A genetic algorithm-based optimization method is proposed for solving the problem of nesting arbitrary shapes. Depending on the number of objects and the size of the search space, realizing an optimal solution within a reasonable time may not be possible. In this paper, a mating concept is introduced to reduce the solution time. Mating between two objects is defined as the positioning of one object relative to the other by merging common features that are assigned by the mating condition between them. A constrained move set is derived from a mating condition that allows the transformation of the object in each mating pair to be fully constrained with respect to the other. Properly mated objects can be placed together, thus reducing the overall computation time. Several examples are presented to demonstrate the efficiency of utilizing the mating concept to solve a nesting optimization problem.

Issue Section:
Technical Papers
Keywords:
genetic algorithms, bin packing
Topics:
Shapes, Algorithms
1.
Zhang, X., and Zhou, J., 1995, “A Heuristic Method for Two-dimensional Layout Problems,” in ASME Design Engineering Technical Conferences, Vol. DE-Vol. 82-1.
2.
Fujita, K., Akagi, S., and Hirokawa, N., 1993, “Hybrid Approach for Optimal Nesting Using a Genetic Algorithm and a Local Minimization Algorithm,” ASME Advances in Design Automation DE-Vol. 65-1.
3.
Jain, S., and Gea, H. C., 1996, “Two-dimensional Packing Problems Using Genetic Algorithms,” Proceedings of the 1996 ASME Design Engineering Technical Conference and Computers in Engineering Conference.
4.
Li, Z., 1994, “Compaction Algorithms for Non-Convex Polygons and Their Applications,” PhD thesis, Harvard University.
5.
Milenkovic, V. J., 1997, “Rotational Polygon Overlap Minimization,” Proceedings of the 13th Annual Symposium on Computational Geometry (SoCG).
6.
Daniels, K. M., 1995, “Containment Algorithms for Non-convex Polygons with Applications to Layout,” PhD thesis, Harvard University, Cambridge, Massachusetts.
7.
Daniels, K., and Milenkovic, V. J., 1996, “Column-based Strip Packing Using Ordered and Compliant Containment,” International Journal on Computational Geometry and Applications (IJCGA). Special issue on Applied Computational Geometry.
8.
Van Camp
,
D. J.
,
Carter
,
M. W.
, and
Vannelli
,
A.
,
1991
, “
A Nonlinear Optimization Approach for Solving Facility Layout Problems
,”
Eur. J. Oper. Res.
,
57
, pp.
174
–
189
.
9.
Heragu
,
S. S.
, and
Alfa
,
A. S.
,
1992
, “
Experimental Analysis of Simulated Annealing Based Algorithms for the Layout Problem
,”
Eur. J. Oper. Res.
,
57
,
190
–
202
.
10.
Yu, C., and Manoochehri, S., 2000, “Optimal Layout of Irregularly Shaped Objects,” ASME Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Baltimore, MD.
11.
Yu, C., and Manoochehri, S., 1999, “Overlap Detection Using Minkowski Sum in Two-dimensional Layout,” Proceedings of ASME Design Engineering Technical Conferences and Design Automation Conference, LasVegas, NV.
12.
de Berg, M., van Kreveld, M., Overmars, M., and Schwarzkopf, O., 1997, Computational Geometry: Algorithms and Applications, Springer.
Copyright © 2002
 by ASME
You do not currently have access to this content.