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Ant Colony Optimization and the Minimum Spanning Tree Problem (2006)
| Venue: | ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY |
| Citations: | 19 - 5 self |
BibTeX
@MISC{Neumann06antcolony,
author = {Frank Neumann and Carsten Witt},
title = { Ant Colony Optimization and the Minimum Spanning Tree Problem},
year = {2006}
}
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Abstract
Ant Colony Optimization (ACO) is a kind of randomized search heuristic that has become very popular for solving problems from combinatorial optimization. Solutions for a given problem are constructed by a random walk on a so-called construction graph. This random walk can be influenced by heuristic information about the problem. In contrast to many successful applications, the theoretical foundation of this kind of randomized search heuristic is rather weak. Theoretical investigations with respect to the runtime behavior of ACO algorithms have been started only recently for the optimization of pseudo-boolean functions. We present the first comprehensive rigorous analysis of a simple ACO algorithms for a combinatorial optimization problem. In our investigations we consider the minimum spanning tree problem and examine the effect of two construction graphs with respect to the runtime behavior. The choice of the construction graph in an ACO algorithm seems to be crucial for the success of such an algorithm. First, we take the input graph itself as the construction graph and analyze the use of a construction procedure that is similar to Broder’s algorithm [1] for choosing a spanning tree uniformly at random. After that, a more incremental construction
Keyphrases
ant colony optimization minimum spanning tree problem construction graph aco algorithm search heuristic random walk runtime behavior so-called construction graph theoretical foundation combinatorial optimization simple aco algorithm incremental construction many successful application construction procedure first comprehensive rigorous analysis heuristic information pseudo-boolean function tree problem broder algorithm combinatorial optimization problem theoretical investigation
