scholarly journals An ADD/DROP procedure for the capacitated plant location problem

2004 ◽  
Vol 24 (1) ◽  
pp. 151-162 ◽  
Author(s):  
Claudio Thomas Bornstein ◽  
Manoel Campêlo
Keyword(s):  
Heuristic Algorithm ◽  
Location Problem ◽  
Lagrangean Relaxation ◽  
Upper Bounds ◽  
Transportation Costs ◽  
Plant Location ◽  
Computational Results ◽  
Lower And Upper Bounds

The capacitated plant location problem with linear transportation costs is considered. Exact rules and heuristics are presented for opening or closing of facilities. A heuristic algorithm based on ADD/DROP strategies is proposed. Procedures are implemented with the help of lower and upper bounds using Lagrangean relaxation. Computational results are presented and comparisons with other algorithms are made.

Lower and upper bounds for a two-level hierarchical location problem in computer networks

2008 ◽  
Vol 35 (6) ◽  
pp. 1982-1998 ◽  
Author(s):  
Aníbal Alberto Vilcapoma Ignacio ◽  
Virgílio José Martins Ferreira Filho ◽  
Roberto Diéguez Galvão
Keyword(s):  
Computer Networks ◽  
Location Problem ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Hierarchical Location

scholarly journals Lagrangean relaxation bounds for point-feature cartographic label placement problem

2006 ◽  
Vol 26 (3) ◽  
pp. 459-471 ◽  
Author(s):  
Glaydston Mattos Ribeiro ◽  
Luiz Antonio Nogueira Lorena
Keyword(s):  
Linear Programming ◽  
Mathematical Formulation ◽  
Lagrangean Relaxation ◽  
Upper Bounds ◽  
Conflict Graph ◽  
Lower And Upper Bounds ◽  
Placement Problem ◽  
Label Placement ◽  
Binary Integer Linear Programming ◽  
Point Feature

The objective of the point-feature cartographic label placement problem (PFCLP) is to give more legibility to an automatic map creation, placing point labels in clear positions. Many researchers consider distinct approaches for PFCLP, such as to obtain the maximum number of labeled points that can be placed without overlapping or to obtain the maximum number of labeled points without overlaps considering that all points must be labeled. This paper considers another variant of the problem in which one has to minimize the number of overlaps while all points are labeled in the map. A conflict graph is initially defined and a mathematical formulation of binary integer linear programming is presented. Commercial optimization packages could not solve large instances exactly using this formulation over instances proposed in the literature. A heuristic is then examined considering a Lagrangean relaxation performed after an initial partition of the conflict graph into clusters. This decomposition allowed us to introduce tight lower and upper bounds for PFCLP.

scholarly journals More on inverse degree and topological indices of graphs

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 165-178
Author(s):  
Suresh Elumalai ◽  
Sunilkumar Hosamani ◽  
Toufik Mansour ◽  
Mohammad Rostami
Keyword(s):  
Upper Bounds ◽  
Topological Indices ◽  
Computational Results ◽  
Randić Index ◽  
Lower And Upper Bounds ◽  
Randic Index ◽  
The Third ◽  
Inverse Degree ◽  
Vertex Degrees ◽  
Chemical Trees

The inverse degree of a graph G with no isolated vertices is defined as the sum of reciprocal of vertex degrees of the graph G. In this paper, we obtain several lower and upper bounds on inverse degree ID(G). Moreover, using computational results, we prove our upper bound is strong and has the smallest deviation from the inverse degree ID(G). Next, we compare inverse degree ID(G) with topological indices (Randic index R(G), geometric-arithmetic index GA(G)) for chemical trees and also we determine the n-vertex chemical trees with the minimum, the second and the third minimum, as well as the second and the third maximum of ID - R. In addition, we correct the second and third minimum Randic index chemical trees in [16].

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

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