Solution Of Subproblems Research Articles

Sum and difference patterns synthesis with common excitation amplitude

This paper focuses on the joint optimization problem of sum and difference patterns with common excitation amplitudes and separate excitation phases. The objective is to reduce the complexity of the antenna system while still maintaining a certain degree-of-freedom (DoF) in synthesizing dual-patterns. The problem is formulated with angular response and common excitation amplitude constraints, making it a nonconvex optimization problem. To address this, we introduce two groups of auxiliary variables to decouple the excitation vector from the complex nonconvex constraints. This allows the original problem to be effectively solved via alternately determining the closed-form solutions for several single-variable optimization subproblems. Additionally, our approach is extended to scenarios involving dynamic range ratio (DRR) reduction, aiming to lower the cost and difficulty of hardware implementation. Theoretical analysis and simulation results are provided to demonstrate that the proposed algorithm can converge to the Karush-Kuhn-Tucker points of the original problem. It is also observed that our approach is capable of generating desired dual-patterns with common excitation amplitudes, regardless of the presence or absence of DRR control.

A model for proppant dynamics in a perforated wellbore

This paper presents a model to simulate behavior of particle-laden slurry in a horizontal perforated wellbore with the goal of quantifying fluid and particle distribution between the perforations. There are two primary phenomena that influence the result. The first one is the non-uniform particle distribution within the wellbore’s cross-section and how it changes along the flow. The second phenomenon is related to the ability of particles to turn from the wellbore to a perforation. Consequently, the paper considers both of these phenomena independently at first, and then they are combined to address the whole problem of flow in a perforated wellbore. A mathematical model for calculating the particle and velocity profiles within the wellbore is developed. The model is calibrated against available laboratory data for various flow velocities, particle diameters, pipe diameters, and particle volume fractions. It predicts a steady-state solution for the particle and velocity profiles, as well as it captures the transition in time from a given state to the steady-state solution. The key dimensionless parameter that quantifies the latter solution is identified and is called dimensionless gravity. When it is small, the particles are fully suspended and the solution is uniform. At the same time, when the aforementioned parameter is large, then the solution is strongly non-uniform and resembles a flowing bed state. A mathematical model for the problem of particle turning is developed and is calibrated against available experimental and computational data. The key parameter affecting the result is called turning efficiency. When the efficiency is close to one, then most of the particles that follow the fluid streamlines going into the perforation are able enter the hole. At the same time, zero efficiency corresponds to the case of no particles entering the perforation. Solutions for the both sub-problems are combined to develop a model for the perforated wellbore. Results are compared (not calibrated) to a series of laboratory and field scale experiments for perforated wellbores. Comparison with the available computational results is presented as well. In addition, the comparison is presented in view of the parametric space defined by the dimensionless gravity and turning efficiency. Such a description allows to explain seemingly contradictory results observed in different tests and also allows to highlight parameters for which perforation orientation plays a significant role.

Distributed appointment assignment and scheduling under uncertainty

We investigate a stochastic distributed appointment assignment and scheduling problem, which consists of assigning appointments to distributed service units and determining service sequences at each service unit. In particular, the service time duration and release time uncertainties are well-considered. The solution to this generic problem finds interesting applications in distributed production systems, healthcare systems, and post-disaster operations. We formulate the problem as a two-stage stochastic program to minimise the total transportation cost and expected makespan, idle time or overtime, and apply the sample average approximation method to make the problem tractable. We then develop a stochastic logic-based Benders decomposition method, decomposing the problem into a master problem and a subproblem. The master problem determines the appointment assignment variables, and the subproblem handles the sequence and service start time variables. Benders optimality cuts are generated from the subproblem's solution and added to the master problem. The developed stochastic logic-based method is advantageous since it can manage many scenarios in parallel. We further consider each appointment's due date, minimise the weighted earliness and tardiness, and adjust the developed method to solve this variant. Experiments on random instances demonstrate the excellent performance of the proposed model and methods.

Worst-Case Complexity of TRACE with Inexact Subproblem Solutions for Nonconvex Smooth Optimization

Worst-Case Complexity of TRACE with Inexact Subproblem Solutions for Nonconvex Smooth Optimization

Secure Hybrid Beamforming for IRS-Assisted Millimeter Wave Systems

This paper investigates the secure hybrid beamforming (HB) design in an intelligent reflecting surface (IRS) assisted millimeter-wave (mmWave) system, where an IRS is deployed to help the legitimate transmission from Alice to Bob under the eavesdropping of Eve. To protect the legitimate transmission, Alice employs HB to send both the information signal and the artificial noise, while the IRS employs passive beamforming (PB) to reconstruct the wireless environment. Aiming at the secrecy capacity (SC) maximization, the joint optimization of HB and PB is formulated as a non-convex problem with constant-modulus constraints. To efficiently solve such a challenging problem, the original problem is decomposed into a PB subproblem and an HB subproblem, then these subproblems are sequentially solved by the proposed algorithms. Particularly, for the PB subproblem, we propose a channel information aided PB algorithm, which is proved to converge at a stationary point. With the solution of PB subproblem, two algorithms are proposed for the HB subproblem: 1) near-optimal SC approaching HB algorithm that achieves a near-optimal solution; 2) low-complexity HB algorithm that achieves a slight lower SC with less computational complexity. Simulation results demonstrate the superior performance of proposed algorithms in comparison with the state-of-the-art works.

Convergence Analysis of Dual Decomposition Algorithm in Distributed Optimization: Asynchrony and Inexactness

Dual decomposition is widely utilized in the distributed optimization of multi-agent systems. In practice, the dual decomposition algorithm is desired to admit an asynchronous implementation due to imperfect communication, such as time delay and packet drop. In addition, computational errors also exist when the individual agents solve their own subproblems. In this paper, we analyze the convergence of the dual decomposition algorithm in the distributed optimization when both the communication asynchrony and the subproblem solution inexactness exist. We find that the interaction between asynchrony and inexactness slows down the convergence rate from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O} (1 / k)$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O} (1 / \sqrt{k})$</tex-math></inline-formula> . Specifically, with a constant step size, the value of the objective function converges to a neighborhood of the optimal value, and the solution converges to a neighborhood of the optimal solution. Moreover, the violation of the constraints diminishes in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O} (1 / \sqrt{k})$</tex-math></inline-formula> . Our result generalizes and unifies the existing ones that only consider either asynchrony or inexactness. Finally, numerical simulations validate the theoretical results.

Variable projection methods for separable nonlinear inverse problems with general-form Tikhonov regularization

The variable projection (VarPro) method is an efficient method to solve separable nonlinear least squares problems. In this paper, we propose a modified VarPro method for solving separable nonlinear least squares problems with general-form Tikhonov regularization. In particular, we apply the Gauss–Newton method to the corresponding reduced problem and investigate its convergence when different approximations of the Jacobian matrix are used. For special cases when computing the generalized singular value decomposition is feasible or a joint spectral decomposition of both forward and regularization operators exists, we provide efficient ways to compute the Jacobians and the solution of the linear subproblems. For large-scale problems, where matrix decompositions are not an option, we compute a reduced Jacobian and apply projection-based iterative methods and generalized Krylov subspace methods to solve the linear subproblems. In all cases, the regularization parameter can be computed automatically at each iteration using generalized cross validation. Several numerical examples highlight the proposed approach’s performance in the quality of the reconstructed image and the reconstructed forward operator, including large-scale two-dimensional imaging problems arising from semi-blind deblurring.

Learning-based near-optimal tracking control for industrial processes with slow and fast modes

This paper devotes to solving the optimal tracking control (OTC) problem of singular perturbation systems in industrial processes under the framework of reinforcement learning (RL) technology. The encountered challenges include the different time scales in system operations and an unknown slow process. The immeasurability of slow process states especially increases the difficulty of finding the optimal tracking controller. To overcome these challenges, a novel off-policy ridge RL method is developed after decomposing the singular perturbed systems using the singular perturbation (SP) theory and replacing unmeasured states using important mathematical manipulations. Theoretical analysis of approximate equivalence of the sum of solutions of subproblems to the solution of the OTC problem is presented. Finally, a mixed separation thickening process (MSTP) and a numerical example are used to verify the effectiveness.

Enhancing Remote Sensing Image Super-Resolution Guided by Bicubic-Downsampled Low-Resolution Image

Image super-resolution (SR) is a significant technique in image processing as it enhances the spatial resolution of images, enabling various downstream applications. Based on recent achievements in SR studies in computer vision, deep-learning-based SR methods have been widely investigated for remote sensing images. In this study, we proposed a two-stage approach called bicubic-downsampled low-resolution (LR) image-guided generative adversarial network (BLG-GAN) for remote sensing image super-resolution. The proposed BLG-GAN method divides the image super-resolution procedure into two stages: LR image transfer and super-resolution. In the LR image transfer stage, real-world LR images are restored to less blurry and noisy bicubic-like LR images using guidance from synthetic LR images obtained through bicubic downsampling. Subsequently, the generated bicubic-like LR images are used as inputs to the SR network, which learns the mapping between the bicubic-like LR image and the corresponding high-resolution (HR) image. By approaching the SR problem as finding optimal solutions for subproblems, the BLG-GAN achieves superior results compared to state-of-the-art models, even with a smaller overall capacity of the SR network. As the BLG-GAN utilizes a synthetic LR image as a bridge between real-world LR and HR images, the proposed method shows improved image quality compared to the SR models trained to learn the direct mapping from a real-world LR image to an HR image. Experimental results on HR satellite image datasets demonstrate the effectiveness of the proposed method in improving perceptual quality and preserving image fidelity.

Rolling Horizon Based Temporal Decomposition for the Offline Pickup and Delivery Problem with Time Windows

The offline pickup and delivery problem with time windows (PDPTW) is a classical combinatorial optimization problem in the transportation community, which has proven to be very challenging computationally. Due to the complexity of the problem, practical problem instances can be solved only via heuristics, which trade-off solution quality for computational tractability. Among the various heuristics, a common strategy is problem decomposition, that is, the reduction of a large-scale problem into a collection of smaller sub-problems, with spatial and temporal decompositions being two natural approaches. While spatial decomposition has been successful in certain settings, effective temporal decomposition has been challenging due to the difficulty of stitching together the sub-problem solutions across the decomposition boundaries. In this work, we introduce a novel temporal decomposition scheme for solving a class of PDPTWs that have narrow time windows, for which it is able to provide both fast and high-quality solutions. We utilize techniques that have been popularized recently in the context of online dial-a-ride problems along with the general idea of rolling horizon optimization. To the best of our knowledge, this is the first attempt to solve offline PDPTWs using such an approach. To show the performance and scalability of our framework, we use the optimization of paratransit services as a motivating example. Due to the lack of benchmark solvers similar to ours (i.e., temporal decomposition with an online solver), we compare our results with an offline heuristic algorithm using Google OR-Tools. In smaller problem instances (with an average of 129 requests per instance), the baseline approach is as competitive as our framework. However, in larger problem instances (approximately 2,500 requests per instance), our framework is more scalable and can provide good solutions to problem instances of varying degrees of difficulty, while the baseline algorithm often fails to find a feasible solution within comparable compute times.

Improving quartet graph construction for scalable and accurate species tree estimation from gene trees.

methods are widely used to estimate species trees from genome-scale data. However, they can fail to produce accurate species trees when the input gene trees are highly discordant because of estimation error and biological processes, such as incomplete lineage sorting. Here, we introduce TREE-QMC, a new summary method that offers accuracy and scalability under these challenging scenarios. TREE-QMC builds upon weighted Quartet Max Cut, which takes weighted quartets as input and then constructs a species tree in a divide-and-conquer fashion, at each step forming a graph and seeking its max cut. The wQMC method has been successfully leveraged in the context of species tree estimation by weighting quartets by their frequencies in the gene trees; we improve upon this approach in two ways. First, we address accuracy by normalizing the quartet weights to account for "artificial taxa" introduced during the divide phase so subproblem solutions can be combined during the conquer phase. Second, we address scalability by introducing an algorithm to construct the graph directly from the gene trees; this gives TREE-QMC a time complexity of [Formula: see text], where n is the number of species and k is the number of gene trees, assuming the subproblem decomposition is perfectly balanced. These contributions enable TREE-QMC to be highly competitive in terms of species tree accuracy and empirical runtime with the leading quartet-based methods, even outperforming them on some model conditions explored in our simulation study. We also present the application of these methods to an avian phylogenomics data set.

Optimizing Comprehensive Cost of Charger Deployment in Multi-hop Wireless Charging

The multi-hop wireless charging technology has attracted a lot of attention, as it largely extends the charging range of chargers. Different from the existing work with single cost optimization, the objective of this article is to optimize the comprehensive cost, which is the combination of energy cost and deployment cost. We decompose the target problem into two sub-problems. The first sub-problem aims to minimize the deployment cost with energy capacity constraints. The proposed algorithm follows the greedy strategy, where the subset of sensor nodes for any charger is determined by finding the capacitated minimum spanning tree. The second sub-problem, which aims to maximize the reduction of comprehensive cost by adding chargers to the solution of the first sub-problem, is proved to be an unconstrained submodular set function maximization problem and can be solved by a 1/2-approximation randomized linear time algorithm for its equivalent problem. Through extensive simulations, we demonstrate that the proposed solution can reduce the comprehensive cost by 57.55% comparing with the benchmark algorithms.

Surrogate-assisted MOEA/D for expensive constrained multi-objective optimization

In this paper, an adaptive surrogate-assisted MOEA/D framework (ASA-MOEA/D) is proposed for solving computationally expensive constrained multi-objective optimization problems, in which three specific search strategies are adaptively implemented based on the optimization states of subproblems to achieve targeted searches for different subproblems. To maintain feasibility, the RBF-based local search models are constructed by comprehensively considering the orthogonal distance difference and constraint satisfaction information for guiding infeasible solutions of the infeasible subproblems into feasible regions. To maintain convergence, the RBF surrogates of the aggregated objective and constraints are employed to construct local search models for locating better feasible solutions. To maintain diversity, the subregions of unexplored subproblems are effectively explored by utilizing the valuable information of their neighboring elite solutions. Moreover, the solution with the maximum overall uncertainty of RBF surrogates is selected for progressively increasing the prediction accuracies of surrogates. Therefore, ASA-MOEA/D strikes an adaptive balance among diversity, feasibility and convergence with the assistance of RBF surrogates as the optimization progresses. Empirical studies on three classical test suites demonstrate that ASA-MOEA/D with tchebycheff approach achieves highly competitive performance over other four state-of-the-art algorithms.

Incremental particle swarm optimization for large-scale dynamic optimization with changing variable interactions

Cooperative coevolutionary algorithms have been developed for large-scale dynamic optimization problems via divide-and-conquer mechanisms. Interacting decision variables are divided into the same subproblem for optimization. Their performance greatly depends on problem decomposition and response abilities to environmental changes. However, existing algorithms usually adopt offline decomposition and hence are insufficient to adapt to changes in the underlying interaction structure of decision variables. Quick online decomposition then becomes a crucial issue, along with solution reconstruction for new subproblems. This paper proposes incremental particle swarm optimization to address the two issues. In the proposed method, the incremental differential grouping obtains accurate groupings by iteratively performing edge contractions on the interaction graph of historical groups. A recombination-based sampling strategy is developed to generate high-quality solutions from historical solutions for new subproblems. In order to coordinate with the multimodal property of the problem, swarms are restarted after convergence to search for multiple high-quality solutions. Experimental results on problem instances up to 1000-D show the superiority of the proposed method to state-of-the-art algorithms in terms of solution optimality. The incremental differential grouping can obtain accurate groupings using less function evaluations.

A fast two-stage algorithm for non-negative matrix factorization in smoothly varying data.

This article reports the study of algorithms for non-negative matrix factorization (NMF) in various applications involving smoothly varying data such as time or temperature series diffraction data on a dense grid of points. Utilizing the continual nature of the data, a fast two-stage algorithm is developed for highly efficient and accurate NMF. In the first stage, an alternating non-negative least-squares framework is used in combination with the active set method with a warm-start strategy for the solution of subproblems. In the second stage, an interior point method is adopted to accelerate the local convergence. The convergence of the proposed algorithm is proved. The new algorithm is compared with some existing algorithms in benchmark tests using both real-world data and synthetic data. The results demonstrate the advantage of the algorithm in finding high-precision solutions.

Efficient computation of extended surface sources

Source extension is a reformulation of inverse problems in wave propagation, that at least in some cases leads to computationally tractable iterative solution methods. The core subproblem in all source extension methods is the solution of a linear inverse problem for a source (right hand side in a system of wave equations) through minimization of data error in the least squares sense with soft imposition of physical constraints on the source via an additive quadratic penalty. For an acoustic formulation for sources supported on a surface, with a soft contraint enforcing concentration at a point, a variant of the time reversal method from photoacoustic tomography provides an approximate solution. This approximate inverse can be used to precondition Krylov space iteration for rapid convergence to the solution of the core subproblem in this setting. Numerical examples illustrate the effectiveness of this preconditioner.

A split-step Fourier pseudo-spectral method for solving the space fractional coupled nonlinear Schrödinger equations

In this paper, we propose a split-step Fourier pseudo-spectral method for solving the space fractional coupled nonlinear Schrödinger (CNLS) equations. The space fractional CNLS equations can be split into two subproblems such that one of them is linear. The solution of the nonlinear subproblem is computed exactly. The Riesz space fractional derivative is approximated by a Fourier pseudo-spectral method. The unconditional stability, convergence, discrete charge and multi-symplectic preserving properties for the proposed method are investigated. Then, the proposed method is extended for solving the two-dimensional problem. Finally, some numerical experiments are performed to confirm our theoretical analysis and illustrate the efficiency of the proposed scheme.

Influence of subproblem solutions on the quality of traveling thief problem solutions

The traveling thief problem (TTP) is a typical combinatorial optimization problem that integrates the computational complexity of the traveling salesman problem (TSP) and the knapsack problem (KP). The interdependent and mutually restrictive relationship between these two sub-problems brings new challenges to the heuristic optimization algorithm for solving the TTP problem. This paper first analyzes the performance of three sub-component combined iterative algorithms: Memetic Algorithm with the Two-stage Local Search (MATLS), S5, and CS2SA algorithms, which all employ the Chained Lin-ighan (CLK) algorithm to generate the circumnavigation path. To investigate the influence of different traveling routes on the performance of TTP solving algorithms, we propose a combinatorial iterative TTP solving algorithm based on the Ant Colony Optimization (ACO) and MAX-MIN Ant System (MMAS). Finally, the experimental investigations suggest that the traveling route generation method dramatically impacts the performance of TTP solving algorithms. The sub-component combined iterative algorithms based on the MMAS algorithm to generate the circumnavigation path has the best practical effect.

Joint computation offloading and resource allocation strategy for D2D-assisted and NOMA-empowered MEC systems

Multi-access edge computing (MEC) emerged as a promising network paradigm that provides computation, storage and networking features within the edge of the pervasive mobile radio access network. This paper jointly considers computation offloading and resource allocation problem in device-to-device (D2D)-assisted and non-orthogonal multiple access (NOMA)-empowered MEC systems, where each mobile device (MD) is allowed to execute its task in one of the three ways, i.e., local computing, MEC offloading or D2D offloading. We invoke orthogonal multiple access (OMA) and NOMA schemes for MDs that select D2D offloading mode, allowing them to assign tasks to their peers using OMA or NOMA. The original problem is formulated as an overall energy consumption minimization problem, which proves to be NP-hard, making it intractable to solve optimally. We start from a simple case, OMA case and transform the original problem into two sub-problems, i.e., resource allocation sub-problem and computation offloading sub-problem and propose two heuristic algorithms to obtain the sub-optimal solutions of both sub-problems. Then, for the MDs selecting D2D offloading mode, we conduct user pairing and apply the NOMA scheme. Finally, simulation results demonstrate the efficiency of the proposed scheme when compared with the related schemes.

A Fast Algorithm for Onboard Atmospheric Powered Descent Guidance

Atmospheric powered descent guidance (APDG) can be solved by successive convexification; however, its onboard application is impeded by high computational cost. When aerodynamic forces are ignored, powered descent guidance (PDG) can be converted to a single convex problem. In contrast, APDG has to be converted into a sequence of convex subproblems, each of which is significantly more complicated. Consequently, the computation increases sharply. A fast real-time interior point method was presented to solve the correlated convex subproblems efficiently onboard in the work. The main contributions are as follows: Firstly, an algorithm was proposed to accelerate the solution of linear systems that cost most of the computation in each iterative step by exploiting the specific problem structure. Secondly, a warm-starting scheme was introduced to refine the initial value of a subproblem with a rough approximate solution of the former subproblem, which lessened the iterative steps required for each subproblem. The method proposed reduced the run time by a factor of 9 compared with the fastest publicly available solver tested in Monte Carlo simulations to evaluate the efficiency of solvers. Runtimes on the order of 0.6 s are achieved on a radiation-hardened flight processor, which demonstrated the potential of the real-time onboard application.