The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
Ant Colony Optimization
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
Ant colony optimization theory: a survey
Theoretical Computer Science
Simulated annealing in convex bodies and an O*(n4) volume algorithm
Journal of Computer and System Sciences - Special issue on FOCS 2003
Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization
Theory of Computing Systems
Randomized local search, evolutionary algorithms, and the minimum spanning tree problem
Theoretical Computer Science
Randomly coloring planar graphs with fewer colors than the maximum degree
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On the runtime analysis of the 1-ANT ACO algorithm
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Information Processing Letters
Rigorous hitting times for binary mutations
Evolutionary Computation
First steps to the runtime complexity analysis of ant colony optimization
Computers and Operations Research
Genetic Programming and Evolvable Machines
Rigorous analyses of fitness-proportional selection for optimizing linear functions
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Rigorous Analyses for the Combination of Ant Colony Optimization and Local Search
ANTS '08 Proceedings of the 6th international conference on Ant Colony Optimization and Swarm Intelligence
Ant Colony Optimization and the Minimum Spanning Tree Problem
Learning and Intelligent Optimization
On the impact of the mutation-selection balance on the runtime of evolutionary algorithms
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
Theoretical analysis of fitness-proportional selection: landscapes and efficiency
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
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
Runtime analysis of an ant colony optimization algorithm for TSP instances
IEEE Transactions on Evolutionary Computation
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
A few ants are enough: ACO with iteration-best update
Proceedings of the 12th annual conference on Genetic and evolutionary computation
The benefit of migration in parallel evolutionary algorithms
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Ant colony optimization and the minimum cut problem
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Necessary and sufficient conditions for success of the metropolis algorithm for optimization
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Ant colony optimization for stochastic shortest path problems
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Theoretical properties of two ACO approaches for the traveling salesman problem
ANTS'10 Proceedings of the 7th international conference on Swarm intelligence
Runtime analysis of a simple ant colony optimization algorithm
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
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The Markov chain Monte Carlo paradigm has developed powerful and elegant techniques for estimating the time until a Markov chain approaches a stationary distribution. This time is known as mixing time. We introduce the reader into mixing time estimations via coupling arguments and use the mixing of pheromone models for analyzing the expected optimization time of ant colony optimization. We demonstrate the approach for plateaus in pseudo-Boolean optimization and derive upper bounds for the time until a target set is found. We also describe how mixing times can be estimated for MMAS ant systems on shortest path problems.