Continuous Problem Research Articles

TRIQS/Nevanlinna: Implementation of the Nevanlinna Analytic Continuation method for noise-free data

We present the TRIQS/Nevanlinna analytic continuation package, an efficient implementation of the methods proposed by J. Fei et al. (2021) [53] and (2021) [55]. TRIQS/Nevanlinna strives to provide a high quality open source (distributed under the GNU General Public License version 3) alternative to the more widely adopted Maximum Entropy based analytic continuation programs. With the additional Hardy functions optimization procedure, it allows for an accurate resolution of wide band and sharp features in the spectral function. Those problems can be formulated in terms of imaginary time or Matsubara frequency response functions. The application is based on the TRIQS C++/Python framework, which allows for easy interoperability with other TRIQS-based applications, electronic band structure codes and visualization tools. Similar to other TRIQS packages, it comes with a convenient Python interface. Program summaryProgram Title:TRIQS/NevanlinnaCPC Library link to program files:https://doi.org/10.17632/4cbzfy5rds.1Developer's repository link:https://github.com/TRIQS/NevanlinnaLicensing provisions: GPLv3Programming language:C++/PythonExternal routines/libraries:TRIQS 3.2[1], Boost >= 1.76.0, Eigen >= 3.4.0, cmake >= 3.20.Nature of problem: Finite-temperature field theories are widely used to study quantum many-body effects and electronic structure of correlated materials. Obtaining physically relevant spectral functions from results in the imaginary time/Matsubara frequency domains requires solution of an ill-posed analytic continuation problem as a post-processing step.Solution method: We present an efficient C++/Python open-source implementation of the Nevanlinna/Caratheodory analytic continuation.

Discrete inverse problem for a hyperbolic equation, properties of the solution to a discrete direct and auxiliary discrete problems

This paper considers the formulation of a discrete inverse problem for a hyperbolic equation. First, the continuous inverse problem is reduced to a convenient form for research. In the inverse problem, the required function is considered even. Since the Dirac delta function is present in the problem data, the structure of a generalized solution to the Cauchy problem for a hyperbolic equation is determined. The solution to the Cauchy problem for a hyperbolic equation is determined only for positive values in time, therefore the solution to the Cauchy problem for negative values in time is determined using odd continuation. After some transformations, the formulation of the continuous inverse problem is reduced to a form convenient for research. A grid domain is introduced, and for all functions in the problem statement the corresponding grid functions and a discrete analogue of the Dirac delta function are determined. Differential operators, initial conditions and additional data of the inverse problem are approximated by finite differences. Assuming that a solution to the discrete inverse problem exists, we prove the data lemma of the discrete inverse problem. In order to study the discrete inverse problem for a hyperbolic equation, a theorem on the existence and uniqueness of the discrete direct problem is proved, as well as on the properties of the solution to this discrete problem. In the course of proving the theorem, a discrete analogue of d'Alembert's formula for solving the Cauchy problem for a hyperbolic equation was obtained. The theorem on the existence of a unique solution to the auxiliary discrete problem and its properties is proved.

Adaptive search space for stochastic opposition-based learning in differential evolution

Differential evolution (DE) is a practical evolutionary algorithm (EA) widely employed for addressing continuous optimization problems. Opposition-based learning (OBL) emerges as a potent method among the techniques enhancing EA performance. The BetaCOBL variant represents a pinnacle in this domain. However, BetaCOBL’s utilization of the promising regions of the search space remains partial, owing to its dependence on a non-adaptive framework. Consequently, its efficacy might dwindle as optimization progresses. We aimed to introduce an enhanced version of BetaCOBL, termed adaptive BetaCOBL (ABetaCOBL). ABetaCOBL commences by adapting the search space based on population distribution and subsequently identifying opposite solutions. We evaluated the efficacy of embedding ABetaCOBL into DE algorithms through experiments. Our experimental results substantiate that ABetaCOBL outperforms its precursor and resilient OBL variants (e.g., ABetaCOBL outperforms iBetaCOBL-eig in 19 out of 58 problems with NL-SHADE-LBC and in 22 out of 58 problems with NL-SHADE-RSP).

Watershed-Based Participatory Sustainable Land Management using Integrated physical SWC Measure in Ilasa Watershed of Goba District, Bale Highland South-Eastern Ethiopia

Soil erosion is among the most challenging and continuous environmental problems in the highlands of Bale particularly in Ilasa Watershed of Goba District. Soil erosion which emanates from both anthropogenic and natural causes currently results decline in agricultural productivity, crop production on the other hand increases downstream flooding and reservoir sedimentation, and loss of valuable plant nutrients. Soil and water conservation (SWC) practices have been carried out to solve land degradation and erosion severity problems in the Ilasa Watershed through participatory approaches the objective of this study was to implement integrated physical SWC practices through participatory approach in the Ilasa watersheds; to rehabilitate degraded watershed using different physical SWC measures and to minimize the risk of soil erosion and increasing soil depth by trapping sediment loss from Ilasa watershed. Hence, different participatory integrated watershed management practices were introduced in the Ilasa watershed for five consecutive years to avert the problem of soil erosion. Community participatory in integrated watershed management particularly soil and water conservation measures interventions for degraded rehabilitation and gulley treatment were capacitated through training, practical field works, and researchable materials support. Awareness creation, increasing knowledge and skill of farmers, providing technical and resource supports, and implementing slope based appropriate SWC structure could help sustainable land management that ensures environmental quality and food security in the study area as well as in the other areas having related biophysical and socioeconomic settings. Among the major types of physical SWC structures and gulley rehabilitation structures constructed in the study watershed were soil bund; stone bund; stone-faced soil bund and cut-off drains, gully reshaping and filling, brushwood check dam, loose stone check dame, sandbag check dam ...

Non-orthogonal multiple access-based MEC for energy-efficient task offloading in e-commerce systems

Mobile edge computing (MEC) reduces the latency for end users to access applications deployed at the edge by offloading tasks to the edge. With the popularity of e-commerce and the expansion of business scale, server load continues to increase, and energy efficiency issues gradually become more prominent. Computation offloading has received widespread attention as a technology that effectively reduces server load. However, how to improve energy efficiency while ensuring computing requirements is an important challenge facing computation offloading. To solve this problem, using non-orthogonal multiple access (NOMA) to increase the efficiency of multi-access wireless transmission, MEC supporting NOMA is investigated in the research. Computing resources will be divided into separate sub-computing that will be handled via e-commerce terminals or transferred to edge sides by reutilizing radio resources, we put forward a Group Switching Matching Algorithm Based on Resource Unit Allocation (GSM-RUA) algorithm that is multi-dimensional. To this end, we first formulate this task allocation problem as a long-term stochastic optimization problem, which we then convert to three short-term deterministic sub-programming problems using Lyapunov optimization, namely, radio resource allocation in a large timescale, computation resource allocating and splitting in a small-time frame. Of the 3 short-term deterministic sub-programming problems, the first sub-programming problem can be remodeled into a 1 to n matching problem, which can be solved using the block-shift-matching-based radio resource allocation method. The latter two sub-programming problems are then transformed into two continuous convex problems by relaxation and then solved easily. We then use simulations to prove that our GSM-RUA algorithm is superior to the state-of-the-art resource management algorithms in terms of energy consumption, efficiency and complexity for e-commerce scenarios.

Performance analyses of weighted superposition attraction-repulsion algorithms in solving difficult optimization problems

ABSTRACT The purpose of this paper is to test the performance of the recently proposed weighted superposition attraction-repulsion algorithms (WSA and WSAR) on unconstrained continuous optimization test problems and constrained optimization problems. WSAR is a successor of weighted superposition attraction algorithm (WSA). WSAR is established upon the superposition principle from physics and mimics attractive and repulsive movements of solution agents (vectors). Differently from the WSA, WSAR also considers repulsive movements with updated solution move equations. WSAR requires very few algorithm-specific parameters to be set and has good convergence and searching capability. Through extensive computational tests on many benchmark problems including CEC’2015 and CEC’2020 performance of the WSAR is compared against WSA and other metaheuristic algorithms. It is statistically shown that the WSAR algorithm is able to produce good and competitive results in comparison to its predecessor WSA and other metaheuristic algorithms.

Modified dung beetle optimizer with multi-strategy for uncertain multi-modal transport path problem

Abstract Uncertain multi-modal transport path optimization (UMTPO) is a combined optimization non-deterministic polynomial-time hard problem. Its goal is to determine a path with the lowest total transportation cost and carbon emissions from the starting point to the destination. To effectively address this issue, this article proposes a modified dung beetle optimizer (DBO) to address it. DBO is a swarm-based metaheuristic optimization algorithm that has the features of a fast convergence rate and high solution accuracy. Despite this, the disadvantages of weak global exploration capability and falling easily into local optima exist. In this article, we propose a modified DBO called MSHDBO for function optimization and to solve the UMTPO problem. However, for the vast majority of metaheuristic algorithms, they are designed for continuous problems and cannot directly solve discrete problems. Therefore, this article employs a priority based encoding and decoding method to solve the UMTPO problem. To verify the performance and effectiveness of the MSHDBO algorithm, we compared it with other improved versions of the DBO algorithm used in the literature. We confirmed the excellent performance of MSHDBO using 41 benchmark test functions from the IEEE CEC 2017 test suite and IEEE CEC 2022 test suite. Additionally, we compared the MSHDBO algorithm with 10 other state-of-the-art metaheuristic optimization algorithms through a practical UMTPO problem. The experimental results indicated that the MSHDBO algorithm achieved very good performance when solving the UMTPO problem.

A Strategy for Preparing Quantum Squeezed States Using Reinforcement Learning

AbstractA scheme leveraging reinforcement learning to engineer control fields for generating non‐classical states is proposed. It is exemplified by the application to prepare spin‐squeezed states for an open collective spin model where a linear control field is designed to govern the dynamics. The reinforcement learning agent determines the temporal sequence of control pulses, commencing from a coherent spin state in an environment characterized by dissipation and dephasing. Compared to the constant control scenario, this approach provides various control sequences maintaining collective spin squeezing and entanglement. It is observed that denser application of the control pulses enhances the performance of the outcomes. However, there is a minor enhancement in the performance by adding control actions. The proposed strategy demonstrates increased effectiveness for larger systems. Thermal excitations of the reservoir are detrimental to the control outcomes. Feasible experiments are suggested to implement this control proposal based on the comparison with the others. The extensions to continuous control problems and another quantum system are discussed. The replaceability of the reinforcement learning module is also emphasized. This research paves the way for its application in manipulating other quantum systems.

Binary metaheuristic algorithms for 0–1 knapsack problems: Performance analysis, hybrid variants, and real-world application

This paper examines the performance of three binary metaheuristic algorithms when applied to two distinct knapsack problems (0–1 knapsack problems (KP01) and multidimensional knapsack problems (MKP)). These binary algorithms are based on the classical mantis search algorithm (MSA), the classical quadratic interpolation optimization (QIO) method, and the well-known differential evolution (DE). Because these algorithms were designed for continuous optimization problems, they could not be used directly to solve binary knapsack problems. As a result, the V-shaped and S-shaped transfer functions are used to propose binary variants of these algorithms, such as binary differential evolution (BDE), binary quadratic interpolation optimization (BQIO), and binary mantis search algorithm (BMSA). These binary variants are evaluated using various high-dimensional KP01 examples and compared to several classical metaheuristic techniques to determine their efficacy. To enhance the performance of those binary algorithms, they are combined with repair operator 2 (RO2) to offer better hybrid variants, namely HMSA, HQIO, and HDE. Those hybrid algorithms are evaluated using several medium- and large-scale KP01 and MKP instances, as well as compared to other hybrid algorithms, to demonstrate their effectiveness. This comparison is conducted using three performance metrics: average fitness value, Friedman mean rank, and computational cost. The experimental findings demonstrate that HQIO is a strong alternative for solving KP01 and MKP. In addition, the proposed algorithms are applied to the Merkle-Hellman Knapsack Cryptosystem and the resource allocation problem in adaptive multimedia systems (AMS) to illustrate their effectiveness when applied to optimize those real applications. The experimental findings illustrate that the proposed HQIO is a strong alternative for handling various knapsack-based applications.

A music recommender system based on compact convolutional transformers

In recent years, music streaming services have garnered a surge in popularity. Maintaining a continuous flow of music that aligns with user preferences, commonly known as the continuity problem, has become a significant issue in this domain. To address this challenge, developing Music Recommender Systems (MRSs) that can automatically search through vast music libraries and suggest appropriate songs to listeners is crucial. To this end, this paper proposes a Compact Convolutional Transformer (CCT) model for improving the feature selection process and thus addressing the continuity problem based on music genres. The model extracts latent features from Mel-spectrograms generated from raw audio songs. Then, the cosine similarity measure determines the similarity between feature maps to recommend the most relevant songs. Several methodologies, including two state-of-the-art CRNN models, are used to benchmark the model’s performance. The experimental results demonstrate that the proposed model significantly outperforms the current state-of-the-art models in terms of precision, recall, F1 score, and overall accuracy while having significantly fewer parameters.

Analysing hyper-heuristics based on Neural Networks for the automatic design of population-based metaheuristics in continuous optimisation problems

When dealing with optimisation problems, Metaheuristics (MHs) quickly come to our minds. A quick literature review reveals a vast universe of MHs. Although the metaphors behind these MHs are always presented as ‘unique’ to justify their novelty, the truth is that many MHs just recombine elements from other techniques. Then, instead of proposing MHs based on what already exists in nature, it is better to follow a standard model for the automatic metaheuristic design by employing simple heuristics. Many approaches have designed algorithms that probe the combination of such heuristics, generating astonishing results compared to generic MHs. Following this idea, our work examines Neural Network (NN) architectures over several control variables to tailor MHs. Our results render an architecture that enhances the results compared to generic MHs at 91%, those MHs produced by Random Search at 81%, and the current state-of-the-art NN model at 66%. We notice a big gap for NN-based models with different architectures, which are worth investigating. Among the benefits of our proposed approach is that it reduces the dependence on human knowledge, moving towards the automatic generation of solving methods that learn from empirical data how to succeed in various continuous optimisation scenarios.

Multi-subswarm cooperative particle swarm optimization algorithm and its application

Particle swarm optimization (PSO) is a classical evolutionary algorithm and has been widely used to solve continuous optimization problems. However, the performance of the PSO algorithm is highly sensitive to its control parameters and learning strategies. To address this problem, a multi-subswarm cooperative particle swarm optimization algorithm (MSC-PSO) is proposed in this paper. In MSC-PSO, firstly, a population muti-subswarm division method is designed to enhance the global exploration capability. Secondly, a level-based particle adaptive inertia weight strategy is introduced to adjust control parameters. Finally, a level-based update learning mechanism is used for particles adaptive selection learning strategy. The performance of the MSC-PSO is evaluated by the CEC2020 test suite, and five heuristic algorithms are compared with the MSC-PSO in the experiments. The experimental results demonstrate that the proposed MSC-PSO algorithm has significant advantages in terms of convergence speed and solving optimal solutions. Furthermore, the proposed MSC-PSO algorithm is used to solve the plant protection unmanned aerial vehicles (UAV) path planning problem. The experimental results proved that the proposed MSC-PSO algorithm effectively solves the real-world UAV path planning problem, and achieves at most a 34 % reduction in round-trip distance and a 24.1 % reduction in total non-spraying time compared to classical PSO.

A computational approach for 2D elliptic singularly perturbed weakly coupled systems of convection–diffusion type with multiple scales and parameters in the diffusion and the convection terms

In this work, we consider the efficient resolution of a 2D elliptic singularly perturbed weakly coupled system of convection–diffusion type, which has small parameters at both the diffusion and the convection terms. We assume that the diffusion parameters can be distinct at each equation of the system, and also, they can have different orders of magnitude, but the convection parameter is the same at both equations of the system. Then, in general, overlapping regular or parabolic boundary layers can appear in the exact solution. The continuous problem is approximated by using the standard upwind finite difference scheme, which is constructed on a special piecewise uniform Shishkin mesh. Then, the numerical scheme is an almost first‐order uniformly convergent method with respect to all the perturbation parameters. Some numerical results, obtained with the numerical algorithm for one test problem, are presented, which show the good performance of the proposed numerical method and also corroborate in practice the theoretical results.

A Metaheuristic Framework with Experience Reuse for Dynamic Multi-Objective Big Data Optimization

Dynamic multi-objective big data optimization problems (DMBDOPs) are challenging because of the difficulty of dealing with large-scale decision variables and continuous problem changes. In contrast to classical multi-objective optimization problems, DMBDOPs are still not intensively explored by researchers in the optimization field. At the same time, there is lacking a software framework to provide algorithmic examples to solve DMBDOPs and categorize benchmarks for relevant studies. This paper presents a metaheuristic software framework for DMBDOPs to remedy these issues. The proposed framework has a lightweight architecture and a decoupled design between modules, ensuring that the framework is easy to use and has enough flexibility to be extended and modified. Specifically, the framework now integrates four basic dynamic metaheuristic algorithms, eight test suites of different types of optimization problems, as well as some performance indicators and data visualization tools. In addition, we have proposed an experience reuse method, speeding up the algorithm’s convergence. Moreover, we have implemented parallel computing with Apache Spark to enhance computing efficiency. In the experiments, algorithms integrated into the framework are tested on the test suites for DMBDOPs on an Apache Hadoop cluster with three nodes. The experience reuse method is compared to two restart strategies for dynamic metaheuristics.

On the long-time behavior of the continuous and discrete solutions of a nonlocal Cahn–Hilliard type inpainting model

In this paper, we study the analytical and numerical long-time stability of a nonlocal Cahn–Hilliard model with a fidelity term for image inpainting introduced in our previous work (Jiang et al., 2024). First, we establish the uniform boundedness of the continuous problem in both L2 and H1 spaces, which is obtained by using the Gagliardo–Nirenberg inequality and the uniform Grönwall lemma. Then, for the temporal semi-discrete scheme, the uniform estimates in L2 and H1 spaces are derived with the aid of the discrete uniform Grönwall lemma under a suitable assumption on the nonlinear potential. This demonstrates the long-time stability of the proposed scheme in L2 and H1 spaces. Finally, we validate the long-time stability and the applicability of our method in signal reconstruction and image inpainting. These numerical experiments demonstrate the high effectiveness of our proposed model.

Continual Observation of Joins under Differential Privacy

The problem of continual observation under differential privacy has been studied extensively in the literature. However, all existing works, with the exception of [28,51], have only studied the simple counting query and its derivatives. Join queries, which are arguably the most important class of queries in relational databases, have only been considered in [28,51], but the solutions offered there have two limitations: First, they only support a few specific graph pattern queries, which are special cases of joins. Second, they require hard degree/frequency constraints on the graph/database instance, and the privatized query answers have errors proportional to these constraints. In this paper, we propose a new differentially private mechanism for continual observation of joins that overcomes these two limitations. Our mechanism supports arbitrary joins and predicates, and do not require any constraints to be given in advance, even over an infinite stream. More importantly, it yields an error that is proportional to the actual maximum degree/frequencies in the graph/database instance at the current time of observation. Such an instance-specific utility guarantee is much preferred for the continual observation problem, where the database size and the query answer may change significantly over time.

A Multi-Time-Step Parallel Computing Method based on Overlapping Particles for DEM

The application of the discrete element method (DEM) to continuous medium problems is becoming increasingly widespread. In this work, a parallel computing method with multiple time steps based on overlapping particles is proposed. The domain decomposition method (DDM) with overlapping particles method is used to increase the speed up and shorten the computation time and meet the consistency requirements during data transmission. The multi-time-step method (MTSM) is adopted to tackle the matching of asynchronous step boundary. Data are exchanged at the boundaries in each subdomain with a message passing interface (MPI). The computational efficiency of different step ratios in both serial and parallel computing is studied respectively. Numerical examples show that the DEM can effectively handle large structure deformation problems, and provides a shorter calculation time than that of the finite element method (FEM). The DEM with multiple time steps in different subdomains effectively reduces the computation time than that with a single time step in the entire domain. Under fixed step ratio conditions, using parallel computing can save more time than serial computing. This work develops ideas for expanding the application of DEM for large engineering problems.

Assessment of a Second-Order Multi-Problem Factor Model Involving Sexual Partners, Marijuana Use, and Post-Arrest Placement Among Persistent Male Adolescent Delinquents

ABSTRACT Problem-behavior theory suggests problem behaviors (e.g. substance use and delinquency) cluster among adolescents. This study explored a second-order problem behavior model of marijuana use, sexual partners, and post-arrest juvenile justice system placement among male adolescents over three waves. Results confirmed a second-order latent factor of problem behaviors, with male adolescents persistently involved in the juvenile justice system experiencing problems with marijuana use, risky sexual behavior, and increased severity of post-arrest placement. Further, older, Hispanic, African American, and urban persistent male delinquents were more likely to demonstrate continued problem behaviors. We discuss implications for future research and practice.

Global Overview of the Application of the Braun-Blanquet Approach in Research

Environmental classifications are of paramount importance for assessing the impacts of land-use changes, for prioritizing conservation efforts, and for developing effective management strategies to mitigate the negative impacts of human activities. The aim of our research was to provide as complete an analysis as possible of the studies that have been carried out using the Braun-Blanquet approach. The global review of studies based on the Braun-Blanquet approach includes 1168 papers and was conducted using the PRISMA 2009 methodological recommendations, strict criteria for the selection/quality of papers, and modern methods of data analysis and visualization using VOSviewer software developed by Nees Jan van Eck and Ludo Waltman (Centre for Science and Technology Studies (CWTS) of Leiden University in the Netherlands) (version 1.6.18), which ensures a representative sample, minimization of subjective judgements, and reliability of conclusions. It was noted that the number of publications on Braun-Blanquet is growing exponentially. This is an indication of the scientific interest in this methodology and its continuous further development. Based on a detailed analysis of the keywords, the main research directions and challenges are identified. These include improving the conceptual and methodological foundations of the Braun-Blanquet approach; improvement in regional vegetation classifications, synthesizing them and producing a comprehensive classification for large areas as a basis for biodiversity conservation and sustainable land use; expansion of the geography; compilation and updating of databases of phytosociological data; management of dynamics and vegetation; discussion of the important problem of continuity and discreteness of vegetation in the context of ecological classifications; and vegetation mapping. The top 20 journals publishing the most cited articles were identified, as well as the top 20 most cited journals whose high citation rate is due to the large number of high-quality articles. The analysis of the bibliographic network of papers in dynamics has shown that the structure of relationships is not constant and has changed significantly. The analysis of the authors’ publication activity showed that the vast majority of researchers have a low publication activity and have published only one to three papers. A peculiarity also emerges: if all the most cited authors are concentrated in Eurasia, then most of the most actively published authors are outside Eurasia. The importance of the Braun-Blanquet approach for the study and classification of forest vegetation should be emphasized. In this case, the Braun-Blanquet approach is integrated into forest typologies, increasing their ecological validity and environmental relevance.

A Stochastic Inexact Sequential Quadratic Optimization Algorithm for Nonlinear Equality-Constrained Optimization

A stochastic algorithm is proposed, analyzed, and tested experimentally for solving continuous optimization problems with nonlinear equality constraints. It is assumed that constraint function and derivative values can be computed but that only stochastic approximations are available for the objective function and its derivatives. The algorithm is of the sequential quadratic optimization variety. Distinguishing features of the algorithm are that it only employs stochastic objective gradient estimates that satisfy a relatively weak set of assumptions (while using neither objective function values nor estimates of them) and that it allows inexact subproblem solutions to be employed, the latter of which is particularly useful in large-scale settings when the matrices defining the subproblems are too large to form and/or factorize. Conditions are imposed on the inexact subproblem solutions that account for the fact that only stochastic objective gradient estimates are employed. Convergence results are established for the method. Numerical experiments show that the proposed method vastly outperforms a stochastic subgradient method and can outperform an alternative sequential quadratic programming algorithm that employs highly accurate subproblem solutions in every iteration. Funding: This material is based upon work supported by the National Science Foundation [Awards CCF-1740796 and CCF-2139735] and the Office of Naval Research [Award N00014-21-1-2532].