scholarly journals An Efficient Two-Stage Sparse Representation Method

Author(s):  
Chengyu Peng ◽  
Hong Cheng ◽  
Manchor Ko

There are a large number of methods for solving under-determined linear inverse problems. For large-scale optimization problem, many of them have very high time complexity. We propose a new method called two-stage sparse representation (TSSR) to tackle it. We decompose the representing space of signals into two parts”, the measurement dictionary and the sparsifying basis. The dictionary is designed to obey or nearly obey the sub-Gaussian distribution. The signals are then encoded on the dictionary to obtain the training and testing coefficients individually in the first stage. Then, we design the basis based on the training coefficients to approach an identity matrix, and we apply sparse coding to the testing coefficients over the basis in the second stage. We verify that the projection of testing coefficients onto the basis is a good approximation of the original signals onto the representing space. Since the projection is conducted on a much sparser space, the runtime is greatly reduced. For concrete realization, we provide an instance for the proposed TSSR. Experiments on four biometric databases show that TSSR is effective compared to several classical methods for solving linear inverse problem.

Author(s):  
Lu Chen ◽  
Handing Wang ◽  
Wenping Ma

AbstractReal-world optimization applications in complex systems always contain multiple factors to be optimized, which can be formulated as multi-objective optimization problems. These problems have been solved by many evolutionary algorithms like MOEA/D, NSGA-III, and KnEA. However, when the numbers of decision variables and objectives increase, the computation costs of those mentioned algorithms will be unaffordable. To reduce such high computation cost on large-scale many-objective optimization problems, we proposed a two-stage framework. The first stage of the proposed algorithm combines with a multi-tasking optimization strategy and a bi-directional search strategy, where the original problem is reformulated as a multi-tasking optimization problem in the decision space to enhance the convergence. To improve the diversity, in the second stage, the proposed algorithm applies multi-tasking optimization to a number of sub-problems based on reference points in the objective space. In this paper, to show the effectiveness of the proposed algorithm, we test the algorithm on the DTLZ and LSMOP problems and compare it with existing algorithms, and it outperforms other compared algorithms in most cases and shows disadvantage on both convergence and diversity.


Author(s):  
Rui Qiu ◽  
Yongtu Liang

Abstract Currently, unmanned aerial vehicle (UAV) provides the possibility of comprehensive coverage and multi-dimensional visualization of pipeline monitoring. Encouraged by industry policy, research on UAV path planning in pipeline network inspection has emerged. The difficulties of this issue lie in strict operational requirements, variable flight missions, as well as unified optimization for UAV deployment and real-time path planning. Meanwhile, the intricate structure and large scale of the pipeline network further complicate this issue. At present, there is still room to improve the practicality and applicability of the mathematical model and solution strategy. Aiming at this problem, this paper proposes a novel two-stage optimization approach for UAV path planning in pipeline network inspection. The first stage is conventional pre-flight planning, where the requirement for optimality is higher than calculation time. Therefore, a mixed integer linear programming (MILP) model is established and solved by the commercial solver to obtain the optimal UAV number, take-off location and detailed flight path. The second stage is re-planning during the flight, taking into account frequent pipeline accidents (e.g. leaks and cracks). In this stage, the flight path must be timely rescheduled to identify specific hazardous locations. Thus, the requirement for calculation time is higher than optimality and the genetic algorithm is used for solution to satisfy the timeliness of decision-making. Finally, the proposed method is applied to the UAV inspection of a branched oil and gas transmission pipeline network with 36 nodes and the results are analyzed in detail in terms of computational performance. In the first stage, compared to manpower inspection, the total cost and time of UAV inspection is decreased by 54% and 56% respectively. In the second stage, it takes less than 1 minute to obtain a suboptimal solution, verifying the applicability and superiority of the method.


Author(s):  
Tianxiang Wang ◽  
Jie Xu ◽  
Jian-Qiang Hu

We consider how to allocate simulation budget to estimate the risk measure of a system in a two-stage simulation optimization problem. In this problem, the first stage simulation generates scenarios that serve as inputs to the second stage simulation. For each sampled first stage scenario, the second stage procedure solves a simulation optimization problem by evaluating a number of decisions and selecting the optimal decision for the scenario. It also provides the estimated performance of the system over all sampled first stage scenarios to estimate the system’s reliability or risk measure, which is defined as the probability of the system’s performance exceeding a given threshold under various scenarios. Usually, such a two-stage procedure is very computationally expensive. To address this challenge, we propose a simulation budget allocation procedure to improve the computational efficiency for two-stage simulation optimization. After generating first stage scenarios, a sequential allocation procedure selects the scenario to simulate, followed by an optimal computing budget allocation scheme that determines the decision to simulate in the second stage simulation. Numerical experiments show that the proposed procedure significantly improves the efficiency of the two-stage simulation optimization for estimating system’s reliability.


2020 ◽  
Author(s):  
Bramka Arga Jafino ◽  
Jan Kwakkel

<p>Climate-related inequality can arise from the implementation of adaptation policies. As an example, the dike expansion policy for protecting rice farmers in the Vietnam Mekong Delta in the long run backfires to the small-scale farmers. The prevention of annual flooding reduces the supply of natural sediments, forcing farmers to apply more and more fertilizers to achieve the same yield. While large-scale farmers can afford this, small-scale farmers do not possess the required economics of scale and are thus harmed eventually. Together with climatic and socioeconomic uncertainties, the implementation of new policies can not only exacerbate existing inequalities, but also induce new inequalities. Hence, distributional impacts to affected stakeholders should be assessed in climate change adaptation planning.</p><p>In this study, we propose a two-stage approach to assess the distributional impacts of policies in model-based support for adaptation planning. The first stage is intended to explore potential inequality patterns that may emerge due to combination of new policies and the realization of exogenous scenarios. This stage comprises four steps: (i) disaggregation of performance indicators in the model in order to observe distributional impacts, (ii) performance of large-scale simulation experimentation to account for deep uncertainties, (iii) clustering of simulation results to identify distinctive inequality patterns, and (iv) application of scenario discovery tools, in particular classification and regression trees, to identify combinations of policies and uncertainties that lead to a specific inequality pattern.</p><p>In the second stage we attempt to asses which policies are morally preferable with respect to the inequality patterns they generate, rather than only descriptively explore the patterns which is the case in the previous stage. To perform a normative evaluation of the distributional impacts, we operationalize five alternative principles of justice: improvement of total welfare (utilitarianism), prioritization of worse-off actors (prioritarianism), reduction of welfare differences across actors (two derivations: absolute inequality and envy measure), and improvement of worst-off actor (Rawlsian difference). The different operationalization of each of these principles forms the so-called social welfare function with which the distributional impacts can be aggregated.</p><p>To test this approach, we use an agricultural planning case study in the upper Vietnam Mekong Delta. Specifically, we assess the distributional impacts of alternative adaptation policies in the upper Vietnam Mekong Delta by using an integrated assessment model. We consider six alternative policies as well as uncertainties related to upstream discharge, sediment supply, and land-use change. Through the first stage, we identify six potential inequality patterns among the 23 districts in the study area, as well as the combinations of policies and uncertainties that result in these types of patterns. From applying the second stage we obtain complete rankings of alternative policies, based on their performance with respect to distributional impacts, under different realizations of scenarios. The explorative stage allows policy-makers to identify potential actions to compensate worse-off actors while the normative stage helps them to easily rank alternative policies based on a preferred moral principle.</p>


2018 ◽  
Vol 7 (3.28) ◽  
pp. 72
Author(s):  
Siti Farhana Husin ◽  
Mustafa Mamat ◽  
Mohd Asrul Hery Ibrahim ◽  
Mohd Rivaie

In this paper, we develop a new search direction for Steepest Descent (SD) method by replacing previous search direction from Conjugate Gradient (CG) method, , with gradient from the previous step,  for solving large-scale optimization problem. We also used one of the conjugate coefficient as a coefficient for matrix . Under some reasonable assumptions, we prove that the proposed method with exact line search satisfies descent property and possesses the globally convergent. Further, the numerical results on some unconstrained optimization problem show that the proposed algorithm is promising. 


1982 ◽  
Vol 10 (1) ◽  
pp. 16-22 ◽  
Author(s):  
H. Hirakawa ◽  
A. Ahagon

Abstract Two-stage mixing when applied to blends of Chlorobutyl Rubber (C1-IIR), Natural Rubber (NR), and Polybutadiene Rubber (BR), can produce tread compounds exhibiting a combination of very low hysteresis, good wet skid resistance, and good abrasion resistance. In the first stage, about half the raw rubber, including all C1-IIR and BR, is mixed with most of the carbon black to form a very high carbon black stock. In the second stage, the first-stage stock is diluted with the remaining NR. Curatives, etc., are added on the mill. Tests on radial tires for automobiles confirm the advantages of the two-stage mixed tri-rubber blend tread compounds.


2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Daniele Peri

PurposeA recursive scheme for the ALIENOR method is proposed as a remedy for the difficulties induced by the method. A progressive focusing on the most promising region, in combination with a variation of the density of the alpha-dense curve, is proposed.Design/methodology/approachALIENOR method is aimed at reducing the space dimensions of an optimization problem by spanning it by using a single alpha-dense curve: the curvilinear abscissa along the curve becomes the only design parameter for any design space. As a counterpart, the transformation of the objective function in the projected space is much more difficult to tackle.FindingsA fine tuning of the procedure has been performed in order to identity the correct balance between the different elements of the procedure. The proposed approach has been tested by using a set of algebraic functions with up to 1,024 design variables, demonstrating the ability of the method in solving large scale optimization problem. Also an industrial application is presented.Originality/valueIn the knowledge of the author there is not a similar paper in the current literature.


2011 ◽  
Vol 41 (9) ◽  
pp. 1819-1826 ◽  
Author(s):  
Piermaria Corona ◽  
Lorenzo Fattorini ◽  
Sara Franceschi

A two-stage sampling strategy is proposed to assess small woodlots outside the forests scattered on extensive territories. The first stage is performed to select a sample of small woodlots using fixed-size sampling schemes, and the second stage is performed to sample trees within woodlots selected at first stage. Usually, fixed- or variable-area plots are adopted to sample trees. However, the use of plot sampling in small patches such as woodlots is likely to induce a relevant amount of bias owing to edge effects. In this framework, sector sampling proves to be particularly effective. The present paper investigates the statistical properties of two-stage sampling strategies for estimating forest attributes of woodlot populations when sector sampling is adopted at the second stage. A two-stage estimator of population totals is derived together with a conservative estimator of its sampling variance. By means of a simulation study, the performance of the proposed estimator is checked and compared with that achieved using traditional plot sampling with edge corrections. Simulation results prove the adequacy of sector sampling and provide some guidelines for the effective planning of the strategy. In some countries, the proposed strategy can be performed with few modifications within the framework of large-scale forest inventories.


2000 ◽  
Vol 7 (5) ◽  
pp. 321-332 ◽  
Author(s):  
Z. Zong ◽  
K.Y. Lam ◽  
Tessa Gan

Biodynamic response of shipboard crew to underwater shock is of a major concern to navies. An underwater shock can produce very high accelerations, resulting in severe human injuries aboard a battleship. Protection of human bodies from underwater shock is implemented by installing onboard isolators. In this paper, the optimal underwater shock isolation to protect human bodies is studied. A simple shock-structure-isolator-human interaction model is first constructed. The model incorporates the effect of fluid-structure interaction, biodynamic response of human body, isolator influence. Based on this model, the optimum shock isolation is then formulated. The performance index and restriction are defined. Thirdly, GA (genetic algorithm) is employed to solve the formulated optimization problem. GA is a powerful evolutionary optimization scheme suitable for large-scale and multi-variable optimization problems that are otherwise hard to be solved by conventional methods. A brief introduction to GA is given in the paper. Finally, the method is applied to an example problem and the limiting performance characteristic is obtained.


Author(s):  
Yukihiro Hamasuna ◽  
Ryo Ozaki ◽  
Yasunori Endo ◽  
◽  
◽  
...  

To handle a large-scale object, a two-stage clustering method has been previously proposed. The method generates a large number of clusters during the first stage and merges clusters during the second stage. In this paper, a novel two-stage clustering method is proposed by introducing cluster validity measures as the merging criterion during the second stage. The significant cluster validity measures used to evaluate cluster partitions and determine the suitable number of clusters act as the criteria for merging clusters. The performance of the proposed method based on six typical indices is compared with eight artificial datasets. These experiments show that a trace of the fuzzy covariance matrixWtrand its kernelizationKWtrare quite effective when applying the proposed method, and obtain better results than the other indices.


Sign in / Sign up

Export Citation Format

Share Document