A Graph-based Ant system and its convergence
Future Generation Computer Systems
Future Generation Computer Systems
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
How to analyse evolutionary algorithms
Theoretical Computer Science - Natural computing
Ant Colony Optimization
Crossover is provably essential for the Ising model on trees
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Ant colony optimization theory: a survey
Theoretical Computer Science
On the runtime analysis of the 1-ANT ACO algorithm
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Approximating covering problems by randomized search heuristics using multi-objective models
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Simulated Annealing versus Metropolis for a TSP instance
Information Processing Letters
Information Processing Letters
First steps to the runtime complexity analysis of ant colony optimization
Computers and Operations Research
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
IEEE Computational Intelligence Magazine
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
A short convergence proof for a class of ant colony optimizationalgorithms
IEEE Transactions on Evolutionary Computation
Ant system: optimization by a colony of cooperating agents
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A few ants are enough: ACO with iteration-best update
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
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
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
Two-stage updating pheromone for invariant ant colony optimization algorithm
Expert Systems with Applications: An International Journal
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
Combinatorial complexity problem reduction by the use of artificial vaccines
Expert Systems with Applications: An International Journal
Runtime analysis of ant colony optimization on dynamic shortest path problems
Proceedings of the 15th annual conference on Genetic and evolutionary computation
Bio-inspired optimization techniques: a critical comparative study
ACM SIGSOFT Software Engineering Notes
An ACO-RFD hybrid method to solve NP-complete problems
Frontiers of Computer Science: Selected Publications from Chinese Universities
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Ant colony optimization (ACO) is a relatively new random heuristic approach for solving optimization problems. The main application of the ACO algorithm lies in the field of combinatorial optimization, and the traveling salesman problem (TSP) is the first benchmark problem to which the ACO algorithm has been applied. However, relatively few results on the runtime analysis of the ACO on the TSP are available. This paper presents the first rigorous analysis of a simple ACO algorithm called (1 + 1) MMAA (Max-Min ant algorithm) on the TSP. The expected runtime bounds for (1 + 1) MMAA on two TSP instances of complete and non-complete graphs are obtained. The influence of the parameters controlling the relative importance of pheromone trail versus visibility is also analyzed, and their choice is shown to have an impact on the expected runtime.