A genetic algorithm with memory for mixed discrete-continuous design optimization

This paper describes a new approach for reducing the number of the fitness function evaluations required by a genetic algorithm (GA) for optimization problems with mixed continuous and discrete design variables. The proposed additions to the GA make the search more effective and rapidly improve the fitness value from generation to generation. The additions involve memory as a function of both discrete and continuous design variables, multivariate approximation of the fitness function in terms of several continuous design variables, and localized search based on the multivariate approximation. The approximation is demonstrated for the minimum weight design of a composite cylindrical shell with grid stiffeners

A Genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint Approximations

This paper describes a new approach for reducing the number of the fitness and constraint function evaluations required by a genetic algorithm (GA) for optimization problems with mixed continuous and discrete design variables. The proposed additions to the GA make the search more effective and rapidly improve the fitness value from generation to generation.The additions involve memory as a function of both discrete and continuous design variables, and multivariate approximation of the individual functions' responses in terms of several continuous design variables. The approximation is demonstrated for the minimum weight design of a composite cylindrical shell with grid stiffeners

Acoustic scattering of broadband echolocation signals from prey of Blainville's beaked whales : modeling and analysis

Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2006Blainville's beaked whales (Mesoplodon densirostris) use broadband, ultrasonic echolocation signals (27 to 57 kHz) to search for, localize, and approach prey that generally consist of mid-water and deep-water fishes and squid. Although it is well known that the spectral characteristics of broadband echoes from marine organisms are a strong function of size, shape, orientation and anatomical group, little is known as to whether or not these or other toothed whales use spectral cues in discriminating between prey and non-prey. In order to study the prey-classification process, a stereo acoustic tag was mounted on a Blainville's beaked whale so that emitted clicks and corresponding echoes from prey could be recorded. A comparison of echoes from prey selected by the whale and those from randomly chosen scatterers suggests that the whale may have, indeed, discriminated between echoes using spectral features and target strengths. Specifically, the whale appears to have favored prey with one or more deep nulls in the echo spectra as well as ones with higher target strength. A three-dimensional, acoustic scattering model is also developed to simulate broadband scattering from squid, a likely prey of the beaked whale. This model applies the distorted wave Born approximation (DWBA) to a weakly-scattering, inhomogeneous body using a combined ray trace and volume integration approach. Scatterer features are represented with volume elements that are small (less than 1/12th of the wavelength) for the frequency range of interest (0 to 120 kHz). Ranges of validity with respect to material properties and numerical considerations are explored using benchmark computations with simpler geometries such as fluid-filled spherical and cylindrical fluid shells. Modeling predictions are compared with published data from live, freely swimming squid. These results, as well as previously published studies, are used in the analysis of the echo spectra of the whale's ensonified targets

Structural optimization of thin shells using finite element method

The objective of the present work was the structural optimization of thin shell structures that are subjected to stress and displacement constraints. In order to accomplish this, the structural optimization computer program DESAP1 was modified and improved. In the static analysis part of the DESAP1 computer program the torsional spring elements, which are used to analyze thin, shallow shell structures, were eliminated by modifying the membrane stiffness matrix of the triangular elements in the local coordinate system and adding a fictitious rotational stiffness matrix. This simplified the DESAP1 program input, improved the accuracy of the analysis, and saved computation time. In the optimization part of the DESAP1 program the stress ratio formula, which redesigns the thickness of each finite element of the structure, was solved by an analytical method. This scheme replaced the iterative solution that was previously used in the DESAP1 program, thus increasing the accuracy and speed of the design. The modified program was used to design a thin, cylindrical shell structure with optimum weight, and the results are reported in this paper

The Number of Cylindrical Shells

Given a set P of n points in three dimensions, a cylindrical shell or zone cylinder is formed by two cylindrical cylinders with the same axis such that all points of P are between the two cylinders. We prove that the number of cylindrical shells enclosing P passing through combinatorially different subsets of P has size Omega(n^3) and O(n^4) (previous known bound was O(n^5) )