# Runtime Analysis of a Simple Ant Colony Optimization Algorithm

@inproceedings{Neumann2006RuntimeAO, title={Runtime Analysis of a Simple Ant Colony Optimization Algorithm}, author={Frank Neumann and Carsten Witt}, booktitle={ISAAC}, year={2006} }

Ant Colony Optimization (ACO) has become quite popular in recent years. In contrast to many successful applications, the theoretical foundation of this randomized search heuristic is rather weak. Building up such a theory is demanded to understand how these heuristics work as well as to come up with better algorithms for certain problems. Up to now, only convergence results have been achieved showing that optimal solutions can be obtained in finite time. We present the first runtime analysis of… Expand

#### Topics from this paper

#### 14 Citations

Runtime Analysis of a Simple Ant Colony Optimization Algorithm

- Computer Science, Mathematics
- Algorithmica
- 2007

This work presents the first runtime analysis of an ACO algorithm, which transfers many rigorous results with respect to the runtime of a simple evolutionary algorithm to the authors' algorithm, and examines the choice of the evaporation factor, a crucial parameter in ACO algorithms, in detail. Expand

Theoretical analysis of two ACO approaches for the traveling salesman problem

- Computer Science
- Swarm Intelligence
- 2011

The rigorous runtime analysis for two ant colony optimization algorithms, based on these two construction procedures, shows that they lead to good approximation in expected polynomial time on random instances. Expand

Runtime Analysis of a Discrete Particle Swarm Optimization Algorithm on Sorting and OneMax

- Computer Science, Mathematics
- FOGA '17
- 2017

Upper and lower bounds on the expected number of function evaluations required by the proposed algorithm to solve the sorting problem and the problem of maximizing the number of ones in a bitstring are proved. Expand

A Hybrid Ant Colony Optimization Algorithm using MapReduce for Arc Routing Problem

- Computer Science
- 2015

This paper extends the implementations of the ACO algorithm with two local search methods and compares two heuristics that guide the HACO algorithms, and experiments with two different pheromone update strategies. Expand

Speeding-Up ACO Implementation by Decreasing the Number of Heuristic Function Evaluations in Feature Selection Problem

- Computer Science
- IWPACBB
- 2008

This paper presents results of applying an improved ACO implementation which focuses on decreasing the number of heuristic function evaluations needed, and major results of using this approach are shown. Expand

Toward a complexity theory for randomized search heuristics

- Computer Science
- 2011

It is shown that analyzing the black-box complexity of the OneMaxn function class—a class often regarded to analyze how heuristics progress in easy parts of the search space—is the same as analyzing optimal winning strategies for the generalized Mastermind game with 2 colors and length-n codewords. Expand

Stochastic Runtime Analysis of a Cross Entropy Algorithm for Traveling Salesman Problems

- Mathematics, Computer Science
- Theor. Comput. Sci.
- 2018

This article investigates the impact of magnitude of the sample size on the runtime to find optimal solutions for TSP instances, and proves a stochastic runtime of O of N ∈ ω ( ln n ) with the vertex-based random solution generation, and two runtimes are very close to the best known expected runtime for variants of Max-Min Ant System with best-so-far reinforcement. Expand

Theoretical Properties of Two ACO Approaches for the Traveling Salesman Problem

- Mathematics, Computer Science
- ANTS Conference
- 2010

This paper investigates ACO algorithms with respect to their runtime behavior for the traveling salesperson (TSP) problem, and presents a new construction graph that has a stronger local property than the given input graph which is often used for constructing solutions. Expand

A novel ACO algorithm for optimization via reinforcement and initial bias

- Computer Science
- Swarm Intelligence
- 2008

The MAF-ACO algorithm, which emulates the foraging behavior of ants found in nature, and an incremental learning component is introduced, which examines how the local stigmergic interaction of the individual ants results in an emergent dynamic programming framework. Expand

Black-box complexities of combinatorial problems

- Computer Science
- GECCO '11
- 2011

This work reveals that the choice of how to model the optimization problem is non-trivial here and comes true where the search space does not consist of bit strings and where a reasonable definition of unbiasedness has to be agreed on. Expand

#### References

SHOWING 1-10 OF 14 REFERENCES

Runtime Analysis of a Simple Ant Colony Optimization Algorithm

- Computer Science, Mathematics
- Algorithmica
- 2007

This work presents the first runtime analysis of an ACO algorithm, which transfers many rigorous results with respect to the runtime of a simple evolutionary algorithm to the authors' algorithm, and examines the choice of the evaporation factor, a crucial parameter in ACO algorithms, in detail. Expand

Ant colony optimization theory: A survey

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2005

A survey on theoretical results on ant colony optimization, which highlights some open questions with a certain interest of being solved in the near future and discusses relations between ant colonies optimization algorithms and other approximate methods for optimization. Expand

Evolutionary Algorithms and the Maximum Matching Problem

- Computer Science
- STACS
- 2003

It is proven that the evolutionary algorithm is a polynomial-time randomized approximation scheme (PRAS) for this optimization problem, although the algorithm does not employ the idea of augmenting paths. Expand

Modeling the Dynamics of Ant Colony Optimization

- Medicine, Computer Science
- Evolutionary Computation
- 2002

Analysis of the dynamics of Ant Colony Optimization (ACO) algorithms shows analytically that the decisions of an ant are influenced in an intriguing way by the use of the pheromone information and the properties of the beryllium matrix. Expand

A GENERALIZED CONVERGENCE RESULT FOR THE GRAPH-BASED ANT SYSTEM METAHEURISTIC

- Mathematics
- Probability in the Engineering and Informational Sciences
- 2003

It is shown that on fairly weak conditions, the current solutions of a metaheuristic following the ant colony optimization paradigm, the graph-based ant system, converge with a probability that can… Expand

Ant Colony Optimization

- Computer Science
- Handbook of Approximation Algorithms and Metaheuristics
- 2007

On the Finite-Time Dynamics of Ant Colony Optimization

- Mathematics
- 2006

An analytical framework for investigating the finite-time dynamics of ant colony optimization (ACO) under a fitness-proportional pheromone update rule on arbitrary construction graphs is developed. A… Expand

On the analysis of the (1+1) evolutionary algorithm

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2002

A step towards a theory on Evolutionary Algorithms, in particular, the so-called (1+1) evolutionary Algorithm, is performed and linear functions are proved to be optimized in expected time O(nlnn) but only mutation rates of size (1/n) can ensure this behavior. Expand

Worst-Case and Average-Case Approximations by Simple Randomized Search Heuristics

- Computer Science
- STACS
- 2005

An average-case analysis for two input distributions reveals that one RSH is convergent to optimality in polynomial time, and it is shown that for both RSHs, parallel runs yield a PRAS. Expand

Randomized local search, evolutionary algorithms, and the minimum spanning tree problem

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2007

It is shown that randomized search heuristics find minimum spanning trees in expected polynomial time without employing the global technique of greedy algorithms. Expand