scholarly journals Optimization of a k-covering of a bounded set with circles of two given radii

2021 ◽  
Vol 11 (1) ◽  
pp. 232-240
Author(s):  
Alexander V. Khorkov ◽  
Shamil I. Galiev
Keyword(s):  
Linear Programming ◽  
Numerical Method ◽  
Lower Bounds ◽  
Integer Linear Programming ◽  
Numerical Results ◽  
Programming Models ◽  
Bounded Set ◽  
The Given

Abstract A numerical method for investigating k-coverings of a convex bounded set with circles of two given radii is proposed. Cases with constraints on the distances between the covering circle centers are considered. An algorithm for finding an approximate number of such circles and the arrangement of their centers is described. For certain specific cases, approximate lower bounds of the density of the k-covering of the given domain are found. We use either 0–1 linear programming or general integer linear programming models. Numerical results demonstrating the effectiveness of the proposed methods are presented.

Mixed Integer Linear Programming Models for Selecting Ground-Level Ozone Control Strategies

2014 ◽  
Vol 19 (6) ◽  
pp. 503-514 ◽  
Author(s):  
Wei-Che Hsu ◽  
Jay M. Rosenberger ◽  
Neelesh V. Sule ◽  
Melanie L. Sattler ◽  
Victoria C. P. Chen
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Control Strategies ◽  
Ground Level ◽  
Programming Models ◽  
Mixed Integer ◽  
Ground Level Ozone ◽  
Ozone Control

scholarly journals Tournaments as Feedback Arc Sets

10.37236/1214 ◽  
1995 ◽  
Vol 2 (1) ◽  
Author(s):  
Garth Isaak
Keyword(s):  
Linear Programming ◽  
Lower Bounds ◽  
Integer Linear Programming ◽  
Minimum Size ◽  
Programming Formulation ◽  
Binary Expansion ◽  
Feedback Arc Set ◽  
Disjoint Cycles ◽  
Linear Programming Formulation ◽  
Integer Linear Programming Formulation

We examine the size $s(n)$ of a smallest tournament having the arcs of an acyclic tournament on $n$ vertices as a minimum feedback arc set. Using an integer linear programming formulation we obtain lower bounds $s(n) \geq 3n - 2 - \lfloor \log_2 n \rfloor$ or $s(n) \geq 3n - 1 - \lfloor \log_2 n \rfloor$, depending on the binary expansion of $n$. When $n = 2^k - 2^t$ we show that the bounds are tight with $s(n) = 3n - 2 - \lfloor \log_2 n \rfloor$. One view of this problem is that if the 'teams' in a tournament are ranked to minimize inconsistencies there is some tournament with $s(n)$ 'teams' in which $n$ are ranked wrong. We will also pose some questions about conditions on feedback arc sets, motivated by our proofs, which ensure equality between the maximum number of arc disjoint cycles and the minimum size of a feedback arc set in a tournament.

Robust mixed-integer linear programming models for the irregular strip packing problem

2016 ◽  
Vol 253 (3) ◽  
pp. 570-583 ◽  
Author(s):  
Luiz H. Cherri ◽  
Leandro R. Mundim ◽  
Marina Andretta ◽  
Franklina M.B. Toledo ◽  
José F. Oliveira ◽  
...  
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Packing Problem ◽  
Programming Models ◽  
Mixed Integer ◽  
Strip Packing
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