TY - JOUR

T1 - Runtime analysis of the 1-ANT ant colony optimizer

A1 - Doerr,Benjamin

A1 - Neumann,Frank

A1 - Sudholt,Dirk

A1 - Witt,Carsten

AU - Doerr,Benjamin

AU - Neumann,Frank

AU - Sudholt,Dirk

AU - Witt,Carsten

PB - Elsevier BV

PY - 2011

Y1 - 2011

N2 - The runtime analysis of randomized search heuristics is a growing field where, in the last two decades, many rigorous results have been obtained. First runtime analyses of ant colony optimization (ACO) have been conducted only recently. In these studies simple ACO algorithms such as the 1-ANT are investigated. The influence of the evaporation factor in the pheromone update mechanism and the robustness of this parameter w.r.t. the runtime behavior have been determined for the example function OneMax.This work puts forward the rigorous runtime analysis of the 1-ANT on the example functions LeadingOnes and BinVal. With respect to Evolutionary Algorithms (EAs), such analyses were essential to develop methods for the analysis on more complicated problems. The proof techniques required for the 1-ANT, unfortunately, differ significantly from those for EAs, which means that a new reservoir of methods has to be built up. Again, the influence of the evaporation factor is analyzed rigorously, and it is proved that its choice has a crucial impact on the runtime. Moreover, the analyses provide insight into the working principles of ACO algorithms. Our theoretical results are accompanied by experimental results that give us a more detailed impression of the 1-ANT’s performance. Furthermore, the experiments also deal with the question whether using many ant solutions in one iteration can decrease the total runtime.

AB - The runtime analysis of randomized search heuristics is a growing field where, in the last two decades, many rigorous results have been obtained. First runtime analyses of ant colony optimization (ACO) have been conducted only recently. In these studies simple ACO algorithms such as the 1-ANT are investigated. The influence of the evaporation factor in the pheromone update mechanism and the robustness of this parameter w.r.t. the runtime behavior have been determined for the example function OneMax.This work puts forward the rigorous runtime analysis of the 1-ANT on the example functions LeadingOnes and BinVal. With respect to Evolutionary Algorithms (EAs), such analyses were essential to develop methods for the analysis on more complicated problems. The proof techniques required for the 1-ANT, unfortunately, differ significantly from those for EAs, which means that a new reservoir of methods has to be built up. Again, the influence of the evaporation factor is analyzed rigorously, and it is proved that its choice has a crucial impact on the runtime. Moreover, the analyses provide insight into the working principles of ACO algorithms. Our theoretical results are accompanied by experimental results that give us a more detailed impression of the 1-ANT’s performance. Furthermore, the experiments also deal with the question whether using many ant solutions in one iteration can decrease the total runtime.

KW - Ant colony optimization

KW - Runtime analysis

KW - Theory

U2 - 10.1016/j.tcs.2010.12.030

DO - 10.1016/j.tcs.2010.12.030

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 17

VL - 412

SP - 1629

EP - 1644

ER -