Search results for "Mathematica"
showing 10 items of 7971 documents
Surrogate-assisted evolutionary multiobjective shape optimization of an air intake ventilation system
2017
We tackle three different challenges in solving a real-world industrial problem: formulating the optimization problem, connecting different simulation tools and dealing with computationally expensive objective functions. The problem to be optimized is an air intake ventilation system of a tractor and consists of three computationally expensive objective functions. We describe the modeling of the system and its numerical evaluation with a commercial software. To obtain solutions in few function evaluations, a recently proposed surrogate-assisted evolutionary algorithm K-RVEA is applied. The diameters of four different outlets of the ventilation system are considered as decision variables. Fr…
Numerical Recovery of Source Singularities via the Radiative Transfer Equation with Partial Data
2013
The inverse source problem for the radiative transfer equation is considered, with partial data. Here we demonstrate numerical computation of the normal operator $X_{V}^{*}X_{V}$ where $X_{V}$ is the partial data solution operator to the radiative transfer equation. The numerical scheme is based in part on a forward solver designed by F. Monard and G. Bal. We will see that one can detect quite well the visible singularities of an internal optical source $f$ for generic anisotropic $k$ and $\sigma$, with or without noise added to the accessible data $X_{V}f$. In particular, we use a truncated Neumann series to estimate $X_{V}$ and $X_{V}^{*}$, which provides a good approximation of $X_{V}^{*…
E-NAUTILUS: A decision support system for complex multiobjective optimization problems based on the NAUTILUS method
2015
Interactive multiobjective optimization methods cannot necessarily be easily used when (industrial) multiobjective optimization problems are involved. There are at least two important factors to be considered with any interactive method: computationally expensive functions and aspects of human behavior. In this paper, we propose a method based on the existing NAUTILUS method and call it the Enhanced NAUTILUS (E-NAUTILUS) method. This method borrows the motivation of NAUTILUS along with the human aspects related to avoiding trading-off and anchoring bias and extends its applicability for computationally expensive multiobjective optimization problems. In the E-NAUTILUS method, a set of Pareto…
Shape Sensitivity Analysis and Gradient-Based Optimization of Large Structures Using MLFMA
2014
A fast method for computing the action of shape-differentiated electric field integral equation (EFIE) system matrix to a vector is derived exploiting the multilevel fast multipole algorithm (MLFMA). The proposed method is used in conjunction with the adjoint-variable method (AVM) to compute the shape gradient of arbitrary objective functions depending on shape of a metallic scatterer. The method is demonstrated numerically by optimizing the shape of a parabolic reflector illuminated with a half-wave dipole.
On shape differentiation of discretized electric field integral equation
2013
Abstract This work presents shape derivatives of the system matrix representing electric field integral equation discretized with Raviart–Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries of the original system matrix. The results are compared to derivatives computed with automatic differentiation technique and finite differences, and are found to be in an excellent agreement. Furthermore, the derived formulas are employed to analyze shape sensitivity of the input impedance of a planar inverted F-antenna, and the results are compared to those obtained using a finite difference approximation.
Interface Detection Using a Quenched-Noise Version of the Edwards-Wilkinson Equation
2015
We report here a multipurpose dynamic-interface-based segmentation tool, suitable for segmenting planar, cylindrical, and spherical surfaces in 3D. The method is fast enough to be used conveniently even for large images. Its implementation is straightforward and can be easily realized in many environments. Its memory consumption is low, and the set of parameters is small and easy to understand. The method is based on the Edwards-Wilkinson equation, which is traditionally used to model the equilibrium fluctuations of a propagating interface under the influence of temporally and spatially varying noise. We report here an adaptation of this equation into multidimensional image segmentation, an…
Linear fusion of interrupted reports in cooperative spectrum sensing for cognitive radio networks
2015
Interrupted reporting has recently been introduced as an effective method to increase the energy efficiency of cooperative spectrum sensing schemes in cognitive radio networks. In this paper, joint optimization of the reporting and fusion phases in a cooperative sensing with interrupted reporting is considered. This optimization aims at finding the best weights used at the fusion center to construct a linear fusion of the received interrupted reports, jointly with Bernoulli distributions governing the statistical behavior of the interruptions. The problem is formulated by using the deflection criterion and as a nonconvex quadratic program which is then solved for a suboptimal solution, in a…
Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models
2017
Abstract European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like the Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a give…
Interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy
2012
Abstract We present an approach to interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy. The approach relies on formulae for lower and upper bounds on coordinates of the outcome of an arbitrary efficient variant corresponding to preference information expressed by the Decision Maker. In contrast to earlier works on that subject, here lower and upper bounds can be calculated and their accuracy controlled entirely within evolutionary computation framework. This is made possible by exploration of not only the region of feasible variants – a standard within evolutionary optimization, but also the region of i…
Genetic programming through bi-objective genetic algorithms with a study of a simulated moving bed process involving multiple objectives
2013
A new bi-objective genetic programming (BioGP) technique has been developed for meta-modeling and applied in a chromatographic separation process using a simulated moving bed (SMB) process. The BioGP technique initially minimizes training error through a single objective optimization procedure and then a trade-off between complexity and accuracy is worked out through a genetic algorithm based bi-objective optimization strategy. A benefit of the BioGP approach is that an expert user or a decision maker (DM) can flexibly select the mathematical operations involved to construct a meta-model of desired complexity or accuracy. It is also designed to combat bloat - a perennial problem in genetic …