A running time analysis of an Ant Colony Optimization algorithm for shortest paths in directed acyclic graphs - Attiratanasunthron, Nattapat; Fakcharoenphol, Jittat (Information processing letters, 2008)
In this paper, we prove polynomial running time bounds for an Ant Colony Optimization (ACO) algorithm for the single-destination shortest path problem on directed acyclic graphs. More specifically, we show that the expected number of iterations required for an ACO-based algorithm with n ants is O ( 1 ρ n 2 m log n ) for graphs with n nodes and m edges, where ρ is an evaporation rate. This result can be modified to show that an ACO-based algorithm for One-Max with multiple ants converges in expected O ( 1 ρ n 2 log n ) iterations, where n is the number of variables. This result stands in sharp contrast with that of Neumann and Witt, where a single-ant algorithm is shown to require an exponential running time if ρ = O ( n − 1 − ε ) for any ε > 0 .