Nonlinear fitting of multi-compartmental data using Hooke and Jeeves direct search method

Compartmental modelling refers to modelling the transport of substances in a system consisting of multiple compartments, which is characterized by the transfer rates among the relevant compartments. In a generalized compartmental system, recycling of substances among the compartments is allowed. Compartmental modelling is a generic technique which is needed in many branches of applied physics. The most challenging task is to determine the transfer rates. The present work described the use of the Hooke and Jeeves (HJ) derivative free direct search method in determining the transfer rates to construct a multi-compartmental model with recycling among the compartments. The use of a direct search method ensures the applicability of the model to functions which are not continuous or differentiable. The present model was successfully validated using previously reported experimental data for distribution of trace elements in four compartments in an animal.

Implementation of image search system for event photo albums

The growing amount of image data (produced in a multitude of different ways – for example, like photo albums from various events) and lack of a direct search method for image information frequently create a situation in which end users of the service that publishes such data want to find themselves but cannot do it faster than looking through all entries one by one. The objective of this study is to develop and implement an approach that would be able to process this kind of data source and extract images similar to those provided by end-users in an on-demand manner. To this end, the modern methods for extract and compressing faces are introduced and applied.

Investigation of a Voronoi Diagram Representation for the Computational Design of Additively Manufactured Discrete Lattice Structures

A lattice structure is defined by a network of interconnected structural members whose architecture exhibits some degree of regularity. Although the overall architecture of a lattice may contain many members, its generation can be a simple process in which a unit cell composed of a small amount of members, in comparison to the overall structure, is mapped throughout the Euclidean space. However, finding the right lattice architecture in a vast search space that customizes the behavior of a design for a given purpose, subject to mechanical and manufacturing constraints, is a challenging task. In response to this challenge, this work investigates a Voronoi diagram-based tessellation of a body-centered cubic cell for applications in structural synthesis and computational design of 3D lattice structures. This work contributes by exploring how the Voronoi tessellation can be utilized to parametrically represent the architecture of a lattice structure and what the implications of the parametrization are on the optimization, for which a global direct search method is used. The work considers two benchmark studies, a cubic and a cantilever lattice structure, as well as the effect of isotropic and anisotropic material property models, stemming from applications to additive manufacturing. The results show that the proposed parameterization generates complex search spaces using only four variables and includes four different lattice structure types, a Kelvin cell, a hexagonal lattice, a diamond-core lattice structure, and a box-boom type lattice structure. The global direct search method applied is shown to be effective considering two different material property models from an additive manufacturing (AM) process.

An Efficient Hybrid Evolution Strategy Algorithm with Direct Search Method for Global Optimization

The main purpose of this article is to demonstrate how evolution strategy optimizers can be improved by incorporating an efficient hybridization scheme with restart strategy in order to jump out of local solution regions. The authors propose a hybrid (μ, λ)ES-NM algorithm based on the Nelder-Mead (NM) simplex search method and evolution strategy algorithm (ES) for unconstrained optimization. At first, a modified NM, called Adaptive Nelder-Mead (ANM) is used that exhibits better properties than standard NM and self-adaptive evolution strategy algorithm is applied for better performance, in addition to a new contraction criterion is proposed in this work. (μ, λ)ES-NM is balancing between the global exploration of the evolution strategy algorithm and the deep exploitation of the Nelder-Mead method. The experiment results show the efficiency of the new algorithm and its ability to solve optimization problems in the performance of accuracy, robustness, and adaptability.

An Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance Company

Catastrophe is a loss that has a low probability of occurring but can lead to high-cost claims. This paper uses the data of fire accidents from a reinsurance company in Thailand for an experiment. Our study is in two parts. First, we approximate the parameters of a Weibull distribution. We compare the parameter estimation using a direct search method with other frequently used methods, such as the least squares method, the maximum likelihood estimation, and the method of moments. The results show that the direct search method approximates the parameters more precisely than other frequently used methods (to four-digit accuracy). Second, we approximate the minimum initial capital (MIC) a reinsurance company has to hold under a given ruin probability (insolvency probability) by using parameters from the first part. Finally, we show MIC with varying the premium rate.