Using an Analytical Computational-Geometry Library to Model Nonoverlap and Boundary-Distance Constraints and their Application to Packing Poly-Bézier Shapes

Paul Morton (pmortonmonarchip.com)

Abstract: In this paper we will show how to model nonoverlap as well as uniform and nonuniform boundary-distance constraints between poly-Bézier shapes using an analytical computational-geometry library. We then use this capability to develop, implement and analyze analytical-optimization solutions to minimum-area rectangular-boundary packing-problems as well as minimum-area one- and two-dimensional puzzle-piece packing-problems. In the process, we will demonstrate the ease and efficiency with which analytical-optimization solutions to complex packing-problems can be formulated, implemented, solved, and analyzed using these models.

Keywords: Modeling Nonoverlap Constraints, Modeling Boundary-distance Constraints, Uniform Boundary-Distance Constraint, Nonuniform Boundary-Distance Constraint, Nonlinear Optimization, Shape Packing, Poly-Bézier Shapes, Puzzle-Piece Packing, Cylindrical Packing, Analytical Computational-Geometry Library, ACGL, IPOPT.

Category 1: Optimization Software and Modeling Systems

Category 2: Nonlinear Optimization (Bound-constrained Optimization )

Category 3: Applications -- Science and Engineering

Citation: MonarchIP P.O. Box 202767 Austin, Texas 78720 December 2021

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Entry Submitted: 12/28/2021
Entry Accepted: 12/30/2021
Entry Last Modified: 02/11/2022

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