key part of our hybrid evolutionary approach lies in the proposed fitness sharing mechanism that is able to smoothly transfer information between the coevolved subpopulations without negatively impacting the specific evolutionary process behavior that characterizes each subpopulation. The proposed MOEA also features an adaptive allocation of fitness evaluations between the coevolved populations to increase robustness and favor the evolutionary search strategy that proves more successful for solving the MOOP at hand. Apart from the new evolutionary algorithm, this paper also contains the description of a new hypervolume and racing-based methodology aimed at providing practitioners from the field of multi-objective optimization with a simple means of analyzing/reporting the general comparative run-time performance of multi-objective optimization algorithms over large problem sets

Performance comparison of generational and steady-state asynchronous multi-objective evolutionary algorithms for computationally-intensive problems.

In the last two decades, multi-objective evolutionary algorithms (MOEAs) have become ever more used in scientific and industrial decision support and decision making contexts the require an a posteriori articulation of preference. The present work is focused on a comparative analysis of the performance of two master–slave parallelization (MSP) methods, the canonical generational scheme and the steady-state asynchronous scheme. Both can be used to improve the convergence speed of multi-objective evolutionary algorithms that must use computationally-intensive fitness evaluation functions. Both previous and present experiments show that a correct choice for one or the other parallelization method can lead to substantial improvements with regard to the overall duration of the optimization process. Our main aim is to provide practitioners of MOEAs with a simple but effective method of deciding which MSP option is better given the particularities of the concrete optimization process. This in turn, would give the decision maker more time for articulating preferences (i.e., more flexibility). Our analysis is performed based on 15 well-known MOOP benchmark problems and two simulation-based industrial optimization processes from the field of electrical drive design. For the first industrial MOOP, when comparing with a preliminary study, applying the steady-state asynchronous MSP enables us to achieve an overall speedup (in terms of total wall-clock computation time) of ≈25%. For the second industrial MOOP, applying the steady-state MSP produces an improvement of ≈12%. We focus our study on two of the best known and most widely used MOEAs: the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and the Strength Pareto Evolutionary Algorithm (SPEA2)

Comparative analysis of two asynchronous parallelization variants for a multi-objective coevolutionary solver.

We describe and compare two steady state asynchronous parallelization variants for DECMO2++, a recently proposed multi-objective coevolutionary solver that generally displays a robust run-time convergence behavior. The two asynchronous variants were designed as trade-offs that maintain only two of the three important synchronized interactions / constraints that underpin the (generation-based) DECMO2++ coevolutionary model. A thorough performance evaluation on a test set that aggregates 31 standard benchmark problems shows that while both parallelization options are able to generally preserve the competitive convergence behavior of the baseline coevolutionary solver, the better parallelization choice is to prioritize accurate run-time search adaptation decisions over the ability to perform equidistant fitness sharing

Walking Faster

The Gröbner Walk is an algorithm that converts a given Gröbner basis of a polynomial ideal I of arbitrary dimension to a Gröbner basis of I with respect to another term order. The conversion is done in several steps (the walk) following a path in the Gröbner fan of I. We report on our experiences with an implementation of the walk. We discuss several algorithmic variations as well as important implementation techniques whose combined effect is to elevate the walk to a new level of performance

Design and Analysis of a 1D Actively Stabilized System with Viscoelastic Damping Support

Passively magnetically stabilized degrees of freedom yield the benefit of reduced complexity and therefore costs. However, the application of passive magnetic bearings (PMBs) also features some drawbacks. The poor damping capability leads to exaggerated deflection amplitudes when passing the resonance speeds of the applied system. This results in the necessity of external damping. Complying with the goal of costs and complexity, viscoelastic materials offer a suitable solution. However, these materials show high frequency and temperature dependent properties which induce the necessity of a proper model. Thus, the design of systems, as presented in this paper, requires accurate modeling of the dynamic behavior including the nonlinear characteristic of damping elements to predict the system displacements. In the investigated setup only two degrees of freedom remain to be controlled actively. These are the axial rotation and the axial position of the rotor which are controlled by the motor and an active magnetic axial bearing (AMB). This article focuses on the rotor dynamic modeling of a radial passively magnetically stabilized system especially considering the nonlinear behavior of viscoelastic damping elements. Finally, the results from the analytic model are verified by measurements on a manufactures test system

On the Walk

The Gröbner Walk is a basis conversion method proposed by Collart, Kalkbrener, and Mall. It converts a given Gröbner basis G of a (possibly positive dimensional) polynomial ideal I to a Gröbner basis G 0 of I with respect to another term order. The target Gröbner basis is approached in several steps (the Walk), each performing a simpler Gröbner basis computation. We address a host of questions associated with this method: alternative ways of presenting the main algorithm, algorithmic variations and refinements, implementation techniques, promising applications, and its practical performance, including a comparison with the FGLM conversion method. Our results show that the Walk has the potential to become a key tool for computing and manipulating ideal bases and solving systems of equations

Scientific Computing in Electrical Engineering

This collection of selected papers presented at the 11th International Conference on Scientific Computing in Electrical Engineering (SCEE), held in St. Wolfgang, Austria, in 2016, showcases the state of the art in SCEE. The aim of the SCEE 2016 conference was to bring together scientists from academia and industry, mathematicians, electrical engineers, computer scientists, and physicists, and to promote intensive discussions on industrially relevant mathematical problems, with an emphasis on the modeling and numerical simulation of electronic circuits and devices, electromagnetic fields, and coupled problems. The focus in methodology was on model order reduction and uncertainty quantification. This extensive reference work is divided into six parts: Computational Electromagnetics, Circuit and Device Modeling and Simulation, Coupled Problems and Multi‐Scale Approaches in Space and Time, Mathematical and Computational Methods Including Uncertainty Quantification, Model Order Reduction, and Industrial Applications. Each part starts with a general introduction, followed by the respective contributions. This book will appeal to mathematicians and electrical engineers. Further, it introduces algorithm and program developers to recent advances in the other fields, while industry experts will be introduced to new programming tools and mathematical methods

A case study of multi-threaded Gröbner basis completion

We investigate sources of parallelism in the Gröbner Basis algorithm for their practical use on the desk-top. Our execution environment is a standard multi-processor workstation, and our parallel programming environment is PARSAC-2 on top of a multi-threaded operating system. We investigate the performance of two main variants of our master parallel algorithm on a standard set of examples. The first version exploits only work parallelism in a strategy compliant way. The second version investigates search parallelism in addition, where large super-linear speedups can be obtained. These speedups are due to improved S-polynomial selection behavior and therefore carry over to single processor machines. Since we obtain our parallel variants by a controlled variation of only a few parameters in the master algorithm, we obtain new insights into the way in which different sources of parallelism interact in Gröbner Basis completion

Fundamental considerations on introducing damping to passively magnetically stabilized rotor systems

When designing passively magnetically stabilized rotor systems, introducing sufficient damping is key. We investigated two different dynamic systemswith one mass and two massesto determine their theoretical optimal behavior and how they can be realized considering real-world specifications and limitations. Based on dimensionless formulations of reduced dynamic systems, we present fundamental correlations between, and the optimal choice of, physical parameters. Furthermore, we compare the two systems in terms of feasibility and efficiency of different damping methods. Our investigations used an eddy current damper and viscoelastic damping elements as exemplary damping methods for the one-mass and two-mass systems, respectively. Passive stabilization was realized by means of permanent magnetic bearings. We found that the two-mass system is preferable due to the broader range of damping possibilities.(VLID)355584