Local convergence of quasi-Newton methods under metric regularity

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity and strong metric regularity. In particular, we show that the Broyden update applied to a generalized equation in Hilbert spaces satisfies the Dennis–Moré condition for q-superlinear convergence. Simple numerical examples illustrate the results.

Integration of modular process simulators under the Generalized Disjunctive Programming framework for the structural flowsheet optimization

The optimization of chemical processes where the flowsheet topology is not kept fixed is a challenging discrete-continuous optimization problem. Usually, this task has been performed through equation based models. This approach presents several problems, as tedious and complicated component properties estimation or the handling of huge problems (with thousands of equations and variables). We propose a GDP approach as an alternative to the MINLP models coupled with a flowsheet program. The novelty of this approach relies on using a commercial modular process simulator where the superstructure is drawn directly on the graphical use interface of the simulator. This methodology takes advantage of modular process simulators (specially tailored numerical methods, reliability, and robustness) and the flexibility of the GDP formulation for the modeling and solution. The optimization tool proposed is successfully applied to the synthesis of a methanol plant where different alternatives are available for the streams, equipment and process conditions.

Multi-objective adaptive evolutionary strategy for tuning compilations

Tuning compilations is the process of adjusting the values of a compiler options to improve some features of the final application. In this paper, a strategy based on the use of a genetic algorithm and a multi-objective scheme is proposed to deal with this task. Unlike previous works, we try to take advantage of the knowledge of this domain to provide a problem-specific genetic operation that improves both the speed of convergence and the quality of the results. The evaluation of the strategy is carried out by means of a case of study aimed to improve the performance of the well-known web server Apache. Experimental results show that a 7.5% of overall improvement can be achieved. Furthermore, the adaptive approach has shown an ability to markedly speed-up the convergence of the original strategy.

Rigorous Design of Complex Distillation Columns Using Process Simulators and the Particle Swarm Optimization Algorithm

We present a derivative-free optimization algorithm coupled with a chemical process simulator for the optimal design of individual and complex distillation processes using a rigorous tray-by-tray model. The proposed approach serves as an alternative tool to the various models based on nonlinear programming (NLP) or mixed-integer nonlinear programming (MINLP) . This is accomplished by combining the advantages of using a commercial process simulator (Aspen Hysys), including especially suited numerical methods developed for the convergence of distillation columns, with the benefits of the particle swarm optimization (PSO) metaheuristic algorithm, which does not require gradient information and has the ability to escape from local optima. Our method inherits the superstructure developed in Yeomans, H.; Grossmann, I. E.Optimal design of complex distillation columns using rigorous tray-by-tray disjunctive programming models. Ind. Eng. Chem. Res.2000, 39 (11), 4326–4335, in which the nonexisting trays are considered as simple bypasses of liquid and vapor flows. The implemented tool provides the optimal configuration of distillation column systems, which includes continuous and discrete variables, through the minimization of the total annual cost (TAC). The robustness and flexibility of the method is proven through the successful design and synthesis of three distillation systems of increasing complexity.

Thermogravimetry and Py–GC/MS techniques as fast qualitative methods for comparing the biochemical composition of Nannochloropsis oculata samples obtained under different culture conditions

Microalgae have many applications, such as biodiesel production or food supplement. Depending on the application, the optimization of certain fractions of the biochemical composition (proteins, carbohydrates and lipids) is required. Therefore, samples obtained in different culture conditions must be analyzed in order to compare the content of such fractions. Nevertheless, traditional methods necessitate lengthy analytical procedures with prolonged sample turn-around times. Results of the biochemical composition of Nannochloropsis oculata samples with different protein, carbohydrate and lipid contents obtained by conventional analytical methods have been compared to those obtained by thermogravimetry (TGA) and a Pyroprobe device connected to a gas chromatograph with mass spectrometer detector (Py–GC/MS), showing a clear correlation. These results suggest a potential applicability of these techniques as fast and easy methods to qualitatively compare the biochemical composition of microalgal samples.

Tuning compilations by multi-objective optimization: Application to Apache web server

Modern compilers present a great and ever increasing number of options which can modify the features and behavior of a compiled program. Many of these options are often wasted due to the required comprehensive knowledge about both the underlying architecture and the internal processes of the compiler. In this context, it is usual, not having a single design goal but a more complex set of objectives. In addition, the dependencies between different goals are difficult to be a priori inferred. This paper proposes a strategy for tuning the compilation of any given application. This is accomplished by using an automatic variation of the compilation options by means of multi-objective optimization and evolutionary computation commanded by the NSGA-II algorithm. This allows finding compilation options that simultaneously optimize different objectives. The advantages of our proposal are illustrated by means of a case study based on the well-known Apache web server. Our strategy has demonstrated an ability to find improvements up to 7.5% and up to 27% in context switches and L2 cache misses, respectively, and also discovers the most important bottlenecks involved in the application performance.

Stability in Linear Optimization Under Perturbations of the Left-Hand Side Coefficients

This paper studies stability properties of linear optimization problems with finitely many variables and an arbitrary number of constraints, when only left hand side coefficients can be perturbed. The coefficients of the constraints are assumed to be continuous functions with respect to an index which ranges on certain compact Hausdorff topological space, and these properties are preserved by the admissible perturbations. More in detail, the paper analyzes the continuity properties of the feasible set, the optimal set and the optimal value, as well as the preservation of desirable properties (boundedness, uniqueness) of the feasible and of the optimal sets, under sufficiently small perturbations.

Optimization of Chemical Processes Using Surrogate Models Based on a Kriging Interpolation

Superstructure approaches are the solution to the difficult problem which involves the rigorous economic design of a distillation column. These methods require complex initialization procedures and they are hard to solve. For this reason, these methods have not been extensively used. In this work, we present a methodology for the rigorous optimization of chemical processes implemented on a commercial simulator using surrogate models based on a kriging interpolation. Several examples were studied, but in this paper, we perform the optimization of a superstructure for a non-sharp separation to show the efficiency and effectiveness of the method. Noteworthy that it is possible to get surrogate models accurate enough with up to seven degrees of freedom.

Dynamic, convex, and robust optimization with Bayesian learning for response-guided dosing

Thesis (Ph.D.)--University of Washington, 2016-08

Understanding human genome regulation through entropic graph-based regularization and submodular optimization

Thesis (Ph.D.)--University of Washington, 2016-06

Optimization and Machine Learning Frameworks for Complex Network Analysis

Thesis (Ph.D.)--University of Washington, 2016-06

Genetic assignment methods for the direct, real-time estimation of migration rate: a simulation-based exploration of accuracy and power

Genetic assignment methods use genotype likelihoods to draw inference about where individuals were or were not born, potentially allowing direct, real-time estimates of dispersal. We used simulated data sets to test the power and accuracy of Monte Carlo resampling methods in generating statistical thresholds for identifying F-0 immigrants in populations with ongoing gene flow, and hence for providing direct, real-time estimates of migration rates. The identification of accurate critical values required that resampling methods preserved the linkage disequilibrium deriving from recent generations of immigrants and reflected the sampling variance present in the data set being analysed. A novel Monte Carlo resampling method taking into account these aspects was proposed and its efficiency was evaluated. Power and error were relatively insensitive to the frequency assumed for missing alleles. Power to identify F-0 immigrants was improved by using large sample size (up to about 50 individuals) and by sampling all populations from which migrants may have originated. A combination of plotting genotype likelihoods and calculating mean genotype likelihood ratios (D-LR) appeared to be an effective way to predict whether F-0 immigrants could be identified for a particular pair of populations using a given set of markers.

Searching oligo sets of human chromosome 12 using evolutionary strategies

DNA Microarray is a powerful tool to measure the level of a mixed population of nucleic acids at one time, which has great impact in many aspects of life sciences research. In order to distinguish nucleic acids with very similar composition by hybridization, it is necessary to design microarray probes with high specificities and sensitivities. Highly specific probes correspond to probes having unique DNA sequences; whereas highly sensitive probes correspond to those with melting temperature within a desired range and having no secondary structure. The selection of these probes from a set of functional DNA sequences (exons) constitutes a computationally expensive discrete non-linear search problem. We delegate the search task to a simple yet effective Evolution Strategy algorithm. The computational efficiency is also greatly improved by making use of an available bioinformatics tool.

Area-under-the-curve monitoring of prednisolone for dose optimization in a stable renal transplant population

Background: Renal transplant recipients were noted to appear cushingoid while on low doses of steroid as part of a triple therapy immunosuppression of cyclosporin A (CsA), prednisolone, and azathioprine. Methods: The study group comprised adult renal transplant recipients with stable graft function who had received their renal allograft a minimum of 1 year previously (43 studies undertaken in 22 men and 20 women) with median daily prednisone dose of 7 mg (range 3-10). The control group was healthy nontransplant subjects [median dose 10 mg (10-30)]. Prednisolone bioavailability was measured using a limited 6-hour area under the curve (AUC), with prednisolone measured using specific HPLC assay. Results: The median prednisolone AUC/mg dose for all transplant recipients was significantly greater than the control group by approximately 50% (316 nmol(.)h/L/mg prednisolone versus 218). AUC was significantly higher in female recipients (median 415 versus 297 for men) and in recipients receiving cyclospotin (348 versus 285). The highest AUC was in women on estrogen supplements who were receiving cyclosporin (median 595). A significantly higher proportion of patients on triple therapy had steroid side effects compared with those on steroid and azathioprine (17/27 versus 4/15), more women than men had side effects (14/16 versus 7/22), and the AUC/mg prednisone was greater in those with side effects than without (median 377 versus 288 nmol-h/L/mg). Discussion: The results are consistent with the hypothesis that CsA increases the bioavailability of prednisolone, most likely through inhibition of beta-glycoprotein. The increased exposure to steroid increased the side-effect profile of steroids in the majority of patients. Because the major contributor to AUC is the maximum postdose concentration, it may be possible to use single-point monitoring (2 hours postdose) for routine clinical studies.

A general-purpose tunable landscape generator

The research literature on metalieuristic and evolutionary computation has proposed a large number of algorithms for the solution of challenging real-world optimization problems. It is often not possible to study theoretically the performance of these algorithms unless significant assumptions are made on either the algorithm itself or the problems to which it is applied, or both. As a consequence, metalieuristics are typically evaluated empirically using a set of test problems. Unfortunately, relatively little attention has been given to the development of methodologies and tools for the large-scale empirical evaluation and/or comparison of metaheuristics. In this paper, we propose a landscape (test-problem) generator that can be used to generate optimization problem instances for continuous, bound-constrained optimization problems. The landscape generator is parameterized by a small number of parameters, and the values of these parameters have a direct and intuitive interpretation in terms of the geometric features of the landscapes that they produce. An experimental space is defined over algorithms and problems, via a tuple of parameters for any specified algorithm and problem class (here determined by the landscape generator). An experiment is then clearly specified as a point in this space, in a way that is analogous to other areas of experimental algorithmics, and more generally in experimental design. Experimental results are presented, demonstrating the use of the landscape generator. In particular, we analyze some simple, continuous estimation of distribution algorithms, and gain new insights into the behavior of these algorithms using the landscape generator.