A new competitive implementation of the electromagnetism-like algorithm for global optimization

The Electromagnetism-like (EM) algorithm is a population- based stochastic global optimization algorithm that uses an attraction- repulsion mechanism to move sample points towards the optimal. In this paper, an implementation of the EM algorithm in the Matlab en- vironment as a useful function for practitioners and for those who want to experiment a new global optimization solver is proposed. A set of benchmark problems are solved in order to evaluate the performance of the implemented method when compared with other stochastic methods available in the Matlab environment. The results con rm that our imple- mentation is a competitive alternative both in term of numerical results and performance. Finally, a case study based on a parameter estimation problem of a biology system shows that the EM implementation could be applied with promising results in the control optimization area.

Use of information on the manufacture of samples for the optical characterization of multilayers through a global optimization

We present a procedure for the optical characterization of thin-film stacks from spectrophotometric data. The procedure overcomes the intrinsic limitations arising in the numerical determination of manyparameters from reflectance or transmittance spectra measurements. The key point is to use all theinformation available from the manufacturing process in a single global optimization process. The method is illustrated by a case study of solgel applications.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

Background: Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results: Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions: Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Identifying the preferred subset of enzymatic profiles in nonlinear kinetic metabolic models via multiobjective global optimization and pareto filters

Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of Saccharomyces cerevisiae.

ContinuousMultimodal Global Optimization with Differential Evolution-Based Methods

Metaheuristic methods have become increasingly popular approaches in solving global optimization problems. From a practical viewpoint, it is often desirable to perform multimodal optimization which, enables the search of more than one optimal solution to the task at hand. Population-based metaheuristic methods offer a natural basis for multimodal optimization. The topic has received increasing interest especially in the evolutionary computation community. Several niching approaches have been suggested to allow multimodal optimization using evolutionary algorithms. Most global optimization approaches, including metaheuristics, contain global and local search phases. The requirement to locate several optima sets additional requirements for the design of algorithms to be effective in both respects in the context of multimodal optimization. In this thesis, several different multimodal optimization algorithms are studied in regard to how their implementation in the global and local search phases affect their performance in different problems. The study concentrates especially on variations of the Differential Evolution algorithm and their capabilities in multimodal optimization. To separate the global and local search search phases, three multimodal optimization algorithms are proposed, two of which hybridize the Differential Evolution with a local search method. As the theoretical background behind the operation of metaheuristics is not generally thoroughly understood, the research relies heavily on experimental studies in finding out the properties of different approaches. To achieve reliable experimental information, the experimental environment must be carefully chosen to contain appropriate and adequately varying problems. The available selection of multimodal test problems is, however, rather limited, and no general framework exists. As a part of this thesis, such a framework for generating tunable test functions for evaluating different methods of multimodal optimization experimentally is provided and used for testing the algorithms. The results demonstrate that an efficient local phase is essential for creating efficient multimodal optimization algorithms. Adding a suitable global phase has the potential to boost the performance significantly, but the weak local phase may invalidate the advantages gained from the global phase.

On the use of convex underestimators in global optimization

Många kvantitativa problem från vitt skilda områden kan beskrivas som optimeringsproblem. Ett mått på lösningens kvalitet bör optimeras samtidigt som vissa villkor på lösningen uppfylls. Kvalitetsmåttet kallas vanligen objektfunktion och kan beskriva kostnader (exempelvis produktion, logistik), potentialenergi (molekylmodellering, proteinveckning), risk (finans, försäkring) eller något annat relevant mått. I min doktorsavhandling diskuteras speciellt icke-linjär programmering, NLP, i ändliga dimensioner. Problem med enkel struktur, till exempel någon form av konvexitet, kan lösas effektivt. Tyvärr kan inte alla kvantitativa samband modelleras på ett konvext vis. Icke-konvexa problem kan angripas med heuristiska metoder, algoritmer som söker lösningar med hjälp av deterministiska eller stokastiska tumregler. Ibland fungerar det här väl, men heuristikerna kan sällan garantera kvaliteten på lösningen eller ens att en lösning påträffas. För vissa tillämpningar är det här oacceptabelt. Istället kan man tillämpa så kallad global optimering. Genom att successivt dela variabeldomänen i mindre delar och beräkna starkare gränser på det optimala värdet hittas en lösning inom feltoleransen. Den här metoden kallas branch-and-bound, ungefär dela-och-begränsa. För att ge undre gränser (vid minimering) approximeras problemet med enklare problem, till exempel konvexa, som kan lösas effektivt. I avhandlingen studeras tillvägagångssätt för att approximera differentierbara funktioner med konvexa underskattningar, speciellt den så kallade alphaBB-metoden. Denna metod adderar störningar av en viss form och garanterar konvexitet genom att sätta villkor på den perturberade Hessematrisen. Min forskning har lyft fram en naturlig utvidgning av de perturbationer som används i alphaBB. Nya metoder för att bestämma underskattningsparametrar har beskrivits och jämförts. I sammanfattningsdelen diskuteras global optimering ur bredare perspektiv på optimering och beräkningsalgoritmer.

Global Optimization Algorithms and their Application to Distributed Systems

In this report, we discuss the application of global optimization and Evolutionary Computation to distributed systems. We therefore selected and classified many publications, giving an insight into the wide variety of optimization problems which arise in distributed systems. Some interesting approaches from different areas will be discussed in greater detail with the use of illustrative examples.

A benchmark method for global optimization problems in structure determination from powder diffraction data

Quasi-Newton-Raphson minimization and conjugate gradient minimization have been used to solve the crystal structures of famotidine form B and capsaicin from X-ray powder diffraction data and characterize the chi(2) agreement surfaces. One million quasi-Newton-Raphson minimizations found the famotidine global minimum with a frequency of ca 1 in 5000 and the capsaicin global minimum with a frequency of ca 1 in 10 000. These results, which are corroborated by conjugate gradient minimization, demonstrate the existence of numerous pathways from some of the highest points on these chi(2) agreement surfaces to the respective global minima, which are passable using only downhill moves. This important observation has significant ramifications for the development of improved structure determination algorithms.

Search space pruning and global optimization of multiple gravity assist trajectories with deep space manoeuvres

This paper deals with the design of optimal multiple gravity assist trajectories with deep space manoeuvres. A pruning method which considers the sequential nature of the problem is presented. The method locates feasible vectors using local optimization and applies a clustering algorithm to find reduced bounding boxes which can be used in a subsequent optimization step. Since multiple local minima remain within the pruned search space, the use of a global optimization method, such as Differential Evolution, is suggested for finding solutions which are likely to be close to the global optimum. Two case studies are presented.

MODELING VERY LONG BASELINE INTERFEROMETRIC IMAGES WITH THE CROSS-ENTROPY GLOBAL OPTIMIZATION TECHNIQUE

We present a new technique for obtaining model fittings to very long baseline interferometric images of astrophysical jets. The method minimizes a performance function proportional to the sum of the squared difference between the model and observed images. The model image is constructed by summing N(s) elliptical Gaussian sources characterized by six parameters: two-dimensional peak position, peak intensity, eccentricity, amplitude, and orientation angle of the major axis. We present results for the fitting of two main benchmark jets: the first constructed from three individual Gaussian sources, the second formed by five Gaussian sources. Both jets were analyzed by our cross-entropy technique in finite and infinite signal-to-noise regimes, the background noise chosen to mimic that found in interferometric radio maps. Those images were constructed to simulate most of the conditions encountered in interferometric images of active galactic nuclei. We show that the cross-entropy technique is capable of recovering the parameters of the sources with a similar accuracy to that obtained from the very traditional Astronomical Image Processing System Package task IMFIT when the image is relatively simple (e. g., few components). For more complex interferometric maps, our method displays superior performance in recovering the parameters of the jet components. Our methodology is also able to show quantitatively the number of individual components present in an image. An additional application of the cross-entropy technique to a real image of a BL Lac object is shown and discussed. Our results indicate that our cross-entropy model-fitting technique must be used in situations involving the analysis of complex emission regions having more than three sources, even though it is substantially slower than current model-fitting tasks (at least 10,000 times slower for a single processor, depending on the number of sources to be optimized). As in the case of any model fitting performed in the image plane, caution is required in analyzing images constructed from a poorly sampled (u, v) plane.

Continuous GRASP with a local active-set method for bound-constrained global optimization

Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic-based on the CGRASP and GENCAN methods-for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP-GENCAN on a set of benchmark multimodal test functions.

Optimization Of Groundwater Remediation With New Efficient Parallel Algorithm For Global Optimization

Application of optimization algorithm to PDE modeling groundwater remediation can greatly reduce remediation cost. However, groundwater remediation analysis requires a computational expensive simulation, therefore, effective parallel optimization could potentially greatly reduce computational expense. The optimization algorithm used in this research is Parallel Stochastic radial basis function. This is designed for global optimization of computationally expensive functions with multiple local optima and it does not require derivatives. In each iteration of the algorithm, an RBF is updated based on all the evaluated points in order to approximate expensive function. Then the new RBF surface is used to generate the next set of points, which will be distributed to multiple processors for evaluation. The criteria of selection of next function evaluation points are estimated function value and distance from all the points known. Algorithms created for serial computing are not necessarily efficient in parallel so Parallel Stochastic RBF is different algorithm from its serial ancestor. The application for two Groundwater Superfund Remediation sites, Umatilla Chemical Depot, and Former Blaine Naval Ammunition Depot. In the study, the formulation adopted treats pumping rates as decision variables in order to remove plume of contaminated groundwater. Groundwater flow and contamination transport is simulated with MODFLOW-MT3DMS. For both problems, computation takes a large amount of CPU time, especially for Blaine problem, which requires nearly fifty minutes for a simulation for a single set of decision variables. Thus, efficient algorithm and powerful computing resource are essential in both cases. The results are discussed in terms of parallel computing metrics i.e. speedup and efficiency. We find that with use of up to 24 parallel processors, the results of the parallel Stochastic RBF algorithm are excellent with speed up efficiencies close to or exceeding 100%.

A common Tabu search algorithm for the global optimization of engineering problems

A novel common Tabu algorithm for global optimizations of engineering problems is presented. The robustness and efficiency of the presented method are evaluated by using standard mathematical functions and hy solving a practical engineering problem. The numerical results show that the proposed method is (i) superior to the conventional Tabu search algorithm in robustness, and (ii) superior to the simulated annealing algorithm in efficiency. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Global optimization approach for the H2-norm model reduction problem

A branch and bound algorithm is proposed to solve the H2-norm model reduction problem for continuous-time linear systems, with conditions assuring convergence to the global optimum in finite time. The lower and upper bounds used in the optimization procedure are obtained through Linear Matrix Inequalities formulations. Examples illustrate the results.

Global optimization for the ℋ∞-norm model reduction problem

A branch and bound algorithm is proposed to solve the [image omitted]-norm model reduction problem for continuous and discrete-time linear systems, with convergence to the global optimum in a finite time. The lower and upper bounds in the optimization procedure are described by linear matrix inequalities (LMI). Also proposed are two methods with which to reduce the convergence time of the branch and bound algorithm: the first one uses the Hankel singular values as a sufficient condition to stop the algorithm, providing to the method a fast convergence to the global optimum. The second one assumes that the reduced model is in the controllable or observable canonical form. The [image omitted]-norm of the error between the original model and the reduced model is considered. Examples illustrate the application of the proposed method.