scholarly journals The Euclidean Steiner Tree Problem: Simulated Annealing and Other Heuristics

2021 ◽  
Author(s):  
◽  
Geoffrey Ross Grimwood
Keyword(s):  
Simulated Annealing ◽  
Steiner Tree ◽  
Heuristic Method ◽  
Distribution Networks ◽  
Network Design Problem ◽  
Steiner Tree Problem ◽  
Viable Solution ◽  
Euclidean Steiner Tree Problem ◽  
Set Of Points

<p>In this thesis the Euclidean Steiner tree problem and the optimisation technique called simulated annealing are studied. In particular, there is an investigation of whether simulated annealing is a viable solution method for the problem. The Euclidean Steiner tree problem is a topological network design problem and is relevant to the design of communication, transportation and distribution networks. The problem is to find the shortest connection of a set of points in the Euclidean plane. Simulated annealing is a generally applicable method of finding solutions of combinatorial optimisation problems. The results of the investigation are very satisfactory. The quality of simulated annealing solutions compare favourably with those of the best known tailored heuristic method for the Euclidean Steiner tree problem</p>

scholarly journals The Euclidean Steiner Tree Problem: Simulated Annealing and Other Heuristics

2021 ◽  
Author(s):  
◽  
Geoffrey Ross Grimwood
Keyword(s):  
Simulated Annealing ◽  
Steiner Tree ◽  
Heuristic Method ◽  
Distribution Networks ◽  
Network Design Problem ◽  
Steiner Tree Problem ◽  
Viable Solution ◽  
Euclidean Steiner Tree Problem ◽  
Set Of Points

<p>In this thesis the Euclidean Steiner tree problem and the optimisation technique called simulated annealing are studied. In particular, there is an investigation of whether simulated annealing is a viable solution method for the problem. The Euclidean Steiner tree problem is a topological network design problem and is relevant to the design of communication, transportation and distribution networks. The problem is to find the shortest connection of a set of points in the Euclidean plane. Simulated annealing is a generally applicable method of finding solutions of combinatorial optimisation problems. The results of the investigation are very satisfactory. The quality of simulated annealing solutions compare favourably with those of the best known tailored heuristic method for the Euclidean Steiner tree problem</p>

GENERALIZED MELZAK'S CONSTRUCTION IN THE STEINER TREE PROBLEM

2002 ◽  
Vol 12 (06) ◽  
pp. 481-488 ◽  
Author(s):  
JIA F. WENG
Keyword(s):  
Steiner Tree ◽  
Euclidean Plane ◽  
Steiner Tree Problem ◽  
Minimal Tree ◽  
Steiner Minimal Tree ◽  
The Core ◽  
Steiner Minimal Trees ◽  
Minimum Networks ◽  
Set Of Points ◽  
The Given

For a given set of points in the Euclidean plane, a minimum network (a Steiner minimal tree) can be constructed using a geometric method, called Melzak's construction. The core of the Melzak construction is to replace a pair of terminals adjacent to the same Steiner point with a new terminal. In this paper we prove that the Melzak construction can be generalized to constructing Steiner minimal trees for circles so that either the given points (terminals) are constrained on the circles or the terminal edges are tangent to the circles. Then we show that the generalized Melzak construction can be used to find minimum networks separating and surrounding circular objects or to find minimum networks connecting convex and smoothly bounded objects and avoiding convex and smoothly bounded obstacles.

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
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