# 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

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#### 16 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

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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

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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

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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

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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

Simple max-min ant systems and the optimization of linear pseudo-boolean functions

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A general upper bound of O((n3 log n)ρ) on the running time for two ACO variants on all linear functions, where ρ determines the pheromone update strength is provided. Expand

Toward a complexity theory for randomized search heuristics

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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.
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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

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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

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