Bounded lower subdifferentiability optimization techniques : applications

In this article we develop a global optimization algorithm for quasiconvex programming where the objective function is a Lipschitz function which may have "flat parts". We adapt the Extended Cutting Angle method to quasiconvex functions, which reduces significantly the number of iterations and objective function evaluations, and consequently the total computing time. Applications of such an algorithm to mathematical programming problems inwhich the objective function is derived from economic systems and location problems are described. Computational results are presented.

Application of identification techniques to determine effect of carbon content in steels on rheological parameters during hot deformation

The objective of the present work is searching for the correlation between the carbon content in steels and the parameters of the rheological models, which are used to describe the materials behavior during hot plastic deformation. This correlation can be expected in the internal variable models, which are based on physical phenomena occurring in the material. Such a model, based on the dislocation density as the internal variable, is investigated in this work. The experiments including hot torsion tests are used for the analysis.
The procedure is composed of three parts. Plastometric tests were performed for steels with various carbon content. Optimization techniques were applied next to determine the coefficients in the internal variable rheological model for these steels. Two versions of the model are considered. One is based on the average dislocation density and the second accounts for the distribution of dislocation densities. Evaluation of correlation between carbon content and such coefficients in the models as activation energy for self diffusion, activation energy for recrystallization, grain boundary mobility, recovery coefficient etc. was the main objective of the work. In consequence, the model which may be used for simulation of hot forming processes for steels with various chemical compositions, is proposed.

Optimization-based formation of autonomous mobile robots

The formation of autonomous mobile robots to an arbitrary geometric pattern in a distributed fashion is a fundamental problem in formation control. This paper presents a new asynchronous, memoryless (oblivious) algorithm to the formation problem via distributed optimization techniques. The optimization minimizes an appropriately defined difference function between the current robot distribution and the target geometric pattern. The optimization processes are performed independently by individual robots in their local coordinate systems. A movement strategy derived from the results of the distributed optimizations guarantees that every movement makes the current robot configuration approaches the target geometric pattern until the final pattern is reached.

Predicting molecular structures: an application of the cutting angle method

The ability to predict molecular geometries has important applications in chemistry. Specific examples include the areas of protein space structure elucidation, the investigation of host–guest interactions, the understanding of properties of superconductors and of zeolites. This prediction of molecular geometries often depends on finding the global minimum or maximum of a function such as the potential energy. In this paper, we consider several well-known molecular conformation problems to which we apply a new method of deterministic global optimization called the cutting angle method. We demonstrate that this method is competitive with other global optimization techniques for these molecular conformation problems.

Learning weights in the generalized OWA operators

This paper discusses identification of parameters of generalized ordered weighted averaging (GOWA) operators from empirical data. Similarly to ordinary OWA operators, GOWA are characterized by a vector of weights, as well as the power to which the arguments are raised. We develop optimization techniques which allow one to fit such operators to the observed data. We also generalize these methods for functional defined GOWA and generalized Choquet integral based aggregation operators.

Global optimisation of neural networks using a deterministic hybrid approach

Selection of the topology of a neural network and correct parameters for the learning algorithm is a tedious task for designing an optimal artificial neural network, which is smaller, faster and with a better generalization performance. In this paper we introduce a recently developed cutting angle method (a deterministic technique) for global optimization of connection weights. Neural networks are initially trained using the cutting angle method and later the learning is fine-tuned (meta-learning) using conventional gradient descent or other optimization techniques. Experiments were carried out on three time series benchmarks and a comparison was done using evolutionary neural networks. Our preliminary experimentation results show that the proposed deterministic approach could provide near optimal results much faster than the evolutionary approach.

A new method for locating the global optimum : application of the cutting angle method to molecular structure prediction

Many problems in chemistry depend on the ability to identify the global minimum or maximum of a function. Examples include applications in chemometrics, optimization of reaction or operating conditions, and non-linear least-squares analysis. This paper presents the results of the application of a new method of deterministic global optimization, called the cutting angle method (CAM), as applied to the prediction of molecular geometries. CAM is shown to be competitive with other global optimization techniques for several benchmark molecular conformation problem. CAM is a general method that can also be applied to other computational problems involving global minima, global maxima or finding the roots of nonlinear equations.

Formation control of weak autonomous robots

Formation of autonomous mobile robots to an arbitrary geometric pattern in a distributed fashion is a fundamental problem in formation control. This paper presents a new fully distributed, memoryless (oblivious) algorithm to the formation control problem via distributed optimization techniques. The optimization minimizes an appropriately defined difference function between the current robot distribution and target geometric pattern. The optimization processes are performed independently by individual robots in their local coordinate system. A movement strategy derived from the results of the distributed optimizations guarantees that every movement makes the current robot configuration approaches the target geometric pattern until the final pattern is reached.

An interactive genetic algorithm approach to MMIC low noise amplifier design using a layered encoding structure

In this paper, an interactive genetic algorithm (IGA) approach is developed to optimize design variables for a monolithic microwave integrated circuit (MMIC) low noise amplifier. A layered encoding structure is employed to the problem representation in genetic algorithm to allow human intervention in the circuit design variable tuning process. The MMIC amplifier design is synthesized using the Agilent Advance Design System (ADS), and the IGA is proposed to tune the design variables in order to meet multiple constraints and objectives such as noise figure, current and simulated power gain. The developed IGA is compared with other optimization techniques from ADS. The results showed that the IGA performs better in achieving most of the involved objectives.

Least squares splines with free knots: global optimization approach

Splines with free knots have been extensively studied in regard to calculating the optimal knot positions. The dependence of the accuracy of approximation on the knot distribution is highly nonlinear, and optimisation techniques face a difficult problem of multiple local minima. The domain of the problem is a simplex, which adds to the complexity. We have applied a recently developed cutting angle method of deterministic global optimisation, which allows one to solve a wide class of optimisation problems on a simplex. The results of the cutting angle method are subsequently improved by local discrete gradient method. The resulting algorithm is sufficiently fast and guarantees that the global minimum has been reached. The results of numerical experiments are presented.

Priority frequency maptable for query optimization using materialized views

In this paper query optimization using materialized views has been analyzed and a comprehensive and efficient technique has been proposed to create Map-table. Materialized views can provide massive improvements in query processing time, especially for aggregation queries over large tables. To realize this potential, a number of existing techniques have been considered regarding the problem of maintaining materialized views as well as optimal searching time and memory overhead. Keeping this in mind, an optimal algorithm has been proposed in this paper for query optimization. It has been demonstrated that the proposed algorithm reduces the searching time substantially and reducing the memory size as well.

Non-smooth optimization methods for computation of the conditional value-at-risk and portfolio optimization

We examine numerical performance of various methods of calculation of the Conditional Value-at-risk (CVaR), and portfolio optimization with respect to this risk measure. We concentrate on the method proposed by Rockafellar and Uryasev in (Rockafellar, R.T. and Uryasev, S., 2000, Optimization of conditional value-at-risk. Journal of Risk, 2, 21-41), which converts this problem to that of convex optimization. We compare the use of linear programming techniques against a non-smooth optimization method of the discrete gradient, and establish the supremacy of the latter. We show that non-smooth optimization can be used efficiently for large portfolio optimization, and also examine parallel execution of this method on computer clusters.

Isolation and characterization of polyunsaturated fatty acid producing Thraustochytrium species : screening of strains and optimization of omega-3 production

An isolation program targeting Thraustochytrids (marine fungoid protists) from 19 different Atlantic Canadian locations was performed. Sixty-eight isolates were screened for biomass, total fatty acid (TFA), eicosapentaenoic acid (EPA), and docosahexaenoic acid (DHA) content. Analysis of fatty acid methyl ester results discerned four distinctive clusters based on fatty acid profiles, with biomass ranging from 0.1 to 2.3 g L−1, and lipid, EPA, and DHA contents ranging from 27.1 to 321.14, 2.97 to 21.25, and 5.18 to 83.63 mg g−1 biomass, respectively. ONC-T18, was subsequently chosen for further manipulations. Identified using 18S rRNA gene sequencing techniques as a Thraustochytrium sp., most closely related to Thraustochytrium striatum T91-6, ONC-T18 produced up to 28.0 g L−1 biomass, 81.7% TFA, 31.4% (w/w biomass) DHA, and 4.6 g L−1 DHA under optimal fermentation conditions. Furthermore, this strain was found to produce the carotenoids and xanthophylls astaxanthin, zeaxanthin, canthaxanthin, echinenone, and β-carotene. Given this strain’s impressive productivity when compared to commercial strains, such as Schizochytrium sp. SR21 (which has only 50% TFA), coupled with its ability to grow at economical nitrogen and very low salt concentrations (2 g L−1), ONC-T18 is seen as an ideal candidate for both scale-up and commercialization.