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This paper addresses a linear programming problem with interval right-hand sides, forming a family of linear programs associated with each realization of the interval data. The paper focuses on the outcome range problem, which seeks the range of an additional function—termed the outcome function—over all possible optimal solutions of such linear programs. We explore the problem's applicability in diverse contexts, discuss its connections to certain existing problems, and analyze its computational complexity and theoretical foundations. Given the inherent computational challenges, we propose three heuristics to solve the problem. The first heuristic employs a reformulation–linearization technique (RLT) to obtain an outer approximation of the range of the outcome function. We also present two algorithms—a gradient-restoration-based approach (GI) and a bases inspection method (BI)—for computing an inner approximation of the range. Computational experiments illustrate the competitive advantage of our proposed approaches versus off-the-shelf solvers. The GI and BI methods present promising results in finding a cheap but tight inner approximation, while the performance of the RLT technique decreases as problem size and uncertainty increase. [ABSTRACT FROM AUTHOR]

How to handle conflict in Dempster-Shafer evidence theory is an open issue. Many approaches have been proposed to solve this problem. The existing approaches can be divided into two kinds. The first is to improve the combination rule, and the second is to modify the data model. A typical method to improve combination rule is to assign the conflict to the total ignorance set Θ . However, it does not make full use of conflict information. A novel combination rule is proposed in this paper, which assigns the conflicting mass to the power set (ACTP). Compared with modifying data model, the advantage of the proposed method is the sequential fusion, which greatly decrease computational complexity. To demonstrate the efficacy of the proposed method, some numerical examples are given. Due to the less information loss, the proposed method is better than other methods in terms of identifying the correct evidence, the speed of convergence and computational complexity. [ABSTRACT FROM AUTHOR]

In this paper, the problem of single-channel blind source separation (SCBSS) is addressed using a novel approach that combines the adaptive mode separation-based wavelet transform (AMSWT) and the density-based clustering with sparse reconstruction. The proposed method is performed in the time–frequency domain and in a reverberant environment. First, using the Fourier transform, the amplitude spectrum of the observed mixture signal is obtained. Then, using variational scaling and wavelet functions, the AMSWT is used to adaptively extract spectral intrinsic components (SICs). To obtain a better time–frequency resolution, the AMSWT is applied to each mode. Thus, the SCBSS problem is transformed into a non-underdetermined. Then, for each frequency bin, the density-based clustering, reformulated to the eigenvector clustering problem, is performed to estimate the mixing matrix. Finally, sparse reconstruction is used to reconstruct the sources. The proposed method is evaluated using objective measures of separation quality. A computational complexity evaluation based on time consumption is also performed. Simulation results show that the proposed method is very effective for solving the SCBSS problem and provides better separation performances than the reference methods. However, the proposed method is computationally expensive. [ABSTRACT FROM AUTHOR]

In this paper, we address the issue of solving problems with multiple components, multiple objectives, and target values for each objective. There are limitations in managing these multi-component, multi-goal problems such as the need for domain expertise to combine or prioritize the goals. In this paper, we propose a domain-independent method, Adaptive Leveling-Weighting-Clustering (ALWC), to manage the exploration of design scenarios of multi-goal, engineering-design problems. Using ALWC, designers explore combinations and priorities of the goals based on their interrelationships. Through iteration, design scenarios are obtained with higher goal achievements and an improved understanding of the relationship among subsystems. This is achieved without increasing computational complexity. This knowledge is helpful for multi-component design. The ALWC method is demonstrated using a thermal-system design problem. [ABSTRACT FROM AUTHOR]

This paper addresses the reconstruction issue of sparse signal by developing centralized and distributed neurodynamic approaches. An l 1 -minimization problem can be employed for reconstructing sparse signal, and for solving this problem, a centralized neurodynamic approach with derivative feedback is designed. Considering the fact that the distributed approaches decompose the large-scale problem into small-scale one without central processing node in centralized ones, it effectively reduces the computational complexity of a single node. According to the distributed consensus and graph theory, the original l 1 -minimization problem can be equivalently transformed as a distributed optimization problem. Then, based on our proposed centralized approach, a distributed neurodynamic approach with derivative feedback is further proposed. Through the convex optimization theory and Lyapunov method, we indicate that the optimal solution of l 1 -minimization problem is equivalent to the equilibrium point of centralized or distributed approach, and that each neurodynamic approach globally converges to its equilibrium point. Furthermore, by comparing with several state-of-the-art neurodynamic approaches, our proposed approaches demonstrate their effectiveness and superiority by simulation results in reconstructing sparse signals and images. [ABSTRACT FROM AUTHOR]

The goal of session-based recommendation is to make item predictions at the next timestamp based on the anonymous ongoing session. Previous work mainly models user's preference by exploring the transition pattern between the interacted items in the session. However, they generally fail to pay enough attention to the item importance in terms of the relevance of the items to user's main purpose. This paper proposes a Session-based Recommendation approach with an Importance Extraction Module, i.e., SR-IEM improved , which can simultaneously consider user's long-term interactions and recent behavior in current session. Specifically, we modify the self-attention mechanism to avoid introducing bias for estimating the importance of each item in the session. Then, the item importances are utilized to produce user's long-term preference, and the sequential signals are incorporated in the long-term interest modeling. Next, the long-term preference and user's current interest which is conveyed by the last interacted item in the session are combined to obtain user's final preference representation. Finally, item predictions are generated using the user preference, where a normalization layer is adopted to solve the long-tail problem. Extensive experiments are conducted on three public benchmark datasets, i.e., Yoochoose 1/64, Yoochoose 1/4 and Diginetica. The experimental results show that SR-IEM improved can outperform the start-of-the-art baselines in terms of Recall and MRR for session-based recommendation. In addition, compared to the state-of-the-art neural methods, SR-IEM improved can obviously reduce the computational complexity. [ABSTRACT FROM AUTHOR]

In a FSS-OFDMA, the OFDM symbol is spread, and the subcarriers are assigned for each user in the frequency band. As the principal subcarrier allocation for each user, localized and interleaved allocations have been proposed, and the interleaved allocation is improved for the BER performance to avoid continuous deep faded subcarrier channels. Also, in the independent channel fluctuation for each user, the MUDiv gain is obtained by the individual and block subcarrier allocations. However, they have a trade-off problem between the BER performance and the computational complexity. To solve this problem, the interleaved block subcarrier allocation has been proposed. On the other hand, the interleaved block is only evaluated for the individual subcarrier and is not evaluated for the several subcarriers. Moreover, the power combination between the subcarrier and the channel is also improved for the BER performance, but the individual and block subcarrier allocations are only evaluated. Therefore, in this paper, we propose the interleaved block subcarrier allocation and the power combination for a FSS-MUDiv/OFDMA. [ABSTRACT FROM AUTHOR]

The reconstruction of time-varying signals on graphs is a prominent problem in graph signal processing community. By imposing the smoothness regularization over the time-vertex domain, the reconstruction problem can be formulated into an unconstrained optimization problem that minimizes the weighted sum of the data fidelity term and regularization term. In this paper, we propose an approximate Newton method to solve the problem in a distributed manner, which is applicable for spatially distributed systems consisting of agents with limited computation and communication capacity. The algorithm has low computational complexity while nearly maintains the fast convergence of the second-order methods, which is evidently better than the existing reconstruction algorithm based on the gradient descent method. The convergence of the proposed algorithm is explicitly proved. Numerical results verify the validity and fast convergence of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, approximation schemes are proposed for handling load uncertainty in compliance-based topology optimization problems, where the uncertainty is described in the form of a set of finitely many loading scenarios. Efficient approximate methods are proposed to approximately evaluate and differentiate either (1) the mean compliance, or (2) a class of scalar-valued function of the individual load compliances such as the weighted sum of the mean and standard deviation. The computational time complexities of the proposed algorithms are analyzed, compared to the exact approaches and then experimentally verified. Finally, some mean compliance minimization problems and some risk-averse compliance minimization problems are solved for verification. [ABSTRACT FROM AUTHOR]

In this paper, we propose to use Artificial Bee Colony (ABC) optimization to solve the joint mode selection, channel assignment, and power allocation (JMSCPA) problem to maximize system throughput and spectral efficiency. JMSCPA is a problem where the allocation of channel and power depends on the mode selection. Such problems require two step solution and are called bi-level optimization problems. As bi-level optimization increases the complexity and computational time, we propose a modified version of single-level ABC algorithm aided with the adaptive transmission mode selection algorithm to allocate the cellular, reuse, and dedicated modes to the DUs along with channel and power allocation based on the network traffic load scenarios. A single variable, represented by the users (CUs and DUs) is used to allocate mode selection, and channel allocation to solve the JMSCPA problem, leading to a simpler solution with faster convergence, and significant reduction in the computational complexity which scales linearly with the number of users. Further, the proposed solution avoids premature stagnation of conventional ABC into local minima by incorporating a modification in its update procedure. The efficacy of the ABC-aided approach, as compared to the results reported in the literature, is validated by extensive numerical investigations under different simulation scenarios. [ABSTRACT FROM AUTHOR]

With low hardware cost and power consumption, direction-of-arrival (DOA) estimation exploiting one-bit quantized array data has become an attractive topic. In this paper, the gridless compressed sensing (CS) with multiple measurement vectors for one-bit DOA estimation is investigated. First, the one-bit quantized signal model is established. Then an atomic norm minimization scheme is proposed based on the output of one-bit quantizer, in which the objective function is reformulated as a semidefinite programming problem combined with a one-sided l 1 -norm constraint, representing the sign inconsistency between the quantized and unquantized measurements. To efficiently solve such a problem and reduce its computational complexity, an accelerated proximal gradient-based algorithm is developed. The proposed approach outperforms the one-bit MUSIC in a small number of measurements, and avoids the grid-mismatch issue of several existing one-bit CS methods. Numerical experiments are conducted to validate the superiorities of the proposed one-bit DOA estimation approach in accuracy and running time. [ABSTRACT FROM AUTHOR]

This paper is devoted to a particular case of applying universal accelerated proximal methods for constructing computationally efficient accelerated versions of methods used for solving optimization problems in various specific statements. A proximally accelerated componentwise gradient method with efficient algorithmic complexity of each iteration is proposed, which effectively takes into account the problem sparseness. An example of applying the proposed approach to solving the optimization problem for a function of form SoftMax is considered. In this problem, the method weakens the dependence of the computational complexity of solution on the problem size by a factor of , and in practice it demonstrates a faster convergence compared with conventional methods. [ABSTRACT FROM AUTHOR]

This paper addresses the camera pose estimation problem from 3D lines and their 2D projections, known as the perspective-n-line (PnL) problem. Although many successful solutions have been presented, it is still a challenging to optimize both computational complexity and accuracy at the same time. In our work, we parameterize the rotation by using the Cayley–Gibbs–Rodriguez (CGR) parameterization and formulate the PnL problem into a polynomial system solving problem. Instead of the Gröbner basis method, which may encounter numeric problems, we seek for an efficient and stability technique—the hidden variable method—to solve the polynomial system and polish the solution via the Gauss–Newton method. The performance of our method is evaluated by using simulations and real images, and results demonstrate that our method offers accuracy and precision comparable or better than existing state-of-the-art methods, but with significantly lower computational cost. [ABSTRACT FROM AUTHOR]

Network Function Virtualization (NFV) is a vital player of modern networks providing different types of services such as traffic optimization, content filtering, and load balancing. More precisely, NFV is a provisioning technology aims at reducing the large Capital Expenditure (CapEx) of network providers by moving services from dedicated hardware to commodity servers using Virtualized Network Functions (VNF). A sequence of VNFs/services following a logical goal is referred to as a Service Function Chain (SFC). The movement toward SFC introduces new challenges to those network services which require high reliability. To address this challenge, redundancy schemes are introduced. Existing redundancy schemes using dedicated protection enhance the reliability of services, however, they do not consider the cost of redundant VNFs. In this paper, we propose a novel reliability enhancement method using a shared protection scheme to reduce the cost of redundant VNFs. To this end, we mathematically formulate the problem as a Mixed Integer Linear Programming (MILP). The objective is to determine optimal reliability that could be achieved with minimum cost. Although the corresponding optimization problem can be solved using existing MILP solvers, the computational complexity is not rational for realistic scenarios. Thereafter, we propose a Reliability-aware and minimum-Cost based Genetic (RCG) algorithm to solve this problem with low computational complexity. In order to evaluate the proposed solution, we have compared it with four different solutions. Simulation results show that RCG achieves near-optimal performance at a much lower complexity compared with the optimal solution. [ABSTRACT FROM AUTHOR]

Increases in the quantity of available data have allowed all fields of science to generate more accurate models of multivariate phenomena. Regression and interpolation become challenging when the dimension of data is large, especially while maintaining tractable computational complexity. Regression is a popular approach to solving approximation problems with high dimension; however, there are often advantages to interpolation. This paper presents a novel and insightful error bound for (piecewise) linear interpolation in arbitrary dimension and contrasts the performance of some interpolation techniques with popular regression techniques. Empirical results demonstrate the viability of interpolation for moderately high-dimensional approximation problems, and encourage broader application of interpolants to multivariate approximation in science. [ABSTRACT FROM AUTHOR]

Kriging has been more and more widely used as a method to construct surrogate models in a variety of areas within the engineering field. The universal Kriging is less appealing than the ordinary Kriging in the case that an informed decision could be hardly made to select the variables for capturing the global trends in responses. The Penalized Blind Kriging (PBK) systematically carries out model selection with penalizing the likelihood function, which leads to improving the predictive performance of a universal Kriging model. However, the PBK demands the execution of an iterative algorithm, which involves repeatedly solving a possibly time-consuming optimization problem to find a varying optimal solution to the correlation coefficient vector. In this paper, the Lasso Kriging (LK) is proposed to not only improve the predictive performance but avoid the iterative computation. The LK selects the important variables fundamentally by solving a Lasso problem using the LARS algorithm with CV. The one-standard error rule is employed to compensate for less penalizing the regression coefficients than the PBK does. Given the selected important variables, unknown Kriging parameters are estimated in the same manner as in the universal Kriging. A linear and a nonlinear mathematical problem and seven highly nonlinear benchmark problems are used to demonstrate the effectiveness of the LK concerning the model selection and predictive performance as well as the computational efficiency. The LK proves to be an effective approach that both improves predictive accuracy as much as the PBK does and requires a little more computational complexity than the universal Kriging. [ABSTRACT FROM AUTHOR]