scholarly journals Mixed integer non-linear programming model for reliable and safer design at an early stage

2021 ◽  
Vol 147 ◽  
pp. 107256
Author(s):  
Daniel Vázquez ◽  
Rubén Ruiz-Femenia ◽  
José A. Caballero
Keyword(s):  
Linear Programming ◽  
Programming Model ◽  
Early Stage ◽  
Linear Programming Model ◽  
Mixed Integer ◽  
Non Linear Programming ◽  
Non Linear

scholarly journals Near optimal minimal convex hulls of disks

2021 ◽  
Author(s):  
Josef Kallrath ◽  
Joonghyun Ryu ◽  
Chanyoung Song ◽  
Mokwon Lee ◽  
Deok-Soo Kim
Keyword(s):  
Linear Programming ◽  
Convex Hull ◽  
Programming Model ◽  
Linear Programming Model ◽  
Mixed Integer ◽  
Convex Hulls ◽  
Non Linear Programming ◽  
Minimal Convex ◽  
Non Linear ◽  
Problem Instances

AbstractThe minimal convex hulls of disks problem is to find such arrangements of circular disks in the plane that minimize the length of the convex hull boundary. The mixed-integer non-linear programming model, named [17], works only for small to moderate-sized problems. Here we propose a polylithic framework of the problem for big problem instances by combining the following algorithms and models: (i) A fast disk-packing algorithm based on Voronoi diagrams, non-linear programming (NLP) models for packing disks, and an NLP model for minimizing the discretized perimeter of convex hull; (ii) A fast convex-hull algorithm to compute the convex hulls of disk arrangements and their perimeter lengths; (iii) A mixed-integer NLP model taking the output of as its input. We present complete analytic solutions for small problems up to four disks and a semi-analytic mixed-integer linear programming model which yields exact solutions for strip packing problems with up to one thousand congruent disks. It turns out that the proposed polylithic approach works fine for large problem instances containing up to 1,000 disks. Monolithic and polylithic solutions using usually outperform other approaches. The polylithic approach yields better solutions than the results in [17] and provides a benchmark suite for further research.

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