PACKING PROBLEM CIRCLES IN RECTANGLE SOFTWARE

For instance, several real life industrial applications require the allocation of a set of pieces to a larger standardized rectangular stock unit. Packing problems constitute a family of natural combinatorial optimization problems, which occur in many fields of study such as computer science, industrial engineering, logistics and manufacturing and production processes. Resultados numéricos son presentados para demostrar la eficiencia del enfoque propuesto y realizar una comparación con los resultados conocidos.

PACKING PROBLEM CIRCLES IN RECTANGLE SOFTWARE

El problema de empaquetamiento se escribe entonces, como un problema de optimización 0–1 a gran escala y es resuelto con software comercial. Se propone una nueva formulación basada en el uso de una malla regular que cubre el contenedor y donde se considera a los nodos de la malla como posiciones potenciales para la asignación de centros de los círculos. Frecuentemente, el problema es formulado como un problema de optimización continua no convexo que es resuelto con técnicas heurísticas combinadas con procedimientos de búsqueda local. Este problema tiene numerosas aplicaciones dentro de la logística, incluyendo la producción y empaquetado para la industria textil, naval, automotriz, aeroespacial y la industria de alimentos. El objetivo es maximizar el número (ponderado) de círculos dentro del contenedor o minimizar el desperdicio de espacio dentro del mismo. Se considera el problema de empaquetar un número limitado de círculos de radios diferentes en un contenedor rectangular de dimensiones fijas. Numerical results are presented to demonstrate the efficiency of the proposed approach. Nesting circles inside one another is also considered. Two families of valid inequalities are proposed to strengthening the formulation. The resulting binary problem is then solved by the commercial software.

The binary variables represent the assignment of centers to the nodes of the grid. The packing problem is then stated as a large scale linear 0–1 optimization problem. A new formulation is proposed based on using a regular grid approximated the container and considering the nodes of the grid as potential positions for assigning centers of the circles. Frequently the problem is formulated as a nonconvex continuous optimization problem which is solved by heuristic techniques combined with the local search procedures. This problem has numerous applications in logistics, including production and packing for the textile, apparel, naval, automobile, aerospace and food industries. The aim is to maximize the (weighted) number of circles placed into the container or minimize the waste. See more Open AccessĪ problem of packing a limited number of unequal circles in a fixed size rectangular container is considered. Measurement devices (pressure, temperature, flow, voltage, frequency etc.), precision engineering, medical devices, instrumentation for education (devices and software), sensor technology, mechatronics and robotics. Solid-state physics, radio engineering, telecommunications, control systems, signal processing, power electronics, electronic devices and circuits and automation. Operations research, systems engineering, management science, complex systems and cybernetics applications and information technologies Electronic Engineering Computer ScienceĬomputer graphics and visualization, programming, human-computer interaction, neural networks, image processing and software engineering. JART classifies research into the following main fields: Material Scienceīiomaterials, carbon, ceramics, composite, metals, polymers, thin films, functional materials and semiconductors. The journal does not charge for submission, processing, publication of manuscripts or for color reproduction of photographs. JART publishes manuscripts describing original research, with significant results based on experimental, theoretical and numerical work. The Journal of Applied Research and Technology (JART) is a bimonthly open access journal that publishes papers on innovative applications, development of new technologies and efficient solutions in engineering, computing and scientific research.

Packing problem circles in rectangle