# On the Invariance of Ant Colony Optimization

@article{Birattari2007OnTI, title={On the Invariance of Ant Colony Optimization}, author={M. Birattari and Paola Pellegrini and Marco Dorigo}, journal={IEEE Transactions on Evolutionary Computation}, year={2007}, volume={11}, pages={732-742} }

Ant colony optimization (ACO) is a promising metaheuristic and a great amount of research has been devoted to its empirical and theoretical analysis. Recently, with the introduction of the hypercube framework, Blum and Dorigo have explicitly raised the issue of the invariance of ACO algorithms to transformation of units. They state (Blum and Dorigo, 2004) that the performance of ACO depends on the scale of the problem instance under analysis. In this paper, we show that the ACO internal state…

## 86 Citations

On the Invariance of Ant System

- Computer ScienceANTS Workshop
- 2006

It is shown that although the internal state of ant system—that is, the pheromone matrix—depends on the scale of the problem instance under analysis, this does not affect the external behavior of the algorithm.

Runtime Analysis of Ant Colony Optimization with Best-So-Far Reinforcement

- Computer Science
- 2008

It turns out that for two of the four studied problems, the expected runtime for the considered class, expressed in terms of the problem size, is of the same order as that for (1+1)-Evolutionary Algorithm.

Cognitive Ant Colony Optimization: A New Framework in Swarm Intelligence

- Computer Science
- 2014

This research develops a novel state transition strategy for Ant Colony Optimization algorithms that can improve the overall performance of the algorithms and uses a new concept of decision-making taken from cognitive behaviour theory to select the transition movements of the ants in the colony.

Simple ant colony algorithm for combinatorial optimization problems

- Computer Science2017 36th Chinese Control Conference (CCC)
- 2017

A novel ACO algorithm called simple ant colony optimization (SACO) is proposed, which can reduce the coupling of parameters and is compared with other novel algorithms based on traveling salesman problems to show the feasibility and effectiveness of improvements.

Two-stage updating pheromone for invariant ant colony optimization algorithm

- Computer ScienceExpert Syst. Appl.
- 2012

Some Combinatorial Optimization Problems on which Ant Colony Optimization is Invariant

- Computer Science
- 2006

In this paper some examples of combinatorial optimization problems to which ant colony optimization can be applied in an invariant fashion are described.

Solving the Traveling Salesman Problem with Ant Colony Optimization: A Revisit and New Efficient Algorithms

- Computer Science
- 2013

This paper revisits the application of ACO techniques to the TSP and proposes two algorithms– Smoothed Max-Min Ant System and Three-Level Ant System– which not only can be easily implemented but also provide better performance, as compared to the well-known Max- Min Ant System.

A Cooperative Ant Colony System and Genetic Algorithm for TSPs

- Computer ScienceICSI
- 2010

Simulation demonstrates that CoACSGA is superior to other ACO related algorithms in terms of convergence, quality of solution, and consistency of achieving the global optimal solution, particularly for small-size TSPs.

An Ant System-Assisted Genetic Algorithm For Solving The Traveling Salesman Problem

- Computer Science
- 2012

A new hybrid algorithm, ant system-assisted genetic algorithm (ASaGA) to handle the travelling salesman problem (TSP) by using the results of ACO to replace that of GA after every certain number of runs during the process.

Solving the traveling salesman problem using cooperative genetic ant systems

- Computer ScienceExpert Syst. Appl.
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