Randomized algorithms
Generating random spanning trees more quickly than the cover time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Introduction to Algorithms
Ant Colony Optimization
Ant colony optimization theory: a survey
Theoretical Computer Science
Minimum spanning trees made easier via multi-objective optimization
Natural Computing: an international journal
Randomized local search, evolutionary algorithms, and the minimum spanning tree problem
Theoretical Computer Science
On the runtime analysis of the 1-ANT ACO algorithm
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Generating random spanning trees
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Comparing variants of MMAS ACO algorithms on pseudo-boolean functions
SLS'07 Proceedings of the 2007 international conference on Engineering stochastic local search algorithms: designing, implementing and analyzing effective heuristics
Simulated annealing beats metropolis in combinatorial optimization
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Worst-case and average-case approximations by simple randomized search heuristics
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Runtime analysis of a simple ant colony optimization algorithm
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Running Time Analysis of ACO Systems for Shortest Path Problems
SLS '09 Proceedings of the Second International Workshop on Engineering Stochastic Local Search Algorithms. Designing, Implementing and Analyzing Effective Heuristics
Using markov-chain mixing time estimates for the analysis of ant colony optimization
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Proceedings of the 13th annual conference companion on Genetic and evolutionary computation
Running time analysis of Ant Colony Optimization for shortest path problems
Journal of Discrete Algorithms
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Ant Colony Optimization (ACO) is a kind of metaheuristic 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 metaheuristic 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 algorithm 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.