Runtime analysis of the 1-ANT ant colony optimizer

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.

[1]  Frank Neumann,et al.  Theoretical Properties of Two ACO Approaches for the Traveling Salesman Problem , 2010, ANTS Conference.

[2]  Julian F. Miller,et al.  Genetic and Evolutionary Computation — GECCO 2003 , 2003, Lecture Notes in Computer Science.

[3]  Dirk Sudholt,et al.  Analysis of different MMAS ACO algorithms on unimodal functions and plateaus , 2009, Swarm Intelligence.

[4]  Dirk Sudholt,et al.  On the runtime analysis of the 1-ANT ACO algorithm , 2007, GECCO '07.

[5]  Dirk Sudholt,et al.  Crossover is provably essential for the Ising model on trees , 2005, GECCO '05.

[6]  Frank Neumann,et al.  Ant Colony Optimization and the minimum spanning tree problem , 2006, Theor. Comput. Sci..

[7]  Ingo Wegener,et al.  Randomized local search, evolutionary algorithms, and the minimum spanning tree problem , 2004, Theor. Comput. Sci..

[8]  Thomas Jansen,et al.  On the analysis of the (1+1) evolutionary algorithm , 2002, Theor. Comput. Sci..

[9]  Rajeev Motwani,et al.  Randomized Algorithms , 1995, SIGA.

[10]  Thomas Stützle,et al.  Ant Colony Optimization Theory , 2004 .

[11]  Ingo Wegener,et al.  Evolutionary Algorithms and the Maximum Matching Problem , 2003, STACS.

[12]  Carsten Witt,et al.  UNIVERSITY OF DORTMUND REIHE COMPUTATIONAL INTELLIGENCE COLLABORATIVE RESEARCH CENTER 531 Design and Management of Complex Technical Processes and Systems by means of Computational Intelligence Methods Worst-Case and Average-Case Approximations by Simple Randomized Search Heuristics , 2004 .

[13]  Marco Dorigo,et al.  Ant colony optimization theory: A survey , 2005, Theor. Comput. Sci..

[14]  Walter J. Gutjahr,et al.  Mathematical runtime analysis of ACO algorithms: survey on an emerging issue , 2007, Swarm Intelligence.

[15]  Frank Neumann,et al.  Design and Management of Complex Technical Processes and Systems by Means of Computational Intelligence Methods Runtime Analysis of a Simple Ant Colony Optimization Algorithm Runtime Analysis of a Simple Ant Colony Optimization Algorithm , 2022 .

[16]  Kenneth A. De Jong,et al.  Design and Management of Complex Technical Processes and Systems by Means of Computational Intelligence Methods on the Choice of the Offspring Population Size in Evolutionary Algorithms on the Choice of the Offspring Population Size in Evolutionary Algorithms , 2004 .

[17]  Frank Neumann,et al.  Randomized Local Search, Evolutionary Algorithms, and the Minimum Spanning Tree Problem , 2004, GECCO.

[18]  Benjamin Doerr,et al.  Refined runtime analysis of a basic ant colony optimization algorithm , 2007, 2007 IEEE Congress on Evolutionary Computation.

[19]  W. Gutjahr,et al.  Runtime Analysis of Ant Colony Optimization with Best-So-Far Reinforcement , 2008 .

[20]  Frank Neumann,et al.  Speeding Up Evolutionary Algorithms through Asymmetric Mutation Operators , 2007, Evolutionary Computation.

[21]  Stephen R. Marsland,et al.  Convergence Properties of (μ + λ) Evolutionary Algorithms , 2011, AAAI.

[22]  Martin Middendorf,et al.  Modeling the Dynamics of Ant Colony Optimization , 2002, Evolutionary Computation.

[23]  W. Gutjahr.  A GENERALIZED CONVERGENCE RESULT FOR THE GRAPH-BASED ANT SYSTEM METAHEURISTIC , 2003, Probability in the Engineering and Informational Sciences.

[24]  Thomas Stützle,et al.  MAX-MIN Ant System , 2000, Future Gener. Comput. Syst..

[25]  Walter J. Gutjahr,et al.  First steps to the runtime complexity analysis of ant colony optimization , 2008, Comput. Oper. Res..

[26]  Benjamin Doerr,et al.  How Single Ant ACO Systems Optimize Pseudo-Boolean Functions , 2008, PPSN.

[27]  Jittat Fakcharoenphol,et al.  A running time analysis of an Ant Colony Optimization algorithm for shortest paths in directed acyclic graphs , 2008, Inf. Process. Lett..