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This work applies Bayesian experimental design to selecting optimal projection geometries in (discretized) parallel beam X-ray tomography assuming the prior and the additive noise are Gaussian. The introduced greedy exhaustive optimization algorithm proceeds sequentially, with the posterior distribution corresponding to the previous projections serving as the prior for determining the design parameters, i.e. the imaging angle and the lateral position of the source-receiver pair, for the next one. The algorithm allows redefining the region of interest after each projection as well as adapting parameters in the (original) prior to the measured data. Both A and D-optimality are considered, with emphasis on efficient evaluation of the corresponding objective functions. Two-dimensional numerical experiments demonstrate the functionality of the approach., 23 pages, 8 figures

Based on decoupling strategy, a novel efficient method is proposed to solve the nonlinear interval uncertainty optimization problem with correlated interval design variables or parameters. This method is applicable to cases where both objective function and constraints are nonlinear with uncertain parameters, and design variables and parameters can be correlated or independent. The uncertainty of design variables and interval parameters is expressed by a multidimensional parallelepiped model, with which the correlated variables and parameters can be converted into independent interval parameters, thus constituting the traditional interval optimization model for independent interval parameters. Based on the idea of sequential optimization and reliability assessment (SORA), the two-layer nested optimization involved in the above interval optimization model can be converted into a single loop problem which can be solved efficiently by the sequential deterministic optimization algorithm. Finally, three numerical examples are investigated to demonstrate the effectiveness of the proposed model.

We propose a game problem formulation for evaluation of general composite system performance under possible external interference and in the presence of protection resources. The problem of finding the guaranteed system performance is reduced to a sequential optimization problem, which is solved by a penalty method. This enables one to find solutions of the defined game for large and complex systems.

For high reliability calculation efficiency and evaluation accuracy, saddlepoint approximation technology has been introduced into design and optimization under uncertainties. When using saddlepoint approximation, there are two prerequisites: all random information is tractable and saddlepoint equations are easy to be solved. However, the above requirements cannot always be met in complex multidisciplinary systems. Random variables sometimes are intractable, or saddlepoint equations are highly nonlinear. To tackle these problems, in this study, an efficient reliability-based multidisciplinary design optimization using the combination method of saddlepoint approximation and third-moment is given. A simplified alternative cumulant generating function can be constructed by saddlepoint approximation and third-moment with the first, second and third moments of a random variable effectively. Then, this cumulant generating function can be utilized to calculate the cumulative distribution function and the probability density function of this random variable approximately. Moreover, to obtain better efficiency, the framework of sequential optimization and reliability analysis is introduced in this study. The corresponding formula of the proposed reliability-based multidisciplinary design optimization is given in detail. Two test problems are solved to show the application of the proposed method.

We prove that the minimum average depth of a decision tree for sorting 8 pairwise different elements is equal to 620160 / 8 ! . We show also that each decision tree for sorting 8 elements, which has minimum average depth (the number of such trees is approximately equal to 8.548 × 10 326365 ), has also minimum depth. Both problems were considered by Knuth (1998). To obtain these results, we use tools based on extensions of dynamic programming which allow us to make sequential optimization of decision trees relative to depth and average depth, and to count the number of decision trees with minimum average depth.

ICDE is extended to the RBDO problem of truss structures by combining ICDE with SORA which gives a so-called the SORA-ICDE.In SORA-ICDE, the optimization loop and reliability assessment loop are decoupled, and hence the efficiency in solving RBDO problems is ensured and improved significantly.Numerical results for five benchmark problems illustrate the effectiveness of the SORA-ICDE in solving the RBDO problem of truss structures. Recently, a Sequential Optimization and Reliability Assessment (SORA) method was proposed and proven to be effective for solving reliability-based design optimization (RBDO) problems. In the SORA, the optimization loop and the reliability assessment loop are decoupled from each other. This helps improve the efficiency of the SORA significantly. However, the SORA still exists two main drawbacks: (1) the optimal solutions are easily trapped within local extremes and (2) the optimal results depend on the initial trial points. To overcome these drawbacks, this paper integrates the SORA with the Improved Constrained Differential Evolution algorithm (ICDE) to give a so-called SORA-ICDE for solving RBDO problems. Due to the global search mechanism, the SORA-ICDE can easily obtain global solutions regardless of initial points. The numerical results obtained in the paper are compared with available results in the literature to illustrate the efficiency, applicability and precision of the SORA-ICDE in solving the RBDO problems for truss structures.

In this note we take a new look at the local convergence of alternating optimization methods for low-rank matrices and tensors. Our abstract interpretation as sequential optimization on moving subspaces yields insightful reformulations of some known convergence conditions that focus on the interplay between the contractivity of classical multiplicative Schwarz methods with overlapping subspaces and the curvature of low-rank matrix and tensor manifolds. While the verification of the abstract conditions in concrete scenarios remains open in most cases, we are able to provide an alternative and conceptually simple derivation of the asymptotic convergence rate of the two-sided block power method of numerical algebra for computing the dominant singular subspaces of a rectangular matrix. This method is equivalent to an alternating least squares method applied to a distance function. The theoretical results are illustrated and validated by numerical experiments., Comment: 20 pages, 4 figures

Convergence improving mechanisms of different MPTP search methods are analyzed.A modified chaos control (MCC) of performance measure function?is proposed.The hybrid chaos control (HCC) method is proposed based on function type criterion.The HCC method is applied for different RBDO approaches. Performance measure approach (PMA) is an effective tool of the reliability-based design optimization (RBDO). And the advanced mean value (AMV) method is widely used for the evaluation of probabilistic constraint due to its simplicity and efficiency. However, the AMV method shows instability and inefficiency when applied to the concave performance measure functions, so do other existing iterative methods. In this paper, to overcome the difficulties, a modified chaos control (MCC) is applied to the AMV iterative procedure through modifying the iterative step of the chaotic dynamics analysis. Since the MCC method is inefficient for convex performance measure functions, a hybrid chaos control (HCC) method is also proposed by employing the AMV method or the MCC method adaptively during the RBDO process. Moreover, we equip PMA and sequential optimization and reliability assessment (SORA) with the HCC method for solving RBDO problems. Numerical examples are presented to demonstrate the simplicity, efficiency and robustness of the HCC method.

In this paper, the constraints of the sequential optimization of the lexicographic approach are relaxed in order to obtain a simple alternative approach to solve multiobjective problems. In other words, we allow the decision-maker to deviate from the optimal solution of each iteration if he/she prefers. Some properties of the obtained solutions are studied and the relationship between these solutions and those of the weighted sum scalarization and the ϵ-constraint scalarization and also the elastic ϵ-constraint scalarization are investigated. Finally, some examples are provided to show more details.

Based on dynamic programming approach we design algorithms for sequential optimization of exact and approximate decision rules relative to the length and coverage [3, 4]. In this paper, we use optimal rules to construct classifiers, and study two questions: i which rules are better from the point of view of classification --exact or approximate; and ii which order of optimization gives better results of classifier work: length, length+coverage, coverage, or coverage+length. Experimental results show that, on average, classifiers based on exact rules are better than classifiers based on approximate rules, and sequential optimization length+coverage or coverage+length is better than the ordinary optimization length or coverage.

The paper provides comparison of three different approaches to on-line tuning of generalized adaptive notch filters (GANFs) - the algorithms used for identification/tracking of quasi-periodically varying dynamic systems. Tuning is needed to adjust adaptation gains, which control tracking performance of GANF algorithms, to the unknown and/or time time-varying rate of system nonstationarity. Two out of three compared approaches are classical solutions - the first one incorporates sequential optimization of adaptation gains while the second one is based on the concept of parallel estimation. The main contribution of the paper is that it suggests the third way - it shows that the best results can be achieved when both approaches mentioned above are combined in a judicious way. Such joint sequential/parallel optimization preserves advantages of both treatments: adaptiveness (sequential approach) and robustness to abrupt changes (parallel approach). Additionally the paper shows how, using the concept of surrogate outputs, one can extend the proposed single-frequency algorithm to the multiple frequencies case, without falling into the complexity trap known as the ''curse of dimensionality''.

The Sequential Optimization and Reliability Assessment (SORA) method is a single-loop method containing a serial of cycles of decoupled deterministic optimization and reliability assessment for improving the efficiency of probabilistic optimization. However, the original SORA method as well as some other existing single-loop methods do not take into account the effect of varying design variance (changing variance) in design problems. In this paper, to enhance the SORA method, three formulations are proposed in order to improve the efficiency for solving problems with changing variance. These formulations are categorized by the different strategies of Inverse Most Probable Point (IMPP) approximation. Mathematical examples and a speed reducer design problem are utilized to test and compare the effectiveness of the proposed formulations. The insight gained from our study on the applicability of different approaches can be extended and utilized in other probabilistic optimization strategies that require IMPP ...

The sequential optimization of lexicographic approach to solving multi-criteria problems is implemented by finding the generalized solutions of a system of inequalities defining the sequential optimization stages. The algorithm effectively generates an optimal solution at every sequential optimization stage.

We explore the small-sample performance of m-step look ahead strategies that only use the k most recent observations, for the Bernoulli two-armed bandit problem. The larger k is not always the better. Strategies with small k and m perform almost as well as the optimal strategies, and they dominate the optimal one over a non-negligible part of the parameter space. Given that they adapt better to unplanned non-stationarities and outperform the optimal one under small prior misspecifications, they will be hard to beat in applications.

Este artigo aborda o problema de locação ótima de torres de transmissão como uma aplicação de métodos de busca em grafos com nós parcialmente ordenados com uma modelagem que aplica a este problema pela primeira vez o conceito de relações de preferência entre nós. São primeiramente apresentados resultados sobre grafos e algoritmos de busca. As restrições eletro-mecânicas e topográficas à obtenção do caminho de custo mínimo são descritas, são definidos os nós, arcos, custos, e caminhos, além de outros componentes do grafo e são descritos os algoritmos de otimização utilizados. O trabalho introduz e demonstra a validade de relações de preferência entre nós, que são utilizadas (juntamente com comparações de custos) no processo de eliminação de caminhos. Este procedimento aumenta a eficiência dos algoritmos de otimização utilizados.This paper focuses on optimal transmission tower spotting as an application of search methods in a graph with partially ordered nodes and for the first time models the problem using preference relations between nodes. First basic results from graph theory and search algorithms are presented. Electro-mechanical and topographical constraints to obtaining the path of minimum cost are described, the nodes, arcs, costs and paths are defined, and the optimization algorithms are shown. The paper introduces and demonstrates the validity of preference relations between nodes. These are used together with cost comparisons to eliminate paths. This procedure increases the efficiency of the optimization algorithms.

Finite Time Thermodynamics is generally associated with the Curzon–Ahlborn approach to the Carnot cycle. Recently, previous publications on the subject were discovered, which prove that the history of Finite Time Thermodynamics started more than sixty years before even the work of Chambadal and Novikov (1957). The paper proposes a careful examination of the similarities and differences between these pioneering works and the consequences they had on the works that followed. The modelling of the Carnot engine was carried out in three steps, namely (1) modelling with time durations of the isothermal processes, as done by Curzon and Ahlborn; (2) modelling at a steady-state operation regime for which the time does not appear explicitly; and (3) modelling of transient conditions which requires the time to appear explicitly. Whatever the method of modelling used, the subsequent optimization appears to be related to specific physical dimensions. The main goal of the methodology is to choose the objective function, which here is the power, and to define the associated constraints. We propose a specific approach, focusing on the main functions that respond to engineering requirements. The study of the Carnot engine illustrates the synthesis carried out and proves that the primary interest for an engineer is mainly connected to what we called Finite (physical) Dimensions Optimal Thermodynamics, including time in the case of transient modelling.

Kelley (1974) claims to give necessary and sufficient conditions for the myopic strategy to be optimal for the two-armed Bernoulli bandit problem with a two-point prior. In this paper we argue that his conditions are not necessary. We further explore the myopicity of the optimal strategy for this particular bandit problem.

In this paper we outline some basic difficulties in the design of fuzzy controllers. We present a new controller concept, which avoids the drawbacks of classical fuzzy controllers. Our concept is suited for an automatic design especially. In order to show how one can develop such a new controller by means of an evolutionary algorithm, we use a simulation of the cart-pole problem with four input variables. In addition, we introduce a procedure, which allows a sequential optimization. Our approach is advantageously with respect to automotive applications.

The Dantzig selector is a linear regression model which aims to sparsely represent a response vector by regressors. This paper introduces two fast algorithms which solve the Dantzig selector. One algorithm is linearized alternating direction method (LADMM) which utilizes the separable structure to solve the Dantzig selector; another is a variant of Dantzig selector with sequential optimization (DASSO) which utilizes the sparsity prior to solve the Dantzig selector. We numerically compare the two algorithms on standard data sets, and show that taking advantage of properties of the problem itself enables designing fast algorithms.

This paper is devoted to the study of algorithms for sequential optimization of approximate inhibitory rules relative to the length, coverage and number of misclassifications. Theses algorithms are based on extensions of dynamic programming approach. The results of experiments for decision tables from UCI Machine Learning Repository are discussed.

A multi-point sampling criterion considering the predictor and its uncertainty simultaneously is proposed based on kriging surrogate model, and a sequential approximation optimization method is developed. Multi-point sampling criterion is used to select the new samples by considering the distributions of the initial samples and the characteristics of the predicted target function. The proposed method selects more than one new sample for each optimization iteration, thus it can be performed by parallel computation or multi-computer runs which improve effectively the computational efficiency. Take tow typical mathematical functions as examples, the proposed method is compared with expected improvement criterion method and the results show the proposed method can effectively search the global optimum.

In order to improve the efficiency of engineering optimization problems, a variety of approximate modeling methods have been developed to express the complex model for reducing the computational expense, but because of the error between approximate model and actual model, optimization results obtained with approximate model are not always consist with that obtained with actual model. In this paper, we adopt support vector regression (SVR) as the new approximate modeling technology, and in order to ensure that approximate optimum solution is consist with actual optimum solution, sequential optimization algorithm is proposed, where the approximate model is persistently updated in the optimization process according to the optimization results, and the approximate optimum solution is gradually approach the actual optimum solution. A numerical example is used to test the proposed algorithm, and experimental results show that the improved sequential optimization algorithm based on SVR is effective to obtain the optimum solution consist with actual optimum solution.

Although controller devices highly improve the seismic performance of civil structures, they usually incur enormous financial costs. A variety of sequential methods for minimizing the cost function have been proposed in the literature. In most of these methods, the control system is optimally designed after the best structural configuration is provided. However, such sequential procedures are unable to yield the best overall design. This paper discusses a combined structural and control optimization approach in which the structural mass and controlled system energy are simultaneously minimized. To this end, a twofold objective function is defined by linearly combining the structural mass and linear quadratic regulator (LQR) performance index. It is shown that the optimal value of this objective function depends on the initial condition, and to circumvent this problem, an alternative objective function is introduced which allows for solving the problem of initial condition dependency. Given the complexity of the problem, a variable neighborhood search (VNS) metaheuristic method is developed. The performance of the developed method is demonstrated through case studies involving the determination of structural responses for shear-type frames. The case studies are presented for evaluating and comparing the effectiveness of the proposed simultaneous technique and the conventional sequential method. The responses of the structures are determined under an array of strong ground motions. The results of the comparative analyses revealed that the simultaneously optimized cases using the proposed methodology had superior dynamic performance compared to the sequentially optimized cases.

In a previous paper (Pastore, 2004), a method for selecting the discount parameter in a gaussian state-space model was introduced. The method is based on a sequential optimization of a Bayes factor and is intended for on-line modelling purposes. In this paper, these results are extended to state-space models where the distribution of the observable variable belongs to the exponential family.

The Sequential Optimization and Reliability Assessment (SORA) method is a single loop method containing a sequence of cycles of decoupled deterministic optimization and reliability assessment for improving the efficiency of probabilistic optimization. However, the original SORA method as well as some other existing single loop methods is not efficient for solving problems with changing variance. In this paper, to enhance the SORA method, three formulations are proposed by taking the effect of changing variance into account. These formulations are distinguished by the different strategies of Inverse Most Probable Point (IMPP) approximation. Mathematical examples and a pressure vessel design problem are used to test and compare the effectiveness of the proposed formulations. The “Direct Linear Estimation Formulation” is shown to be the most effective and efficient approach for dealing with problems with changing variance. The gained insight can be extended and utilized to other optimization strategies that require MPP or IMPP estimations.Copyright © 2005 by ASME

Purpose: To develop a Sequential Optimization script that generates HDR‐like dose distribution for hypofractionated prostate treatment with CyberKnife® RoboticRadiosurgery System and evaluate its consistency over different patients. Method and Materials: Sequential Optimization is the latest optimization algorithm available for CyberKnife treatment planning. The optimization is performed sequentially, as a series of individual optimization steps. Each step corresponds to a specific clinical objective. First, dose constraints to organs at risk are defined that cannot be violated by during the optimization. Additional constraints are defined to the maximum Monitor Units for each beam, for each robot position, and for the entire treatment plan. Then the objectives of each optimization step are specified. The result of each step represents the optimal value for this objective that is achievable within the existing constraints. Each result is retained as an additional constraint for all subsequent steps. In this manner the treatment plan is built up one clinical objective at a time, with a gradual improvement observed at each step. A sequence of optimization steps (script) was created that generates HDR‐like dose distribution for prostate treatment delivering 38 Gy in 4 fractions. Treatment plans were generated with the same script and with the Iris Variable Aperture Collimator for 10 prostates. Results: Prostate volumes ranged from 25–70 cc. Prostate V100, V125 and V150 are ∼95%, 50% and 15%. Urethra Dmax and D10 are

The structure of many sequential optimization problems over a finite or infinite horizon can be summarized in the mapping that defines the related dynamic programming algorithm. In this paper we take as a starting point this mapping and obtain results that are applicable to a broad class of problems. This approach has also been taken earlier by Denardo under contraction assumptions. The analysis here is carried out without contraction assumptions and thus the results obtained can be applied, for example, to the positive and negative dynamic programming models of Blackwell and Strauch. Most of the existing results for these models are generalized and several new results are obtained relating mostly to the convergence of the dynamic programming algorithm and the existence of optimal stationary policies.

Factorial designs are arguably the most widely used designs in scientific investigations. Generalized minimum aberration (GMA) and uniformity are two important criteria for evaluating both regular and non-regular designs. The generation of GMA designs is a non-trivial problem due to the sequential optimization nature of the criterion. Based on an analytical expression between the generalized wordlength pattern and a uniformity measure, this paper converts the generation of GMA designs to a constrained optimization problem, and provides effective algorithms for solving this particular problem. Moreover, many new designs with GMA or near-GMA are reported, which are also (nearly) optimal under the uniformity measure.

Publisher Summary An algorithm for the solution of the linear problem has been developed, and computer simulation resulted in fast convergence to within the desired limits of accuracy. It has been found that it is necessary that the initial values of the adjoint variables ϕ (0) = λ must be within a given region to ensure convergence. Two methods have been programmed to ensure this condition. Both include first running the unbounded-control problem and then using the optimal λs found for the initial conditions on the bounded-control problem. The first method varies the bounds sequentially using the final λs from one bounded problem as the initial values for a more restricted bound until the desired bounded problem is reached. The second method utilizes the continuity of the optimal lambdas with the control bounds and a curve-fitting routine to predict the desired initial values after running the unbounded case and two slightly bounded cases. The application of the linear-problem approach to the nonlinear control problem appears feasible. Preliminary studies in the algorithm for control iteration have indicated convergence for simple problems. Considerable programming and further study are necessary to verify the application to nonlinear problems.