Refined runtime analysis of a basic ant colony optimization algorithm

Neumann and Witt (2006) analyzed the runtime of the basic ant colony optimization (ACO) algorithm 1-Ant on pseudo-Boolean optimization problems. For the problem OneMax they showed how the runtime depends on the evaporation factor. In particular, they proved a phase transition from exponential to polynomial runtime. In this work, we simplify the view on this problem by an appropriate translation of the pheromone model. This results in a profound simplification of the pheromone update rule and, by that, a refinement of the results of Neumann and Witt. In particular, we show how the exponential runtime bound gradually changes to a polynomial bound inside the phase of transition.

[1]  M. Dorigo,et al.  Ant System: An Autocatalytic Optimizing Process , 1991 .

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

[3]  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 .

[4]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[5]  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 .

[6]  Benjamin Doerr,et al.  Faster Evolutionary Algorithms by Superior Graph Representation , 2007, 2007 IEEE Symposium on Foundations of Computational Intelligence.

[7]  Mihalis Yannakakis,et al.  On the complexity of local search , 1990, STOC '90.

[8]  W. Gutjahr.  On the Finite-Time Dynamics of Ant Colony Optimization , 2006 .

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

[10]  Frank Neumann,et al.  Speeding Up Evolutionary Algorithms Through Restricted Mutation Operators , 2006, PPSN.

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

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

[13]  Mark Jerrum,et al.  The Metropolis Algorithm for Graph Bisection , 1998, Discret. Appl. Math..

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

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

[16]  Noga Alon,et al.  The Probabilistic Method, Second Edition , 2004 .

[17]  Frank Neumann.  Expected runtimes of evolutionary algorithms for the Eulerian cycle problem , 2004, IEEE Congress on Evolutionary Computation.

[18]  Benjamin Doerr,et al.  Adjacency list matchings: an ideal genotype for cycle covers , 2007, GECCO '07.

[19]  Dirk Sudholt,et al.  On the influence of pheromone updates in ACO algorithms , 2007 .

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

[21]  Frank R. Neumann.  Runtime Analysis of Ant Colony Optimization Algorithms , 2007 .