A genetic algorithm for the two-dimensional Single Large Object Placement Problem

The two-dimensional Single Large Object Placement Problem (SLOPP) problem consists of determining a cutting pattern of a set of n small rectangular piece types (little object) on a rectangular stock plate (large object) of length L and width W, as to maximize the sum of the profits of the pieces to be cut. Each piece type i, i = 1, . . ., m, is characterized by a length li , a width wi , a profit (or weight) ci and an upper demand value bi . Only guillotine cuts are allowed and the pieces may be rotated by 90°. In this paper two heuristic alghoritm were applied to constrained two-dimensional cutting problems and the results were compared.

[1]  Ralph E. Gomory,et al.  The Theory and Computation of Knapsack Functions , 1966, Oper. Res..

[2]  John E. Beasley,et al.  Algorithms for Unconstrained Two-Dimensional Guillotine Cutting , 1985 .

[3]  A. Bagchi,et al.  Best-First Search Methods for Constrained Two-Dimensional Cutting Stock Problems , 1993, Oper. Res..

[4]  Günther R. Raidl,et al.  Solving a Real-World Glass Cutting Problem , 2004, EvoCOP.

[5]  S. Jakobs,et al.  European Journal Ofoperational Research on Genetic Algorithms for the Packing of Polygons , 2022 .

[6]  Gerhard Wäscher,et al.  An improved typology of cutting and packing problems , 2007, Eur. J. Oper. Res..

[7]  Mhand Hifi,et al.  Approximate and Exact Algorithms for Constrained (Un) Weighted Two-dimensional Two-staged Cutting Stock Problems , 2001, J. Comb. Optim..

[8]  Nicos Christofides,et al.  An Algorithm for Two-Dimensional Cutting Problems , 1977, Oper. Res..

[9]  Mhand Hifi,et al.  Strip generation algorithms for constrained two-dimensional two-staged cutting problems , 2004, Eur. J. Oper. Res..

[10]  Harald Dyckhoff,et al.  A typology of cutting and packing problems , 1990 .

[11]  Mhand Hifi.  An improvement of viswanathan and bagchi's exact algorithm for constrained two-dimensional cutting stock , 1997, Comput. Oper. Res..

[12]  L. Fogel,et al.  European Journal Ofoperational Research on Genetic Algorithms for the Packing of Polygons , 1996 .

[13]  John E. Beasley,et al.  An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure , 1985, Oper. Res..

[14]  P. Y. Wang,et al.  Two Algorithms for Constrained Two-Dimensional Cutting Stock Problems , 1983, Oper. Res..

[15]  J. O. Berkey,et al.  Two-Dimensional Finite Bin-Packing Algorithms , 1987 .

[16]  Kathryn A. Dowsland,et al.  Genetic Algorithms-a Tool for OR? , 1996 .

[17]  Hongfei Teng,et al.  An improved BL-algorithm for genetic algorithm of the orthogonal packing of rectangles , 1999, Eur. J. Oper. Res..