Search Results (27)

The construction industry remains one of the main contributors to environmental degradation due to its high material consumption and massive waste generation. This study introduces Granizzo, a hybrid methodological framework that integrates artificial intelligence (AI), parametric design, and digital fabrication to transform construction and demolition waste (CDW) into sustainable architectural mosaics. The workflow involves material selection, AI-driven classification of fragments, generative design algorithms for pattern optimization, and CNC-based experimental prototyping. A dataset comprising brick, cement, marble, glass, and stone fragments was analyzed using a Random Forest classifier, achieving an average accuracy above 90%. Parametric design algorithms based on circle packing and tessellation achieved up to 92% surface coverage, reducing voids and optimizing formal diversity compared to manually assembled mosaics. Prototypes fabricated with CNC molds exhibited 35% shorter assembly times and 20% fewer voids, confirming the technical feasibility of the proposed process. A preliminary Life Cycle Assessment (LCA) revealed measurable environmental benefits in energy savings and CO₂ reduction. The findings suggest that Granizzo constitutes a replicable methodological platform that merges digital precision and sustainable materiality, enabling a circular approach to architectural production and aligning with contemporary challenges of design innovation, material reuse, and computational creativity. Full article

There exists an extensive and fairly comprehensive discrete analytic function theory which is based on circle packing. This paper introduces a faithful discrete analogue of the classical Schwarzian derivative to this theory and develops its basic properties. The motivation comes from the current lack of circle packing algorithms in spherical geometry, and the discrete Schwarzian derivative may provide for new approaches. A companion localized notion called an intrinsic schwarzian is also investigated. The main concrete results of the paper are limited to circle packing flowers. A parameterization by intrinsic schwarzians is established, providing an essential packing criterion for flowers. The paper closes with the study of special classes of flowers that occur in the circle packing literature. As usual in circle packing, there are pleasant surprises at nearly every turn, so those not interested in circle packing theory may still enjoy the new and elementary geometry seen in these flowers. Full article

The proliferation of wireless sensor networks in remote and inaccessible areas demands efficient data collection approaches that minimize energy consumption while ensuring comprehensive coverage. Traditional data retrieval methods face significant challenges when sensors are sparsely distributed across extensive areas, particularly in scenarios where direct sensor access is impractical due to terrain constraints or operational limitations. This research addresses these challenges through a novel hybrid optimization framework that combines integer linear programming (ILP) with multiple traveling salesperson problem (mTSP) algorithms for drone-based data collection in wireless sensor networks (WSNs). The methodology employs a two-phase approach, where ILP optimally determines strategic access point locations for sensor clustering based on communication capabilities, followed by mTSP optimization to generate efficient inter-AP flight trajectories rather than individual sensor visits. Comprehensive simulations across diverse network configurations and drone quantities demonstrate consistent performance improvements, with travel distance reductions reaching 32% compared to conventional mTSP implementations. Comparative evaluation against established clustering algorithms including Voronoi, DBSCAN, Constrained K-Means, Graph-Based clustering, and Greedy Circle Packing confirms that ILP consistently achieves optimal access point allocation while maintaining superior routing efficiency. Additionally, a novel quality assessment metric quantifies sensor grouping effectiveness, revealing that ILP-based clustering advantages become increasingly pronounced with higher sensor densities, providing substantial operational benefits for large-scale wireless sensor network deployments. Full article

This study presents a novel, two-stage algorithm that minimizes the number of machines and operators required to produce multiple product types repeatedly in cyclic scheduling. Our algorithm treats the problem of minimum machines as a bin packing problem (BPP), and the problem of determining the number of operators required is also modeled as the BPP, but with constraints. The BPP is NP-hard, but with suitable heuristic algorithms, the proposed model allocates multiple product types to machines and multiple machines to operators without overlapping setup times (machine interference). The production schedule on each machine is represented as a circle (donut). By using lower bounds, it is possible to assess whether the number of machines required by our model is optimal; if not, the optimality gap can be quantified. The algorithm has been validated using real-world data from an industrial facility producing 17 types of products. The results of our algorithm led to significant cost savings and improved scheduling performance. The outcomes demonstrate the effectiveness of the proposed algorithm in optimizing resource utilization by reducing the number of machines and operators required. Although this study focuses on a manufacturing system, the model can also be applied to other contexts. Full article

This paper addresses the maximum coverage location problem in a generalized setting, where both facilities (service areas) and regional demand are modeled as continuous entities. Unlike traditional formulations, our approach allows for arbitrary shapes for both service areas and demand regions, with additional constraints on facility placement. The key novelty of this work is its ability to handle complex, irregularly shaped service areas, including approximating them as unions of centrally symmetric shapes. This enables the use of an analytical approach based on spatial symmetry, which allows for efficient estimation of the covered area. The problem is formulated as a nonlinear optimization task. We analyze the properties of the objective function and leverage the Shapely library in Python 3.13.3 for efficient geometric computations. To improve computational efficiency, we develop an extended elastic model that significantly reduces processing time. This model generalizes the well-known quasi-physical, quasi-human algorithm for circle packing, extending its applicability to more complex spatial configurations. The effectiveness of the proposed approach is validated through test cases in which service areas take the form of circles, ellipses, and irregular polygons. Our method provides a robust and adaptable solution for various settings of practically interesting continuous maximum coverage location problems involving irregular regional demand and service areas. Full article

Traditional classifications of global development, such as the developed/developing dichotomy or Global North/South, often oversimplify the intricate landscape of human development. This paper leverages computational tools, advanced visualization techniques, and mathematical modeling to challenge these conventional categories and reveal a continuous development spectrum among nations. By applying hierarchical clustering, multidimensional scaling, and interactive visualizations to Human Development Index (HDI) data, we identify “development neighborhoods”—clusters of countries that exhibit similar development patterns, sometimes across geographical boundaries. Our methodology combines network theory, statistical physics, and digital humanities approaches to model development as a continuous field, introducing novel metrics for development potential and regional inequality. Through analysis of HDI data from 193 countries (1990–2022), we demonstrate significant regional variations in development trajectories, with Africa showing the highest mean change rate (28.36%) despite maintaining the lowest mean HDI (0.557). The implementation of circle packing and radial dendrogram visualizations reveals both population dynamics and development continuums, while our mathematical framework provides rigorous quantification of development distances and cluster stability. This approach not only uncovers sophisticated developmental progressions but also emphasizes the importance of continuous frameworks over categorical divisions. The findings highlight how digital humanities tools can enhance our understanding of global development, providing policymakers with insights that traditional methods might overlook. Our methodology demonstrates the potential of computational social science to offer more granular analyses of development, supporting policies that recognize the diversity within regional and developmental clusters, while our mathematical framework provides a foundation for future quantitative studies in development economics. Full article

In this study, we investigated circle design in a bubble chart. The bubble chart that we designed has a unit circle at the center and is surrounded by a series of layered circle rings. In order to add the next layer of circles, there is always a silhouette circle that is tangential to all circles in the newest layer. The extension of the circle is partitioned into two classes: one in which each layer has the same number of circles with the same radii, and another in which the new layer has circles with different radii. We solve this problem geometrically and/or algebraically if the problem is simple and present a heuristic algorithm for solving more complex problems. Full article

Wireless Sensor Networks are used in an ever-increasing range of applications, thanks to their ability to monitor and transmit data related to ambient conditions in almost any area of interest. The optimization of coverage and the assurance of connectivity are fundamental for the efficiency and consistency of Wireless Sensor Networks. Optimal coverage guarantees that all points in the field of interest are monitored, while the assurance of the connectivity of the network nodes assures that the gathered data are reliably transferred among the nodes and the base station. In this research article, a novel algorithm based on Particle Swarm Optimization is proposed to ensure coverage and connectivity in Wireless Sensor Networks. The objective function is derived from energy function minimization methodologies commonly applied in bounded space circle packing problems. The performance of the novel algorithm is not only evaluated through both simulation and statistical tests that demonstrate the efficacy of the proposed methodology but also compared against that of relative algorithms. Finally, concluding remarks are drawn on the potential extensibility and actual use of the algorithm in real-world scenarios. Full article

We review and present several challenging model classes arising in the context of finding optimized object packings (OP). Except for the smallest and/or simplest general OP model instances, it is not possible to find their exact (closed-form) solution. Most OP problem instances become increasingly difficult to handle even numerically, as the number of packed objects increases. Specifically, here we consider classes of general OP problems that can be formulated in the framework of nonlinear optimization. Research experience demonstrates that—in addition to utilizing general-purpose nonlinear optimization solver engines—the insightful exploitation of problem-specific heuristics can improve the quality of numerical solutions. We discuss scalable OP problem classes aimed at packing general circles, spheres, ellipses, and ovals, with numerical (conjectured) solutions of non-trivial model instances. In addition to their practical relevance, these models and their various extensions can also serve as constrained global optimization test challenges. Full article

Malfatti’s problem is the problem of fitting three circles into a triangle such that they are tangent to each other and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to include T_n = 1 + 2 + … + n circles inside the triangle with special tangency properties among the circles and triangle sides; this problem is referred to as the extended Malfatti problem or the Tri(T_n) problem. In the extended Malfatti problem, the number of circles in the triangle is a triangle number because the tangency properties between the internal circles and the three sides of the triangle have a special type of structure; that is, the corner circle is tangent to two sides of the triangle and two other circles, the boundary circles are tangent to one side of the triangle and four other circles, and the inner circles are always tangent to six other circles. The circles we find in the extended Malfatti problem have the following property: the smallest and largest radii of the circles differ to a great extent. In the study presented herein, we propose algorithms to solve the problem that the tangency properties between the circles and the sides of the triangle are not fixed, so that the number of circles in the triangle is not necessarily a triangle number. The purpose of this change is to attempt to establish the radii of the circles in the triangle within a small range. Full article

This research identifies the relationship between industrial engineering and environmental sustainability knowledge components. A combination of a systematic literature review (SLR) and applied thematic analysis (ATA) is employed to uncover the pertinent literature associated with the purpose of this research. Whilst various forms of strategies, theories, methods, and practices were uncovered in each of the knowledge components, only a few were overlapping. These overlapping components include green supply chain operations, circular economy, and technology management. This study is the first in a series of studies contextualising industrial engineering knowledge in terms of its applicability to environmental sustainability. These results reveal concepts from industrial engineering and environmental sustainability knowledge components that can be used to systematically design methodologies or practically implement them in an industry or organisation. Methods and practices were a dedicated theme in the analysis, and these can be used by practitioners. A circle packing diagram is crafted using the IISE Body of Knowledge as a means of categorisation. This study considered industrial engineering as a catalyst in creating new forms of transdisciplinary knowledge areas. It also considers how industrial engineering knowledge can contribute to meeting environmental challenges. Full article

Malfatti’s problem involves three circles (called Malfatti circles) that are tangent to each other and two sides of a triangle. In this study, our objective is to extend the problem to find 6, 10, … $\sum _1^{n}i$ (n > 2) circles inside the triangle so that the three corner circles are tangent to two sides of the triangle, the boundary circles are tangent to one side of the triangle, and four other circles (at least two of them being boundary or corner circles) and the inner circles are tangent to six other circles. We call this problem the extended general Malfatti’s problem, or the Tri(T_n) problem, where Tri means that the boundary of these circles is a triangle, and T_n is the number of circles inside the triangle. In this paper, we propose an algorithm to solve the Tri(T_n) problem. Full article

We describe a series of parallel lenses with constant proportions packed in a circle. To construct n lenses, a regular 2(n + 1)-gon is drawn with a central diagonal of 2r length, followed by an array of n parallel diagonals perpendicular to the former. These diagonals and the central angle of the pair of peripherals, the shortest diagonals, are used to construct n rhombi. The rhombi define the shape of lenses tangential to them. To construct the arcs of the lenses, beams perpendicular to the sides of each rhombus are drawn. Four beams radiating from the top and bottom vertices of each rhombus intersect in the centers of a pair of coaxal circles. Thus, the vertical axis of each rhombus coincides with the radical axis of the pair. The intersection of the pair represents the corresponding lens. All n lenses form a tangential sequence along the central diagonal. Their cusps circumscribe the polygon and the lenses themselves. The area covered by the lenses converges to (2/3) πr². Full article

Background: Fibonacci patterns and tubular forms both arose early in the phylogeny of multicellular organisms. Tubular forms offer the advantage of a regulated internal milieu, and Fibonacci forms may offer packing efficiencies. The underlying mechanisms behind the cellular genesis of Fibonacci and tubular forms remain unknown. Methods: In a multicellular organism, cells adhere to form a macrostructure and to coordinate further replication. We propose and prove simple theorems connecting cell replication and adhesion to Fibonacci forms and simplicial topology. Results: We identify some cellular and molecular properties whereby the contact inhibition of replication by adhered cells may approximate Fibonacci growth patterns. We further identify how a component $2\to 3$ cellular multiplication step may generate a multicellular structure with some properties of a two-simplex. Tracking the homotopy of a two-simplex to a circle and to a tube, we identify some molecular and cellular growth properties consistent with the morphogenesis of tubes. We further find that circular and tubular cellular aggregates may be combinatorially favored in multicellular adhesion over flat shapes. Conclusions: We propose a correspondence between the cellular and molecular mechanisms that generate Fibonacci cell counts and those that enable tubular forms. This implies molecular and cellular arrangements that are candidates for experimental testing and may provide guidance for the synthetic biology of hollow morphologies. Full article

An intelligent assembly method was designed to realize the intelligent assembly of the profiled thermal battery pack and improve its assembly accuracy. Firstly, as the number and size of different monomer batteries vary, this paper takes the monomer thermal battery assembly as the object, with a common shape circle assembly screw arrangement and an established process model. Then, the assembly also has an improved differential evolution algorithm for assembly arrangement and process on the number, location, tightening of the screw assembly, torque, and the order of solutions. According to this scheme, the assembly and the flatness test were carried out. The results showed that the bottom plate of the assembly frame was “concave in the middle and warped around”, and the flatness error was large. The scheme was optimized by numerical simulation analysis. After optimization, the average offset of the floor plane was 0.04 mm, and the offset accounted for 0.028% of the overall height; the maximum offset was 0.094 mm and the offset was reduced by 0.312%. Full article