Steiner Trees in Industry pp 441-466 | Cite as

# A First Level Scatter Search Implementation for Solving the Steiner Ring Problem in Telecommunications Network Design

## Abstract

In this paper, we consider a combinatorial optimization problem in a graph *G*(*V*, *E*) where *V* represents the node set and *E* denotes the edge set. *V* is partitioned into two subsets *V* _{1} and *V* _{2}, which denote the “Steiner” node set and “Target” node set respectively. Similarly, *E* is partitioned into sets of *E* _{1} and *E* _{2}, where *E* _{1} is the set of edges that join two Steiner nodes, and *E* _{2} is the set of edges that join one Steiner node and one target node. No edges exist between two target nodes. The problem is to select a non-empty Steiner set *S* ⊂ *V* _{1} such that each target node must be linked to exactly one selected Steiner node. Meanwhile, all selected (active) Steiner nodes must be connected to form a *Hamiltonian* tour of minimum connection cost which is called *Traveling Salesman (TSP)* tour. The objective of the problem is to minimize the total costs (which we will describe in detail subsequently).

## Keywords

Tabu Search Target Node Vehicle Route Problem Scatter Search Path Relinking## Preview

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