Flexible Polyhedron Method Research Articles

Most important phases of development optimization of complex structure

The paper is concerned with most important phases of formation and development optimization of complex structure. A formal approach to multidisciplinary optimization of complex devices is developed. The stages of optimization of complex devices: the choice of models of analysis, design variables, functional objectives and constraints. Optimization techniques are classified as direct; the first and second order; stochastic; linear and nonlinear programming. The applications of different types of Super Computer Simulation and Optimization Based Design / Engineering (multidimensional, structural, topological, parametric, multicriteria) are shown. On the basis of a mathematical model that takes into account the spatial and temporal fields of different nature (electrical, magnetic, elastic deformation, mechanical and thermal) with use of optimization genetic algorithms and the flexible polyhedron method, the complex structure is developed, which is characterized of reduced weight and size and high efficiency.

High-efficiency impact electromechanical converter

An algorithm for choosing the parameters of the impact electromechanical converter based on the genetic algorithms and the flexible polyhedron method joint use is developed. The spatial-temporal distribution of integral and local electrodynamics forces that act on the accelerated anchor is found.

Parameter estimation for LLDPE gas-phase reactor models

Product development and advanced control applications require models with good predictive capability. However, in some cases it is not possible to obtain good quality phenomenological models due to the lack of data or the presence of important unmeasured effects. The use of empirical models requires less investment in modeling, but implies the need for larger amounts of experimental data to generate models with good predictive capability. In this work, nonlinear phenomenological and empirical models were compared with respect to their capability to predict the melt index and polymer yield of a low-density polyethylene production process consisting of two fluidized bed reactors connected in series. To adjust the phenomenological model, the optimization algorithms based on the flexible polyhedron method of Nelder and Mead showed the best efficiency. To adjust the empirical model, the PLS model was more appropriate for polymer yield, and the melt index needed more nonlinearity like the QPLS models. In the comparison between these two types of models better results were obtained for the empirical models.

MATHEMATICAL MODELING, AUTOMATION AND CONTROL OF THE BIOCONVERSION OF SORBITOL TO SORBOSE IN THE VITAMIN C PRODUCTION PROCESS I. MATHEMATICAL MODELING

In 1990, the Biotechnology and the Control Systems Groups of IPT started developing a system for the control and automation of fermentation processes, applied to the oxidation of sorbitol to sorbose by the bacteria Gluconobacter oxydans, the microbial step of the vitamin C production process, that was chosen as a case study. Initially, a thirteen-parameter model was fitted to represent the batch operation of the system utilizing a nonlinear regression analysis, the flexible polyhedron method. Based on these results, a model for the continuous process (with the same kinetic equations) was constructed and its optimum operating point obtained

On the application of the flexible polyhedron method to solve mathematical programming problems

On the application of the flexible polyhedron method to solve mathematical programming problems

An analog of the flexible polyhedron method for scheduling problems

An analog of the flexible polyhedron method for scheduling problems

AN ALGORITHM FOR THE OPTIMAL SYNTHESIS OF COMPLEX FUNCTION GENERATORS

This article presents an effective algorithm for the optimum synthesis of complex function generators. Bagci's linear superposition technique is applied to obtain feasible initial estimates. In the optimum synthesis, the sum of squares of the structural errors at every design point is used as the objective function, subject to the constraints or the ratios of link lengths and the constraints of closure. Results are obtained by the constrained flexible polyhedron method. This algorithm can not only carry out the optimum synthesis effectively but also can get rid of the problems of branch defects and degeneracy.

ANDAL: A Nonparametric Discrimination And Learning Algorithm for Recognition in Imperfectly Supervised Environments

The problem of recognition in nonparametric environments under imperfect supervision is not amenable to solution through classical statistical approaches based on identification of finite mixtures, which require an a priori knowledge of the probabilistic descriptions of the classes. Accordingly, the problem is viewed in this study as one of optimal linear/nonlinear partitioning of the imperfectly labeled training sample set. This optimal partitioning is accomplished by defining an appropriate optimality criterion, which takes into account the imperfectness of supervision, and solving the resultant optimization problem through the Improved Flexible Polyhedron Method (IFPM). Possible alternatives to compensate for the inherent bias in this criterion towards equipopulation clusters are developed and evaluated using an illustrative example. Details of the methodology involved in implementing the approach are presented. Results of simulation experiments, which confirm the validity and effectiveness of this new technique in accomplishing optimal, linear/nonlinear discriminant learning in imperfectly supervised, nonparametric environments, are included.

OPAL: A new algorithm for optimal partitioning and learning in non parametric unsupervised environments

A nonlinear programming approach to the problem of learning in nonparametric and unsupervised environments is put forth in this study. The approach exploits the concept of optimal partitioning of the given data set as the objective of such nonparametric unsupervised learning. This partitioning or clustering is achieved by the application of the recently developed improved flexible polyhedron method (IFPM) to the associated optimization problem. The optimization problem is defined here in terms of a new, conceptually innovative optimality criterion based on intergroup and intragroup distinct scatters. Details of this new approach, a procedure for deriving an initial partition, and application of the algorithm to two numerical examples are presented.

Swift — a new constrained optimization technique

In this paper a new technique for constrained optimization called SWIFT (Sequential Weight Increasing Factor Technique) is presented and compared with some test problems available in the literature. This procedure uses an Improved Flexible Polyhedron Method as the basic algorithm for unconstrained optimization. SWIFT significantly differs. from existing constrained optimization techniques, including SUMT, in the way it penalizes the objective function. This, in effect, has brought about extreme simplification, elegance and fast convergence to the problem of constrained optimization.