Algorithm For Domains Research Articles

Inverse power method for the principal eigenvalue of the Robin [formula omitted]-Laplacian

In this paper, a numerical algorithm to compute the first eigenvalue and the corresponding eigenfunction of the p-Laplacian eigenvalue problem with Robin boundary conditions is developed. The algorithm generates a sequence of numbers and functions. It is established that the sequence of numbers is decreasing and converges to the first eigenvalue, while the sequence of functions converges to the corresponding eigenfunction. The method is easier to implement in comparison with the current methods.The order of convergence for the algorithm is investigated. Several numerical experiments reveal the robustness and the efficacy of the algorithm for domains of various geometries. Our results provide deeper insights for the limiting cases p→1 and ∞.

Analysis of the Computational Cost of PolyFront: an Algorithm for Planar Triangulation

The triangulation of planar domains is a relevant and largely studied problem in many applied sciences. This paper analyzes the computational time of a triangulation algorithm for plane domains with holes, introduced in a previous paper. This algorithm is based on the normal offsetting technique starting from a polygonal approximation of the domain boundary. It is shown that the computational time is linear with respect to the number of vertices of the triangulation. Experimental results confirm the theoretical upper bound obtained for the computational time.

Appropriate noise addition to metaheuristic algorithms can enhance their performance

Nature-inspired swarm-based algorithms are increasingly applied to tackle high-dimensional and complex optimization problems across disciplines. They are general purpose optimization algorithms, easy to implement and assumption-free. Some common drawbacks of these algorithms are their premature convergence and the solution found may not be a global optimum. We propose a general, simple and effective strategy, called heterogeneous Perturbation–Projection (HPP), to enhance an algorithm’s exploration capability so that our sufficient convergence conditions are guaranteed to hold and the algorithm converges almost surely to a global optimum. In summary, HPP applies stochastic perturbation on half of the swarm agents and then project all agents onto the set of feasible solutions. We illustrate this approach using three widely used nature-inspired swarm-based optimization algorithms: particle swarm optimization (PSO), bat algorithm (BAT) and Ant Colony Optimization for continuous domains (ACO). Extensive numerical experiments show that the three algorithms with the HPP strategy outperform the original versions with 60–80% the times with significant margins.

A method for fast economic optimization of large hybrid ground source heat pump systems

This paper presents a novel simulation-based method for fast economic optimization of large hybrid ground source heat pump systems. Rapid evaluation of the objective function is achieved by the joint use of previously developed efficient algorithms, including Delaunay triangulation, successive flux estimation and fast spectral convolution. The resulting objective function is concave and composed only of continuous parameters. The global optimal solution of a problem composed of several dozens of boreholes operating over a 30 year time span is found using the Ant Colony Optimization algorithm for continuous domains, and convergence is achieved in under 12 min of computation time. Results show that optimization is key for proposing a financially viable hybrid ground source heat pump project for large commercial buildings. We also show that proper project financing, such as government guaranteed loans, can significantly contribute towards achieving better economic performance. The proposed approach is fast, convergent, practical, and can help promoters present hybrid GSHP projects under a less risky type of business.

Multi-Uav Trajectory Planning for 3d Visual Inspection of Complex Structures

This paper presents a new trajectory planning algorithm for 3D autonomous UAV volume coverage and visual inspection. The algorithm is an extension of a state-of-the-art Heat Equation Driven Area Coverage (HEDAC) multi-agent area coverage algorithm for 3D domains. With a given target exploration density field, the algorithm designs a potential field and directs UAVs to the regions of higher potential, i.e., higher values of remaining density. Collisions between the agents and agents with domain boundaries are prevented by implementing the distance field and correcting the agent's directional vector when the distance threshold is reached. A unit cube test case is considered to evaluate this trajectory planning strategy for volume coverage. For visual inspection applications, the algorithm is supplemented with camera direction control. A field containing the nearest distance from any point in the domain to the structure surface is designed. The gradient of this field is calculated to obtain the camera orientation throughout the trajectory. Three different test cases of varying complexities are considered to validate the proposed method for visual inspection. The simplest scenario is a synthetic portal-like structure inspected using three UAVs. The other two inspection scenarios are based on realistic structures where UAVs are commonly utilized: a wind turbine and a bridge. When deployed to a wind turbine inspection, two simulated UAVs traversing smooth spiral trajectories have successfully explored the entire turbine structure while cameras are directed to the curved surfaces of the turbine's blades. In the bridge test case an efficacious visual inspection of a complex structure is demonstrated by employing a single UAV and five UAVs. The proposed methodology is successful, flexible and applicable in real-world UAV inspection tasks.

Relational Boosted Bandits

Contextual bandits algorithms have become essential in real-world user interaction problems in recent years. However, these algorithms represent context as attribute value representation, which makes them infeasible for real world domains like social networks, which are inherently relational. We propose Relational Boosted Bandits (RB2), a contextual bandits algorithm for relational domains based on (relational) boosted trees. RB2 enables us to learn interpretable and explainable models due to the more descriptive nature of the relational representation. We empirically demonstrate the effectiveness and interpretability of RB2 on tasks such as link prediction, relational classification, and recommendation.

An enhanced chimp optimization algorithm for continuous optimization domains

Chimp optimization algorithm (ChOA) is a recently proposed metaheuristic. Interestingly, it simulates the social status relationship and hunting behavior of chimps. Due to the more flexible and complex application fields, researchers have higher requirements for native algorithms. In this paper, an enhanced chimp optimization algorithm (EChOA) is proposed to improve the accuracy of solutions. First, the highly disruptive polynomial mutation is used to initialize the population, which provides the foundation for global search. Next, Spearman’s rank correlation coefficient of the chimps with the lowest social status is calculated with respect to the leader chimp. To reduce the probability of falling into the local optimum, the beetle antennae operator is used to improve the less fit chimps while gaining visual capability. Three strategies enhance the exploration and exploitation of the native algorithm. To verify the function optimization performance, EChOA is comprehensively analyzed on 12 classical benchmark functions and 15 CEC2017 benchmark functions. Besides, the practicability of EChOA is also highlighted by three engineering design problems and training multilayer perceptron. Compared with ChOA and five state-of-the-art algorithms, the statistical results show that EChOA has strong competitive capabilities and promising prospects.

Approaches for Optimizing the Performance of Adaptive Neuro-Fuzzy Inference System and Least-Squares Support Vector Machine in Precipitation Modeling

This study employs two heuristic algorithms, including the genetic algorithm (GA) and ant colony optimization for continuous domains (ACOR), for optimizing the parameters of two soft computing models, namely adaptive neuro-fuzzy inference system (ANFIS) and least-squares support vector machine (LSSVM), which were used for modeling monthly precipitation for all 12 months of the year. Data from 40 meteorological stations situated in different parts of Iran were used. The effectiveness of input data was determined by internal correlation-coefficient and nonlinear sensitivity analysis. Selected input data were further evaluated by another sensitivity analysis method, cosine amplitude (CA). Considering different evaluation months, LSSVM was more accurate and reliable than ANFIS. It was also found that both algorithms improved the performance of models for most months of the year. ACOR was better and more reliable than was GA in optimizing the models. ACOR produced the best results in autumn that led to the improvement of performance of ANFIS in terms of correlation coefficient (R) and root-mean square error (RMSE) by 35% and 0.40 mm for October; 42% and 0.99 mm for November; and 31% and 0.74 mm for December. The performance of LSSVM was enhanced by 6% and 0.28 mm for October; 22% and 0.20 mm for November; and 4% and 0.10 mm for December, respectively. For July and August, the suggested algorithms could not improve the performance of ANFIS. The algorithms did optimize LSSVM in all months, so the RMSE and mean absolute error were improved by 0.15 and 0.28 mm for July and 0.28 and 0.56 mm for August, respectively.

Evolutionary and adaptive inheritance enhanced Grey Wolf Optimization algorithm for binary domains

This paper introduces a new binary Grey Wolf Optimization (GWO) algorithm, which is one of the recent swarm intelligence-based metaheuristic algorithms. Its various extensions have been reported in the related literature. Despite numerous successful applications in real-valued optimization problems, the canonical GWO algorithm cannot directly handle binary optimization problems. To this end, transformation functions are commonly employed to map the real-valued solution vector to the binary values; however, this approach brings about the undesired problem of spatial disconnect. In this study, evolutionary and adaptive inheritance mechanisms are employed in the GWO algorithm so as to operate in the binary domain directly. To mimic the leadership hierarchy procedure of the GWO, multi-parent crossover with two different dominance strategies is developed while updating the binary coordinates of the wolf pack. Furthermore, adaptive mutation with exponentially decreasing step-size is adopted to avoid premature convergence and to establish a balance between intensification and diversification. The performance of the proposed algorithm is tested on the well-known binary benchmark suites comprised of the Set-Union Knapsack Problem (SUKP) that extends the 0–1 Knapsack Problem and the Uncapacitated Facility Location Problem (UFLP). Comprehensive experimental study including real-life applications and statistical analyses demonstrate the effectiveness of the proposed algorithm.

Q-Learning Based Failure Detection and Self-Recovery Algorithm for Multi-Robot Domains

Task allocation is the essential part of multi-robot coordination researches and it plays a significant role to achieve desired system performance. Uncertainties in multi-robot systems’ working environment due to nature of them are the major hurdle for perfect coordination. When learning-based task allocation approaches are used, firstly robots learn about their working environment and then they benefit from their experiences in future task allocation process. These approaches provide useful solutions as long as environmental conditions remain unchanged. If permanent changes in environment characteristics or some failure in multi-robot system occur undesirably e.g. in disaster response which is a good example to represent such cases, the previously-learned information becomes invalid. At this point, the most important mission is to detect the failure and to recover the system initial learning state. For this purpose, Q-learning based failure detection and self-recovery algorithm is proposed in this study. According to this approach, multi-robot system checks whether these variations permanent, then recover the system to learning state if it is required. So, it provides dynamic task allocation procedure having great advantages against unforeseen situations. The experimental results verify that the proposed algorithm offer efficient solutions for multi-robot task allocation problem even in systemic failure cases. DOI: 10.5755/j01.eie.25.2.23197

Mesh Parametrization Driven by Unit Normal Flow

AbstractBased on mesh deformation, we present a unified mesh parametrization algorithm for both planar and spherical domains. Our approach can produce intermediate frames from the original meshes to the targets. We derive and define a novel geometric flow: ‘unit normal flow (UNF)’ and prove that if UNF converges, it will deform a surface to a constant mean curvature (CMC) surface, such as planes and spheres. Our method works by deforming meshes of disk topology to planes, and spherical meshes to spheres. Our algorithm is robust, efficient, simple to implement. To demonstrate the robustness and effectiveness of our method, we apply it to hundreds of models of varying complexities. Our experiments show that our algorithm can be a competing alternative approach to other state‐of‐the‐art mesh parametrization methods. The unit normal flow also suggests a potential direction for creating CMC surfaces.

Evolutionary Heuristic A* Search: Pathfinding Algorithm with Self-Designed and Optimized Heuristic Function

The performance and efficiency of A* search algorithm heavily depends on the quality of the heuristic function. Therefore, designing an optimal heuristic function becomes the primary goal of developing a search algorithm for specific domains in artificial intelligence. However, it is difficult to design a well-constructed heuristic function without careful consideration and trial-and-error, especially for complex pathfinding problems. The complexity of a heuristic function increases and becomes unmanageable to design when an increasing number of parameters are involved. Existing approaches often avoid complex heuristic function design: they either trade-off the accuracy for faster computation or taking advantage of the parallelism for better performance. The objective of this paper is to reduce the difficulty of complex heuristic function design for A* search algorithm. We aim to design an algorithm that can be automatically optimized to achieve rapid search with high accuracy and low computational cost. In this paper, we present a novel design and optimization method for a Multi-Weighted-Heuristics function (MWH) named Evolutionary Heuristic A* search (EHA*) to: (1) minimize the effort on heuristic function design via Genetic Algorithm (GA), (2) optimize the performance of A* search and its variants including but not limited to WA* and MHA*, and (3) guarantee the completeness and optimality. EHA* algorithm enables high performance searches and significantly simplifies the processing of heuristic design. We apply EHA* to multiple grid-based pathfinding benchmarks to evaluate the performance. Our experiment result shows that EHA* (1) is capable of choosing an accurate heuristic function that provides an optimal solution, (2) can identify and eliminate inefficient heuristics, (3) is able to automatically design multi-heuristics function, and (4) minimizes both the time and space complexity.

Q-Learning Based Failure Detection and Self-Recovery Algorithm for Multi-Robot Domains

Task allocation is the essential part of multi-robot coordination researches and it plays a significant role to achieve desired system performance. Uncertainties in multi-robot systems’ working environment due to nature of them are the major hurdle for perfect coordination. When learning-based task allocation approaches are used, firstly robots learn about their working environment and then they benefit from their experiences in future task allocation process. These approaches provide useful solutions as long as environmental conditions remain unchanged. If permanent changes in environment characteristics or some failure in multi-robot system occur undesirably e.g. in disaster response which is a good example to represent such cases, the previously-learned information becomes invalid. At this point, the most important mission is to detect the failure and to recover the system initial learning state. For this purpose, Q-learning based failure detection and self-recovery algorithm is proposed in this study. According to this approach, multi-robot system checks whether these variations permanent, then recover the system to learning state if it is required. So, it provides dynamic task allocation procedure having great advantages against unforeseen situations. The experimental results verify that the proposed algorithm offer efficient solutions for multi-robot task allocation problem even in systemic failure cases.DOI: 10.5755/j01.eie.25.1.22728

Reducing dimensionality to model 2D rotating and standing waves in a delayed nonlinear optical system with thin annulus aperture

The purpose of the paper is to theoretically investigate 2D wave patterns in a nonlinear optical system with diffractive feedback. We consider a delayed functional differential diffusion equation on a thin annulus with Neumann boundary conditions. To study pattern formation phenomena, we construct the Faria normal form of a Hopf bifurcation, which is necessarily degenerate because the equation exhibits O(2) symmetry. The coefficients of the normal form determine the excitation of rotating or standing waves with the prescribed spatio-temporal characteristics, but these coefficients can be expressed only implicitly. However, for sufficiently thin annuli, the equation corresponds to a limit 1D model on a circle, which was carefully analysed in our previous papers and whose normal form was explicitly calculated. 2D wave stability predictions that we make based on the normal form of the limit 1D model are in good agreement with direct numerical simulations of the 2D model. To accelerate computation, we elaborated an efficient fast finite Hankel transform algorithm for thin annular domains.

Adaptive Algorithm for Three-Dimensional Mesh Generation Based on Constrained Delaunay

Mesh generation is a key step for many areas. Here, an adaptive mesh generation algorithm for piecewise linear domains based on constrained Delaunay is proposed. We focus on improving the quality of the meshes generated and make them conforming to an isotropic size function which is specified by the user. The preliminary mesh with boundaries conforming is generated first. We try to add points to split the mesh either bad shape or not conforming to the size function. The new point can be added to the domain only if it is not close to the existing point in the domain. Finally, local meshes are reconstructed to make all meshes comply with the constrained Delaunay. Experimental comparisons show that the new algorithm is advantageous in generating adaptive mesh. The presented method can be used in a wide range of areas such as computer vision, finite element method and many other areas.

Transferable Contextual Bandit for Cross-Domain Recommendation

Traditional recommendation systems (RecSys) suffer from two problems: the exploitation-exploration dilemma and the cold-start problem. One solution to solving the exploitation-exploration dilemma is the contextual bandit policy, which adaptively exploits and explores user interests. As a result, the contextual bandit policy achieves increased rewards in the long run. The contextual bandit policy, however, may cause the system to explore more than needed in the cold-start situations, which can lead to worse short-term rewards. Cross-domain RecSys methods adopt transfer learning to leverage prior knowledge in a source RecSys domain to jump start the cold-start target RecSys. To solve the two problems together, in this paper, we propose the first applicable transferable contextual bandit (TCB) policy for the cross-domain recommendation. TCB not only benefits the exploitation but also accelerates the exploration in the target RecSys. TCB's exploration, in turn, helps to learn how to transfer between different domains. TCB is a general algorithm for both homogeneous and heterogeneous domains. We perform both theoretical regret analysis and empirical experiments. The empirical results show that TCB outperforms the state-of-the-art algorithms over time.

Deriving ICD-11 personality disorder domains from dsm-5 traits: initial attempt to harmonize two diagnostic systems.

The personality disorder domains proposed for the ICD-11 comprise Negative Affectivity, Detachment, Dissociality, Disinhibition, and Anankastia, which are reasonably concordant with the higher-order trait domains in the Alternative DSM-5 Model for Personality Disorders. We examined (i) whether designated DSM-5 trait facets can be used to describe the proposed ICD-11 trait domains, and (ii) how these ICD-11 trait features are hierarchically organized. A mixed Danish derivation sample (N=1541) of 615 psychiatric out-patients and 925 community participants along with a US replication sample (N=637) completed the Personality Inventory for DSM-5 (PID-5). Sixteen PID-5 traits were designated to cover features of the ICD-11 trait domains. Exploratory structural equationmodeling (ESEM) analyzes showed that the designated traits were meaningfully organized in the proposed ICD-11 five-domain structure as well as other recognizable higher-order models of personality and psychopathology. Model fits revealed that the five proposed ICD-11 personality disorder domains were satisfactorily resembled, and replicated in the independent US sample. The proposed ICD-11 personality disorder domains can be accurately described using designated traits from the DSM-5 personality trait system. A scoring algorithm for the ICD-11 personality disorder domains is provided in appendix.

All-quad meshing without cleanup

We present an all-quad meshing algorithm for general domains. We start with a strongly balanced quadtree. In contrast to snapping the quadtree corners onto the geometric domain boundaries, we move them away from the geometry. Then we intersect the moved grid with the geometry. The resulting polygons are converted into quads with midpoint subdivision. Moving away avoids creating any flat angles, either at a quadtree corner or at a geometry–quadtree intersection. We are able to handle two-sided domains, and more complex topologies than prior methods. The algorithm is provably correct and robust in practice. It is cleanup-free, meaning we have angle and edge length bounds without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is fast and predictable. This paper has better quality bounds, and the algorithm is demonstrated over more complex domains, than our prior version.

Partition of unity interpolation on multivariate convex domains

In this paper, we present an algorithm for multivariate interpolation of scattered data sets lying in convex domains [Formula: see text], for any [Formula: see text]. To organize the points in a multidimensional space, we build a [Formula: see text]-tree space-partitioning data structure, which is used to efficiently apply a partition of unity interpolant. This global scheme is combined with local radial basis function (RBF) approximants and compactly supported weight functions. A detailed description of the algorithm for convex domains and a complexity analysis of the computational procedures are also considered. Several numerical experiments show the performances of the interpolation algorithm on various sets of Halton data points contained in [Formula: see text], where [Formula: see text] can be any convex domain, like a 2D polygon or a 3D polyhedron. Finally, an application to topographical data contained in a pentagonal domain is presented.

An optimal mesh generation algorithm for domains with Koch type boundaries

In this paper we propose a mesh algorithm to generate a regular and conformal family of nested triangulations for a planar domain divided into two non-convex polygonal subdomains by a prefractal Koch type interface. The presence of the interface, a polygonal curve, induces a natural triangulation in which the vertices of the prefractal are also nodes of the triangulation. In order to achieve an optimal rate of convergence of the numerical approximation a suitably refined mesh around the reentrant corners is required. This is achieved by generating a mesh compliant with the Grisvard's condition. We present the mesh algorithm and a detailed proof of the Grisvard conditions.