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Item response tree (IRTree) models form a family of psychometric models that allow researchers to control for multiple response processes, such as different sorts of response styles, in the measurement of latent traits. While IRTree models can capture quantitative individual differences in both the latent traits of interest and the use of response categories, they maintain the basic assumption that the nature and weighting of latent response processes are homogeneous across the entire population of respondents. In the present research, we therefore propose a novel approach for detecting heterogeneity in the parameters of IRTree models across subgroups that engage in different response behavior. The approach uses score‐based tests to reveal violations of parameter heterogeneity along extraneous person covariates, and it can be employed as a model‐based partitioning algorithm to identify sources of differences in the strength of trait‐based responding or other response processes. Simulation studies demonstrate generally accurate Type I error rates and sufficient power for metric, ordinal, and categorical person covariates and for different types of test statistics, with the potential to differentiate between different types of parameter heterogeneity. An empirical application illustrates the use of score‐based partitioning in the analysis of latent response processes with real data. [ABSTRACT FROM AUTHOR]

To enhance the power generation efficiency of the photovoltaic system, it is necessary to ensure that it can operate stably at the global maximum power point (MPP). This paper presents a study on the maximum power point tracking(MPPT) technology of photovoltaic system and a new MPPT technique based on the improved multi‐subgroup parallel optimization algorithm with shuffled frog leaping algorithm (IMSPO‐SFLA) is proposed, which combines the improved multi‐subgroup parallel optimization algorithm with the shuffled frog leaping algorithm. Moreover, the developed MPPT technique improves the tracking accuracy of the MPP, increased the speed of MPP tracking, the problem of the traditional frog leaping algorithm being prone to falling into a local optimum is successfully overcame by it. In order to verify the effectiveness of the method, a simulation model is established in MATLAB in this paper. The Simulation results show that the method proposed in this paper can make the photovoltaic power generation system be operated more efficiently, which contributes to the development of the renewable energy field and promotes the progress of clean energy technology. Compared with the traditional algorithm, it has obvious advantages in realizing the MPPT of PV power generation system. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

Terrain analysis plays an important role in computer graphics, hydrology and geomorphology. In particular, analyzing the path of material flow over a terrain with consideration of local depressions is a precursor to many further tasks in erosion, river formation, and plant ecosystem simulation. For example, fluvial erosion simulation used in terrain modeling computes water discharge to repeatedly locate erosion channels for soil removal and transport. Despite its significance, traditional methods face performance constraints, limiting their broader applicability. In this paper, we propose a novel GPU flow routing algorithm that computes the water discharge in 풪(log n) iterations for a terrain with n vertices (assuming n processors). We also provide a depression routing algorithm to route the water out of local minima formed by depressions in the terrain, which converges in 풪(log2 n) iterations. Our implementation of these algorithms leads to a 5× speedup for flow routing and 34 × to 52 × speedup for depression routing compared to previous work on a 10242 terrain, enabling interactive control of terrain simulation. [ABSTRACT FROM AUTHOR]

Runge–Kutta algorithms with adaptive step size control provide reliable tools for the solution of initial value problems with diagonally implicit Runge‐Kutta (DIRK) methods as the most common approach. In this contribution, the new low‐order explicit last‐stage diagonally implicit Runge–Kutta (ELDIRK) methods are investigated, combining implicit schemes with an additional explicit evaluation as an explicit last stage. This results in Butcher tableaus with two solutions of different convergence orders suitable for embedded methods, where the higher‐order solution is achieved by additional explicit evaluations. Thus, the iterative solution of non‐linear systems is omitted for the additional stage, presenting a major reduction in computational cost for the determination of a local error estimate. The key contribution is the application of the novel Butcher tableaux to phase‐field problems, solved with the finite‐element method, leading to substantial numerical investigations with an efficient approach for DIRK schemes. The most important aspects are the investigations of stability properties which lead to the novel class of A‐stable ELDIRK methods. In accordance, the study of the convergence orders is presented. A local error estimator is presented, such that adaptive step size control for the new low‐order embedded schemes based on an empirical approach for error estimation is achieved. A suitable parallel algorithm is presented with conclusive two‐dimensional phase‐field simulations based on a Kobayashi‐Warren‐Carter model. The higher‐order convergence suggested by the novel schemes is confirmed, and their effective results are demonstrated, resulting in a valuable semi‐explicit addition to the family of Runge–Kutta time integration schemes. [ABSTRACT FROM AUTHOR]

In this article, a model‐free parallel reinforcement learning method is proposed to solve the suboptimal control problem for the Markov jump singularly perturbed systems. First, since fast and slow dynamics coexist in Markov jump singularly perturbed systems, it may lead to ill‐conditioned numerical problems during the controller design process. Therefore, the original system can be decomposed into independent subsystems at different time‐scales by employing the reduced order method. In addition, two model‐free parallel reinforcement learning algorithms are designed to obtain the optimal controllers for the fast and slow subsystems, respectively. Moreover, within the framework of reinforcement learning, the controllers of the Markov jump singularly perturbed systems can be acquired without the systems dynamics. Finally, a numerical example is introduced to prove the effectiveness of proposed algorithms. [ABSTRACT FROM AUTHOR]

The assessment of compound blood‐brain barrier (BBB) permeability poses a significant challenge in the discovery of drugs targeting the central nervous system. Conventional experimental approaches to measure BBB permeability are labor‐intensive, cost‐ineffective, and time‐consuming. In this study, we constructed six machine learning classification models by combining various machine learning algorithms and molecular representations. The model based on ExtraTree algorithm and random partitioning strategy obtains the best prediction result, with AUC value of 0.932±0.004 and balanced accuracy (BA) of 0.837±0.010 for the test set. We employed the SHAP method to identify important features associated with BBB permeability. In addition, matched molecular pair (MMP) analysis and representative substructure derivation method were utilized to uncover the transformation rules and distinctive structural features of BBB permeable compounds. The machine learning models proposed in this work can serve as an effective tool for assessing BBB permeability in the drug discovery for central nervous system disease. [ABSTRACT FROM AUTHOR]

Summary: In the paper, we compute some lower bounds on time of parallel solving of the subset sum problem on a big number of processors by several versions of dynamic programming algorithm Balsub proposed before by Pisinger. Based on these lower bounds, we propose a version of Balsub which could be possibly effectively parallelized. [ABSTRACT FROM AUTHOR]

Summary: The breadth‐first search procedure is an algorithm that traverses the vertices of a graph, determining the distance from each vertex to the initial vertex. The distance is infinite for a non‐reachable vertex from the starting vertex. Despite having an efficient serial version, this important algorithm is irregular, making its effective parallel implementation a daunting task. This paper shows the results of an OpenMP‐based implementation of the breadth‐first search procedure using the bag data structure. Furthermore, the code relied on the C++ programming language. This paper reimplements an existing proposal coded using the Cilk++ programming language. The experiments relied on 32 strongly connected graphs and 31 disconnected graphs in executions performed on two machines. The first machine contained 28 cores and two threads per core. The second machine comprised 48 processing cores, with hyperthreading disabled. Regarding the serial version, the parallel implementation yielded a speedup of up to 20× when using 28 processing cores and up to 25× when using 56 threads in tests performed on a machine with the first generation of Intel® Xeon® Scalable processors. Furthermore, the new parallel implementation yielded speedups of up to 45× when using 48 cores in experiments performed on a machine with the second generation of Intel® Xeon® Scalable processors. [ABSTRACT FROM AUTHOR]

Summary: The t$$ t $$‐admissibility is a min‐max problem that concerns to determine whether a graph G$$ G $$ contains a spanning tree T$$ T $$ in which the distance between any two adjacent vertices of G$$ G $$ is at most t$$ t $$ in T$$ T $$. The stretch index of G$$ G $$, σ(G)$$ \sigma (G) $$, is the smallest t$$ t $$ for which G$$ G $$ is t$$ t $$‐admissible. This problem is in P for t≤2$$ t\le 2 $$, NP‐complete for σ(G)≤t$$ \sigma (G)\le t $$, t≥4$$ t\ge 4 $$, and remaining open for t=3$$ t=3 $$. In a very recent development, Couto et al. (Inf Process Lett, 2022; 177: 106265) introduced both sequential and parallel algorithms for constructing spanning trees. Additionally, they proposed two greedy heuristics for generating a candidate solution tree, but they left unresolved the issue of how to decide between two vertices when both have equal chances of being chosen in a greedy step. This criterion is important, since different branches can yield different stretch indexes. In response to this question, we developed nine new heuristics that use the concept of vertex importance in complex networks. Our research evaluates results on several types of graphs, including Barabási‐Albert, Erdős‐Rényi, Watts‐Strogatz, and bipartite graphs. Furthermore, we introduce a new parallel algorithm that employs a method using induced cycle of the graph to compare its performance with previously proposed algorithms. We develop a deep analysis on the proposed strategies (parallel and heuristics) comparing all of them to the other ones in the literature and as a result we obtain the best results so far in order to obtain exact values (or heuristics) of stretch indexes. [ABSTRACT FROM AUTHOR]

This paper presents a novel Bayesian method for backcalculation of pavement dynamic modulus, stiffness, thickness, and damping using falling weight deflectometer (FWD) data. The backcalculation procedure yields estimates and uncertainties for each pavement property of interest. As a by‐product of the Bayesian procedure, information about measurement error is recovered. The Bayesian method is tested on simulated FWD backcalculations and compared with a state‐of‐the‐art trust‐region optimization algorithm, and it achieves estimation errors that are nearly an order of magnitude lower than the trust‐region solver. Confidence intervals are computed from thousands of simulated backcalculations and are shown to quantify uncertainty in estimated pavement properties. To cope with the computational expense of backcalculation, a fully parallel transitional Markov chain Monte Carlo procedure is developed. The fully parallel algorithm scales well to computation with many processor cores, and it yields up to a 50% reduction in computation time when compared to existing parallel implementations. [ABSTRACT FROM AUTHOR]

Spread spectrum technology has been widely employed for positioning and communicating with autonomous underwater vehicles (AUVs), but conventional spread spectrum sequences lack confidentiality and reliability in UWA channel. Considering the limitations of conventional sequences and the characteristics of underwater acoustic (UWA) channel, a composite chaotic orthogonal sequence (CCOS) based on the UWA channel is proposed. The confidentiality of the CCOS is superior to that of the m‐sequence, while the autocorrelation performance of the CCOS is superior to that of the orthogonal sequence. Moreover, the CCOS can compensate for the imbalance of logistic chaotic sequence when assigned certain initial values. Acquisition is a crucial component of accessing the spread spectrum signal; therefore, the acquisition performance indicates the applicability of the CCOS. The source–target model is established to simulate communication with an underwater moving target. To simulate the acquisition process, a parallel algorithm based on fast Fourier transform is adopted, and the entire simulation process is completed based on the BELLHOP ray acoustic model. Through data processing, the Doppler shift error is less than half of the frequency‐search element. Furthermore, the acquisition probabilities of the CCOS with different numbers of bits are over 90%, which demonstrates the reliability of the CCOS. [ABSTRACT FROM AUTHOR]

As urban population increases, integrated underground–aboveground complexes are being constructed at growing paces in major cities. The seismic analysis of such complexes is crucial for the safety and functionality in the threat of potential earthquake disasters. However, fine‐grained numerical modeling and analysis of such large and complex structures are still inefficient due to the consideration of the soil–structure interaction (SSI). To address this challenge, an efficient approach for numerical modeling of large‐scale seismic SSI analysis is presented in this paper to overcome the limitations of existing finite element analysis (FEA) software. Moreover, a multi‐graphic processing unit (GPU) parallel explicit algorithm is implemented for the nonlinear dynamic SSI problems to further increase the computational efficiency. A large underground–aboveground complex project in China is used as an example to demonstrate the capability of the integrated method. The accuracy and reliability of the multi‐GPU parallel explicit finite element algorithm for SSI analysis (GFEA‐SSIA) are verified through a comparative analysis of the linear‐elastic and nonlinear dynamic response of the building calculated by GFEA‐SSIA and common FEA software. Finally, the structural response and structural damage of the underground–aboveground complex are analyzed under multidirectional seismic motions, and the damage distributions of the structures are provided. [ABSTRACT FROM AUTHOR]

Summary: The Oak Ridge Leadership Computing Facility (OLCF) has been preparing the nation's first exascale system, Frontier, for production and end users. Frontier is based on HPE Cray's new EX architecture and Slingshot interconnect and features 74 cabinets of optimized 3rd Gen AMD EPYC CPUs for HPC and AI and AMD Instinct 250X accelerators. As a part of this preparation, "real‐world" user codes have been selected to help assess the functionality, performance, and usability of the system. This article describes early experiences using the system in collaboration with the Hamburg Observatory for two selected codes, which have since been adopted in the OLCF test harness. Experiences discussed include efforts to resolve performance variability and per‐cycle slowdowns. Results are shown for a performance portable astrophysical magnetohydronamics code, AthenaPK, and a mini‐application stressing the core functionality of a performance portable block‐structured adaptive mesh refinement framework, Parthenon‐Hydro. These results show good scaling characteristics to the full system. At the largest scale, the Parthenon‐Hydro miniapp reaches a total of 1.7×1013 zone‐cycles/s on 9216 nodes (73,728 logical GPUs) at ≈92% weak scaling parallel efficiency (starting from a single node using a second‐order, finite‐volume method). [ABSTRACT FROM AUTHOR]

Summary: Wireless sensor and actor networks (WSANs) consist of nodes associated in an ad hoc manner to perform sensing tasks for information gathering and acting functions on the basis of gathered information. Connectivity is an essential requirement of large‐scale wireless networks, and WSANs are supposed to stay connected. The nodes in hostile environments are prone to failures such as battery depletion, physical damage, or hardware malfunction. The failure of some nodes, like cut vertex nodes, can partition the network into multiple network segments. Most of the solutions for network partition recovery proposed in the literature depend on the assumption that the network is obstacle‐free. However, an obstacle‐free environment is not possible in real‐life situations. In the last few decades, UAVs or drones have been engaged in various applications such as industrial inspections, remote sensing, agriculture, military, disaster relief, and so forth, UAVs can be employed to strengthen the connections in wireless networks by coordinating with ground nodes since they can render services in rough areas where ground nodes cannot provide services. Thus, our research is based on using UAVs as relay nodes to reconnect the disjoint partitions. This paper proposes two algorithms: Drone assisted partition recovery algorithm (DAPRA) and drone assisted detection and partition recovery algorithm (DADPRA). In both algorithms, partitions are detected by the sink node. In DAPRA sink node determines the failed cut‐vertex node and sends UAV to the location of the failed cut‐vertex node. In DADPRA algorithm, UAV identifies the failed cut‐vertex node and reconnects the disjoint network segments. DAPRA and DADPRA are analyzed according to the state‐of‐the‐art parameters, that is, recovery and detection time, UAV's travel distance, and the total messages transmitted. The proposed algorithms are compared with similar Distributed Partition Detection and Recovery using UAV (DPDRU) approach. The simulation results show the proposed algorithms detect network partitioning in less time as compared to DPDRU approach. [ABSTRACT FROM AUTHOR]

High‐resolution gravity field models of the Moon established from Gravity Recovery and Interior Laboratory satellite gravity data have been playing an important role in understanding the interior structure and tectonic evolution of the Moon. Due to the correlations in the high degree and order term coefficients of the gravity field models, the difference between satellite flight orbits, and the random noise of instruments, the high‐resolution gravity anomalies data derived from the models of high degree and order usually present serious multi‐directional striping and random noise, which clearly affect the subsequent interpretation of the data. We provide an omnidirectional filtering method based on the polynomial‐fitting principle to remove multi‐directional striping noise in the lunar satellite gravity anomalies data. A set of azimuth parameters are chosen to suppress all the directions of striping noise. The algorithms of data partitioning and iterative optimization are utilized to make our method suitable and stable for large‐scale data sets. Tests on the synthetic data and the real data from the Moon's Rümker region and globally verified the feasibility of our method with a better destriping effect than the traditional Gaussian filtering or degree‐order‐truncation methods. Plain Language Summary: High‐resolution gravity anomalies derived from gravity field models are often disrupted by interference such as multi‐directional striping and random noise. The omnidirectional filtering method for destriping lunar satellite gravity data can solve this annoying problem by introducing a set of azimuth parameters and the algorithms of data partitioning and iterative optimization. Through theoretical model experiments and high‐precision satellite gravity data tests in the Moon's Rümker region, this study demonstrates our method has a better performance in striping and random noise removal compared to previous methods. This method holds potential for application to satellite gravity data of other planets or other satellite geophysical data. Key Points: The omnidirectional filtering method based on the polynomial‐fitting principle to remove multi‐directional striping noise in the lunar satellite gravity anomalies dataA set of azimuth parameters are chosen to suppress all the directions of striping noiseThe algorithms of data partitioning and iterative optimization are used to make our method suitable and stable for large‐scale data sets [ABSTRACT FROM AUTHOR]

In supervised learning, feature selection methods identify the most relevant predictors to include in a model. For linear models, the inclusion or exclusion of each variable may be represented as a vector of bits playing the role of the genetic material that defines the model. Genetic algorithms reproduce the strategies of natural selection on a population of models to identify the best. We derive the distribution of the importance scores for parallel genetic algorithms under the null hypothesis that none of the features has predictive power. They, hence, provide an objective threshold for feature selection that does not require the visual inspection of a bubble plot. We also introduce the eradication strategy, akin to forward stepwise selection, where the genes of useful variables are sequentially forced into the models. The method is illustrated on real data, and simulation studies are run to describe its performance. [ABSTRACT FROM AUTHOR]

Primary healthcare plays a pivotal role in enhancing health conditions. In Singapore, such services are predominantly manifested through the implementation of the Community Health Assistance Scheme (CHAS). CHAS is an initiative aimed at providing fundamental preventive and therapeutic services, especially for those seniors and low‐income adults with chronic diseases. In spite of considerable efforts in policy and research in this domain, there is a dearth of studies focusing on the spatial optimization of these primary healthcare services. In this study, an innovative multi‐objective medical service facility siting model has been developed based on coarse‐grained parallel genetic algorithm to address the intricate challenges associated with the optimization of locations for CHAS clinics. The proposed optimization model aims to simultaneously maximize accessibility, minimize inequity, and minimize the number of clinics. The successful application of this model in the siting of CHAS clinics in Singapore demonstrates its effectiveness in enhancing residents' access to healthcare services. Apart from its novel academic contributions to the field of spatial optimization of primary healthcare facilities in general, we have also discussed the inherent limitations and identified certain aspects as the future directions of this research. [ABSTRACT FROM AUTHOR]

This paper introduces a modified sequential version method for optimizing a linear function over an integer efficient set, as well as a new exact parallel algorithm. The performance of parallel programming in this context is clear and shown through different instances with different sizes. Each procedure builds a finite monotonous sequence of values for the main criterion to be optimized, in a reasonable amount of CPU execution time. This latter remains much better. For the first time, the Algerian IBNBADIS cluster—CERIST—was used with this type of problem. Significant results are obtained by both proposed techniques, particularly with the parallel one. [ABSTRACT FROM AUTHOR]

Summary: Clustering ensemble is a popular approach for identifying data clusters that combines the clustering results from multiple base clustering algorithms to produce more accurate and robust data clusters. However, the performance of clustering ensemble algorithms is highly dependent on the quality of clustering members. To address this problem, this paper proposes a member enhancement‐based clustering ensemble (MECE) algorithm that selects the ensemble members by considering their distribution consistency. MECE has two main components, called heterocluster splitting and homocluster merging. The first component estimates two probability density functions (p.d.f.s) estimated on the sample points of an heterocluster and represents them using a Gaussian distribution and a Gaussian mixture model. If the random numbers generated by these two p.d.f.s have different probability distributions, the heterocluster is then split into smaller clusters. The second component merges the clusters that have high neighborhood densities into a homocluster, where the neighborhood density is measured using a novel evaluation criterion. In addition, a co‐association matrix is presented, which serves as a summary for the ensemble of diverse clusters. A series of experiments were conducted to evaluate the feasibility and effectiveness of the proposed ensemble member generation algorithm. Results show that the proposed MECE algorithm can select high quality ensemble members and as a result yield the better clusterings than six state‐of‐the‐art ensemble clustering algorithms, that is, cluster‐based similarity partitioning algorithm (CSPA), meta‐clustering algorithm (MCLA), hybrid bipartite graph formulation (HBGF), evidence accumulation clustering (EAC), locally weighted evidence accumulation (LWEA), and locally weighted graph partition (LWGP). Specifically, MECE algorithm has the nearly 23% higher average NMI, 27% higher average ARI, 15% higher average FMI, and 10% higher average purity than CSPA, MCLA, HBGF, EAC, LWEA, and LWGA algorithms. The experimental results demonstrate that MECE algorithm is a valid approach to deal with the clustering ensemble problems. [ABSTRACT FROM AUTHOR]

Summary: We are concerned with the mapping on high performance hybrid architectures of a parallel software implementing a two level overlapping domain decomposition, that is, along space and time directions, of the four dimensional variational data assimilation model. The reference architecture belongs to the SCoPE (Sistema Cooperativo Per Elaborazioni scientifiche multidisciplinari) data center, located at University of Naples Federico II. We consider the initial boundary problem of the shallow water equation and analyse both strong and weak scaling. Keeping the efficiency always greater than 60%$$ 60\% $$ and about 90%$$ 90\% $$ in most cases, we experimentally find that the isoefficiency function grows a little more than linearly with respect to the number of processes. Results, obtained by using the parallel computing toolbox of MATLABR2013a, are in agreement with the algorithm's performance prevision based on the scale up factor, confirming the appropriate mapping of the algorithm on the hybrid architecture. [ABSTRACT FROM AUTHOR]

In literature, the cost of a partitioned fluid‐structure interaction scheme is typically assessed by the number of coupling iterations required per time step, while ignoring the internal iterations within the nonlinear subproblems. In this work, we demonstrate that these internal iterations have a significant influence on the computational cost of the coupled simulation. Particular attention is paid to how limiting the number of iterations within each solver call can shorten the overall run time, as it avoids polishing the subproblem solution using unconverged coupling data. Based on systematic parameter studies, we investigate the optimal number of subproblem iterations per coupling step. In addition, this work proposes a new convergence criterion for partitioned algorithms that is based solely on the number of subproblem iterations required to reach the subproblem residual tolerances and therefore does not require any additional convergence tolerance for the coupling loop. [ABSTRACT FROM AUTHOR]

Firstly, the Canny operator combined with circle fitting is used to position the working surface. Secondly, the median filter and the Laplacian operator are selected for preprocessing. Due to uneven illumination, surface texture, or environmental dust, the extracted scratches exhibit fragmentation, and traditional morphological operations cannot handle scratches well, so an improved Canny operator combined with probabilistic Hough transform is proposed for scratch connection. A bidirectional connection is introduced to optimize the edge detection process of the Canny operator, and a parallel algorithm is introduced to shorten the detection time. Finally, the standard Hough transform needs to traverse the entire parameter space, and the calculation is complicated, and the probability Hough transform is selected. The experimental results show that compared with the traditional Canny algorithm, the precision, recall, and F1‐score of the improved Canny algorithm are increased by 3.2%, 13.2%, and 6.0%, respectively. After adding parallel processing, the average detection time was reduced by 45 ms. Finally, the accuracy of scratches extracted using this algorithm reached 97.96%, the leak rate, and mistake rate of this study are only 3.33% and 2.00%, which provides a more accurate and efficient theoretical support for the research on brake disc scratch detection. [ABSTRACT FROM AUTHOR]

The sea surface is a complex superposition of various wave systems, thus, analysing their characteristics provides more meaningful and accurate information compared to conventional integrated wave parameter approaches. The concept of wave family—a population of wave systems within a specific region in spectral space—provides the foundation for investigating the long‐term climatology of wave systems. This study adopts a wave family approach to investigate the climatology of wave systems and their long‐term climate controllers at the location of a coastal buoy in the western North Atlantic Ocean. The frequency‐direction wave spectrum is constructed for a historical 20‐year period by applying the Maximum Entropy Method on directional buoy measurements acquired from the National Data Buoy Center station 44025, located in the New York Bight. The two‐dimensional wave spectrum is partitioned, using the watershed partitioning algorithm, and the occurrence distribution of spectral partitions is calculated to identify predominant wave families. Each of the four identified wave families carries unique characteristics based on spatial formation and duration of propagation prior to arrival at the study site. The study quantifies long‐term trends and variability in wave height of each wave family on a monthly, seasonal and annual level, and their relative importance to the bulk sea‐state climatology. The nexus between the bulk or wave family seasonal wave heights and the climate indices is quantified to identify the wave climate controllers in the study area. [ABSTRACT FROM AUTHOR]

This article considers an identical parallel‐machine task scheduling problem motivated by operations management of online services. A task with an integer processing time can be split into sub‐tasks with integer processing times. Each task has multiple integer milestones and at each milestone a nonnegative penalty will occur. The penalty value of a task at a milestone is a convex nonincreasing function of the completed amount by this milestone. Our objective is to determine a feasible schedule for all the tasks on given identical parallel machines, such that the sum of all tasks' total penalty at all milestones is minimized. We prove the NP‐hardness of this problem in the ordinary sense and develop a branch‐and‐price algorithm. Computational experiments utilizing data from an online service operations survey show that this algorithm is singularly efficient and promising. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to construct a common solution of the split null point problem associated with the maximal monotone operators and the fixed point problem associated with a finite family of k‐demicontractive operators in Hilbert spaces. We compute the optimal common solution via inertial parallel hybrid algorithm under a suitable set of control conditions. The viability of parallel implementation of the algorithm is demonstrated for various theoretical as well as numerical results. The results presented in this paper improve various existing results in the current literature. [ABSTRACT FROM AUTHOR]

The phase field approach to fracture becomes popular for complicated fracture problems in recent years. However, its widespread application is hindered by its high computational cost. In this article, we propose an efficient parallel explicit‐implicit solution scheme for the phase field approach to dynamic fracture based on a domain decomposition method, specifically, the dual‐primal finite element tearing and interconnecting (FETI‐DP) method. In this scheme, the displacement field is updated by an explicit algorithm in parallel, and the phase field is implicitly solved by the FETI‐DP method. In particular, Lagrange multipliers are introduced to ensure the interface continuity of the phase field. In the computational process, the information exchange among subdomains merely exists in a few substeps, which renders the cost for communication very small. Moreover, the size of equations to be solved is proportional to the total area of subdomain interfaces, which is significantly reduced compared with a typical single‐domain solution procedure. The solution scheme is able to perform phase field simulations with a million of degrees of freedom using only 0.034 core hours per load step, and has flexible extensibility for existing phase field codes. Several numerical examples demonstrate the accuracy and efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

Summary: Backtracking branch‐and‐prune (BP) algorithms and their variants are exhaustive search tree techniques widely employed to solve optimization problems in many scientific areas. However, they characteristically often demand significant amounts of computing power for problem sizes representative of real‐world scenarios. Given that their search domains can often be partitioned, these algorithms are frequently designed to execute in parallel by harnessing distributed computing systems. However, to achieve efficient parallel execution times, an effective strategy is required to balance the nonuniform partition workloads across the available resources. Furthermore, with the increasing integration of servers with heterogeneous resources and the adoption of resource sharing, balancing workloads is becoming complex. This paper proposes a strategy to execute parallel BP algorithms more efficiently on even shared or heterogeneous distributed systems. The approach integrates a self‐adjusting dynamic partitioning method in the BP algorithm with a dynamic scheduler, provided by an application middleware, which manages the parallel execution while addressing any issues of imbalance. Empirical results indicate better scalability with efficiencies above 90% for instances of an application case study for the discretizable molecular distance geometry problem (DMDGP). Improvements of up to 38% were obtained in execution speed‐ups compared to a more traditional parallel BP implementation for DMDGP. [ABSTRACT FROM AUTHOR]

Summary: A new synthetic floating simulator topology is proposed which realizes lossy parallel inductance (R‐L), lossy parallel capacitance (R‐C), lossy parallel C‐D, and lossless floating capacitance multiplier (FCM) circuits using only three current feedback operational amplifiers (CFOA) as active elements and three impedances. In all the presented circuits, the value of L, C, and D is independently controllable through a single resistance without requiring any matching condition for passive elements. A novel feature of the proposed circuit involves a straightforward adjustment in the CFOA connections, allowing the circuit to function as either a floating lossless immittance simulator or a floating series‐type lossy immittance simulator. Various application examples of the presented circuits such as lead compensator, lag compensator, first‐order high‐pass filter, and fourth‐order Butterworth filter are also given to justify the theoretical analysis. To validate the workability of the proposed circuits, several analyses are conducted, including frequency analysis, transient analysis, Monte‐Carlo analysis, and temperature analysis, using the macro‐model of AD844 in the SPICE simulation tool. Experimental results of the parallel R‐L simulator and application examples are also provided using commercially available IC AD844‐type integrated CFOAs. [ABSTRACT FROM AUTHOR]

Summary: This article proposes a high efficiency video coding (HEVC) standard hardware using block matching motion estimation algorithm. A hybrid parallel spiral and adaptive threshold star diamond search algorithm (Hyb PS‐ATSDSA) proposes for fast motion estimation in HEVC. Parallel spiral search approach utilizes spiral pattern for searching from center to the surroundings and adaptive threshold SDA consists of two phases, they are adaptive threshold and star diamond algorithm. To lower computational complexities in HEVC architecture, parallel spiral search algorithm uses several blocks matching schemes. Adaptive threshold and star diamond algorithm are used to reduce the matching errors and remove the invalid blocks early from the procedure of motion estimation and finally predicts the final motion of the image. Speed is increased while using this hybrid algorithm. Proposed structure is carried out in Xilinx; ISE 14.5 design suit, then the experimental outcomes are analyzed to existing motion estimation strategies in field‐programmable gate array devices. Experimental performance of the proposed Hyb‐PS‐ATSDSA‐ME‐HEVC method attains lower delay 33.97%, 32.97%, 62.97, and 26.97%, and lower area 34.867%, 45.97%, 27.97%, and 43.967% compared with the existing methods, such as FSA‐ME‐HEVC, TZSA‐ME‐HEVC, hyb TZSA‐IME‐HEVC, and IBMSA‐ME‐HEVC, respectively. [ABSTRACT FROM AUTHOR]

Fully implicit Runge–Kutta methods offer the possibility to use high order accurate time discretization to match space discretization accuracy, an issue of significant importance for many large scale problems of current interest, where we may have fine space resolution with many millions of spatial degrees of freedom and long time intervals. In this work, we consider strongly A‐stable implicit Runge–Kutta methods of arbitrary order of accuracy, based on Radau quadratures. For the arising large algebraic systems we introduce efficient preconditioners, that (1) use only real arithmetic, (2) demonstrate robustness with respect to problem and discretization parameters, and (3) allow for fully stage‐parallel solution. The preconditioners are based on the observation that the lower‐triangular part of the coefficient matrices in the Butcher tableau has larger in magnitude values, compared to the corresponding strictly upper‐triangular part. We analyze the spectrum of the corresponding preconditioned systems and illustrate their performance with numerical experiments. Even though the observation has been made some time ago, its impact on constructing stage‐parallel preconditioners has not yet been done and its systematic study constitutes the novelty of this article. [ABSTRACT FROM AUTHOR]

We consider here a cell‐centered finite difference approximation of the Richards equation in three dimensions, averaging for interface values the hydraulic conductivity K=K(p)$$ K=K(p) $$, a highly nonlinear function, by arithmetic, upstream and harmonic means. The nonlinearities in the equation can lead to changes in soil conductivity over several orders of magnitude and discretizations with respect to space variables often produce stiff systems of differential equations. A fully implicit time discretization is provided by backward Euler one‐step formula; the resulting nonlinear algebraic system is solved by an inexact Newton Armijo–Goldstein algorithm, requiring the solution of a sequence of linear systems involving Jacobian matrices. We prove some new results concerning the distribution of the Jacobians eigenvalues and the explicit expression of their entries. Moreover, we explore some connections between the saturation of the soil and the ill conditioning of the Jacobians. The information on eigenvalues justifies the effectiveness of some preconditioner approaches which are widely used in the solution of Richards equation. We also propose a new software framework to experiment with scalable and robust preconditioners suitable for efficient parallel simulations at very large scales. Performance results on a literature test case show that our framework is very promising in the advance toward realistic simulations at extreme scale. [ABSTRACT FROM AUTHOR]

We construct a space‐time parallel method for solving parabolic partial differential equations by coupling the parareal algorithm in time with overlapping domain decomposition in space. The goal is to obtain a discretization consisting of "local" problems that can be solved on parallel computers efficiently. However, this introduces significant sources of error that must be evaluated. Reformulating the original parareal algorithm as a variational method and implementing a finite element discretization in space enables an adjoint‐based a posteriori error analysis to be performed. Through an appropriate choice of adjoint problems and residuals the error analysis distinguishes between errors arising due to the temporal and spatial discretizations, as well as between the errors arising due to incomplete parareal iterations and incomplete iterations of the domain decomposition solver. We first develop an error analysis for the parareal method applied to parabolic partial differential equations, and then refine this analysis to the case where the associated spatial problems are solved using overlapping domain decomposition. These constitute our time parallel algorithm and space‐time parallel algorithm respectively. Numerical experiments demonstrate the accuracy of the estimator for both algorithms and the iterations between distinct components of the error. [ABSTRACT FROM AUTHOR]

Brain tumour diagnosis is significant for both physicians and patients, but the low contrast and the artefacts of MRI glioma images always affect the diagnostic accuracy. The existing mainstream image enhancement methods are insufficient in improving contrast and suppressing artefacts simultaneously. To enrich the field of glioma image enhancement, this research proposed a glioma image enhancement method based on histogram modification and total variational using stochastic parallel gradient descent (SPGD) algorithm. Firstly, this method modifies the cumulative distribution function on the image histogram and performs gamma correction on the image according to the modified histogram to obtain a contrast‐enhanced image. Then, the method suppresses the artefacts of glioma images by total variational and wavelet denoising algorithm. To get better enhancement images, the optimal parameters in the proposed method are searched by the SPGD algorithm. The statistical studies performed on 580 real glioma images demonstrate that the authors' approach can outperform the existing mainstream image enhancement methods. The results show that the proposed method increases the discrete entropy of the image by 8.9% and the contrast by 2.8% compared to original images. The enhanced images are produced by the proposed method with a natural appearance, appealing contrast, less degradation, and reasonable detail preservation. [ABSTRACT FROM AUTHOR]

We extend a two‐level task partitioning previously applied to the inversion of dense matrices via Gauss–Jordan elimination to the more challenging QR factorization as well as the initial orthogonal reduction to band form found in the singular value decomposition. Our new task‐parallel algorithms leverage the tasking mechanism currently available in OpenMP to exploit "nested" task parallelism, with a first outer level that operates on matrix panels and a second inner level that processes the matrix either by μ$$ \mu $$‐panels or by tiles, in order to expose a large number of independent tasks. We present a detailed performance analysis, including execution traces, which shows that the two‐level refinement into fine grain tasks allows for an improved load balancing and delivers high performance on current general‐purpose many‐core processors (CPUs) from Intel and AMD. [ABSTRACT FROM AUTHOR]

Optimal control musculoskeletal simulation is a valuable approach for studying fundamental and clinical aspects of human movement. However, the high computational demand has long presented a substantial challenge, creating a need to improve simulation performance. The OpenSim Moco software package permits musculoskeletal simulation problems to be solved in parallel on multicore processors using the CasADi optimal control library, potentially reducing the computational demand. However, the computational performance of this framework has not been thoroughly examined. Thus, we aimed to investigate the computational speed‐up obtained via multicore parallel computing relative to solving problems serially (i.e., using a single core) in optimal control simulations of human movement in OpenSim Moco. Simulations were solved using up to 18 cores with a variety of temporal mesh interval densities and using two different initial guess strategies. We examined a range of musculoskeletal models and movements that included two‐ and three‐dimensional models, tracking and predictive simulations, and walking and reaching tasks. The maximum overall parallel speed‐up was problem specific and ranged from 1.7 to 7.7 times faster than serial, with most of the speed‐up achieved by about 6 processor cores. Parallel speed‐up was generally greater on finer temporal meshes, while the initial guess strategy had minimal impact on speed‐up. Considerable speed‐up can be achieved for some optimal control simulation problems in OpenSim Moco by leveraging the multicore processors often available in modern computers. However, since improvements are problem specific, achieving optimal computational performance will require some degree of exploration by the end user. [ABSTRACT FROM AUTHOR]

Objective: This study aimed to develop and validate a scoring system for predicting the need for esophagogastroduodenoscopy (EGD) in clinical practice to enhance accuracy and reduce misapplications. Methods: From February 2021 to April 2022, outpatients scheduled for EGD at the Department of Gastroenterology in our hospital were recruited. Patients completed the system evaluation by providing clinical symptoms, relevant medical history, and endoscopic findings. Patients were randomly divided into the training and validation cohorts (at 2:1 ratio). The optimal algorithm was selected from five alternatives including a parallel test. Six physicians participated in a human‐computer comparative validation. Sensitivity and negative likelihood ratio (−LR) were used as the primary indicators. Results: Altogether 865 patients were enrolled, with 578 in the training cohort and 287 in the validation cohort. The scoring system comprised 21 variables, including age, 13 typical clinical symptoms, and seven medical history variables. The parallel test was selected as the final algorithm. Positive EGD findings were reported in 54.5% of the training cohort and 62.7% of the validation cohort. The scoring system demonstrated a sensitivity of 79.0% in the training cohort and 83.9% in the validation cohort, with −LR being 0.627 and 0.615, respectively. Compared to physicians, the scoring system exhibited higher sensitivity (84.0% vs 68.7%, P = 0.02) and a lower −LR (1.11 vs 2.41, P = 0.439). Conclusions: We developed a scoring system to predict the necessity of EGD using a parallel test algorithm, which was user‐friendly and effective, as evidenced by single‐center validation. [ABSTRACT FROM AUTHOR]

This document is a summary of a special issue of the journal Concurrency and Computation: Practice and Experience, which contains eight selected papers from the 14th International Conference on Parallel Processing and Applied Mathematics (PPAM 2022). The conference focused on topics related to high-performance computing (HPC) and included discussions on emerging technologies, algorithms, and software tools. The selected papers cover a range of subjects, including the convergence of iterative methods for solving nonlinear equations, testing interval arithmetic libraries, automatic performance tuning for symmetric eigenvalue problems, GPU computing, simulation of molecular magnetism, load balancing in distributed memory systems, predicting execution time of computational workloads, and resource selection for cloud-based applications. The papers provide valuable insights and advancements in the field of HPC. [Extracted from the article]

Summary: Sequence alignment is a critical computational problem in various domains, including genomics, proteomics, and natural language processing. The Needleman‐Wunsch (NW) algorithm is a classical dynamic programming approach for finding the optimal global alignment between two sequences. However, its quadratic time and space complexity make it impractical for aligning large‐scale sequences, which are increasingly common in modern applications. In this article, we propose a parallel variation of the NW algorithm that enables scalable global sequence alignment with customizable scoring schemes. Our approach re‐formulates the dependencies in the NW algorithm to enable parallel execution, thereby leveraging the computational power of modern parallel architectures, such as graphics processing unit (GPU). Furthermore, our algorithm supports arbitrary linear scoring schemes, which allows us to use domain‐specific knowledge to improve alignment accuracy. We establish the correctness of our algorithm and evaluate its performance using real DNA and user trajectory sequences on GPUs. Our parallel algorithm has shown impressive results in our experiments, with a peak performance of 27.99 GCUPS (giga cell updates per second) and a maximum speedup of 48.18 times compared to the traditional sequential implementation. Additionally, our algorithm demonstrates remarkable scalability, enabling the alignment of sequences of any length while ensuring balanced work distribution and optimal utilization of resources. Our primary objective is to harness the computational capabilities of a single GPU and fully utilize the processing power of multi‐core CPUs. [ABSTRACT FROM AUTHOR]

Due to the limited sample sizes and highly complicated performance functions, how to improve the reliability calculation accuracy and efficiency is an important issue for complex equipment working in harsh environments. This paper proposes an active learning reliability algorithm based on the double‐mutation slap swarm algorithm‐optimized (DMSSA) Kriging surrogate model, parallel infilling strategy and subset simulation (SS). In the method, the uniform design (UD) is employed to select the initial sampling points and their real responses of performance functions are estimated. The DMSSA integrates Cauchy and Gauss mutation to explore the optimal hyperparameter of Kriging model with high accuracy. The parallel infilling strategy combines the expected improvement (EI), minimizing prediction (MP) and mean squared error (MSE) criteria to find new sampling points, which are adaptively added into the database in each iteration to update the design of experiment (DoE). Ultimately, the SS method is employed to deal with the small failure probability problems. Five various examples are analyzed to verify the calculation accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The data‐independent acquisition mass spectrometry (DIA‐MS) has rapidly evolved as a powerful alternative for highly reproducible proteome profiling with a unique strength of generating permanent digital maps for retrospective analysis of biological systems. Recent advancements in data analysis software tools for the complex DIA‐MS/MS spectra coupled to fast MS scanning speed and high mass accuracy have greatly expanded the sensitivity and coverage of DIA‐based proteomics profiling. Here, we review the evolution of the DIA‐MS techniques, from earlier proof‐of‐principle of parallel fragmentation of all‐ions or ions in selected m/z range, the sequential window acquisition of all theoretical mass spectra (SWATH‐MS) to latest innovations, recent development in computation algorithms for data informatics, and auxiliary tools and advanced instrumentation to enhance the performance of DIA‐MS. We further summarize recent applications of DIA‐MS and experimentally‐derived as well as in silico spectra library resources for large‐scale profiling to facilitate biomarker discovery and drug development in human diseases with emphasis on the proteomic profiling coverage. Toward next‐generation DIA‐MS for clinical proteomics, we outline the challenges in processing multi‐dimensional DIA data set and large‐scale clinical proteomics, and continuing need in higher profiling coverage and sensitivity. [ABSTRACT FROM AUTHOR]

This paper proposes a multi‐objective hybrid evolutionary search algorithm to simultaneously optimize the number of workstations, the idle index and the quantity of the production equipment required for the parallel production line balancing problem including disassembly and assembly tasks. The proposed algorithm uses the crossover operation and the mutation operation to generate neighborhood individuals of the current evolutionary population. Based on the mixed population composed of the current evolutionary population and the newly generated neighborhood population, a novel population update method is developed. The individuals of the new generation population are composed of Pareto dominant individuals filtered from the mixed population and several individuals randomly selected from the dominated individuals. Then the local search strategy based on simulated annealing operation is applied to the new generation of population individuals to overcome the defect of premature convergence of the proposed algorithm. By solving test examples of different scales and comparing them with a variety of classical algorithms, the advantages in the aspects of the diversity, the convergence, and the distribution of the solution results of the proposed algorithm are proved. Finally, the established mathematical model and the developed algorithm are applied to the parallel production line designed for the bogie remanufacturing production line of a railway freight car maintenance company. The advantages of the parallel production line in improving the production efficiency and reducing the production cost are identified. [ABSTRACT FROM AUTHOR]

This paper presents a parallel algorithm for massive direct simulations of fluidized beds. It is based on an implicit–explicit (IMEX) technique for efficient and stable time integration of the incompressible Navier–Stokes equations in a domain that fits the boundaries of the particles at any time moment. The only modelling element in the algorithm is the model for particle–particle collisions, which is of the so‐called soft‐sphere type. The parallel performance of this technique is comparable to the performance of fully explicit methods. The numerical simulations of fluidized beds show very realistic effects that demonstrate the relevance of the simulation approach. [ABSTRACT FROM AUTHOR]

In view of the known problems of parameter sensitivity, local optimum, and slow convergence in the ant colony optimization (ACO), we aim to improve the performance of the ACO. To solve the traveling salesman problem (TSP) quickly with accurate results, we propose a fully parallel ACO (FP-ACO). Based on the max–min ant system (MMAS), we initiate a compensation mechanism for pheromone to constrain its value, guarantee the correctness of results and avoid a local optimum, and further enhance the convergence ability of ACO. Moreover, based on the compute unified device architecture (CUDA), the ACO is implemented as a kernel function on a graphics processing unit (GPU), which shortens the running time of massive iterations. Combined with the roulette wheel selection mechanism, FP-ACO has powerful search capabilities and is committed to obtaining better solutions. The experimental results show that, compared with the effective strategies ACO (ESACO) that runs on CPU, the speed-up ratio of the proposed algorithm reaches 35, and the running time is less than that of the max–min ant system-roulette wheel method-bitmask tabu (MMAS-RWM-BT) that runs on GPU. Furthermore, our algorithm outperforms the other two algorithms in the speed-up ratio and less runtime, proving that the proposed FP-ACO is more suitable for solving TSP. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show that Kahan's and Gill‐Møller compensated summation algorithms that allow to achieve high accuracy of summing long sequences of floating‐point numbers can be efficiently vectorized and parallelized using Intel AVX‐512 intrinsics together with OpenMP constructs in order to utilize SIMD extension of modern multicore processors. Numerical experiments show that the new implementations of the algorithms achieve much better accuracy than ordinary summation in both double and single precision and their performance is comparable with the performance of the ordinary summation algorithm optimized automatically. The vectorized Gill‐Møller algorithm is faster than the vectorized Kahan's algorithm. However, in case of single precision, the accuracy of the Gill‐Møller algorithm is worse than Kahan's but it can be fixed by the use of mixed‐precision. Then the accuracy of both compensated summation algorithms is the same and the Gill‐Møller algorithm is still faster than Kahan's. [ABSTRACT FROM AUTHOR]

Morphological operations are among the most popular classic image filters. The filter assumes the maximum or minimum value within a window and is often used for light object thickening and thinning operations, which are important components of various workflows, such as object recognition and stylization. Circular windows are preferred over rectangular windows for obtaining isotropic filter results. However, the existing efficient algorithms focus on rectangular or binary input images. Efficient morphological operations with circular windows for grayscale images remain challenging. In this study, we present a fast grayscale morphology heuristic computation algorithm that decomposes circular windows using the convex hull of circles. We significantly accelerate traditional methods based on Minkowski addition by introducing new decomposition rules specialized for circular windows. As our morphological operation using a convex hull can be computed independently for each pixel, the algorithm is efficient for modern multithreaded hardware. [ABSTRACT FROM AUTHOR]

Multiple‐Input‐Multiple‐Output (MIMO) radar has the characteristic of multiple antenna channels, bringing on a big data volume for signal processing. Therefore, the trade‐off between detection ability and computational efficiency is always considered. In this article, an optimisation system is proposed to enhance the real‐time performance of frequency division MIMO radar without compromising accuracy. For the scenario of low‐altitude small target detection, a signal processing acceleration method is proposed and a MIMO radar optimisation system based on graphics processing unit (GPU) architecture is built. The signal model of frequency division MIMO radar is first established, improving the classical signal processing flow efficiency from the perspective of reducing fast Fourier transform (FFT) times and windowing operation times. To achieve an advanced acceleration, the parallel architecture of ArrayFire‐library in GPU is then employed. Distinct minimum parallel units are extracted by analysing the principle of digital beamforming (DBF), pulse compression, moving target detection (MTD), and constant false‐alarm rate (CFAR) algorithms. And the corresponding parallel algorithms are designed to constitute a parallel acceleration system of frequency division MIMO. Simulation results indicate that the proposed method significantly improves the efficiency of MIMO system with a maximum acceleration ratio of 65 times, meeting the real‐time processing requirements. [ABSTRACT FROM AUTHOR]

The Lovász local lemma (LLL) is a keystone principle in probability theory, guaranteeing the existence of configurations which avoid a collection ℬ$$ \mathcal{B} $$ of "bad" events which are mostly independent and have low probability. A seminal algorithm of Moser and Tardos (J. ACM, 2010, 57, 11) (which we call the MT algorithm) gives nearly‐automatic randomized algorithms for most constructions based on the LLL. However, deterministic algorithms have lagged behind. We address three specific shortcomings of the prior deterministic algorithms. First, our algorithm applies to the LLL criterion of Shearer (Combinatorica, 1985, 5, 241–245); this is more powerful than alternate LLL criteria and also leads to cleaner and more legible bounds. Second, we provide parallel algorithms with much greater flexibility. Third, we provide a derandomized version of the MT‐distribution, that is, the distribution of the variables at the termination of the MT algorithm. We show applications to non‐repetitive vertex coloring, independent transversals, strong coloring, and other problems. [ABSTRACT FROM AUTHOR]

Performance and energy are the two most important objectives for optimization on heterogeneous high performance computing platforms. This work studies a mathematical problem motivated by the bi‐objective optimization of data‐parallel applications on such platforms for performance and energy. First, we formulate the problem and present an exact algorithm of polynomial complexity solving the problem where all the application profiles of objective type one are continuous and strictly increasing, and all the application profiles of objective type two are linear increasing. We then apply the algorithm to develop solutions for two related optimization problems of parallel applications on heterogeneous hybrid platforms, one for performance and dynamic energy and the other for performance and total energy. Our proposed solution methods are then employed to solve the two bi‐objective optimization problems for two data‐parallel applications, matrix multiplication and gene sequencing, on a hybrid platform employing five heterogeneous processors, namely, two different Intel multicore CPUs, an Nvidia K40c GPU, an Nvidia P100 PCIe GPU, and an Intel Xeon Phi. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a mesh‐based partitioning algorithm (MBPA) to solve bilinear matrix inequality (BMI) problems is proposed, where the main idea is to divide the solution space of a non‐convex BMI problem into smaller parts in the form of Simplexes through meshing the space. In each simplex, only the concave part of BMI constraints is approximated by piecewise affine matrix (PAM), which eventually leads to a convex sub‐problem. After that, the feasible solution can be easily obtained in each simplex through the linear matrix inequality (LMI) optimization. Although the proposed MBPA exploits PAM approximation, it relaxes several restrictive conditions used in other methods, so, it can be used as an effective approach for solving BMI problems. Various numerical examples on systems from COMPleib library to design static output feedback controller are provided to validate the proposed MBPA. Simulation results reveal the satisfactory performance of MBPA in several examined problems and provide acceptable performance compared to other existing BMI solution algorithms. Comparing the percentage of superiority of MBPA with some existing prominent BMI algorithms in several control problems including spectral abscissa optimization problems, H∞$$ {H}_{\infty } $$ and H2$$ {H}_2 $$ optimization problems for the closed‐loop systems of COMPleib show that the proposed algorithm is more successful than the previous ones. [ABSTRACT FROM AUTHOR]