Search

The present comment concerns the correct presentation of an algorithm proposed in the above paper for the glow-curve deconvolution in the case of continuous distribution of trapping states. Since most researchers would use directly the proposed algorithm as published, they should be notified of its correct formulation during the fitting of TL glow curves of materials with continuous trap distribution using this Equation. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in algorithms that take in input an arbitrary graph G , and that enumerate in output all the (inclusion-wise) maximal "subgraphs" of G which fulfil a given property Π. All over this paper, we study several different properties Π , and the notion of subgraph under consideration (induced or not) will vary from a result to another. More precisely, we present efficient algorithms to list all maximal split subgraphs, maximal induced cographs and maximal threshold graphs of a given input graph. All the algorithms presented here run in polynomial delay, and moreover for split graphs it only requires polynomial space. In order to develop an algorithm for maximal split (edge-)subgraphs, we establish a bijection between the maximal split subgraphs and the maximal stable sets of an auxiliary graph. For cographs and threshold graphs, the algorithms rely on a framework recently introduced by Conte & Uno (2019) called Proximity Search. Finally we consider the extension problem, which consists in deciding if there exists a maximal induced subgraph satisfying a property Π that contains a set of prescribed vertices and that avoids another set of vertices. We show that this problem is NP-complete for every non-trivial hereditary property Π. We extend the hardness result to some specific edge version of the extension problem. [ABSTRACT FROM AUTHOR]

This paper proposes a novel nature-inspired meta-heuristic algorithm, named Snow Geese Algorithm. It is inspired by the migratory behavior of snow geese and emulates the distinctive "Herringbone" and "Straight Line" shaped flight patterns observed during their migration. The algorithm is structured into three main phases for benchmark testing. In the first phase, the Snow Geese Algorithm's numerical results are compared with those of several classical meta-heuristic algorithms using the same test functions and original data from these algorithms. In the second phase, in order to minimize potential variations during the comparison, all algorithms undergo evaluation on a standardized testing platform. In the third phase, this paper applies the Snow Geese Algorithm to solve four widely recognized engineering optimization problems: the tubular column design, piston lever optimization design, reinforced concrete beam design and car side impact design. These real-world engineering problems serve as test cases to assess Snow Geese Algorithm problem-solving capabilities. The primary objective of the Snow Geese Algorithm is to provide an alternative perspective for tackling complex optimization problems. Please note that the complete source code for the Snow Geese Algorithm is publicly available at https://github.com/stones3421/SGA-project. • Snow Geese Algorithm: A novel meta-heuristic approach inspired by snow geese flight behavior, tackling optimization problems. • Two-stage Strategy: Mimics snow geese exploration and exploitation patterns, setting it apart from traditional methods. • Performance Evaluation: Multiple algorithms are assessed on different problems. • Algorithm Features: Experimental results validate the effectiveness of the Snow Geese Algorithm. • Practical Applications: Snow Geese Algorithm shows potential in engineering optimization, aiding accurate decision-making. [ABSTRACT FROM AUTHOR]

In this paper, based on the Lagrange multiplier method, we construct a maximum principle preserving scheme for the time-fractional Allen-Cahn equation of 2- α (0 < α < 1) order. The correction energy of this scheme is increased by a term compared to the original energy, which is O (τ α). We prove that our scheme is unconditionally stable related to the corrected energy and verify the convergence, maximum principle, and energy conservation properties of the algorithm through numerical examples. We also find that the larger the α , the faster the evolution of the time-fractional Allen-Cahn equation. [ABSTRACT FROM AUTHOR]

Diffeomorphic registration is a widely used technique for finding a smooth and invertible transformation between two coordinate systems, which are measured using template and reference images. The point-wise volume-preserving constraint det ⁡ (∇ φ (x)) = 1 is effective in some cases, but may be too restrictive in others, especially when local deformations are relatively large. This can result in poor matching when enforcing large local deformations. In this paper, we propose a new bi-variant diffeomorphic image registration model that introduces a soft constraint on the Jacobian equation det ⁡ (∇ φ (x)) = f (x) > 0. This allows local deformations to shrink and grow within a flexible range 0 < κ m < det ⁡ (∇ φ (x)) < κ M. The Jacobian determinant of transformation is explicitly controlled by optimizing the relaxation function f (x). To prevent deformation folding and improve the smoothness of the transformation, a positive constraint is imposed on the optimization of the relaxation function f (x) , and a regularizer is used to ensure the smoothness of f (x). Furthermore, the positivity constraint ensures that f (x) is as close to one as possible, which helps to achieve a volume-preserving transformation on average. We also analyze the existence of the minimizer for the variational model and propose a penalty-splitting algorithm with a multilevel strategy to solve this model. Numerical experiments demonstrate the convergence of the proposed algorithm and show that the positivity constraint can effectively control the range of relative volume without compromising the accuracy of the registration. Moreover, the proposed model generates diffeomorphic maps for large local deformations and outperforms several existing registration models in terms of performance. • A novel bi-variant diffeomorphic image registration model with relaxed Jacobian determinant constraints is proposed. • The existence of the minimizer for the variational model is proved. • A penalty splitting algorithm with a multilevel strategy is designed to solve the new model. • Numerical experiments show that the proposed algorithm is convergent and the new model has good performance. [ABSTRACT FROM AUTHOR]

In this paper, we devise a stochastic extragradient-like algorithm incorporated with inertial terms, which requires a single projection onto our feasible set and employs a stochastic approximation version of an Armijo-type line search scheme along a feasible direction, for solving pseudomonotone stochastic variational inequalities. In the algorithm, two different stepsize strategies are employed to update steplength sequences without using the prior knowledge of the Lipschitz constant of involved operators. In the process of the stochastic approximation, we iteratively reduce the variance of stochastic errors. The almost sure convergence, the complexity analysis, and rates are provided in a dimensional space under reasonable conditions. Finally, some numerical experiments with graphical illustrations are reported to demonstrate the applicability and the efficiency of our algorithm in comparison with some projection type methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper we provide a tetrahedra-free algorithm to compute low-cardinality quadrature rules with a given degree of polynomial exactness, positive weights and interior nodes on a polyhedral element with arbitrary shape. The key tools are the notion of Tchakaloff discretization set and the solution of moment-matching equations by Lawson-Hanson iterations for NonNegative Least-Squares. Several numerical tests are presented. The method is implemented in Matlab as open-source software. [ABSTRACT FROM AUTHOR]

A k -class domination coloring (k -cd-coloring) is a partition of the vertex set of a graph G into k independent sets V 1 , ... , V k , where each V i is dominated by some vertex u i of G. The least integer k such that G admits a k -cd-coloring is called the cd-chromatic number, χ c d (G) , of G. A subset S of the vertex set of a graph G is called a subclique in G if d G (x , y) ≠ 2 for every x , y ∈ S. The cardinality of a maximum subclique in G is called the subclique number, ω s (G) , of G. In this paper, we present algorithms to compute an optimal cd-coloring and a maximum subclique of (i) trees with time complexity O (n) and (ii) co-bipartite graphs with time complexity O (n 2. 5). This improves O (n 3) algorithms by Shalu et al. (2017, 2020). In addition, we prove tight upper bounds for the subclique number of the class of (i) P 5 -free graphs and (ii) double-split graphs. [ABSTRACT FROM AUTHOR]

Earth observation satellite (EOS) scheduling is critical for improving the performance of Earth observation system. Most of the existing studies on satellite observation scheduling problems focus on static tasks and real-time dynamic tasks also known as emergency tasks while few attempts have been made for common dynamic tasks yet. The common dynamic tasks are characterized by uncertain arrival times and delayable observations while the emergency tasks require immediate observations. The number of common dynamic tasks is rapidly increasing with the expansion of satellite observation applications, which poses great challenges to EOS observation scheduling. To address this issue, this paper investigates the satellite observation scheduling problem with common dynamic tasks. Firstly, a centralized onboard dynamic scheduling framework based on a periodic-triggered rolling horizontal optimization (RHO) strategy is proposed and a novel two-stage mathematical model is established for the periodic rescheduling problem. Secondly, we propose a low-complexity onboard periodic rescheduling algorithm (OPR), which consists of a greedy-based task allocation algorithm, a pointer network (Ptr-network) based task scheduling algorithm and an iterative local search algorithm. In the greedy-based task allocation algorithm, we define a Task-EOS Fitness Indicator (TEFI) and each task is greedily allocated to the EOS with maximum TEFI. In the Ptr-network based task scheduling algorithm, the allocated task sets of all EOSs are fed into the Ptr-network in parallel to generate the observation scheduling result. Afterward, an iterative local search algorithm is proposed to further improve the quality of the observation scheduling result. Finally, extensive experiments are conducted to demonstrate the superiority of the OPR algorithm for the satellite observation scheduling problem with common dynamic tasks. [ABSTRACT FROM AUTHOR]

• OCR-detected characters or words in an image require line segmentation to reunite into word or sentence. • Projection based line segmentation cannot be applied to Chinese historical texts. • Columns in Chinese historical texts exhibit a sub-divided column format. • Adjacent character detection (ACD) algorithm can deal with the unique column structure. • Performance of ACD algorithm as a post-processing of OCR is discussed. In recent times, the advent of AI-based optical character recognition (OCR) has garnered significant attention in the realm of digital text conversion. However, it is imperative to note that OCR solely identifies individual characters or words, and lacks the ability to reunite them into cohesive units such as words or sentences. Consequently, the manual sorting of them to establish the appropriate reading order has emerged as a bottleneck. In this paper, we present an algorithm termed adjacent character detection (ACD), designed to serve as a post-processing of OCR, facilitating automatic digital text conversion. The algorithm involves line segmentation through a quad-ACD scan (up-down-down-up), allowing it to consecutively discern characters within a column based on their adjacency relations. Conventional projection profile analyses have struggled to effectively partition the distinct internal structure of Chinese historical text, where two annotation columns often subdivide from a single body column. In contrast, our ACD algorithm employs an approach, reuniting adjacent characters rather than fragmenting the entire text into isolated entities. Additionally, ACD algorithm enabled body/annotation classification for OCR-detected characters based on the pattern analysis of its quad scan. This cumulative information empowers the conversion of digital text in a desired reading order. To assess the efficacy of the proposed algorithm, a set of ground-truth OCR result was subjected to rigorous testing, culminating in a reading order accuracy of 98.6%. Noteworthy robustness was also demonstrated in the face of misaligned columns, experimentally induced by applying tilt, warp, and wavy noises to the original digital images. Lastly, the algorithm was integrated with two pre-developed OCR models, resulting in a reading order accuracy of 97.7%. [Display omitted] [ABSTRACT FROM AUTHOR]

• Dynamics of multi-layer membrane structure with elastic spacers is studied. • An optimization criterion to eliminate the crossing modes is proposed. • The optimal spacer positions are calculated by Particle Swarm Optimizer algorithm. In recent years, there has been a growing interest in the dynamics of space membrane structures. However, existing research primarily focuses on single-layer membrane structures, leaving a significant research gap in the study of multi-layer structures with elastic spacers. To address this gap, this paper studies the dynamics and interlayer spacing accuracy of multi-layer membrane structures with elastic spacers. Specifically, the research focuses on the placement optimization of elastic spacers. A novel optimization criterion for the elastic spacers has been proposed, and the Particle Swarm Optimizer (PSO) algorithm has been utilized to calculate the optimal spacers positions. Results show that optimally placed elastic spacers can eliminate the crossing modes and improve the interlayer spacing accuracy during vibration. [ABSTRACT FROM AUTHOR]

Two key challenges in optimal control include efficiently solving high-dimensional problems and handling optimal control problems with state-dependent running costs. In this paper, we consider a class of optimal control problems whose running costs consist of a quadratic on the control variable and a convex, non-negative, piecewise affine function on the state variable. We provide the analytical solution for this class of optimal control problems as well as a Hopf-type representation formula for the corresponding Hamilton-Jacobi partial differential equations. Finally, we propose efficient numerical algorithms based on our Hopf-type representation formula, convex optimization algorithms, and min-plus techniques. We present several high-dimensional numerical examples, which demonstrate that our algorithms overcome the curse of dimensionality. We also describe a field-programmable gate array (FPGA) implementation of our numerical solver whose latency scales linearly in the spatial dimension and that achieves approximately a 40 times speedup compared to a parallelized central processing unit (CPU) implementation. Thus, our numerical results demonstrate the promising performance boosts that FPGAs are able to achieve over CPUs. As such, our proposed methods have the potential to serve as a building block for solving more complicated high-dimensional optimal control problems in real-time. [ABSTRACT FROM AUTHOR]

This paper analyzes a parareal approach based on fractional-step methods for the nonstationary Navier-Stokes equations. As an efficient parallel computing framework, the coarse propagator often determines the performance of the parareal algorithm. We present a parareal algorithm using the fractional-step method, a very efficient time discrete scheme for the Naiver-Stokes equations, as the coarse propagator for the Navier-Stokes equations. Then we give the specific stability and convergence analysis of this specific parareal algorithm. Finally, numerical experiments are done to show efficiency and illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, elliptic control problems with the integral constraint on the gradient of the state and the box constraint on the control are considered. The optimality conditions for the problem are proved. To numerically solve the problem, a finite element duality-based inexact majorized accelerated block coordinate descent (FE-dABCD) algorithm is proposed. Specifically, both the state and the control are discretized by piecewise linear functions. An inexact majorized ABCD algorithm is employed to solve the discretized problem via its dual, which is a multi-block unconstrained convex optimization problem, but the primal variables are also generated in each iteration. Thanks to the inexactness of the FE-dABCD algorithm, the subproblems at each iteration are allowed to be solved inexactly. For the smooth subproblem, we use the preconditioned generalized minimal residual (GMRES) method to solve it. For the two nonsmooth subproblems, one of them has a closed form solution through introducing an appropriate proximal term, and another one is solved by the line search Newton's method. Based on these efficient strategies, we prove that our proposed FE-dABCD algorithm enjoys O (1 k 2 ) iteration complexity. Moreover, to make the algorithm more efficient and further reduce its computation cost, based on the mesh-independence of ABCD method, we propose an FE-dABCD algorithm with a warm-start strategy (wFE-dABCD). Some numerical experiments are done and the numerical results show the efficiency of the FE-dABCD algorithm and wFE-dABCD algorithm. [ABSTRACT FROM AUTHOR]

Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory dynamics, like spiral waves, relaxation oscillations and spatio-temporal Turing instability. Inspired by the classical "divide and conquer" approach, we propose a piecewise version of DMD (pDMD) to overcome this problem. The main idea is to split the original dataset in N submatrices and then apply the exact (randomized) DMD method in each subset of the obtained partition. We describe the pDMD algorithm in detail and we introduce some error indicators to evaluate its performance when N is increased. Numerical experiments show that very accurate reconstructions are obtained by pDMD for datasets arising from time snapshots of certain reaction-diffusion PDE systems, like the FitzHugh-Nagumo model, a λ - ω system and the DIB morpho-chemical system for battery modeling. Finally, a discussion about the overall computational load and the future prediction features of the new algorithm is also provided. [ABSTRACT FROM AUTHOR]

This paper investigates the convergence behavior of the Dirichlet-Neumann and Neumann-Neumann waveform relaxation algorithms for time-fractional sub-diffusion and diffusion-wave equations. The algorithms are applied to regular domains in 1D and 2D for multiple subdomains, and the impact of different constant values of the generalized diffusion coefficient on the algorithms' convergence is analyzed. The convergence rate of the algorithms is analyzed as the fractional order of the time derivative changes. The paper demonstrates that the algorithms exhibit slow superlinear convergence when the fractional order is close to zero, almost finite step convergence (exact finite step convergence for wave case) when the order approaches two, and faster superlinear convergence as the fractional order increases in between. The transitional nature of the algorithms' behavior is effectively captured through estimates with changes in the fractional order, and the results are verified by numerical experiments. [ABSTRACT FROM AUTHOR]

• A novel combined interval prediction algorithm is proposed in this paper. • Hybrid feature selection strategy is designed in the proposed system. • Multi-objective optimization mechanism reflects strong search capabilities. • Four interval prediction models cover the inherent modes of sequence. Traditional point prediction approaches can not reflect the uncertainty, which brings greater risks to decision-makers. To fill this gap, this paper extends a feature selection strategy that relies solely on correlation and redundant feature judgment, proposes a novel combined interval prediction algorithm, 3-Mcip (Combined Interval Prediction Based on Maximize Relevancy, Minimize Redundancy and Maximize Synergy) system, and solves the tradeoff between prediction accuracy and interval width. This system first designs a hybrid feature selection strategy to optimally select candidate variables and reduce model input redundancy. Secondly, the structure of the four ANN models is improved to accommodate the results of feature selection, and an optimization mechanism is introduced to search for the Pareto optimal solution set. In order to measure the comprehensive performance of the 3-Mcip system, hourly power load data and related candidate variables from Pittsburgh and Washington, D.C are considered. The numerical results show that the 3-Mcip system has coverage rates of 53.3333, 90.1667, and 99.4479 for Site 1 at different levels of interval width coefficients, which not only achieves perfect prediction of power load but also analyzes uncertainty. It is also helpful for power system managers to better capture the fluctuation range of future load and improve the flexibility of smart grid dispatching. [ABSTRACT FROM AUTHOR]

In this paper, the multi-parameter time fractional radially symmetric anomalous diffusion model used in porous media with initial singularity is considered. Both the direct numerical solution problem and the multi-parameter identification inverse problem are studied. Given the singularity in the initial time, a stable numerical scheme on nonuniform grid mesh is derived by using the L 2 − 1 σ method. To conduct the multi-parameter inversion problem, a novel hybrid Black Widow Optimization and Cuckoo Search (BWOCS) algorithm is proposed to combine the advantages of both the BWO algorithm and the CS algorithm, in order to improve the convergence speed and to achieve high-accuracy optimal results. Numerical examples are given to verify the efficiency and accuracy of the proposed numerical scheme and parameter inversion algorithm. Results show that the nonuniform grid L 2 − 1 σ scheme is efficient to deal with the time fractional radially symmetric anomalous diffusion problem with initial singularity, and the hybrid BWOCS algorithm has high precision and well convergence speed, compared with both the BWO and CS algorithms, which can be extended to other fractional inverse problems. [ABSTRACT FROM AUTHOR]

We address the problem of Multi-Source Domain Adaptation (MSDA), which trains a neural network using multiple labeled source datasets and an unlabeled target dataset, and expects the trained network to well classify the unlabeled target data. The main challenge in this problem is that the datasets are generated by relevant but different joint distributions. In this paper, we propose to address this challenge by estimating and minimizing the mutual information in the network latent feature space, which leads to the alignment of the source joint distributions and target joint distribution simultaneously. Here, the estimation of the mutual information is formulated into a convex optimization problem, such that the global optimal solution can be easily found. We conduct experiments on several public datasets, and show that our algorithm statistically outperforms its competitors. Video and code are available at https://github.com/sentaochen/Mutual-Information-Estimation-and-Minimization. [ABSTRACT FROM AUTHOR]

Heat exchanger network (HEN) synthesis is a vibrant research field in process system engineering, with substantial contributions to energy conservation and emissions reduction initiatives. The optimal design of a heat exchanger network is not an easy task due to the abundance of local optima in the solution space caused by the non-linear, non-convex, and discontinuous nature of the problem. Generally, several heuristic algorithms employ a greedy evolutionary mechanism, optimize through greedily accepting the decrease in the objective function, and converge to obtain the optimal solution. The Random Walk algorithm has a simple evolutionary mechanism, is prone to mutation, and exhibits high flexibility. However, the algorithm's inherent persistent greediness in searching restrict the scope of the search. Thus, this paper proposes an anti-greedy concept based on the Random Walk method to serve as the basis of a new synthesis approach called the Anti-greedy Random Walk algorithm. Two strategies are proposed in the algorithm, which broaden the solution domain by slowing down rapid unit reduction and accepting imperfect solutions, respectively. One strategy is to thoroughly search for the integer and continuous variables of the HEN problem by covering a much larger search space. Another is to escape the local extrema and move forward to discover more possibilities. Quantitative data demonstrates the algorithm's ability to avoid the local extrema and enhance the search effectiveness. Three different scales of classical cases are used in this work and the obtained results are superior to the published ones. [Display omitted] • An improved Random Walk algorithm is presented for heat exchanger network synthesis. • Two anti-greedy strategies are proposed from an objective and structural perspective. • Both integer and continuous variables are explored by covering a larger search space. • Three benchmark cases were solved with better results than previously literature. [ABSTRACT FROM AUTHOR]

The concept of jump system, introduced by Bouchet and Cunningham (1995), is a set of integer points satisfying a certain exchange property. We consider the minimization of a separable convex function on a jump system. It is known that the problem can be solved by a greedy algorithm. In this paper, we are interested in whether the greedy algorithm has the geodesic property, which means that the trajectory of the solutions generated by the algorithm is a geodesic from the initial solution to a nearest optimal solution. We show that a special implementation of the greedy algorithm enjoys the geodesic property, while the original algorithm does not. As a corollary to this, we present a new greedy algorithm for linear optimization on a delta-matroid and show that the algorithm has the geodesic property. [ABSTRACT FROM AUTHOR]

Neural network ensembling is a common and robust way to increase model efficiency. In this paper, we propose a new neural network ensemble algorithm based on Audibert's empirical star algorithm. We provide optimal theoretical minimax bound on the excess squared risk. Additionally, we empirically study this algorithm on regression and classification tasks and compare it to most popular ensembling methods. [ABSTRACT FROM AUTHOR]

In this paper, we present a variable sample-size operator extrapolation algorithm for solving a class of stochastic mixed variational inequalities. One distinctive feature of our algorithm is that it updates a single search sequence by solving a prox-mapping subproblem and computing an evaluation of the expected mapping at each iteration and hence it may significantly reduce computation load. In particular, the iteration sequence generated by our algorithm always belongs to the feasible region. We show that, under some moderate conditions, the proposed algorithm can achieve O (1 / T) ergodic convergence rate in terms of the expected restricted gap function, where T denotes the number of iterations. We derive some results related to the convergence rate of the Bregman distance between iterates and solutions, the iteration complexity, and the oracle complexity for the proposed algorithm when the sample size increases at a geometric rate. We also investigate the sublinear convergence rate in terms of the residual function under the generalized monotonicity condition. Numerical experiments on stochastic network game, stochastic sparse traffic assignment problems and sparse classification problem indicate that the proposed algorithm is promising compared with some existing algorithms. [ABSTRACT FROM AUTHOR]

In this paper, several local and parallel finite element algorithms are proposed and analyzed for the 2D/3D stationary inductionless incompressible magnetohydrodynamic (MHD) equations. The core concept is to guarantee the charge-conservation property by choosing mixed finite element spaces in H 0 (div , Ω) × L 0 2 (Ω) to approximate (J , ϕ) , meantime combining the idea of domain decomposition method to realize parallel operation. The characteristic of the proposed algorithms is that the computational complexity is greatly reduced while ensuring the accuracy of the numerical simulation. With the local a prior estimate as the technical means of theoretical analysis, we give the error estimates of the algorithms. Finally, several numerical experiments are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Actor–critic methods are leading in many challenging continuous control tasks. Advantage estimators, the most common critics in the actor–critic framework, combine state values from bootstrapping value functions and sample returns. Different combinations balance the bias introduced by state values and the variance returned by samples to reduce estimation errors. The bias and variance constantly fluctuate throughout training, leading to different optimal combinations. However, existing advantage estimators usually use fixed combinations that fail to account for the trade-off between minimizing bias and variance to find the optimal estimate. Our previous work on adaptive advantage estimation (AAE) analyzed the sources of bias and variance and offered two indicators. This paper further explores the relationship between the indicators and their optimal combination through typical numerical experiments. These analyses develop a general form of adaptive combinations of state values and sample returns to achieve low estimation errors. Empirical results on simulated robotic locomotion tasks show that our proposed estimators achieve similar or superior performance compared to previous generalized advantage estimators (GAE). [ABSTRACT FROM AUTHOR]

• Bi-level hierarchical distribution of resources is reformulated. • Hooke-Jeeves and Scatter Search algorithms are implemented. • A multi-objective perspective is introduced to tackle the problem. • A multi-objective scatter search algorithm delivers best results for both objectives. • Tailored-made instances were crafted for the problem. The decision regarding the hierarchical distribution of resources is crucial for many organizations that want to allocate such resources efficiently. At the upper level of the hierarchy, a decision-maker may have an objective and a set of feasible solutions partially determined by the lower level. Nevertheless, the upper level can influence but not control the decision-maker at the lower level. Moreover, the objectives of the upper and lower levels are conflicting. Hence, the hierarchical distribution of resources can be formulated as a bi-level programming model. This paper reformulates the hierarchical allocation of resources. The Hooke-Jeeves (HJ) algorithm and the hybrid scatter search–Nelder-Mead (SSNM) method are proposed to solve the newly formulated problem. The problem is also analyzed from a multi-objective perspective to equally prioritize the upper and lower levels while subjecting each to an interdependent set of constraints; a multi-objective scatter search algorithm (MSSA) was developed for that purpose. Tailor-made instances were also designed for the implementation of the developed algorithms. The findings demonstrated that the HJ algorithm provides the best solution according to the upper-level objective function. However, it does not guarantee the best result for the lower level. In comparison, MSSA has a set of best possible solutions for both objectives. The hybrid SSNM method could not match the results provided by the former methods. [ABSTRACT FROM AUTHOR]

Exploring special multi-scroll chaotic systems is meaningful work. This paper studies an expanded multi-scroll chaotic system consisting of eight terms with one nonlinearity. It is generated by modifying the nonlinear term of the newly constructed chaotic system by a polynomial function. The unique mathematical model makes the unstable index-2 equilibria increase in four dimensions, which contributes to the number of scrolls expanding in each phase plane unidirectionally. Dynamic analysis finds that the system can yield complex nested multi-scroll attractors and has single-parameter-based synchronization control of amplitude and offset boosting behavior. Moreover, circuit implementation verifies the physical existence of the proposed system. Also, an image encryption algorithm for remote sensing images is established. Permutation and diffusion operations are performed using new pixel coordinates derived from the data of the chaotic matrix, which comes from the same position as the pixel matrix. Relevant tests suggest that the algorithm is secure and able to resist undesirable interference. • Simple multiscroll chaotic system with various signal control features is proposed. • Complex dynamics, circuit implementation of the proposed system is studied. • New chaos-based image encryption algorithm with high security is designed. [ABSTRACT FROM AUTHOR]

This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method and post-processing technique. The most valuable highlights of the present algorithm are that (1) a global continuous approximate solution is generated via the partition of unity method; (2) by adding an extra coarse grid correction step, the smoothness of the approximate solution is improved; (3) it has a good parallel performance since there requires little communication in solving a series of residual problems in the subdomain of interest. We theoretically derive the L 2 -error estimates both for the approximate velocity and pressure and H 1 -error estimate for the velocity under some necessary conditions. Meanwhile, we numerically perform various test examples to validate the theoretically predicted convergence rate and illustrate the high efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Based on the convex combination technique, we propose a projection-based hybrid conjugate gradient algorithm for solving nonlinear equations with convex constraints in this paper. The conjugate parameter of the proposed algorithm is a convex combination of the modified Polak-Ribière-Polyak and Dai-Yuan type conjugate parameters, and the search direction has the sufficient descent property without the use of a line search strategy. The proposed hybrid algorithm's global convergence is established under appropriate assumptions. The numerical experiments demonstrate that the proposed algorithm is more efficient and competitive than existing methods under some benchmark test problems. Furthermore, it is also extended to solve the sparse signal and impulse noise image restoration problem that arises in compressive sensing. [ABSTRACT FROM AUTHOR]

In this paper, we propose a proximal fully parallel splitting method with a relaxation factor for solving separable convex minimization model with linear constraints, where the objective function is the sum of m individual functions without coupled variables. With a full Jacobian decomposition, we decompose the subproblem associated with the augmented Lagrangian method into m smaller subproblems and then add a quadratic proximal term to each decomposed subproblem, which makes the resulting ones easier to solve for many applications. In order to accelerate the numerical performance, we attach a positive relaxation factor to update the Lagrange multiplier, which also allows more flexibility in the design of algorithms. Moreover, we refine the step size of the underrelaxation step, which enlarges several existing ones in the literature. We prove that the proposed method is globally convergent, and show the worst-case O (1 / k) convergence rate in a nonergodic sense. Finally, the efficiency and robustness of the proposed method are also demonstrated by solving the ℓ 1 norm problem, the ℓ 1 -regularized least squares problem, the exchange problem and the total variation image restoration problem. [ABSTRACT FROM AUTHOR]

Generally, the central air conditioners are centralized in a refrigeration room in public buildings. The proportion of energy consumption of the refrigeration room is about 40% of entire building. This paper aims to propose an energy plus and self-designed simulator to reduce the energy consumption of a large electronic factory in Zhuhai City, Guangdong province, China. In this paper, the real data collected from the electronic factory in February and the group control method used in the refrigeration room based on the kernel ridge regression algorithm. The correctness of the kernel ridge regression algorithm was verified with the experimental results. Compared to traditional PID control method, the kernel ridge regression algorithm could dynamically adjust those parameters, such as temperature and frequency to match the high efficiency zone of each device. The overall average COP of the system is increased from 4.17 to 7.04. The electricity of the refrigeration room could save 64 MWh with the cooling load forecast error being below 7% in February. The power consumption is expected to reduce by 8.2% and 562.3 MWh in 2022. [ABSTRACT FROM AUTHOR]

As is known, the problem of finding a three-dimensional stable matching with cyclic preferences (3DSM-CYC) always has a solution, if the number of objects of each type (i.e., the problem size n) does not exceed 5. According to the conjecture proposed by Eriksson et al. (2006), this is true for any n. However, Lam and Plaxton (2019) have proposed an algorithm for constructing preference lists in 3DSM-CYC which has allowed them to disprove the mentioned conjecture. The size of the initially constructed counterexample equals 90; however, according to the results obtained by us recently for the problem with incomplete preference lists, one can use the same construction for getting a counterexample of size 45. The main contribution of this paper consists of reducing the size of the counterexample to n = 20. We summarize results of the application of the technique developed by us for constructing counterexamples for 3DSM-CYC. In the final section of the paper we discuss a new variant of 3DSM, whose solution always exists and can be found within the same time as that required for solving 2DSM. [ABSTRACT FROM AUTHOR]

Topology optimization has seen increased interest with the rise of additive manufacturing (AM) as a fabrication method, because of its ability to exploit the geometric complexity that AM offers. However, AM still imposes some geometric restrictions on the design, most notably on minimum feature size, overhang angles, and enclosed voids. Enclosed voids are problematic because for many AM methods it is impossible to remove supports, unmelted powder or uncured liquid from them. This paper introduces a filter based on a cumulative sum flood fill algorithm to alleviate this issue in a flexible manner. This filter produces a density field where every enclosed void element is rendered solid. It successfully eliminates enclosed voids in both 2D and 3D problems, with low computational cost due to its geometric nature. In addition we demonstrate direct control over the location, amount, and size of powder removal features by varying boundary conditions for the filter, running additional flood fills, and adding morphology operators, respectively. • The cumulative sum flood fill approach is introduced in topology optimization. • The approach works as a filter and successfully eliminates enclosed voids. • Direct control can be achieved over the amount, location, and size of access channels. • Due to its geometric nature it adds little computational effort. [ABSTRACT FROM AUTHOR]

• Variational Quantum Circuits (VQCs) play a key role in several applications. • VQCs are parameterized quantum circuits trained by using classical optimizers. • The paper proposes to apply memetic algorithms to train VQCs. • The designed memetic algorithm outperforms the state-of-the-art classical optimizers. Among the ready-to-implement quantum algorithms, Variational Quantum Circuits (VQCs) play a key role in several applications, including machine learning. Their strength lies in the use of a parameterized quantum circuit that is trained by means of an optimization algorithm run on a classical computer. In such a scenario, there is a strong need to design appropriate classical optimization schemes that deal efficiently with VQCs and pave the way for quantum advantage in machine learning. Among possible optimization schemes, those based on evolutionary computation are finding increasing interest, given the unconventional and nonanalytical nature of the problem to be solved. This paper proposes to apply memetic algorithms to train VQCs used as quantum classifiers and shows the benefits of exploiting this evolutionary optimization technique through a comparative experimental session. [ABSTRACT FROM AUTHOR]

Given a graph G = (V , E) , an L (2 , 1) -labeling of the graph is an assignment ℓ from the vertex set to the set of nonnegative integers such that for any pair of vertices (u , v) , | ℓ (u) − ℓ (v) | ≥ 2 if u and v are adjacent, and ℓ (u) ≠ ℓ (v) if u and v are at distance 2. The L (2 , 1) -labeling problem is to minimize the range of ℓ (i.e., max u ∈ V (ℓ (u)) − min u ∈ V (ℓ (u)) + 1). Although the problem is generally hard to approximate within any constant factor, it was known to be approximable within factor 10.67 for unit disk graphs. This paper designs a new way of partitioning the plane into squares for periodic labeling, based on which we present an 8-approximation polynomial-time algorithm for L (2 , 1) -labeling of unit disk graphs. • An 8-approximation algorithm of L(2,1)-labeling for unit disk graphs with geometric representations is presented. • The previously known bound is 10.67. • The presented algorithm gives a simple periodic labeling based on a new way of partitioning the plane into squares. [ABSTRACT FROM AUTHOR]

In this paper, a novel spectral method is presented and studied for the fourth order problem with mixed boundary in a cylindrical domain. The basic idea of our approach is to reduce the original problem into a series of decoupled two-dimensional fourth-order problems first, by using the cylindrical coordinate transformation and Fourier expansion, and then adopt the standard spectral method to solve the decoupled problems. A new essential pole condition is proposed to overcome the difficulty caused by the introduction of singularity and variable coefficients in cylindrical coordinate transformation. Existence and uniqueness of the weak solution and the discrete numerical solution are proved, and error estimates of the spectral method are derived. Furthermore, the efficient implementation of our algorithm is discussed, where a set of effective basis functions are constructed to ensure the sparsity of the mass matrix and stiffness matrix. Numerical examples are presented to validate the theoretical findings and the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we present a two-grid lumped mass finite element algorithm for 2D Allen-Cahn equations, where Crank-Nicolson scheme and piecewise linear element are utilized for temporal and spatial discretization, respectively. Both the maximum-norm boundedness and H 1 -norm error estimates of the proposed two-grid scheme are discussed. Finally, a numerical example is given to verify the theoretical results. By comparing with the finite element scheme and the two-grid finite element scheme, we found that our scheme has a great advantage in calculation time. [ABSTRACT FROM AUTHOR]