A greedy random adaptive search procedure for the weighted maximal planar graph problem

2003 ◽  
Vol 45 (4) ◽  
pp. 635-651 ◽  
Author(s):  
Ibrahim H. Osman ◽  
Baydaa Al-Ayoubi ◽  
Musbah Barake
Keyword(s):  
Planar Graph ◽  
Search Procedure ◽  
Adaptive Search ◽  
Maximal Planar Graph ◽  
Graph Problem

An algorithm and upper bounds for the weighted maximal planar graph problem

2015 ◽  
Vol 66 (8) ◽  
pp. 1399-1412 ◽  
Author(s):  
Amir Ahmadi-Javid ◽  
Amir Ardestani-Jaafari ◽  
Leslie R Foulds ◽  
Hossein Hojabri ◽  
Reza Zanjirani Farahani
Keyword(s):  
Planar Graph ◽  
Upper Bounds ◽  
Maximal Planar Graph ◽  
Graph Problem

Facility Layout Planning

2013 ◽  
pp. 212-223
Author(s):  
Hossein Hojabri ◽  
Elnaz Miandoabchi
Keyword(s):  
Mathematical Models ◽  
Planar Graph ◽  
Facility Layout ◽  
Layout Design ◽  
Simple Graph ◽  
Layout Planning ◽  
Adjacency Graph ◽  
Manufacturing Plants ◽  
Maximal Planar Graph ◽  
Facilities Layout

The weighted maximal planar graph (WMPG) appears in many applications. It is currently used to design facilities layout in manufacturing plants. Given an edge-weighted complete simple graph G, the WMPG involves finding a sub-graph of G that is planar in the sense that it could be embedded on the plane such that none of its edges intersect, and is maximal in the sense that no more edges can be added to it unless its planarity is violated. Finally, it is optimal in the sense that the resulting maximal planar graph holds the maximum sum of edge weights. In this chapter, the aim is to explain the application of planarity in facility layout design. The mathematical models and the algorithms developed for the problem so far are explained. In the meanwhile, the corollaries and theorems needed to explain the algorithms and models are briefly given. In the last part, an explanation on how to draw block layout from the adjacency graph is given.

scholarly journals Jobs scheduling within Industry 4.0 with consideration of worker’s fatigue and reliability using Greedy Randomized Adaptive Search Procedure

2019 ◽  
Vol 52 (19) ◽  
pp. 85-90
Author(s):  
I. El Mouayni ◽  
G. Demesure ◽  
H. Bril-El Haouzi ◽  
P. Charpentier ◽  
A. Siadat
Keyword(s):  
Industry 4.0 ◽  
Search Procedure ◽  
Adaptive Search

Finding weaknesses in networks using Greedy Randomized Adaptive Search Procedure and Path Relinking

2020 ◽  
Vol 37 (6) ◽  
Author(s):  
Sergio Pérez‐Peló ◽  
Jesús Sánchez‐Oro ◽  
Abraham Duarte
Keyword(s):  
Path Relinking ◽  
Search Procedure ◽  
Adaptive Search

scholarly journals The maximum Wiener index of maximal planar graphs

2020 ◽  
Vol 40 (4) ◽  
pp. 1121-1135
Author(s):  
Debarun Ghosh ◽  
Ervin Győri ◽  
Addisu Paulos ◽  
Nika Salia ◽  
Oscar Zamora
Keyword(s):  
Planar Graph ◽  
Connected Graph ◽  
Planar Graphs ◽  
Wiener Index ◽  
Maximal Planar Graph

Abstract The Wiener index of a connected graph is the sum of the distances between all pairs of vertices in the graph. It was conjectured that the Wiener index of an n-vertex maximal planar graph is at most $$\lfloor \frac{1}{18}(n^3+3n^2)\rfloor $$ ⌊ 1 18 ( n 3 + 3 n 2 ) ⌋ . We prove this conjecture and determine the unique n-vertex maximal planar graph attaining this maximum, for every $$ n\ge 10$$ n ≥ 10 .

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