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  Ant Colony Optimization and the Minimum Spanning Tree Problem

Neumann, F., & Witt, C. (2006). Ant Colony Optimization and the Minimum Spanning Tree Problem. Electronic Colloquium on Computational Complexity (ECCC): Report Series, 143, 1-12.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0019-E477-D Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0024-5AE8-A
Genre: Journal Article

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http://eccc.hpi-web.de/report/2006/143/ (Any fulltext)
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 Creators:
Neumann, Frank1, Author           
Witt, Carsten2, Author
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              
2External Organizations, ou_persistent22              

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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 for choosing a spanning tree uniformly at random. After that, a more incremental construction procedure is analyzed. It turns out that this procedure is superior to the Broder-based algorithm and produces additionally in a constant number of iterations a minimum spanning tree if the influence of the heuristic information is large enough.

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Language(s): eng - English
 Dates: 2006-11-28
 Publication Status: Published online
 Pages: -
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 Table of Contents: -
 Rev. Type: -
 Identifiers: Report Nr.: TR06-143
BibTex Citekey: NeuWittMST2006
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Title: Electronic Colloquium on Computational Complexity (ECCC) : Report Series
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Source Genre: Journal
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Publ. Info: Potsdam : Hasso-Plattner-Institut für Softwaretechnik GmbH
Pages: - Volume / Issue: 143 Sequence Number: - Start / End Page: 1 - 12 Identifier: ISSN: 1433-8092