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. Keywords: Circle Packing, Integer Programming, Large Scale Optimization. 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. * de Ingeniería Mecánica y Eléctrica, Universidad Autónoma de Nuevo León, Monterrey, Nuevo León, México.Ī problem of packing a limited number of unequal circles in a fixed size rectangular container is considered. Approximate Packing Circles in a Rectangular Container: Valid Inequalities and Nestingġ Complex Systems Department, Computing Center of Russian Academy of Sciences, Moscow, Russia.
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