Packing of Polygonal Pieces

Besides problems of optimal packing rectangular-shaped objects, as considered in previous chapters, the optimal arrangement of non-rectangular pieces is frequently of interest. Here we address aspects concerning the mutual position of polygonal pieces and the containment within a polygonal region. Moreover, we discuss the basic principles of heuristic solution approaches.

[1]  Y. Stoyan,et al.  Mathematical model and solution method of optimization problem of placement of rectangles and circles taking into account special constraints , 1998 .

[2]  Gerhard Wäscher,et al.  Cutting and packing , 1995, Eur. J. Oper. Res..

[3]  Tom M. Cavalier,et al.  A new algorithm for the two-polygon containment problem , 1997, Comput. Oper. Res..

[4]  Graham Kendall,et al.  Complete and robust no-fit polygon generation for the irregular stock cutting problem , 2007, Eur. J. Oper. Res..

[5]  Victor J. Milenkovic,et al.  Rotational polygon containment and minimum enclosure using only robust 2D constructions , 1999, Comput. Geom..

[6]  Sivan Toledo,et al.  External Polygon Containment Problems , 1994, Comput. Geom..

[7]  T. M. Cavalier,et al.  Containment of a single polygon using mathematical programming , 1996 .

[8]  Thomas Lengauer,et al.  Computing closely matching upper and lower bounds on textile nesting problems , 1998, Eur. J. Oper. Res..

[9]  Joaquim A. Jorge,et al.  Marker-making using automatic placement of irregular shapes for the garment industry , 1990, Comput. Graph..

[10]  Julia A. Bennell,et al.  Optimal clustering of a pair of irregular objects , 2015, J. Glob. Optim..

[11]  Julia A. Bennell,et al.  Tools of mathematical modeling of arbitrary object packing problems , 2010, Ann. Oper. Res..

[12]  K. Dowsland,et al.  Solution approaches to irregular nesting problems , 1995 .

[13]  Yu. G. Stoyan,et al.  A method of optimal lattice packing of congruent oriented polygons in the plane , 2000, Eur. J. Oper. Res..

[14]  Thiago de Castro Martins,et al.  Rotational placement of irregular polygons over containers with fixed dimensions using simulated annealing and no-fit polygons , 2008 .

[15]  Richard Carl Art.  An approach to the two dimensional irregular cutting stock problem. , 1966 .

[16]  Zhenyu Li,et al.  The Complexity of the Compaction Problem , 1993, CCCG.

[17]  Matteo Fischetti,et al.  Mixed-integer programming models for nesting problems , 2009, J. Heuristics.

[18]  Julia A. Bennell,et al.  The geometry of nesting problems: A tutorial , 2008, Eur. J. Oper. Res..

[19]  T. M. Cavalier,et al.  A new algorithm for the minimal-area convex enclosure problem , 1995 .

[20]  J.J.S. Sentieiro,et al.  A system for the compaction of two-dimensional irregular shapes based on simulated annealing , 1991, Proceedings IECON '91: 1991 International Conference on Industrial Electronics, Control and Instrumentation.

[21]  Antonio Albano,et al.  Optimal Allocation of Two-Dimensional Irregular Shapes Using Heuristic Search Methods , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[22]  Jacek Blazewicz,et al.  Using a tabu search approach for solving the two-dimensional irregular cutting problem , 1993, Ann. Oper. Res..

[23]  V. Milenkovic,et al.  Translational polygon containment and minimal enclosure using mathematical programming , 1999 .

[24]  Alberto L. Sangiovanni-Vincentelli,et al.  A Parallel Simulated Annealing Algorithm for the Placement of Macro-Cells , 1987, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[25]  Yu. G. Stoyan,et al.  Regular packing of congruent polygons on the rectangular sheet , 1999, Eur. J. Oper. Res..

[26]  Hiroshi Nagamochi,et al.  An iterated local search algorithm based on nonlinear programming for the irregular strip packing problem , 2009, Discret. Optim..

[27]  M. V. Novozhilova,et al.  Mathematical model and method of searching for a local extremum for the non-convex oriented polygons allocation problem , 1996 .

[28]  K. Dowsland.  Some experiments with simulated annealing techniques for packing problems , 1993 .

[29]  Yaodong Cui.  Dynamic programming algorithms for the optimal cutting of equal rectangles , 2005 .

[30]  Indrajit Mukherjee,et al.  A review of optimization techniques in metal cutting processes , 2006, Comput. Ind. Eng..

[31]  Giorgio Fasano,et al.  A global optimization point of view to handle non-standard object packing problems , 2013, J. Glob. Optim..

[32]  Victor J. Milenkovic,et al.  Densest translational lattice packing of non-convex polygons , 2002, Comput. Geom..