Two-dimensional interpolation using a cell-based searching procedure

In this paper we present an efficient algorithm for bivariate interpolation, which is based on the use of the partition of unity method for constructing a global interpolant. It is obtained by combining local radial basis function interpolants with locally supported weight functions. In particular, this interpolation scheme is characterized by the construction of a suitable partition of the domain in cells so that the cell structure strictly depends on the dimension of its subdomains. This fact allows us to construct an efficient cell-based searching procedure, which provides a significant reduction of CPU times. Complexity analysis and numerical results show such improvements on the algorithm performances

Hybridization of multi-objective deterministic particle swarm with derivative-free local searches

The paper presents a multi-objective derivative-free and deterministic global/local hybrid algorithm for the efficient and effective solution of simulation-based design optimization (SBDO) problems. The objective is to show how the hybridization of two multi-objective derivative-free global and local algorithms achieves better performance than the separate use of the two algorithms in solving specific SBDO problems for hull-form design. The proposed method belongs to the class of memetic algorithms, where the global exploration capability of multi-objective deterministic particle swarm optimization is enriched by exploiting the local search accuracy of a derivative-free multi-objective line-search method. To the authors best knowledge, studies are still limited on memetic, multi-objective, deterministic, derivative-free, and evolutionary algorithms for an effective and efficient solution of SBDO for hull-form design. The proposed formulation manages global and local searches based on the hypervolume metric. The hybridization scheme uses two parameters to control the local search activation and the number of function calls used by the local algorithm. The most promising values of these parameters were identified using forty analytical tests representative of the SBDO problem of interest. The resulting hybrid algorithm was finally applied to two SBDO problems for hull-form design. For both analytical tests and SBDO problems, the hybrid method achieves better performance than its global and local counterparts

Hull-form optimization of a luxury yacht under deterministic and stochastic operating conditions via global derivative-free algorithms

Simulation-based design optimization (SBDO) techniques are used in the shape design of complex engineering systems. SBDO methods integrate an optimization algorithm, a tool for the design modification, and analysis tools. In the context of ship/ocean applica- tions the objective function is often noisy, its derivatives are not directly provided and local minima cannot be excluded, therefore global derivative-free algorithms are widely used. The objective of this work is to investigate the efficiency of three global deterministic derivative-free optimization algorithms for the deterministic and stochastic hull-form optimization of a luxury yacht. Particle Swarm Optimization (DPSO), Dolphin Pod Optimization (DPO), and DIviding RECTangles (DIRECT) are applied to reduce the total resistance over a variety of conditions. The approach includes a comparison of the performances of the optimization algorithms, based on deterministic results for two separate operating conditions. DPSO is identified as the most promising optimization algorithm and is used for the robust design optimization (RDO) per- formed considering a stochastic variation of the cruise speed with uniform distribution within a speed range from 8 to 16 kn. The resistance curve of deterministic and robust solutions is finally presented

Curvature based sampling of curves and surfaces

Efficient sampling methods enable the reconstruction of a generic surface with a limited amount of points. The reconstructed surface can therefore be used for inspection purpose. In this paper a sampling method that enables the reconstruction of a curve or surface is proposed. The input of the proposed algorithm is the number of required samples. The method takes into account two factors: the regularity of the sampling and the complexity of the object. A higher density of samples is assigned where there are some significant features, described by the curvature. The analysed curves and surfaces are described through the B-splines spaces. The sampling of surfaces generated by two or more curves is also discussed

SF-SFD: Stochastic Optimization of Fourier Coefficients to Generate Space-Filling Designs

Due to the curse of dimensionality, it is often prohibitively expensive to generate deterministic space-filling designs. On the other hand, when using na{\"i}ve uniform random sampling to generate designs cheaply, design points tend to concentrate in a small region of the design space. Although, it is preferable in these cases to utilize quasi-random techniques such as Sobol sequences and Latin hypercube designs over uniform random sampling in many settings, these methods have their own caveats especially in high-dimensional spaces. In this paper, we propose a technique that addresses the fundamental issue of measure concentration by updating high-dimensional distribution functions to produce better space-filling designs. Then, we show that our technique can outperform Latin hypercube sampling and Sobol sequences by the discrepancy metric while generating moderately-sized space-filling samples for high-dimensional problems

Multi-query Path Planning for an Unmanned Fixed-Wing Aircraft

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106491/1/AIAA2013-4791.pd