Alternating Optimization Procedure Research Articles

Decentralized Multiarea Robust Generation Unit and Tie-Line Scheduling Under Wind Power Uncertainty

The growing interconnections of regional power systems and the large-scale integration of wind energy bring about the critical need to coordinate multiarea generation unit and tie-line scheduling (MAUTS). It is recognized that because of the limitations on private data exchange and model management, it is suitable to address the multiarea power scheduling problem in a decentralized way. In this paper, the MAUTS problem is formulated using the adaptive robust optimization (RO) scheme to account for uncertain wind energy. Our model is decomposed into regional subproblems by augmented Lagrangian decomposition (ALD), which enables a fully distributed computation within an alternating direction multiplier method framework. To address the nonconvexity issue, a tractable alternating optimization procedure (AOP) is developed to obtain high-quality solutions with finite convergence for the nonconvex mixed-integer problem. Simulations on different test systems are conducted to show the computational performance, the solution quality, and scalability of the proposed method.

Click Prediction for Web Image Reranking Using Multimodal Sparse Coding

Image reranking is effective for improving the performance of a text-based image search. However, existing reranking algorithms are limited for two main reasons: 1) the textual meta-data associated with images is often mismatched with their actual visual content and 2) the extracted visual features do not accurately describe the semantic similarities between images. Recently, user click information has been used in image reranking, because clicks have been shown to more accurately describe the relevance of retrieved images to search queries. However, a critical problem for click-based methods is the lack of click data, since only a small number of web images have actually been clicked on by users. Therefore, we aim to solve this problem by predicting image clicks. We propose a multimodal hypergraph learning-based sparse coding method for image click prediction, and apply the obtained click data to the reranking of images. We adopt a hypergraph to build a group of manifolds, which explore the complementarity of different features through a group of weights. Unlike a graph that has an edge between two vertices, a hyperedge in a hypergraph connects a set of vertices, and helps preserve the local smoothness of the constructed sparse codes. An alternating optimization procedure is then performed, and the weights of different modalities and the sparse codes are simultaneously obtained. Finally, a voting strategy is used to describe the predicted click as a binary event (click or no click), from the images' corresponding sparse codes. Thorough empirical studies on a large-scale database including nearly 330 K images demonstrate the effectiveness of our approach for click prediction when compared with several other methods. Additional image reranking experiments on real-world data show the use of click prediction is beneficial to improving the performance of prominent graph-based image reranking algorithms.

Calculating hansen solubility parameters of polymers with genetic algorithms

ABSTRACTIn materials engineering, it is often essential to know what are the best solvents to process any polymer, and employing methods based on Hansen solubility parameters are an effective way to find them. In this work the Hansen solubility parameters of polyether sulfone, lignin, and bitumen have been calculated by an alternative optimization procedure. It has been shown that, by applying an evolutionary strategy to Hansen's correlation method, it is possible to improve the fitting of solubility spheres. Compared with previous calculations, most quality‐of‐fit parameters are optimized. As a result, the sphere radii are reduced and, except for lignin, at least one of the solubility parameters is considerably changed (by 0.9–1.5 MPa1/2). Shortcomings of the correlation method are also pointed out, such as lack of data quality evaluation on set of solvents and uncertain character for partially solving solvents. At least the former could be handled by a proposed parameter called fill factor. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 39696.

An improved solution to the replenishment policy for the EMQ model with rework and multiple shipments

Recently, Chiu et al. (2012) [1] present an alternative optimization procedure to derive the optimal replenishment lot size for an economic manufacturing quantity (EMQ) model with rework and multiple shipments. This inventory model was proposed by Chiu et al. (2011) [2]. Both papers do not consider the determining of the number of shipments. This paper determines both the optimal replenishment lot size and the optimal number of shipments jointly. The solution of this paper is better than the solutions of Chiu et al. [1,2].

A modification of the k-means method for quasi-unsupervised learning

Since the advent of data clustering, the original formulation of the clustering problem has been enriched to incorporate a number of twists to widen its range of application. In particular, recent heuristic approaches have proposed to incorporate restrictions on the size of the clusters, while striving to minimize a measure of dissimilarity within them. Such size constraints effectively constitute a way to exploit prior knowledge, readily available in many scenarios, which can lead to an improved performance in the clustering obtained.In this paper, we build upon a modification of the celebrated k-means method resorting to a similar alternating optimization procedure, endowed with additive partition weights controlling the size of the partitions formed, adjusted by means of the Levenberg–Marquardt algorithm. We propose several further variations on this modification, in which different kinds of additional information are present. We report experimental results on various standardized datasets, demonstrating that our approaches outperform existing heuristics for size-constrained clustering. The running-time complexity of our proposal is assessed experimentally by means of a power-law regression analysis.

Pairwise constraints based multiview features fusion for scene classification

Recently, we have witnessed a surge of interests of learning a low-dimensional subspace for scene classification. The existing methods do not perform well since they do not consider scenes' multiple features from different views in low-dimensional subspace construction. In this paper, we describe scene images by finding a group of features and explore their complementary characteristics. We consider the problem of multiview dimensionality reduction by learning a unified low-dimensional subspace to effectively fuse these features. The new proposed method takes both intraclass and interclass geometries into consideration, as a result the discriminability is effectively preserved because it takes into account neighboring samples which have different labels. Due to the semantic gap, the fusion of multiview features still cannot achieve excellent performance of scene classification in real applications. Therefore, a user labeling procedure is introduced in our approach. Initially, a query image is provided by the user, and a group of images are retrieved by a search engine. After that, users label some images in the retrieved set as relevant or irrelevant with the query. The must-links are constructed between the relevant images, and the cannot-links are built between the irrelevant images. Finally, an alternating optimization procedure is adopted to integrate the complementary nature of different views with the user labeling information, and develop a novel multiview dimensionality reduction method for scene classification. Experiments are conducted on the real-world datasets of natural scenes and indoor scenes, and the results demonstrate that the proposed method has the best performance in scene classification. In addition, the proposed method can be applied to other classification problems. The experimental results of shape classification on Caltech 256 suggest the effectiveness of our method.

Joint Optimization of Source Power Allocation and Distributed Relay Beamforming in Multiuser Peer-to-Peer Relay Networks

In this paper, we consider the joint optimization of the source power allocation and relay beamforming weights in distributed multiuser peer-to-peer (MUP2P) relay networks applying the amplify-and-forward (AF) protocol. We adopt a quality-of-service (QoS) based approach, in which the total power transmitted from all sources and relays is minimized while guaranteeing the prescribed QoS requirement of each source-destination pair. The QoS is modeled as a function of the receive signal-to-interference-plus-noise ratio (SINR) at the destinations. Unlike the existing contributions, the transmitted powers of the sources and the beamforming weights of the relays are optimized jointly in this paper. Introducing an appropriate transformation of variables, the QoS based source power allocation and distributed relay beamforming (PADB) problem can be equivalently transformed into a difference of convex (DC) program, which can be efficiently solved with local optimality using the constrained concave convex procedure (CCCP). Based on this procedure, we also propose an iterative feasibility search algorithm (IFSA) to find an initial feasible point of the DC program. The analytic study of the proposed solution confirms that it converges to a local optimum of the PADB problem. Numerical results show that our solution outperforms (in terms of the total transmitted power) the alternating optimization procedure and the exact penalty based DC algorithm. In addition, the proposed IFSA outperforms the alternating optimization algorithm in finding feasible points of the DC program (i.e., the equivalence of the PADB problem).

Achieving the Outage Capacity of the Diamond Relay Network to Within One Bit and Even Less

A new forwarding strategy is proposed for the wireless diamond relay network under slow fading. The key feature is that it can adaptively switch between decode-forward and compress-forward according to the instantaneous received signal strength. It has four control parameters, which can be optimized by an alternating optimization procedure. Its outage performance is compared with two lower bounds. Analytically, it is proven to achieve the outage capacity to within 1 bit and within 50% for any signal-to-noise ratio (SNR). Empirically, it is shown to be nearly optimal for some fading scenarios.

Beamforming Design for Simplified Analog Antenna Combining Architectures

Analog antenna combining architectures have recently received increased interest due to their reduced size and power consumption, in comparison with the conventional multiple-input-multiple-output (MIMO) approach that operates in the baseband. In this paper, we design algorithms for three new radio-frequency (RF) architectures that are based on different combinations of phase shifters and variable gain amplifiers. From a baseband point of view, each architecture poses a different beamforming design problem in which the transmit/receive beamformers are constrained to have constant-modulus complex, real, or nonnegative real weights, respectively. Assuming perfect channel knowledge, we consider the problem of designing these constrained RF beamformers under orthogonal frequency-division-multiplexing (OFDM) transmissions. For the general MIMO case, the resulting optimization problems are not convex and are, therefore, difficult to solve. However, the single-input-multiple-output (SIMO) and multiple-input-single-output cases either have a closed-form solution or can be reformulated as convex problems. Exploiting this fact, an alternating optimization procedure is used to find a suboptimal solution for the MIMO case. The performance of the different RF-MIMO architectures is compared by means of Monte Carlo simulations, which allows us to conclude that the architecture based solely on phase shifters (RF equal-gain beamforming) provides the best results.

Supervised learning of local projection kernels

We formulate a supervised, localized dimensionality reduction method using a gating model that divides up the input space into regions and selects the dimensionality reduction projection separately in each region. The gating model, the locally linear projections, and the kernel-based supervised learning algorithm which uses them in its kernels are coupled and their training is performed with an alternating optimization procedure. Our proposed local projection kernel projects a data instance into different feature spaces by using the local projection matrices, combines them with the gating model, and performs the dot product in the combined feature space. Empirical results on benchmark data sets for visualization and classification tasks validate the idea. The method is generalizable to regression estimation and novelty detection.

Fast optimization of statistical potentials for structurally constrained phylogenetic models

BackgroundStatistical approaches for protein design are relevant in the field of molecular evolutionary studies. In recent years, new, so-called structurally constrained (SC) models of protein-coding sequence evolution have been proposed, which use statistical potentials to assess sequence-structure compatibility. In a previous work, we defined a statistical framework for optimizing knowledge-based potentials especially suited to SC models. Our method used the maximum likelihood principle and provided what we call the joint potentials. However, the method required numerical estimations by the use of computationally heavy Markov Chain Monte Carlo sampling algorithms.ResultsHere, we develop an alternative optimization procedure, based on a leave-one-out argument coupled to fast gradient descent algorithms. We assess that the leave-one-out potential yields very similar results to the joint approach developed previously, both in terms of the resulting potential parameters, and by Bayes factor evaluation in a phylogenetic context. On the other hand, the leave-one-out approach results in a considerable computational benefit (up to a 1,000 fold decrease in computational time for the optimization procedure).ConclusionDue to its computational speed, the optimization method we propose offers an attractive alternative for the design and empirical evaluation of alternative forms of potentials, using large data sets and high-dimensional parameterizations.

Polynomial Spline Estimation and Inference of Proportional Hazards Regression Models with Flexible Relative Risk Form

The Cox proportional hazards model usually assumes an exponential form for the dependence of the hazard function on covariate variables. However, in practice this assumption may be violated and other relative risk forms may be more appropriate. In this article, we consider the proportional hazards model with an unknown relative risk form. Issues in model interpretation are addressed. We propose a method to estimate the relative risk form and the regression parameters simultaneously by first approximating the logarithm of the relative risk form by a spline, and then employing the maximum partial likelihood estimation. An iterative alternating optimization procedure is developed for efficient implementation. Statistical inference of the regression coefficients and of the relative risk form based on parametric asymptotic theory is discussed. The proposed methods are illustrated using simulation and an application to the Veteran's Administration lung cancer data.

Soft vector quantization and the EM algorithm

The relation between hard c-means (HCM), fuzzy c-means (FCM), fuzzy learning vector quantization (FLVQ), soft competition scheme (SCS) of Yair et al. (1992) and probabilistic Gaussian mixtures (GM) have been pointed out recently by Bezdek and Pal (1995). We extend this relation to their training, showing that learning rules by these models to estimate the cluster centers can be seen as approximations to the expectation–maximization (EM) method as applied to Gaussian mixtures. HCM and unsupervised, LVQ use 1-of- c type competition. In FCM and FLVQ, membership is the −2/( m−1)th power of the distance. In SCS and GM, Gaussian function is used. If the Gaussian membership function is used, the weighted within-groups sum of squared errors used as the fuzzy objective function corresponds to the maximum likelihood estimate in Gaussian mixtures with equal priors and covariances. The fuzzy clustering method named fuzzy c-means alternating optimization procedure (FCM-AO) proposed to optimize the former is then equivalent to batch EM and SCS's update rule is a variant of the online version of EM. The advantages of the probabilistic framework are: (i) we no longer have spurious spread parameters that needs fine tuning as m in fuzzy vector quantization or β in SCS; instead we have a variance term that has a sound interpretation and that can be estimated from the sample; (ii) EM guarantees that the likelihood does not decrease, thus it converges to the nearest local optimum; (iii) EM also allows us to estimate the underlying distance norm and the cluster priors which we could not with the other approaches. We compare Gaussian mixtures trained with EM with LVQ (HCM), SCS and FLVQ on the IRIS dataset and see that it is more accurate due to its being able to take into account the covariance information. We finally note that vector quantization is generally an intermediate step before finding a final output for which supervision may be possible. Thus, instead of an uncoupled approach where an unsupervised method is used first to find the cluster parameters followed by supervised training of the mapping based on the memberships, we advocate a coupled approach where the cluster parameters and mapping are trained supervised in a coupled way. The uncoupled approach ignores the error at the outputs which may not be ideal.

Discontinuous optimization in a class of multi-stage production systems

An alternative and efficient optimization procedure for discontinuous optimization in batch production systems is presented. This method, namely, the direct pattern search method (DPSM) is an alternative approach to that suggested by Imo and Leech (1984), the sequential unconstrained minimization technique (SUMT) to minimize the processing time per unit of a finished product in a class of multi-stage production systems. Moreover, the scope for the extension of the Imo and Leech (1984) model is explained with reference to the application to just-in-time (JIT) manufacturing systems and flexible manufacturing systems (FMS). Furthermore, the model can be enriched with an objective to model more realistic production systems incorporating the cost due to queueing of batches, and batch splitting and forming using the concept of equivalent transformation. The main purpose is to motivate the extension of the model in order to enhance the scope and application of the model for modern production systems and the use ...

Analytic optimization of Dyson optics

A prototype of a 248-nm optical projection printer based on the unit magnification Dyson configuration was designed and built [J. Vac. Sci. Technol. 9, 3108 (1991)]. Iterative computer methods were used to optimize the geometry of the system to provide minimum aberrations over a given field. Here we present an alternative optimization procedure and use it to design a 193-nm system. This new procedure yields useful insights into the design process and allows us to see why modifications in geometry are required for optimum performance. An understanding of the trade-offs involved in the optimization allows us to suggest and evaluate future design changes.