Optimization Online


Packing Ovals In Optimized Regular Polygons

F.J. Kampas(frank***at***physicistatlarge.com)
J.D. Pintér(jdp416***at***lehigh.edu)
I. Castillo(icastillo***at***wlu.ca)

Abstract: We present a model development framework and numerical solution approach to the general problem-class of packing convex objects into optimized convex containers. Specifically, here we discuss the problem of packing ovals (egg-shaped objects, defined here as generalized ellipses) into optimized regular polygons in R". Our solution strategy is based on the use of embedded Lagrange multipliers, followed by nonlinear (global-local) optimization. The numerical results are attained using randomized starting solutions refined by a single call to a local optimization solver. We obtain credible, tight packings for packing 4 to 10 ovals into regular polygons with 3 to 10 sides in all (224) test problems presented here, and for other similarly difficult packing problems.

Keywords: Object Packings ∙ Generalized Ellipses (Ovals, Eggs) ∙ Regular Polygon Containers ∙ Model Development Using Embedded Lagrange Multipliers ∙ Global-Local Nonlinear Optimization ∙ Numerical Test Results

Category 1: Global Optimization

Category 2: Optimization Software and Modeling Systems

Category 3: Global Optimization (Applications )

Citation: Research Report, November 2018. Submitted for publication.

Download: [PDF]

Entry Submitted: 11/27/2018
Entry Accepted: 11/27/2018
Entry Last Modified: 11/27/2018

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society