Browsing by Subject "Robustness"
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Item Open Access Approximate MLFMA as an efficient preconditioner(IEEE, 2007) Malas, Tahir; Ergül, Özgür; Gürel, LeventIn this work, we propose a preconditioner that approximates the dense system operator. For this purpose, we develop an approximate multilevel fast multipole algorithm (AMLFMA), which performs a much faster matrix-vector multiplication with some relative error compared to the original MLFMA. We use AMLFMA to solve a closely related system, which makes up the preconditioner. Then, this solution is embedded in the main solution that uses MLFMA. By taking into account the far-field elements wisely, this preconditioner proves to be much more effective compared to the near-field preconditioners.Item Open Access Benchmarking the robustness of instance segmentation models(Institute of Electrical and Electronics Engineers , 2023-08-29) Dalva, Y.; Pehlivan, H.; Altındiş, Said Fahri; Dündar, AyşegülThis article presents a comprehensive evaluation of instance segmentation models with respect to real-world image corruptions as well as out-of-domain image collections, e.g., images captured by a different set-up than the training dataset. The out-of-domain image evaluation shows the generalization capability of models, an essential aspect of real-world applica tions, and an extensively studied topic of domain adaptation. These presented robustness and generalization evaluations are important when designing instance segmentation models for real-world applications and picking an off-the-shelf pretrained model to directly use for the task at hand. Specifically, this benchmark study includes state-of-the-art network architectures, network backbones, normalization layers, models trained starting from scratch versus pretrained networks, and the effect of multitask training on robustness and generalization. Through this study, we gain several insights. For example, we find that group normalization (GN) enhances the robustness of networks across corruptions where the image contents stay the same but corruptions are added on top. On the other hand, batch normalization (BN) improves the generalization of the models across different datasets where statistics of image features change. We also find that single-stage detectors do not generalize well to larger image resolutions than their training size. On the other hand, multistage detectors can easily be used on images of different sizes. We hope that our comprehensive study will motivate the development of more robust and reliable instance segmentation models.Item Open Access A capacitated hub location problem under hose demand uncertainty(Elsevier, 2017) Meraklı, M.; Yaman, H.In this study, we consider a capacitated multiple allocation hub location problem with hose demand uncertainty. Since the routing cost is a function of demand and capacity constraints are imposed on hubs, demand uncertainty has an impact on both the total cost and the feasibility of the solutions. We present a mathematical formulation of the problem and devise two different Benders decomposition algorithms. We develop an algorithm to solve the dual subproblem using complementary slackness. In our computational experiments, we test the efficiency of our approaches and we analyze the effects of uncertainty. The results show that we obtain robust solutions with significant cost savings by incorporating uncertainty into our problem.Item Open Access Effects of skewness and kurtosis on model selection criteria(Elsevier BV, 1998) Başçı, S.; Zaman, A.We consider the behavior of model selection criteria in AR models where the error terms are not normal by varying skewness and kurtosis. The probability of estimating the true lag order for varying degrees of freedom (k) is the interest. For both small and large samples skewness does not effect the performance of criteria under consideration. On the other hand, kurtosis does effect some of the criteria considerably. In large samples and for large values of k the usual asymptotic theory results for normal models are confirmed. Moreover, we showed that for small sample sizes performance of some newly introduced criteria which were not considered in Monte Carlo studies before are better. (C) 1998 Elsevier Science S.A.Item Open Access Efficient and robust approach for the derivation of closed-form Green's functions(IEEE, 1995) Aksun, M. İrşadiSpatial domain Green's functions for multilayer, planar geometries are cast into closed forms with two-level approximation of the spectral domain representation of the Green's functions. This approach is very robust and much faster compared to the original one-level approximation.Item Open Access Essays on bilateral trade with discrete types(Bilkent University, 2019-10) Mohammadinezhad, Kamyar KargarBilateral trade is probably the most common market interaction problem and can be considered as the simplest form of two sided markets where a seller and a buyer bargain over an indivisible object subject to incomplete information on the reservation values of participants. We treat this problem as a combinatorial optimization problem and re-establish some results of economic theory that are well-known under continuous valuations assumptions for the case of discrete valuations using linear programming techniques. First, we propose mathematical formulation for the problem under dominant strategy incentive compatibility (DIC) and ex-post individual rationality (EIR) properties. Then we derive necessary and sufficient conditions under which ex-post efficiency can be obtained together with DIC and EIR. We also define a new property called Allocation Maximality and prove that the Posted Price mechanism is the only mechanism that satisfies DIC, EIR and allocation maximality. In the final part we consider ambiguity in the problem framework originating from different sets of priors for agents types and derive robust counterparts. Next, we study the bilateral trade problem with an intermediary who wants to maximize her expected gains. Using network programming we transform the initial linear program into one from which the structure of mechanism is transparent. We then relax the risk-neutrality assumption of the intermediary and consider the problem from the perspective of risk-averse intermediary. The effects of risk-averse approach are presented using computational experiments. Finally, we broaden the scope of the problem and discuss the case in which the seller is also a producer at the same time and consider benefit and cost functions for the respective parties. Starting by a non-convex optimization problem, we obtain an equivalent convex optimization problem from which the problem is solved easily. We also reconsider the same problem under dominant strategy incentive compatibility and ex-post individual rationality constraints to preserve the practicality of all obtained solutions.Item Open Access Generating a robust model for production and inventory control(Bilkent University, 1993) Sencer, AslıIn tills stud}', we generate a production and inventory control model which gives h'obust‘ solutions against demand estimation errors. This model is applied to a real production and inventory system; howe\’er, it is a general model where the demand rate is stochastic with a known probability distribution and other parameters of the system are constant. The proposed model is a bi-objective chicision making model, with two decision variables. .A ‘compromised* solution is found for the problem using the trade-off curve generated by a constrained sequential optimization technique, applied on a nonlinear programming model parametrically. Robustness against parameter estimation errors is tested by sensitivity analysis. Here a new dimension is added to sensitivity analysis methodology by including a sensitivity measure as a ‘cost of error* of parameter estimation. By so doing, the proposed model is tested against the classical EOQ model and it is shown that the proposed model ])erforms far better.Item Open Access Generating robust and stable schedules in a single machine environment(IIE, 2004) Gören, Selçuk; Sabuncuoğlu, İhsanScheduling is a decision making process that concerns with allocation of limited resources (machines, material handling equipment, operators, tools, etc.) to competing tasks (operations of jobs) over time with the goal of optimizing one or more objectives. The output of this process is time/machine/operation assignments. In the scheduling theory, the objective is generally to optimize one or more regular performance measures such as makespan, flow-time, and tardiness. Recently, two new measures have been also used in scheduling applications: "robustness" and "stability". In this paper, we develop a new surrogate measure to achieve robustness and stability. This measure is embedded in a tabu search algorithm to generate schedules in a single machine environment subject to random machine breakdowns. The results of extensive computational experiments indicate that the proposed method performs better than the average slack method used in the literature.Item Open Access Hedging production schedules against uncertainty in manufacturing environment with a review of robustness and stability research(Taylor & Francis, 2009) Sabuncuoglu, I.; Goren, S.Scheduling is a decision-making process that is concerned with the allocation of limited resources to competing tasks (operations of jobs) over a time period with the goal of optimising one or more objectives. In theory, the objective is usually to optimise some classical system performance measures such as makespan, tardiness/earliness and flowtime under deterministic and static assumptions. In practice, however, scheduling systems operate in dynamic and stochastic environments. Hence, there is a need to incorporate both uncertainty and dynamic elements into the scheduling process. In this paper, the major issues involved in scheduling decisions are discussed and the basic approaches to tackle these problems in manufacturing environments are analysed. Proactive scheduling is then focused on and several robustness and stability measures are presented. Previous research on scheduling robustness and stability is also reviewed and further research directions are suggested.Item Open Access Hub location proplems under polyhedral demand uncertainty(Bilkent University, 2015-07) Meraklı, MerveHubs are points of consolidation and transshipment in many-to-many distribution systems that bene t from economies of scale. In hub location problems, the aim is to locate hub facilities such that each pairwise demand is satis ed and the total cost is minimized. The problem usually arises in the strategic planning phase prior to observing actual demand values. Hence incorporating robustness into hub location decisions under data uncertainty is crucial for achieving a reliable hub network design. In this thesis, we study hub location problems under polyhedral demand uncertainty. We consider uncapacitated multiple allocation p-hub median problem under hose and hybrid demand uncertainty and capacitated multiple allocation hub location problem under hose demand uncertainty. We propose mixed integer linear programming formulations and devise several exact solution algorithms based on Benders decomposition in order to solve large-scale problem instances. Computational experiments are performed on instances of three benchmark data sets from the literature.Item Open Access Integral action based Dirichlet boundary control of Burgers equation(IEEE, 2003) Efe, M. Ö.; Özbay, HitayModeling and boundary control for Burgers Equation is studied in this paper. Modeling has been done via processing of numerical observations through singular value decomposition with Galerkin projection. This results in a set of spatial basis functions together with a set of Ordinary Differential Equations (ODEs) describing the temporal evolution. Since the dynamics described by Burgers equation is nonlinear, the corresponding reduced order dynamics turn out to be nonlinear. The presented analysis explains how boundary condition appears as a control input in the ODEs. The controller design is based on the linearization of the dynamic model. It has been demonstrated that an integral controller, whose gain is a function of the spatial variable, is sufficient to observe reasonably high tracking performance with a high degree of robustness.Item Open Access Linear huber M-estimator under ellipsoidal data uncertainty(Springer, 2002) Pınar, M. Ç.The purpose of this note is to present a robust counterpart of the Huber estimation problem in the sense of Ben-Tal and Nemirovski when the data elements are subject to ellipsoidal uncertainty. The robust counterparts are polynomially solvable second-order cone programs with the strong duality property. We illustrate the effectiveness of the robust counterpart approach on a numerical example.Item Open Access Microfabricated ultrasonic transducers: towards robust models and immersion devices(IEEE, 1996-11) Ladabaum, I.; Jin, X.; Soh, H. T.; Pierre, F.; Atalar, Abdullah; Khuri-Yakub, B. T.The successful fabrication of ultrasonic immersion transducers is reported. Transducers are observed to operate from 1 MHz to 20 MHz in water, with the frequency range limited by electronics, not the transducers. Transmission results are included which show that a single pair of transducers is able to operate in water at 4, 6, and 8 MHz with a signal to noise ratio of at least 48 dB. The same transducer pair is shown to operate in air at 6 MHz. A model is introduced which highlights the significant parameters of transducer design. The model enables the design of optimized transducers.Item Open Access On robust solutions to linear least squares problems affected by data uncertainty and implementation errors with application to stochastic signal modeling(Elsevier, 2004) Pınar, M. Ç.; Arıkan, OrhanEngineering design problems, especially in signal and image processing, give rise to linear least squares problems arising from discretization of some inverse problem. The associated data are typically subject to error in these applications while the computed solution may only be implemented up to limited accuracy digits, i.e., quantized. In the present paper, we advocate the use of the robust counterpart approach of Ben-Tal and Nemirovski to address these issues simultaneously. Approximate robust counterpart problems are derived, which leads to semidefinite programming problems yielding stable solutions to overdetermined systems of linear equations affected by both data uncertainty and implementation errors, as evidenced by numerical examples from stochastic signal modeling.Item Open Access Optimization of schedule robustness and stability under random machine breakdowns and processing time variability(Taylor & Francis, 2010) Goren, S.; Sabuncuoglu, I.In practice, scheduling systems are subject to considerable uncertainty in highly dynamic operating environments. The ability to cope with uncertainty in the scheduling process is becoming an increasingly important issue. This paper takes a proactive scheduling approach to study scheduling problems with two sources of uncertainty: processing time variability and machine breakdowns. Two robustness (expected total flow time and expected total tardiness) and three stability (the sum of the squared and absolute differences of the job completion times and the sum of the variances of the realized completion times) measures are defined. Special cases for which the measures can be easily optimized are identified. A dominance rule and two lower bounds for one of the robustness measures are developed and subseqently used in a branch-and-bound algorithm to solve the problem exactly. A beam search heuristic is also proposed to solve large problems for all five measures. The computational results show that the beam search heuristic is capable of generating robust schedules with little average deviation from the optimal objective function value (obtained via the branch-and-bound algorithm) and it performs significantly better than a number of heuristics available in the literature for all five measures.Item Open Access Rapid and robust image reconstruction for magnetic particle imaging(Bilkent University, 2020-06) Kurt, SemihMagnetic Particle Imaging (MPI) is a rapidly developing medical imaging modality, which can image with high resolution, contrast, and sensitivity the spatial distribution of superparamagnetic iron oxide nanoparticles. Several applications of MPI have been introduced on angiography, cancer imaging, and stem cell tracking. Due to the safety limits on time-varying magnetic fields, MPI images are obtained by dividing the field-of-view (FOV) into numerous relatively small partial FOVs (pFOVs). Each pFOV suffers from a DC loss due to direct feedthrough interference caused by simultaneous excitation and signal reception. The standard x-space image reconstruction first processes each pFOV separately, and then combines them by enforcing smoothness and non-negativity constraints on the final image. These steps require the pFOVs to overlap, and can amplify the effects of non-ideal signal conditions, such as harmonic interference, noise, and nanoparticle relaxation. This thesis proposes two robust x-space image reconstruction techniques. The first technique, pFOV center imaging (PCI), first forms a raw image of the entire FOV by directly mapping the signal to pFOV centers. The final image is then reconstructed by deconvolving this raw image with a known, compact kernel. The second technique, harmonic dispersion x-space (HD-X), takes advantage of the dispersion in signal harmonics in the case of rapid scan trajectories. Followed by a sharp bandstop filtering of the fundamental harmonic, this technique directly grids the signal to form the final image, and does not require overlapping pFOVs. PCI offers robustness against harmonic interferences, and HD-X enables x-space reconstruction of rapid and sparse trajectories with non-overlapping pFOVs. Extensive simulations and imaging experiments show that both proposed methods outperform standard x-space reconstruction in terms of robustness against non-ideal signal conditions and image quality.Item Open Access Robust antiwindup compensation for high-precision tracking of a piezoelectric nanostage(Institute of Electrical and Electronics Engineers Inc., 2016) Liu, P.; Yan, P.; Zhang Z.; Özbay, HitayUltrahigh-precision tracking in nanomanipulations poses major challenges for mechanical design as well as servo control, due to the general confliction between the precision requirement and large stroke tracking. The situation is further complicated by input saturation, which is almost inevitable for microactuators. This paper presents a novel control architecture combining a parallel internal-model-based tracking design and a robust antiwindup control structure, such that asymptotic tracking can be achieved for nanoservo systems in the presence of saturation nonlinearity and model uncertainties. For the augmented system with internal-model dynamics, an I/O-based equivalent representation from control (free of saturation) to system output is derived by incorporating the dead-zone nonlinearity, saturation compensation blocks, as well internal-model units. The robustness condition on the saturation compensator is also derived based on the sector bound criterion and an H∞-optimal design is developed accordingly. The proposed robust antiwindup tracking control architecture is deployed on a customize-designed nanostage driven by a piezoelectric (PZT) actuator, where numerical simulations and real-time experiments demonstrate excellent tracking performance and saturation compensation capability, achieving tracking precision error less than 0.23%.Item Open Access A robust approach for the derivation of closed-form Green's functions(Institute of Electrical and Electronics Engineers, 1996-05) Aksun, M. I.Spatial-domain Green's functions for multilayer, planar geometries are cast into closed forms with two-level approximation of the spectral-domain representation of the Green's functions. This approach is very robust and much faster compared to the original one-level approximation. Moreover, it does not require the investigation of the spectral-domain behavior of the Green's functions in advance to decide on the parameters of the approximation technique, and it can be applied to any component of the dyadic Green's function with the same ease.Item Open Access Robust auction design under multiple priors by linear and integer programming(Springer New York LLC, 2018) Koçyiğit, Ç.; Bayrak, Halil İbrahim; Pınar, Mustafa ÇelebiIt is commonly assumed in the optimal auction design literature that valuations of buyers are independently drawn from a unique distribution. In this paper we study auctions under ambiguity, that is, in an environment where valuation distribution is uncertain itself, and present a linear programming approach to robust auction design problem with a discrete type space. We develop an algorithm that gives the optimal solution to the problem under certain assumptions when the seller is ambiguity averse with a finite prior set P and the buyers are ambiguity neutral with a prior f∈ P. We also consider the case where all parties, the buyers and the seller, are ambiguity averse, and formulate this problem as a mixed integer programming problem. Then, we propose a hybrid algorithm that enables to compute an optimal solution for the problem in reduced time.Item Open Access Robust bilateral trade with discrete types(Springer, 2018) Kargar, Kamyar; Bayrak, Halil İbrahim; Pınar, Mustafa ÇelebiBilateral trade problem is the most common market interaction in which a seller and a buyer bargain over an indivisible object, and the valuation of each agent about the object is private information. We investigate the cases where mechanisms satisfying Dominant Strategy Incentive Compatibility (DIC) and Ex-post Individual Rationality (EIR) properties can exhibit robust performance in the face of imprecision in prior structure. We start with the general mathematical formulation for the bilateral trade problem with DIC, EIR properties. We derive necessary and sufficient conditions for DIC, EIR mechanisms to be Ex-post efficient at the same time. Then, we define a new property—Allocation Maximality—and prove that the Posted Price mechanisms are the only mechanisms that satisfy DIC, EIR and Allocation Maximal properties. We also show that Posted Price mechanism is not the only mechanism that satisfies DIC and EIR properties. The last part of the paper introduces different sets of priors for agents’ types and consequently allows ambiguity in the problem framework. We derive robust counterparts and solve them numerically for the proposed objective function under box and ϕ-divergence ambiguity specifications. Results suggest that restricting the feasible set to Posted Price mechanisms can decrease the objective value to different extents depending on the uncertainty set.