Multidimensional Optimization Algorithm Research Articles

A new line search technique

In this paper the problem of line search, an important step in most multidimensional optimization algorithms, is considered. If conjugate gradient descent is to be used in producing a descent sequence for a given functional f on a Hilbert space H, then at every step in the sequence one is faced with the problem of finding α, the step length to minimize f(x (k) + αP (k)) where x (k), P (k) ∈ H are the k-th elements of the descent sequence and k-th descent direction, respectively. This is usually accomplished by a one-dimensional search. It is the purpose of this paper to discuss a method of search that determines, by a synergy of analytic-synthetic procedures, a sequence {α (k)} such that the sequence {f(x (k) + α (k) P (k))} converges to f(x *(k)), the minimum of f(x). Specifically, the step in Fletcher-Reeve's algorithm that employs the geometric mean of the past values of α (k) as initial estimate is replaced by their harmonic mean to yield initially a low order accuracy formula. The efficiency of this technique is confirmed by numerical experimentation.

On Using Global Optimization to Obtain Better Performance of a MART Algorithm in 3D X-ray Tomography

In this article an improvement to a current methodology for testing iterative reconstruction methods is presented. This improvement consists in the use of a multidimensional global optimization algorithm for the best estimate of the free parameters of the reconstruction process. This algorithm is based on a probabilistic random search method. The global optimization algorithms allow us to achieve the best performance of the reconstruction algorithms in order to compare them under the optimal conditions. This methodology has been applied for the testing of a MART (Multiplicative Algebraic Reconstruction Technique) algorithm performance using the classical cubic-shaped voxels and spherical symmetric basis functions, also known as blobs, as the basis functions for the image representation in 3D X-ray cone-beam transmission tomography.

Developments towards a fully automated AMS system

The possibilities of computer-assisted and automated accelerator mass spectrometry (AMS) measurements were explored. The goal of these efforts is to develop fully automated procedures for “routine” measurements at the Vienna Environmental Research Accelerator (VERA), a dedicated 3-MV Pelletron tandem AMS facility. As a new tool for automatic tuning of the ion optics we developed a multi-dimensional optimization algorithm robust to noise, which was applied for 14C and 10Be. The actual isotope ratio measurements are performed in a fully automated fashion and do not require the presence of an operator. Incoming data are evaluated online and the results can be accessed via Internet. The system was used for 14C, 10Be, 26Al and 129I measurements.

On convergence of "divide the best" global optimization algorithms

In this paper a new class of multidimensional global optimization algorithms (called "divide the best" algorithms) is proposed. The class unifies and generalizes the classes of the characteristic methods and the adaptive partition algorithms introduced by Grishagin and Pinter respectively. The new scheme includes also some methods which do not fit either the characteristic or the adaptive partition families. A detailed convergence study is presented. A special attention is paid to cases where sufficient conditions of everywhere dense, local and global convergence are fulfilled only over subregions of the search domain.

Array surveying using matched-field processing

In this paper, the problem of localizing a vertical line array of sensors is studied in the context of matched-field processing. A broadcasting source is assumed deployed in a known environment at a known location from a vertical line array. Array surveying is discussed and a simple procedure using a correlation measure and a standard multidimensional optimization algorithm is proposed to resolve the array shape. First, this procedure is used on simulated data and convergence is demonstrated. Then, the method is used on data collected at sea in September 1987 with a 900-m-long array with 120 sensors. The derived array sensor positions are found consistent with previous analysis results. The positions found by the optimization procedure have a noisy character which is thought to be due to deviations of the individual array element gain and phase characteristics from their nominal calibrations.

Self‐surveying techniques for matched‐field processing

The classic problem of matched‐field processing is the detection and localization of (unknown) sources assuming a known oceanic environment and a calibrated vertical line array of known shape. If a broadcasting source is deployed at a known location, the array shape can be determined through assumptions on the environment, or the environmental characteristics (such as the sound‐speed profile) can be determined if the array shape is known. These two problems are investigated in the framework of matched‐field processing. First, the array shape calibration is discussed and a simple procedure, using a correlation measure and a standard multidimensional optimization algorithm, is proposed. This procedure is used on simulated data (where convergence is observed) and on real data collected at sea in September 1987 with a 900‐m‐long array with 120 sensors. The experimental results are found consistent with those obtained through previous analysis. Then, the problem of calibrating the oceanic environment is studied using a normal mode formulation. Bucker's self‐cohering approach to correct for tame environmental mismatch in the matched‐field processor output [H. Bucker, 4th MFP Workshop, 6–8 Sept. 1989, Victoria, Canada], provides a convenient measure of the environmental mismatch for a range‐independent medium. An approach to tomography, using a vertical line array that samples well the normal modes, is proposed. The preliminary simulation results show that the Bucker correction factors provide a smooth measure of sound‐speed mismatch and that the inversion for the sound‐speed profile should be possible through optimization. [Work supported by ONR.]

Application of multi-dimensional optimization to laboratory control

Multidimensional optimization algorithms are shown to be useful in control of experimental apparatus. We describe an interface to a BBC microcomputer which permits the simultaneous operation of up to five stepper-motors, and describe the algorithms used to position apparatus to obtain the extremum of a computer-acquired signal. For reliability and efficiency it is most important to handle correctly effects due to signal noise. One particular example, a nulling ellipsometer, is described in detail.

Meat emulsion functionality related to fat-protein ratio and selected dairy and cereal products

The influence of fat-protein ratio, moisture content, buttermilk powder, modified wheat flour, corn starch and modified waxy maize flour in processed meat emulsions upon their sensory attributes, textural profile parameters, and selected functional properties were investigated. These properties were optimized using regression models, canonical analysis, response surface methodology, and a multidimensional optimization algorithm.

A minimax search plan for constrained optimization problems

A minimax search strategy is described for locating the boundary point of a region on a line joining a feasible point to an infeasible point. Asymptotic strategies, useful when the number of experiments to be used in the search is not predetermined, are also given. These strategies are useful subroutines for many multidimensional optimization algorithms.