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The efficient arrangement of patterns on a substrate surface is of paramount importance across diverse domains, including manufacturing, design, nanotechnology, and printed electronics. This paper introduces three distinct strategies for pattern arrangement within the realm of two-dimensional cutting and packing challenges. Firstly, for irregular patterns, we have developed a modified genetic algorithm that effectively determines the spatial relationships between patterns, facilitating subsequent packing processes. Secondly, we present the “MaxiRectPack” method designed for rectangular patterns. This method utilizes partitioning techniques and a variety of orientation schemes to maximize pattern packing efficiency. Lastly, we propose a technique based on normalized 2-D cross-correlation for patterns of diverse shapes, allowing precise placement while accounting for variations in substrate and pattern energy. These methodologies are adaptable, catering to irregular, rectangular, and diverse pattern shapes, offering versatile solutions for pattern placement in the context of two-dimensional cutting and packing. With a strong emphasis on resource conservation and spatial efficiency, this research equips practitioners and researchers with practical tools for optimizing material utilization and pattern arrangement on substrates.

This article proposes a novel discrete grey wolf optimization for the packing problem, called the two-dimensional strip packing (2DSP) problem without guillotine constraint. The 2DSP involves cutting pieces from a stock sheet with the objective of minimizing waste. To solve the 2DSP problem by the discrete grey wolf algorithm, many strategies are originally proposed. The searching and attacking operators in the algorithm are redesigned to guarantee coding effectiveness. A novel approach to measure the distance between the wolves is presented. In addition, an improved best-fit strategy is developed to solve this packing problem. The best-fit strategy divides the situation into five cases based on the width and length of the rectangle. Computational results on widely used benchmark instances show that the novel discrete grey wolf algorithm can solve the 2DSP problem effectively, and surpasses most of the previously reported meta-heuristic algorithms.

For large power systems, a continual challenge is to display wide-area data in a way that maximizes human users’ situational awareness. This paper describes a new visualization technique that draws a mosaic of colored tiles to represent multiple data fields for electric grid objects, arranged to preserve geographic context. The key problem in creating these diagrams is packing the tiles onto the display space, minimizing the total displacement while forbidding overlaps. This paper formulates that problem and presents a horizontal-packing algorithm which is able to produce a feasible, quality solution at an interactive time scale. Illustrative examples are shown for using mosaics to monitor wide-area generator status and dispatch, bus voltages, and line and transformer limits. Mosaics can be customized in numerous ways to show different aspects of the system state, providing for human users a simultaneous sense of the wide-area summary, regional trends, and prominent outliers.

This paper addresses the issue of placing a simple polygon (upon translation and rotation) on an isometric triangular grid such that the polygon contains the maximum number of triangles in its closure. This solves the problem left open in two recent papers titled “On the problem of the automated design of large-scale robot skin” and “An improved algorithm for the automated design of large scale robot skin” published in the IEEE Transactions on Automation Science and Engineering . Based on the properties of the grid, an improved algorithm is also presented. We also present some experimental results describing the use of this algorithm. [ABSTRACT FROM AUTHOR]

An optimization procedure for the layout assessment of electrically large but finite planar arrays is presented. The synthesis takes into account the desired directivity pattern that is prescribed employing bound constraints. Moreover, the size of the radiators is taken into account, which results in a hard nonoverlapping, between the elements, constraint. The latter should not be violated if we want the attained solution not only to obey the far-field mask, but also to be physically realizable. As stated, the optimization problem is twofold. An antenna design is associated with a packing problem. In order to take the constraints on the layout into account and solve the whole problem, we propose the constraint relaxation approach, which is equipped with a packing algorithm. Our study is applied to various initial geometries, and the resulting arrays appear to comply with the desired pattern and the nonoverlapping constraint. Several examples for different cases including symmetric arrays and a study on maximally sparse arrays are presented, which show the applicability and merit of the method. [ABSTRACT FROM PUBLISHER]

A hybrid genetic approach is proposed for container loading in order to meet the up-to-date customer requirements in the logistics industry. Container loading is usually modeled as a three-dimensional packing problem which is known to be NP-complete. By combining an order-based genetic algorithm with a novel heuristic placement method, the complicated and highly constrained packing problem is transformed into a simple permutation problem with a much smaller searching domain. It is guaranteed that every box is stable after placement inside the container. From the simulation results, it is demonstrated that optimal results can be duly obtained in a reasonably short period of time. [ABSTRACT FROM AUTHOR]