Subproblems Of Smaller Size Research Articles

Deterministic Beamforming for Unmanned Aerial Vehicle Array

This paper addresses the deterministic beamforming for unmanned aerial vehicle (UAV) array (UAVA), which is equipped with an antenna for each UAV. Unlike conventional array, the UAVA can obtain extra degrees-of-freedom for beamforming by flexibly controlling the topology of UAVs, which motivates us to consider an off-grid array layout to improve the beamformer. To effectively control the load of UAVs, we incorporate the dynamic range ratio (DRR) of weighting coefficients of UAVA. On these basis, we formulate a new optimization model aiming to minimize the maximum sidelobe level under the constraints of mainlobe ripple, DRR, layout spacing and array aperture. However, the resulting NP-hard problem is quite challenging due to the exponential form of layout vector and the non-convexity of mainlobe ripple and DRR. In this respect, we reformulate this multi-constrained problem into a new iteration form of combining alternating direction penalty method and majorization-minimization via introducing a series of auxiliary variables. In each iteration, the tractable and small-sized subproblems can almost globally be solved. Numerical results confirm that our method is more suitable for deterministic beamforming of UAVA than the state-of-the-art methods.

A learning-based solution method for practical slab allocation problem in multiple hot rolling lines

Steel slabs are key in-process products in the steel production process. The slab allocation problem is to allocate slabs to suitable orders by considering complicated technical restrictions and multiple management requirements. In practice, thousands of slabs in multiple production lines should be allocated to orders. Due to the complexity and large scale of the problem, it takes planners a long time to make decisions, and the obtained allocation schemes are usually ineffective because of the myopic nature of the rule-based methods. In this article, we present a learning-based solution method for solving a practical slab allocation problem in multiple hot rolling lines. We formulate the problem as an integer programming model, then a data-based method is adopted to evaluate the mismatching cost between slabs and orders. To effectively solve the large-sized problem, a learning-based decomposition strategy is proposed to decompose the original problem into several small-sized subproblems. Then, a branch-and-price algorithm is proposed to optimally solve the subproblems. To further speed up the solution process, a primal heuristics based on column generation is designed to solve the large-sized subproblems. The solution methods have been implemented in a steel company and effectively increased slab utilization and reduced production cost.

Proximal ADMM for nonconvex and nonsmooth optimization

By enabling the nodes or agents to solve small-sized subproblems to achieve coordination, distributed algorithms are favored by many networked systems for efficient and scalable computation. While for convex problems, substantial distributed algorithms are available, the results for the more broad nonconvex counterparts are extremely lacking. This paper develops a distributed algorithm for a class of nonconvex and nonsmooth problems featured by (i) a nonconvex objective formed by both separate and composite components regarding the decision variables of interconnected agents, (ii) local bounded convex constraints, and (iii) coupled linear constraints. This problem is directly originated from smart buildings and is also broad in other domains. To provide a distributed algorithm with convergence guarantee, we revise the powerful alternating direction method of multiplier (ADMM) method and proposed a proximal ADMM. Specifically, noting that the main difficulty to establish the convergence for the nonconvex and nonsmooth optimization with ADMM is to assume the boundness of dual updates, we propose to update the dual variables in a discounted manner. This leads to the establishment of a so-called sufficiently decreasing and lower bounded Lyapunov function, which is critical to establish the convergence. We prove that the method converges to some approximate stationary points. We besides showcase the efficacy and performance of the method by a numerical example and the concrete application to multi-zone heating, ventilation, and air-conditioning (HVAC) control in smart buildings.

Block-Term Tensor Decomposition: Model Selection and Computation

The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a scenario encountered in numerous and diverse applications. Its uniqueness and approximation have thus been thoroughly studied. Nevertheless, the challenging problem of estimating the BTD model structure, namely the number of block terms and their individual ranks, has only recently started to attract significant attention. In this paper, a novel method of BTD model selection and computation is proposed, based on the idea of imposing column sparsity \emph{jointly} on the factors and in a \emph{hierarchical} manner and estimating the ranks as the numbers of factor columns of non-negligible magnitude. Following a block successive upper bound minimization (BSUM) approach for the proposed optimization problem is shown to result in an alternating hierarchical iteratively reweighted least squares (HIRLS) algorithm, which is fast converging and enjoys high computational efficiency, as it relies in its iterations on small-sized sub-problems with closed-form solutions. Simulation results for both synthetic examples and a hyper-spectral image de-noising application are reported, which demonstrate the superiority of the proposed scheme over the state-of-the-art in terms of success rate in rank estimation as well as computation time and rate of convergence.

Spatial–temporal out-of-order execution for advanced planning and scheduling in cyber-physical factories

Cyber-Physical System (CPS) is one of the most promising directions of Industry 4.0 smart manufacturing. Abundant manufacturing data and information are available for decision-makers in real-time thanks to the application of various frontier technologies in CPS. However, the inherent complexity and uncertainty of manufacturing optimization still plague scholars and practitioners and impede further progress of smart manufacturing. The production planning and scheduling is such a complex and stochastic problem that has received considerable research attention. Whereas how to leverage the strengths of CPS for breaking the bottleneck of complexity and uncertainty, is still a question that needs further exploration. This paper proposes a novel “divide and conquer” approach, Spatial–Temporal Out-Of-Order execution (ST-OOO), for achieving real-time planning and scheduling in cyber-physical factories. ST-OOO divides the space and time scopes of a factory into finite areas and intervals to reduce complexity and localize uncertainties so that the original complex optimization problem is decomposed into a set of subproblems with different spatial and temporal characteristics. These small-size subproblems can be assembled using data and information visibility and traceability, and then solved in a rolling spatiotemporal manner to generate a global solution. A case study shows that ST-OOO has a well-balanced and more stable performance compared to traditional strategies. Sensitivity analysis is carried out to study the impacts of spatial and temporal scales on the results.

Fast Multi-View Clustering via Nonnegative and Orthogonal Factorization.

The rapid growth of the number of data brings great challenges to clustering, especially the introduction of multi-view data, which collected from multiple sources or represented by multiple features, makes these challenges more arduous. How to clustering large-scale data efficiently has become the hottest topic of current large-scale clustering tasks. Although several accelerated multi-view methods have been proposed to improve the efficiency of clustering large-scale data, they still cannot be applied to some scenarios that require high efficiency because of the high computational complexity. To cope with the issue of high computational complexity of existing multi-view methods when dealing with large-scale data, a fast multi-view clustering model via nonnegative and orthogonal factorization (FMCNOF) is proposed in this paper. Instead of constraining the factor matrices to be nonnegative as traditional nonnegative and orthogonal factorization (NOF), we constrain a factor matrix of this model to be cluster indicator matrix which can assign cluster labels to data directly without extra post-processing step to extract cluster structures from the factor matrix. Meanwhile, the F-norm instead of the L2-norm is utilized on the FMCNOF model, which makes the model very easy to optimize. Furthermore, an efficient optimization algorithm is proposed to solve the FMCNOF model. Different from the traditional NOF optimization algorithm requiring dense matrix multiplications, our algorithm can divide the optimization problem into three decoupled small size subproblems that can be solved by much less matrix multiplications. Combined with the FMCNOF model and the corresponding fast optimization method, the efficiency of the clustering process can be significantly improved, and the computational complexity is nearly O(n) . Extensive experiments on various benchmark data sets validate our approach can greatly improve the efficiency when achieve acceptable performance.

Efficient Downlink Power Allocation Algorithms for Cell-Free Massive MIMO Systems

Cell-free Massive MIMO systems consist of a large number of geographically distributed access points (APs) that serve the users by coherent joint transmission. The spectral efficiency (SE) achieved by each user depends on the power allocation: which APs that transmit to which users and with what power. In this article, we revisit the max-min and sum-SE power allocation policies, which have previously been approached using high-complexity general-purpose solvers. We develop and compare several different high-performance low-complexity power allocation algorithms that are appropriate for use in large systems. We propose two new algorithms for sum-SE power optimization inspired by weighted minimum mean square error (WMMSE) minimization and fractional programming (FP). Further, one new FP-based algorithm is proposed for max-min fair power allocation. The alternating direction method of multipliers (ADMM) is used to solve specific convex subproblems in the proposed algorithms. Our ADMM reformulations lead to multiple small-sized subproblems with closed-form solutions. The proposed algorithms find global or local optimal power allocation solutions for large-scale systems but with reduced computational time compared to previous work.

Beampattern Synthesis via the Constrained Subarray Layout Optimization

This article deals with a joint design of subarray layout vector (LV) and weighted coefficient of radiation element (RE) to achieve desired beampattern for a new array architecture. We first present an architecture of thinned array composed of multiple regular subarrays (ACMRS) and establish corresponding subarray layout and beampattern models. Then, we formulate a new optimization problem aiming to minimize the peak sidelobe level (PSL) and the LV norm under the constraints of power beampattern and subarray layout. The resulting problem is quite challenging to solve due to the highly nonconvex discrete LV and double-sided quadratic constraints. In this respect, we formulate the resultant hybrid optimization problem into a new alternating direction method of multipliers (ADMM) form via introducing a series of auxiliary variables, and propose an approximation algorithm based on ADMM. In each iteration of the proposed ADMM, the tractable and small-sized subproblems are globally or locally solved in parallel. Finally, numerical simulations show that the proposed method can obtain a lower PSL beampattern and a thinner (i.e., fewer REs or subarrays) array while satisfying the given constraints. Furthermore, fullwave simulation also shows that it has good reliability in the application of beampattern synthesis for real array.

Hyperspectral image classification based on sparse modeling of spectral blocks

Hyperspectral images provide abundant spatial and spectral information that is very valuable for material detection in diverse areas of practical science. The high-dimensions of data lead to many processing challenges that can be addressed via existent spatial and spectral redundancies. In this paper, a sparse modeling framework is proposed for hyperspectral image classification. Spectral blocks are introduced to be used along with spatial groups to jointly exploit spectral and spatial redundancies. To reduce the computational complexity of sparse modeling, spectral blocks are used to break the high-dimensional optimization problems into small-size sub-problems that are faster to solve. Furthermore, the proposed sparse structure enables to extract the most discriminative spectral blocks and further reduce the computational burden. Experiments on three benchmark datasets, i.e., Pavia University, Indian Pines and Salinas images verify that the proposed method leads to a robust sparse modeling of hyperspectral images and improves the classification accuracy compared to several state-of-the-art methods. Moreover, the experiments demonstrate that the proposed method requires less processing time.

Optimal Task Allocation Algorithms for Energy Constrained Multihop Wireless Networks

In recent years, multihop wireless networks have been playing a key role in many Internet of Things applications. Due to the limited resources of wireless nodes, extending the network lifetime is one of the most crucial issues, which needs to be concerned. This paper aims to maximize the network lifetime by appropriately distributing the tasks of the applications for each node in the network. First, a centralized optimal task allocation algorithm for multihop wireless networks (COTAM) is proposed by modeling the problem of maximizing the network lifetime as a linear programming (LP) problem. As the centralized algorithm requires knowing all the network parameters in advance, COTAM is mostly restricted to the off-line optimization in known environments. To extend the usability of the approach, this paper further proposes a distributed optimal task allocation algorithm (DOTAM) based on Dantzig–Wolf decomposition. DOTAM divides the centralized large-sized LP problem into small-sized subproblems, which are independently executed by each node. The proposed COTAM and DOTAM are tested by applying both the artificially generated applications and a realistic application. The extensive results demonstrate that DOTAM achieves the same performance as COTAM. Comparing with existing methods, they provide significant improvements on extending the network lifetime.

Wideband MIMO Radar Waveform Design

We consider the design of wideband multiple-input multiple-output (MIMO) radar waveforms to approximate a desired beampattern and achieve prescribed space-frequency nulling in a space-frequency region of interest. A general design model involving modulus, power, and energy constraints on the probing waveforms is introduced. To deal with the resulting non-convex design, a novel iterative algorithm with low computational complexity is proposed. In each iteration, the non-convex design is approximated successively through a series of convex subproblems. Then, each convex subproblem is reformulated in a new alternating direction method of multipliers form, with small-sized subproblems solved in parallel with closed-form solutions via utilizing the Karush-Kuhn-Tucker conditions. Numerical results are provided to demonstrate the effectiveness of the proposed algorithm.

Efficient Due-Date Quoting and Production Scheduling for Integrated Circuit Packaging With Reentrant Processes

The advances in packaging technology in the past decade have overcome a few engineering limitations in integrated circuit (IC) manufacturing. This has greatly complicated the manufacturing process and created a huge challenge in the operations management of the semiconductor back-end production. In particular, the modern demand of lighter and smaller products expedites the multichip packaging technology, which requires reentrant processes and hence makes resource scheduling more difficult. Apart from the fact that IC packaging shares many key features with the semiconductor front-end production, the cycle time of back-end production is significantly shorter than that of the front-end production. Therefore, there is an urgent need of a rapid solution procedure to generate a reliable production schedule for IC packaging. To respond to customer requests efficiently, this paper models the production scheduling of IC packaging as an optimization model and formulates a hybrid genetic algorithm (GA) to solve the problem efficiently. The embedded structure of our model enables the decomposition of the original problems into many small-sized subproblems, which can be solved by available optimization solvers. These subproblems communicate via a master problem, which is solved by a GA to determine the due dates assigned to subproblems. The master and the subproblems are iteratively solved in turn to obtain a satisfactory solution. Computational experiments and an empirical study are performed to validate the efficiency and the feasibility of the proposed approach.

An Ensemble Approach to Link Prediction

A network with $n$ nodes contains $O(n^2)$ possible links. Even for networks of modest size, it is often difficult to evaluate all pairwise possibilities for links in a meaningful way. Further, even though link prediction is closely related to missing value estimation problems, it is often difficult to use sophisticated models such as latent factor methods because of their computational complexity on large networks. Hence, most known link prediction methods are designed for evaluating the link propensity on a specified subset of links, rather than on the entire networks. In practice, however, it is essential to perform an exhaustive search over the entire networks. In this article, we propose an ensemble enabled approach to scaling up link prediction, by decomposing traditional link prediction problems into subproblems of smaller size. These subproblems are each solved with latent factor models, which can be effectively implemented on networks of modest size. By incorporating with the characteristics of link prediction, the ensemble approach further reduces the sizes of subproblems without sacrificing its prediction accuracy. The ensemble enabled approach has several advantages in terms of performance, and our experimental results demonstrate the effectiveness and scalability of our approach.

ADMM-Based Fast Algorithm for Multi-Group Multicast Beamforming in Large-Scale Wireless Systems

Multi-group multicast beamforming in wireless systems with large antenna arrays and massive audience is investigated in this paper. Multicast beamforming design is a well-known non-convex quadratically constrained quadratic programming (QCQP) problem. A conventional method to tackle this problem is to approximate it as a semi-definite programming problem via semi-definite relaxation, whose performance, however, deteriorates considerably as the number of per-group users goes large. A recent attempt is to apply convex-concave procedure (CCP) to find a stationary solution by treating it as a difference of convex programming problem, whose complexity, however, increases dramatically as the problem size increases. In this paper, we propose a low-complexity high-performance algorithm for multi-group multicast beamforming design in large-scale wireless systems by leveraging the alternating direction method of multipliers (ADMM) together with CCP. In specific, the original non-convex QCQP problem is first approximated as a sequence of convex subproblems via CCP. Each convex subproblem is then reformulated as a novel ADMM form. Our ADMM reformulation enables that each updating step is performed by solving multiple small-size subproblems with closed-form solutions in parallel. Numerical results show that our fast algorithm maintains the same favorable performance as state-of-the-art algorithms but reduces the complexity by orders of magnitude.

Implementation of an integrated production and electricity optimization system in melt shop

The production of stainless steel begins by melting of scrap in melt shop that is known as one of the most electricity intensive processes. Volatile and uncertain renewable energy sources cause high fluctuations in electricity prices and thus usually higher costs for the final user such as a melt shop. This paper presents an integrated production and electricity optimization system that can help the melt shop to adjust its production schedule to volatile electricity prices and thus lower its costs. An existing production scheduling optimization system based on a continuous-time mixed-integer linear programming model has been further developed to account for electricity costs as well. It deploys an intelligent heuristics which decomposes the overall optimization problem into several sub-problems of smaller size in order to achieve faster and more robust solution. The electricity-aware optimization system has been successfully tested and implemented in a melt shop where it managed to reduce electricity costs by around 3%. At the same time, the system has improved coordination between different production stages, and thus made the entire melt shop more flexible, agile and responsive to unexpected events. The system has also been recognized as a very useful tool for running various simulations, what-if analysis and business scenarios on the melt shop in order to identify bottlenecks and further increase its production rate.

XGRouter: high-quality global router in X-architecture with particle swarm optimization

This paper presents a high-quality very large scale integration (VLSI) global router in X-architecture, called XGRouter, that heavily relies on integer linear programming (ILP) techniques, partition strategy and particle swarm optimization (PSO). A new ILP formulation, which can achieve more uniform routing solution than other formulations and can be effectively solved by the proposed PSO is proposed. To effectively use the new ILP formulation, a partition strategy that decomposes a large-sized problem into some small-sized sub-problems is adopted and the routing region is extended progressively from the most congested region. In the post-processing stage of XGRouter, maze routing based on new routing edge cost is designed to further optimize the total wire length and mantain the congestion uniformity. To our best knowledge, XGRouter is the first work to use a concurrent algorithm to solve the global routing problem in X-architecture. Experimental results show that XGRouter can produce solutions of higher quality than other global routers. And, like several state-of-the-art global routers, XGRouter has no overflow.

COVARIANCE ASSISTED SCREENING AND ESTIMATION.

Consider a linear model Y = X β + z, where X = Xn,p and z ~ N(0, In ). The vector β is unknown and it is of interest to separate its nonzero coordinates from the zero ones (i.e., variable selection). Motivated by examples in long-memory time series (Fan and Yao, 2003) and the change-point problem (Bhattacharya, 1994), we are primarily interested in the case where the Gram matrix G = X'X is non-sparse but sparsifiable by a finite order linear filter. We focus on the regime where signals are both rare and weak so that successful variable selection is very challenging but is still possible. We approach this problem by a new procedure called the Covariance Assisted Screening and Estimation (CASE). CASE first uses a linear filtering to reduce the original setting to a new regression model where the corresponding Gram (covariance) matrix is sparse. The new covariance matrix induces a sparse graph, which guides us to conduct multivariate screening without visiting all the submodels. By interacting with the signal sparsity, the graph enables us to decompose the original problem into many separated small-size subproblems (if only we know where they are!). Linear filtering also induces a so-called problem of information leakage, which can be overcome by the newly introduced patching technique. Together, these give rise to CASE, which is a two-stage Screen and Clean (Fan and Song, 2010; Wasserman and Roeder, 2009) procedure, where we first identify candidates of these submodels by patching and screening, and then re-examine each candidate to remove false positives. For any procedure β̂ for variable selection, we measure the performance by the minimax Hamming distance between the sign vectors of β̂ and β. We show that in a broad class of situations where the Gram matrix is non-sparse but sparsifiable, CASE achieves the optimal rate of convergence. The results are successfully applied to long-memory time series and the change-point model.

Improved algorithm about NSFOT

For the purpose of further saving computing time, an improved algorithm about NSFOT is provided in this paper. That is, by introducing the simple operations such as preprocessing or after-processing, Haar and Walsh transforms are performed conveniently on the multiprocessor. As a result, one large size problem is divided into several small size sub-problems, load on every processor not only decreases greatly but also gets so uniform that much time is saved. Both the theoretical analysis and experimental results demonstrate the effectiveness of the proposed approach.

Goal-oriented optimal subset selection of correlated multimedia streams

A multimedia analysis system utilizes a set of correlated media streams, each of which, we assume, has a confidence level and a cost associated with it, and each of which partially helps in achieving the system goal. However, the fact that at any instant, not all of the media streams contribute towards a system goal brings up the issue of finding the best subset from the available set of media streams. For example, a subset of two video cameras and two microphones could be better than any other subset of sensors at some time instance to achieve a surveillance goal (e.g. event detection). This article presents a novel framework that finds the optimal subset of media streams so as to achieve the system goal under specified constraints. The proposed framework uses a dynamic programming approach to find the optimal subset of media streams based on three different criteria: first, by maximizing the probability of achieving the goal under the specified cost and confidence; second, by maximizing the confidence in the achieved goal under the specified cost and probability with which the goal is achieved; and third, by minimizing the cost to achieve the goal with a specified probability and confidence. Each of these problems is proven to be NP-Complete. From an AI point of view, the solution we propose is heuristic-based, and for each criterion, utilizes a heuristic function which for a given problem, combines optimal solutions of small-sized subproblems to yield a potential near-optimal solution to the original problem. The proposed framework allows for a tradeoff among the aforementioned three criteria, and offers the flexibility to compare whether any one set of media streams of low cost would be better than any other set of higher cost, or whether any one set of media streams of high confidence would be better than any other set of low confidence. To show the utility of our framework, we provide the experimental results for event detection in a surveillance scenario.

A SURROGATE‐PARAMETER APPROACH TO MODELING GROUNDWATER BASINS1

ABSTRACT: A surrrogate‐prarmeter approach to modeling groundwater basins is presented, which has the following advantages over current simulation‐type methods: (i) conducivness to modeling nonhomogeneous and nonisotropic basins; (ii) there is no need to guess boundary conditions if accurate information is not available; (iii) the model is amenable to systematic calibration or identification through the use of optimization techniques; and (iv) compatibility with systematic algorithms for analyzing a wide range of management strategies. Since the parameter identification problem is large‐scale and nonconvex, it is decomposed through application of generalized duality theory, into several subproblems of smaller size which are solved independently a number of times in order to achieve an overall solution. Results are presented for a hypothetical system of four interacting wells.