Controlled Random Search Research Articles

Simulating sedimentary burial cycles – Part 2: Elemental-based multikinetic apatite fission-track interpretation and modelling techniques illustrated using examples from northern Yukon

Abstract. Compositionally dependent apatite fission track (AFT) annealing is a common but underappreciated cause for AFT age dispersion in sedimentary samples. We present an interpretation and modelling strategy for samples with variable apatite composition that exploits multikinetic AFT annealing to obtain thermal histories that can provide more detail and better resolution compared to conventional methods. We illustrate our method using a Permian and a Devonian sample from northern Yukon, Canada, both with complicated geological histories and long residence times in the AFT partial annealing zone. Effective Cl values (eCl; converted from rmr0 values) derived from detailed apatite elemental data are used to define AFT statistical kinetic populations with significantly different total annealing temperatures (∼110–185 ∘C) and ages that agree closely with the results of age mixture modelling. These AFT populations are well resolved using eCl values but exhibit significant overlap with respect to the conventional parameters of Cl content or Dpar. Elemental analyses and measured Dpar for Phanerozoic samples from Yukon and the Northwest Territories confirm that Dpar has low precision and that Cl content alone cannot account for the compositional and associated kinetic variability observed in natural samples. An inverse multikinetic AFT model, AFTINV, is used to obtain thermal-history information by simultaneously modelling multiple kinetic populations as distinct thermochronometers with different temperature sensitivities. A nondirected Monte Carlo scheme generates a set of statistically acceptable solutions at the 0.05 significance level and then these solutions are updated to the 0.5 level using a controlled random search (CRS) learning algorithm. The smoother, closer-fitting CRS solutions allow for a more consistent assessment of the eCl values and thermal-history styles that are needed to satisfy the AFT data. The high-quality Devonian sample (39 single-grain ages and 202 track lengths) has two kinetic populations that require three cycles of heating and cooling (each subsequent event of lower intensity) to obtain close-fitting solutions. The younger and more westerly Permian sample with three kinetic populations only records the latter two heating events. These results are compatible with known stratigraphic and thermal maturity constraints, and the QTQt software produces similar results. Model results for these and other samples suggest that elemental-derived eCl values are accurate within the range 0–0.25 apfu (atoms per formula unit, with rmr0 values of 0.73–0.84), which encompasses most of the data from annealing experiments. Outside of this range, eCl values for more exotic compositions may require adjustment relative to better-constrained apatite compositions when trying to fit multiple kinetic populations. Our results for natural and synthetic samples suggest that an element-based multikinetic approach has great potential to dramatically increase the temperature range and resolution of thermal histories relative to conventional AFT thermochronology.

Development of Local IDF-formula Using Controlled Random Search Method for Global Optimization

The aim of the study is to present the effective and relatively simple empirical approach to rainfall intensity-duration-frequency-formulas development, based on Controlled Random Search (CRS) for global optimization. The approach is mainly dedicated to the cases in which the commonly used IDF-relationships do not provide satisfactory fit between simulations and observations, and more complex formulas with higher number of parameters are advisable. Precipitation data from Gdansk gauge station were analyzed as the example, with use of peak-overthreshold method and Chomicz scale for rainfall intensity. General forms of the IDF-function were chosen and the parameter calibration with use of CRS algorithm was developed. The compliance of the obtained IDFformulas with precipitation data and the efficiency of the algorithm were analyzed. The study confirmed the proposed empirical approach may be an interesting alternative for probabilistic ones, especially when IDFrelationship has more complex form and precipitation data do not match “typical” hydrological distributions.

VES/TEM 1D joint inversion by using Controlled Random Search (CRS) algorithm

Electrical (DC) and Transient Electromagnetic (TEM) soundings are used in a great number of environmental, hydrological, and mining exploration studies. Usually, data interpretation is accomplished by individual 1D models resulting often in ambiguous models. This fact can be explained by the way as the two different methodologies sample the medium beneath surface. Vertical Electrical Sounding (VES) is good in marking resistive structures, while Transient Electromagnetic sounding (TEM) is very sensitive to conductive structures. Another difference is VES is better to detect shallow structures, while TEM soundings can reach deeper layers. A Matlab program for 1D joint inversion of VES and TEM soundings was developed aiming at exploring the best of both methods. The program uses CRS – Controlled Random Search – algorithm for both single and 1D joint inversions. Usually inversion programs use Marquadt type algorithms but for electrical and electromagnetic methods, these algorithms may find a local minimum or not converge. Initially, the algorithm was tested with synthetic data, and then it was used to invert experimental data from two places in Paraná sedimentary basin (Bebedouro and Pirassununga cities), both located in São Paulo State, Brazil. Geoelectric model obtained from VES and TEM data 1D joint inversion is similar to the real geological condition, and ambiguities were minimized. Results with synthetic and real data show that 1D VES/TEM joint inversion better recovers simulated models and shows a great potential in geological studies, especially in hydrogeological studies.

Optimization Algorithms for Kinematically Optimal Design of Parallel Manipulators

Optimal design is an inevitable step for parallel manipulators. The formulated optimal design problems are generally constrained, nonlinear, multimodal, and even without closed-form analytical expressions. Numerical optimization algorithms are thus applied to solve the problems. However, the optimization algorithms are usually chosen ad arbitrium. This paper aims to provide a guideline to choose algorithms for optimal design problems. Typical algorithms, the sequential quadratic programming (SQP) with multiple initial points, the controlled random search (CRS), the genetic algorithm (GA), the differential evolution (DE), and the particle swarm optimization (PSO), are investigated in detail for their convergence performances by using two canonical design examples, the Delta robot and the Gough-Stewart platform. It is shown that SQP with multiple initial points can be efficient for simple design problems, while DE and PSO perform effectively and steadily for all design problems. CRS can be used to generate good initial points since it exhibits excellent convergence evolution in the starting period.

NUMERICAL STUDIES OF SOME GENERALIZED CONTROLLED RANDOM SEARCH ALGORITHMS

This paper presents motivations and algorithmic details of some generalized controlled random search (CRS) algorithms for global optimization. It also carries out an extensive numerical study of the generalized CRS algorithms to demonstrate their superiorities over their original counterparts. The numerical study is carried out using a set of 50 test problems many of which are inspired by practical applications. Numerical experiments indicate that the generalized algorithms are considerably better than the previous versions. The algorithms are also compared with the DIRECT algorithm (Jones et al., 1993). The comparison shows that the generalized CRS algorithms are better than the DIRECT algorithm in high dimensional problems. Thus, they offer a reasonable alternative to many currently available stochastic algorithms, especially for problems requiring "direct search type" methods.

Identification of minimal metabolic pathway models consistent with phenotypic data

In metabolic systems, the cellular network of metabolic reactions together with constraints of (ir)reversibility of enzymes determines the space of all possible steady-state phenotypes. Analysis of large metabolic models, however, is not feasible in real-time and identification of a smaller model without loss of accuracy is desirable for model-based bioprocess optimization and control. To this end, we propose two search algorithms for systematic identification of a subset of pathways that match the observed cellular phenotype relevant for a particular process condition. Central carbon metabolism of Escherichia coli was used as a case-study together with three phenotypic datasets obtained from the literature. The first search method is based on ranking pathways and the second is a controlled random search (CRS) algorithm. Since we wish to obtain a biologically realistic subset of pathways, the objective function to be minimized is a trade-off between the error and investment costs. We found that the CRS outperforms the ranking algorithm, as it is less likely to fall into local minima. In addition, we compared two pathway analysis methods (elementary modes versus generating vectors) in terms of modelling accuracy and computational intensity. We conclude that generating vectors have preference over elementary modes to describe a particular phenotype. Overall, the original model containing 433 generating vectors or 2706 elementary modes could be reduced to a system of one to three pathways giving a good correlation with the measured datasets. We consider this work as a first step towards the use of detailed metabolic models to improve real-time optimization, monitoring, and control of biological processes.

Selection of Elementary Modes for Bioprocess Control

The lack of model-based information in bioreactor monitoring and control can have a profound impact on biological systems. We therefore aim to develop a model using elementary modes (EMs) that represents the observed phenotype in given environmental conditions suited for bioprocess control. Challenges in the model development were the high number of possible phenotypes of stoichiometric models and the high computational intensity.Two methods were compared to reduce the number of EMs to match the observed cellular phenotype. The first method is based on ranking modes and the second is a controlled random search (CRS) algorithm. Since we wish to obtain a biologically realistic subset of EMs, the objective function to be minimized is a trade-off between the error, efficiency of the modes, and model size.The case study considered the central carbon metabolism of Escherichia coli. The original model containing 2706 modes for case 1 and 11718 for case 2 was reduced to a system of one for case 1 and three modes for case 2 giving a good correlation with the measured data. Furthermore, considering also intracellular besides extracellular metabolites, results in a better fit of the measured rates. Finally, the CRS outperformed the ranking algorithm.

Synthesis of the [formula omitted]-distribution as an aid to stochastic global optimization

The β -distribution is used as a point generation scheme in global optimization. Two population set-based global optimization algorithms are considered. These are the differential evolution (DE) and the controlled random search (CRS) algorithms. The point generation schemes of DE and CRS are hybridized with the β random variate. The hybridization uses a probabilistic combination of the point generation by the β -distribution and the point generation by DE or CRS. Numerical experiments are carried out using both test and practical problems. Numerical results suggest that the resulting algorithms are superior to their respective original counterpart.

Some Variants of the Controlled Random Search Algorithm for Global Optimization

We suggested some modifications to the controlled random search (CRS) algorithm for global optimization. We introduce new trial point generation schemes in CRS, in particular, point generation schemes using linear interpolation and mutation. Central to our modifications is the probabilistic adaptation of point generation schemes within the CRS algorithm. A numerical study is carried out using a set of 50 test problems many of which are inspired by practical applications. Numerical experiments indicate that the resulting algorithms are considerably better than the previous versions. Thus, they offer a reasonable alternative to many currently available stochastic algorithms, especially for problems requiring direct search type methods.

Controlled random search technique for estimation of convective heat transfer coefficient

This paper is concerned with a method for solving inverse heat conduction problem. The method is based on the controlled random search (CRS) technique in conjunction with modified Newton–Raphson method. The random search procedure does not need the computation of derivative of the function to be evaluated. Therefore, it is independent of the calculation of the sensitivity coefficient for nonlinear parameter estimation. The algorithm does not depend on the future-temperature information and can predict convective heat transfer coefficient with random errors in the input temperature data. The technique is first validated against an analytical solution of heat conduction equation for a typical rocket nozzle. Comparison with an earlier analysis of inverse heat conduction problem of a similar experiment shows that the present method provides solutions, which are fully consistent with the earlier results. Once validated, the technique is used to investigate another estimation of heat transfer coefficient for an experiment of short duration, high heating rate, and employing indepth temperature measurement. The CRS procedure, in conjunction with modified Newton–Raphson method, is quite useful in estimating the value of the convective heat-transfer coefficient from the measured transient temperature data on the outer surface or imbedded thermocouple inside the rocket nozzle. Some practical examples are illustrated, which demonstrate the stability and accuracy of the method to predict the surface heat flux.

Scaled Up Pulsed Deposition Technology: Carburization Resistant Ablation Coatings for Ethylene Pyrolysis Coils

ABSTRACTProducts derived from ethylene have and will continue to replace metallic materials traditionally used for transportation, building materials, and products we use in our everyday lives. As the demand continues to increase, a more suitable material for the outlet coils of ethylene pyrolysis heaters will have to be identified. In this study, we discuss utilization of scaled up pulsed deposition technology to deposit adherent carburization resistant coatings on the inner diameter of ethylene pyrolysis tubing with the intent of extending tube life. Ablation target material selection was based primarily on elevated temperature properties and the ability of the coating to prevent transformation of the inherent protective chromium oxide surface film to metal carbides while in service. The near optimal settings of the processing parameters for pulsed laser deposition of ceramic SiC on heat resistant tubing traditionally used for ethylene service were investigated using a semi quantitative controlled random search methodology. Minimization of the objective function which was based on width, thickness and coverage of the thin film resulted in an optimal deposition time of 4.3 minutes and surface finish of 272 nm.

On success rates for controlled random search

Controlled Random Search (CRS) is a simple population based algorithm which despite its attractiveness for practical use, has never been very popular among researchers on Global Optimization due to the difficulties in analysing the algorithm. In this paper, a framework to study the behaviour of algorithms in general is presented and embedded into the context of our view on questions in Global Optimization. By using as a reference a theoretical ideal algorithm called N-points Pure Adaptive Search (NPAS) some new analytical results provide bounds on speed of convergence and the Success Rate of CRS in the limit once it has settled down into simple behaviour. To relate the performance of the algorithm to characteristics of functions to be optimized, constructed simple test functions, called extreme cases, are used.

Constrained inversion of seismic refraction data using the controlled random search

When designing models for 2-D seismic refraction inversion, it is desirable to frame the models as polygonal units with well‐defined geophysical characteristics. Such inversion is strongly nonlinear. Random search methods for nonlinear inversion, such as the genetic algorithm and simulated annealing, have received much attention in recent years. Such methods are well suited when the model space is large and contains multiple global minima to the misfit function. Constraints are necessary in the automatic construction of polygonal models. Controlled random search (CRS) is a member of this class of methods that has not been widely exploited. CRS is an iterative process based on the polytope algorithm, which offers a means by which linear constraints may be used. The CRS samples large model spaces, resists local minima, and can find multiple global minima. A new program has been developed for inversion of 2-D seismic refraction data which incorporates geologic compatibility constraints for polygon‐based models. A theoretical example and practical applications of this technique to environmental investigations illustrate its characteristics.

Detection of gravitational waves from coalescing binaries in the time domain

We propose a multistep procedure for the on-line detection and analysis of gravitational wave signals emitted during the coalescence of compact binaries. This procedure, based on a hierarchical strategy, consists of a rough analysis of the gravitational wave signal using adaptive line enhancers (ALE) filters and the controlled random search (CRS) optimization algorithm followed by a refined analysis using the classic matched-filtering technique. The results of simulations for the rough analysis are quite promising both for the relatively small computational power needed and for the robustness of the algorithms used, so that it could be very helpful for gravitational wave detection with very large baseline interferometric detectors like LIGO and VIRGO.

A Numerical Comparison of Some Modified Controlled Random Search Algorithms

In this paper we propose a new version of the Controlled Random Search (CRS) algorithm of Price. The new algorithm has been tested on thirteen global optimization test problems. Numerical experiments indicate that the resulting algorithm performs considerably better than the earlier versions of the CRS algorithms. The algorithm, therefore, could offer a reasonable alternative to many currently available stochastic algorithms, especially for problems requiring `direct search'' type methods. Also a classification of the CRS algorithms is made based on `global technique'' -- `local technique'' and the relative performance of classes is numerically explored.

Speed Control of a DC Motor Using Global Search Optimization Method

There are two aspect to this study. Firstly a new global search method is introduced which was developed by combining the two well-known global search methods, namely Controlled Random Search (CRS), Global Search Using Brownian Motion. Next, this new method has been applied to design of optimal controller for the speed control of a dc motor. The design has been done for various controller structures (PID, Cascade PID and nonlinear feedback) and their performances are compared with each other. Moreover, the results are also compared with the ones obtained by the application of classical optimal control theory and it is seen that the methodology has some merits.