Continuous Problem Research Articles

Greater cane rat algorithm (GCRA): A nature-inspired metaheuristic for optimization problems

This paper introduces a new metaheuristic technique known as the Greater Cane Rat Algorithm (GCRA) for addressing optimization problems. The optimization process of GCRA is inspired by the intelligent foraging behaviors of greater cane rats during and off mating season. Being highly nocturnal, they are intelligible enough to leave trails as they forage through reeds and grass. Such trails would subsequently lead to food and water sources and shelter. The exploration phase is achieved when they leave the different shelters scattered around their territory to forage and leave trails. It is presumed that the alpha male maintains knowledge about these routes, and as a result, other rats modify their location according to this information. Also, the males are aware of the breeding season and separate themselves from the group. The assumption is that once the group is separated during this season, the foraging activities are concentrated within areas of abundant food sources, which aids the exploitation. Hence, the smart foraging paths and behaviors during the mating season are mathematically represented to realize the design of the GCR algorithm and carry out the optimization tasks. The performance of GCRA is tested using twenty-two classical benchmark functions, ten CEC 2020 complex functions, and the CEC 2011 real-world continuous benchmark problems. To further test the performance of the proposed algorithm, six classic problems in the engineering domain were used. Furthermore, a thorough analysis of computational and convergence results is presented to shed light on the efficacy and stability levels of GCRA. The statistical significance of the results is compared with ten state-of-the-art algorithms using Friedman's and Wilcoxon's signed rank tests. These findings show that GCRA produced optimal or nearly optimal solutions and evaded the trap of local minima, distinguishing it from the rival optimization algorithms employed to tackle similar problems. The GCRA optimizer source code is publicly available at: https://www.mathworks.com/matlabcentral/fileexchange/165241-greater-cane-rat-algorithm-gcra.

Optimal Approximation of Unique Continuation

AbstractWe consider numerical approximations of ill-posed elliptic problems with conditional stability. The notion of optimal error estimates is defined including both convergence with respect to discretisation and perturbations in data. The rate of convergence is determined by the conditional stability of the underlying continuous problem and the polynomial order of the approximation space. A proof is given that no approximation can converge at a better rate than that given by the definition without increasing the sensitivity to perturbations, thus justifying the concept. A recently introduced class of primal-dual finite element methods with weakly consistent regularisation is recalled and the associated error estimates are shown to be optimal in the sense of this definition.

Surrogate-assisted evolutionary algorithms for expensive combinatorial optimization: a survey

As potent approaches for addressing computationally expensive optimization problems, surrogate-assisted evolutionary algorithms (SAEAs) have garnered increasing attention. Prevailing endeavors in evolutionary computation predominantly concentrate on expensive continuous optimization problems, with a notable scarcity of investigations directed toward expensive combinatorial optimization problems (ECOPs). Nevertheless, numerous ECOPs persist in practical applications. The widespread prevalence of such problems starkly contrasts the limited development of relevant research. Motivated by this disparity, this paper conducts a comprehensive survey on SAEAs tailored to address ECOPs. This survey comprises two primary segments. The first segment synthesizes prevalent global, local, hybrid, and learning search strategies, elucidating their respective strengths and weaknesses. Subsequently, the second segment furnishes an overview of surrogate-based evaluation technologies, delving into three pivotal facets: model selection, construction, and management. The paper also discusses several potential future directions for SAEAs with a focus towards expensive combinatorial optimization.

Continuity of inner-outer factorization and cross sections from invariant subspaces to inner functions

Let H∞ be the Banach algebra of bounded analytic functions on the unit open disc D equipped with the supremum norm. As well known, inner functions play an important role in the study of bounded analytic functions. In this paper, we are interested in the study of inner functions. Following by the canonical inner-outer factorization decomposition, define Qinn and Qout the maps from H∞ to I the set of inner functions and F the set of outer functions, respectively. In this paper, we study the H2-norm continuity and H∞-norm discontinuity of Qinn and Qout on some subsets of H∞. On the other hand, the Beurling theorem connects inner functions and invariant subspaces of the multiplication operator Mz. We show the nonexistence of continuous cross section from some certain invariant subspaces to inner functions in the supremum norm. The continuity problem of Qinn and Qout on Hol(D‾), the set of all analytic functions in the closed unit disk, are considered. In addition, we also study the factor maps Q[inn] and Q[out] from H∞ to I/T and F/T, where I/T is the quotient space of I mod T and F/T is the quotient space of F mod T.

Robust design for mixture experiments: an efficient class of exchangeable designs for Scheffé polynomials

Modern industry, engineering, and science seek to explore new methods to determine the composition that optimally describes certain product features. The goal of mixture design is to determine the proportions that optimize some property of the response. Most practitioners adopt a classical design approach since they vaguely know the model form prior to running their experiments. This work is focused on finding optimal designs for Scheffé polynomials where the parametric description of the response function may be inadequate. Our purpose is to obtain an analytical solution to the continuous problem (when possible) and to otherwise provide a numerical alternative. Theoretical results are proven for binary blends, while other strategies based on imposing restrictions and numerical approaches are provided for ternary blends. A real example illustrates the favorability of the results for a three-salt mixture setup. The geometrical properties observed in the designs encouraged the investigation of a class of exchangeable designs. The results reveal that this class of restricted designs may be widely recommended for their simplicity, high performance, and computational efficiency.

Advancing feature ranking with hybrid feature ranking weighted majority model: a weighted majority voting strategy enhanced by the Harris hawks optimizer

Abstract Feature selection (FS) is vital in improving the performance of machine learning (ML) algorithms. Despite its importance, identifying the most important features remains challenging, highlighting the need for advanced optimization techniques. In this study, we propose a novel hybrid feature ranking technique called the Hybrid Feature Ranking Weighted Majority Model (HFRWM2). HFRWM2 combines ML models with the Harris Hawks Optimizer (HHO) metaheuristic. HHO is known for its versatility in addressing various optimization challenges, thanks to its ability to handle continuous, discrete, and combinatorial optimization problems. It achieves a balance between exploration and exploitation by mimicking the cooperative hunting behavior of Harris’s hawks, thus thoroughly exploring the search space and converging toward optimal solutions. Our approach operates in two phases. First, an odd number of ML models, in conjunction with HHO, generate feature encodings along with performance metrics. These encodings are then weighted based on their metrics and vertically aggregated. This process produces feature rankings, facilitating the extraction of the top-K features. The motivation behind our research is 2-fold: to enhance the precision of ML algorithms through optimized FS and to improve the overall efficiency of predictive models. To evaluate the effectiveness of HFRWM2, we conducted rigorous tests on two datasets: “Australian” and “Fertility.” Our findings demonstrate the effectiveness of HFRWM2 in navigating the search space and identifying optimal solutions. We compared HFRWM2 with 12 other feature ranking techniques and found it to outperform them. This superiority was particularly evident in the graphical comparison of the “Australian” dataset, where HFRWM2 showed significant advancements in feature ranking.

Numerical modelling of continuous casting of round billets with turbulence in the melt

The present work aims to solve the continuous casting benchmark problem in axisymmetry with turbulence in the melt by the meshless method. The physical model of the liquid-solid system that involves mass, momentum and energy conservation is formulated in the mixture continuum approximation. The melt is assumed Newtonian and incompressible. A k-epsilon Reynolds averaged Navier-Stokes turbulence model is implemented with Abe-Kondoh-Nagano closures. The mushy region is modelled as a Darcy porous media with the Kozeny-Carman permeability model. The solution of partial differential equations is implemented locally using collocation with radial basis functions and explicit time-stepping. The velocity pressure coupling is performed using the fractional step method. The validation of the model is assessed by comparing its outcomes with the results of the finite volume method. A sensitivity study of the varying casting speed and temperature on the velocity, temperature, and solid fraction fields is shown.

Exploring High School English Teaching Strategies for Continuation Writing based on Discourse Cohesion Theory

As a new type of question under the background of the new college entrance examination, continuation writing requires the writer to continue the article based on the context provided in the previous text, supplemented by the situational context of the article, and ensuring the logical coherence of the content. Discourse cohesion theory focuses on the coherence of grammar and vocabulary in discourse organization, aiming to construct a complete and coherent discourse text. The cohesive means under this theory can help writers to produce a well-structured, logically clear, and coherent article to a certain extent. Starting from the concept and existing problems of continuation writing, this article analyzes and explores the points of convergence between discourse cohesion theory and continuation writing, and proposes several teaching strategies to better guide writing teaching and improve students' writing ability. From the perspective of discourse cohesion theory, teachers can guide students to select appropriate referencing methods, plan the overall layout, pay attention to smooth connections, maintain logical clarity, and skillfully use substitution and ellipsis to refine language, making the writing process more efficient.

Targeting TRPV4 Channels for Cancer Pain Relief.

Despite the unique and complex nature of cancer pain, the activation of different ion channels can be related to the initiation and maintenance of pain. The transient receptor potential vanilloid 4 (TRPV4) is a cation channel broadly expressed in sensory afferent neurons. This channel is activated by multiple stimuli to mediate pain perception associated with inflammatory and neuropathic pain. Here, we focused on summarizing the role of TRPV4 in cancer etiology and cancer-induced pain mechanisms. Many studies revealed that the administration of a TRPV4 antagonist and TRPV4 knockdown diminishes nociception in chemotherapy-induced peripheral neuropathy (CIPN). Although the evidence on TRPV4 channels' involvement in cancer pain is scarce, the expression of these receptors was reportedly enhanced in cancer-induced bone pain (CIBP), perineural, and orofacial cancer models following the inoculation of tumor cells to the bone marrow cavity, sciatic nerve, and tongue, respectively. Effective pain management is a continuous problem for patients diagnosed with cancer, and current guidelines fail to address a mechanism-based treatment. Therefore, examining new molecules with potential antinociceptive properties targeting TRPV4 modulation would be interesting. Identifying such agents could lead to the development of treatment strategies with improved pain-relieving effects and fewer adverse effects than the currently available analgesics.

A Reentry Trajectory Planning Algorithm via Pseudo-Spectral Convexification and Method of Multipliers

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve online trajectory planning. In the proposed algorithm, the Chebyshev pseudo-spectral method with high-accuracy approximation performance is first employed to discretize the continuous dynamic equations. Subsequently, based on the multipliers and linearization methods, the original nonconvex trajectory planning problem is transformed into a series of relaxed convex subproblems in the form of an augmented Lagrange function. Then, the interior point method is utilized to iteratively solve the relaxed convex subproblem until the expected convergence precision is achieved. The convex-optimization-based and multipliers methods guarantee the promotion of fast convergence precision, making it suitable for online trajectory planning applications. Finally, numerical simulations are conducted to verify the performance of the proposed algorithm. The simulation results show that the algorithm possesses better convergence performance, and the solution time can reach the level of seconds, which is more than 97% less than nonlinear programming algorithms, such as the sequential quadratic programming algorithm.

Broiler sound signal filtering method based on improved wavelet denoising and effective pulse extraction

There is little attention paid to signal filtering in existing broiler health monitoring or broiler sound signal classification research, and the only few studies still have issues such as lack of specific, in-depth, and specialized details. In response to these problems, the authors conducted a depth analysis of the signal characteristics of effective signal components and noises, and proposed a broiler sound signal filtering method based on improved wavelet denoising and effective pulse extraction. This method consists of two parts. The first part is wavelet denoising, which is used to remove the widely distributed noises in broiler sound signals. Specifically, a wavelet denoising algorithm based on continuous differentiable threshold function and scale threshold has been proposed. The disadvantages in existing hard threshold function, soft threshold function, and semi-soft threshold function have been effectively addressed, and the smoothness of broiler sound signals has been ensured. The second part is pulse extraction processing, which is used to remove sudden noises that appears as independent pulses in broiler sound signals. Specifically, a two-stage variable multi-threshold pulse extraction algorithm has been proposed. The main advantages of existing three-threshold pulse extraction algorithm and double-threshold pulse extraction algorithm have been referenced, the threshold setting standard has been clarified, the continuous multi-pulse problem has been given special attention, and the effective signal components in broiler sound signals have been accurately extracted. In this way, the noises in broiler sound signals were removed, and the effective signal components were highlighted. The signal-to-noise ratio (SNR) and root mean square error (RMSE) from signal detection field, as well as the classification accuracy and F1-score from machine learning field, were used to comprehensively evaluate the effect of the signal filtering method proposed in this paper. A large number of tests shown that, compared to existing signal filtering methods, the broiler sound signal processed by the signal filtering method proposed in this paper achieved the maximum SNR and the minimum RMSE. On feature data sets created from broiler sound signals processed by different signal filtering methods, three classifiers all achieved the highest classification accuracy and F1-score on the feature data set corresponding to the signal filtering method proposed in this paper. The feasibility, practicality, and superiority of the signal filtering method proposed in this paper have been widely verified. This study is an important supplement to the broiler health monitoring and broiler sound signal classification research, providing important references for signal filtering research in similar fields.

Reentry trajectory planning for hypersonic vehicles via an improved sequential convex programming method

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem. The solution efficiency and convergence properties of the planning algorithm become an essential point when considering the practical application scenarios. In this paper, an augmented-Lagrange-based improved sequential convex programming algorithm is proposed to solve it and achieve superior solutions with higher accuracy and efficiency. Firstly, the mapped Chebyshev pseudo-spectral method is utilized to convert the continuous optimal control problem into a highly approximately discretized one. In this framework, the discretization technique is employed to discretize the states and control variables at the time interval, which leads to the improvement of ill-conditioned differential matrix and better approximation properties of the variables. Moreover, by introducing slack variables, automatically updated penalty parameters and Lagrange multipliers during the convexification processing, the original nonconvex problem is transformed into an augmented-Lagrange-function-formed relaxed convex one. Then, the arrived convex subproblem can be solved iteratively by the matured interior-point method until the predetermined precision is satisfied. Based on this transformation, it can effectively alleviate the numerical difficulty and improve the convergence property of the proposed improved sequential convex programming algorithm. Finally, Rigorous theoretical analysis is conducted to prove that the solution sequence generated by the proposed algorithm could converge to an approximate global solution of the original problem. Numerical simulations are also presented, and it is demonstrated that the solution time of the proposed algorithm is more than 95% less than that of the traditional nonlinear programming methods without losing the merits of high precision.

On Classifying Continuous Constraint Satisfaction Problems

A continuous constraint satisfaction problem (CCSP) is a constraint satisfaction problem (CSP) with an interval domain $U \subset \mathbb{R}$. We engage in a systematic study to classify CCSPs that are complete of the Existential Theory of the Reals, i.e., ER-complete. To define this class, we first consider the problem ETR, which also stands for Existential Theory of the Reals. In an instance of this problem we are given some sentence of the form $\exists x_1, \ldots, x_n \in \mathbb{R} : \Phi(x_1, \ldots, x_n)$, where $\Phi$ is a well-formed quantifier-free formula consisting of the symbols $\{0, 1, +, \cdot, \geq, >, \wedge, \vee, \neg\}$, the goal is to check whether this sentence is true. Now the class ER is the family of all problems that admit a polynomial-time many-one reduction to ETR. It is known that NP $\subseteq$ ER $\subseteq$ PSPACE. We restrict our attention on CCSPs with addition constraints ($x + y = z$) and some other mild technical conditions. Previously, it was shown that multiplication constraints ($x \cdot y = z$), squaring constraints ($x^2 = y$), or inversion constraints ($x\cdot y = 1$) are sufficient to establish ER-completeness. We extend this in the strongest possible sense for equality constraints as follows. We show that CCSPs (with addition constraints and some other mild technical conditions) that have any one well-behaved curved equality constraint ($f(x,y) = 0$) are ER-complete. We further extend our results to inequality constraints. We show that any well-behaved convexly curved and any well-behaved concavely curved inequality constraint ($f(x,y) \geq 0$ and $g(x,y) \geq 0$) imply ER-completeness on the class of such CCSPs.

A computational method for calculating the electrical and thermal conductivity of random composites

In the present work, for the first time, the electrical–thermal conductivity of a composite random material is correlated with the number of conductive paths, the mean path length, and the mean effective path width measured in a representative surface element (RSE) by Monte Carlo sampling. This work is organized in two parts. The theoretical calculation takes place in the first part for the correlation of conductive paths by adopting three approaches (incremental with respect to accuracy and complexity) based on: (i) one-component straight paths; (ii) one-component non-straight paths; (iii) multi-component non-straight paths. In the second part, a novel numerical methodology for the calculation of the conductance of the RSE through the conductive paths, mean path length and the mean effective path is developed for the general model of multi-component non-straight line paths based on Ohm’s law. In addition, a methodology that reduces the calculated conductivity from the microscale to the macroscale is proposed, that takes into account the probability of percolation for finite sizes and the average value of the conductivity from the samples in which percolation occurs. After the necessary consistency steps and verification of the method and its implementation on random binary material systems, it is further applied to solve synthetic continuous percolation problems at the microscale and macroscale. The results and the accuracy of the calculations are in close agreement with existing models. The electrical Direct Current (DC) and thermal conductivity follow the same scaling relation and the proposed methodology can be applied at the same stage without additional cost. In a random binary medium the simulations showed that a scaling law of conductivity is followed by an exponent value close to 1.3. In addition, the number of conductive paths, the average length of the paths, and the effective width follow scaling laws with exponents 1.44±0.01 , −0.25±0.01 and −0.39±0.01, respectively.

A hybrid multi-objective evolutionary algorithm with high solving efficiency for UAV defense programming

Emerging Unmanned Aerial Vehicle (UAV) application patterns, including the Loyal Wingman and Unmanned Swarms, have significantly challenged the administration and defense against illegal or trespassing UAVs. The weapon-target assignment (WTA) problem, a famous combinatorial optimization problem in military operations research, is decisive for the success of UAV defense programming. Related investigations face two main challenges: 1) Constructing a multi-objective optimization model reflecting the complexities of new UAV application patterns, and 2) solving the time-consuming WTA problem with high-dimension decision variables as it is NP-complete. This paper introduces a modified differential evolution based on a new mapping method called Pareto-Optimal-Matching that solves multi-objective binary optimization problems and constructs a 3 objective Sensor-Weapon-Target Assignment model. The proposed algorithm overcomes the inherent limitation of traditional differential evolution, which only performs well in continuous problems. Promising results were obtained based on different simulation metrics under various problems (proposed model, MOKP, and ZDT5), validating the superior performance of the proposed algorithm.

An energy-efficient GMRES–multigrid solver for space-time finite element computation of dynamic poroelasticity

We present and analyze computationally Geometric MultiGrid (GMG) preconditioning techniques for Generalized Minimal RESidual (GMRES) iterations to space-time finite element methods (STFEMs) for a coupled hyperbolic–parabolic system modeling, for instance, flow in deformable porous media. By using a discontinuous temporal test basis, a time marching scheme is obtained. Higher order approximations that offer the potential to inherit most of the rich structure of solutions to the continuous problem on computationally feasible grids increase the block partitioning dimension of the algebraic systems, comprised of generalized saddle point blocks. Our V-cycle GMG preconditioner uses a local Vanka-type smoother. Its action is defined in an exact mathematical way. Due to nonlocal coupling mechanisms of 348 unknowns, the smoother is applied on patches of elements. This ensures damping of higher order error frequencies. By numerical experiments of increasing complexity, the efficiency of the solver for STFEMs of different polynomial order is illustrated and confirmed. Its parallel scalability is analyzed. Beyond this study of classical performance engineering, the solver’s energy efficiency is investigated as an additional and emerging dimension in the design and tuning of algorithms on the hardware.

Pediatric Population Management Classification for Children with Medical Complexity.

Improving the overall care of children with medical complexity (CMC) is often beset by challenges in proactively identifying the population most in need of clinical management and quality improvement. The objective of the current study was to create a system to better capture longitudinal risk for sustained and elevated utilization across time using real-time electronic health record (EHR) data. A new Pediatric Population Management Classification (PPMC), drawn from visit diagnoses and continuity problem lists within the EHR of a tristate health system, was compared with an existing complex chronic conditions (CCC) system for agreement (with weighted κ) on identifying CCMC, as well as persistence of elevated charges and utilization from 2016 to 2019. Agreement of assignment PPMC was lower among primary care provider (PCP) populations than among other children traversing the health system for specialty or hospital services only (weighted κ 62% for PCP vs. 82% for non-PCP). The PPMC classification scheme, displaying greater precision in identifying CMC with persistently high utilization and charges for those who receive primary care within a large integrated health network, may offer a more pragmatic approach to selecting children with CMC for longitudinal care management.

Enhancing forest optimization algorithm with gravitational search for nonlinear continuous optimization

Meta-heuristic algorithms have great role in solving problems related to optimization. Meta-heuristic method cannot solve problems related to optimization due to No Free Lunch theory. Hence different optimization methods are proposed by various researchers each year in order to solve optimization problems. Forest Optimization Algorithm (FOA) is an evolutionary optimization algorithm that is appropriate for continuous nonlinear optimization problems. The algorithm drawbacks include entrapment in local optimum and failure in achieving global optimum. The paper proposes hybrid algorithm called FOAGSA, in which the Gravitational Search Algorithm (GSA) is employed to improve the FOA performance in order to solve nonlinear continuous problems. The FOAGSA was evaluated through 39 benchmark optimization functions and two engineering problems. The experimental results proved that the FOAGSA exhibited acceptable results compared to state-of-art and well-known Meta-heuristic algorithms. Friedman ranking algorithm was utilized to compare FOAGSA with existing methods. The FOAGSA was ranked first on that basis.

Athens or Rome? A New Perspective on the Political Philosophy of H. Arendt

Hannah Arendt is widely known as a philosopher who attempted to rehabilitate the ancient Greek conception of politics. According to established readings of The Human Condition, Arendt is generally regarded as a ‘Graecophile’ whose thought is underwritten by ‘Athenian nostalgia’. Arendt’s sympathies for the Greeks are hard to deny: she did indeed turn to the Athenian understanding of politics in an attempt to crystallise in it the core elements of authentic politics. However, this interpretation is excessively one-sided. In Arendt’s view, the greatest contribution to the understanding of politics was offered by the Romans, not the Greeks. The Romans were much better at dealing with the problem of stability, continuity and order of politics. In Arendt’s view, an exclusive focus on action, spontaneity and extraordinary deeds threatens to destabilise the life of the political community. By introducing concepts such as tradition, authority, the sacredness of foundation, the law (lex), as well as the political significance of promise and forgiveness, the Romans opened up a dimension of political sedimentation which was alien to the Greeks. Political sedimentation provides safeguards, without which a sustainable political existence would become impossible.

Oscillatory Neural Network-Based Ising Machine Using 2D Memristors.

Neural networks are increasingly used to solve optimization problems in various fields, including operations research, design automation, and gene sequencing. However, these networks face challenges due to the nondeterministic polynomial time (NP)-hard issue, which results in exponentially increasing computational complexity as the problem size grows. Conventional digital hardware struggles with the von Neumann bottleneck, the slowdown of Moore's law, and the complexity arising from heterogeneous system design. Two-dimensional (2D) memristors offer a potential solution to these hardware challenges, with their in-memory computing, decent scalability, and rich dynamic behaviors. In this study, we explore the use of nonvolatile 2D memristors to emulate synapses in a discrete-time Hopfield neural network, enabling the network to solve continuous optimization problems, like finding the minimum value of a quadratic polynomial, and tackle combinatorial optimization problems like Max-Cut. Additionally, we coupled volatile memristor-based oscillators with nonvolatile memristor synapses to create an oscillatory neural network-based Ising machine, a continuous-time analog dynamic system capable of solving combinatorial optimization problems including Max-Cut and map coloring through phase synchronization. Our findings demonstrate that 2D memristors have the potential to significantly enhance the efficiency, compactness, and homogeneity of integrated Ising machines, which is useful for future advances in neural networks for optimization problems.