Concatenation-Based Greedy Heuristics for the Euclidean Steiner Tree Problem

Algorithmica ◽  
1999 ◽  
Vol 25 (4) ◽  
pp. 418-437 ◽  
Author(s):  
M. Zachariasen ◽  
P. Winter
Keyword(s):  
Steiner Tree ◽  
Steiner Tree Problem ◽  
Greedy Heuristics ◽  
Euclidean Steiner Tree Problem

scholarly journals Hybrid greedy genetic algorithm for the Euclidean Steiner tree problem

2019 ◽  
Author(s):  
Andrey Oliveira ◽  
Danilo Sanches ◽  
Bruna Osti
Keyword(s):  
Genetic Algorithm ◽  
Steiner Tree ◽  
Optimization Problem ◽  
Spanning Trees ◽  
Evolutionary Strategies ◽  
Steiner Tree Problem ◽  
Minimum Length ◽  
Genetic Operators ◽  
Steiner Points ◽  
Euclidean Steiner Tree Problem

This paper presents a genetic algorithm for the Euclidean Steiner tree problem. This is an optimization problem whose objective is to obtain a minimum length tree to interconnect a set of fixed points, and for this purpose to be achieved, new auxiliary points, called Steiner points, can be added. The proposed heuristic uses a genetic algorithm to manipulate spanning trees, which are then transformed into Steiner trees by inserting and repositioning the Steiner points. Greedy genetic operators and evolutionary strategies are tested. Results of numerical experiments for benchmark library problem (OR-Library) are presented and discussed.This paper presents a genetic algorithm for the Euclidean Steiner tree problem. This is an optimization problem whose objective is to obtain a minimum length tree to interconnect a set of fixed points, and for this purpose to be achieved, new auxiliary points, called Steiner points, can be added. The proposed heuristic uses a genetic algorithm to manipulate spanning trees, which are then transformed into Steiner trees by inserting and repositioning the Steiner points. Greedy genetic operators and evolutionary strategies are tested. Results of numerical experiments for benchmark library problem (OR-Library) are presented and discussed.

On a nonconvex MINLP formulation of the Euclidean Steiner tree problem in n-space: missing proofs

2018 ◽  
Vol 14 (2) ◽  
pp. 409-415 ◽  
Author(s):  
Claudia D’Ambrosio ◽  
Marcia Fampa ◽  
Jon Lee ◽  
Stefan Vigerske
Keyword(s):  
Steiner Tree ◽  
Steiner Tree Problem ◽  
Euclidean Steiner Tree Problem ◽  
Missing Proofs

Solving the prize‐collecting Euclidean Steiner tree problem

2020 ◽  
Author(s):  
David Whittle ◽  
Marcus Brazil ◽  
Peter A. Grossman ◽  
J. Hyam Rubinstein ◽  
Doreen A. Thomas
Keyword(s):  
Steiner Tree ◽  
Steiner Tree Problem ◽  
Prize Collecting ◽  
Euclidean Steiner Tree Problem

Convex relaxation and variational approximation of the Steiner problem: theory and numerics

2018 ◽  
Vol 3 (1) ◽  
pp. 19-27 ◽  
Author(s):  
M. Bonafini
Keyword(s):  
Steiner Tree ◽  
Convex Relaxation ◽  
Steiner Tree Problem ◽  
Variational Approximation ◽  
Steiner Problem ◽  
Convex Relaxations ◽  
Numerical Schemes ◽  
Steiner Minimal Trees ◽  
Euclidean Steiner Tree Problem

Abstract We survey some recent results on convex relaxations and a variational approximation for the classical Euclidean Steiner tree problem and we see how these new perspectives can lead to effective numerical schemes for the identification of Steiner minimal trees.

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