Ants easily solve stochastic shortest path problems

Abstract

The recent theoretical analysis (Horoba, Sudholt (GECCO 2010)) of an ant colony optimizer for the stochastic shortest path problem suggests that ant system experiences significant difficulties when the input data is prone to noise. In this work, we propose a slightly different ant optimizer to deal with noise.We prove that, under mild conditions, it finds the paths with shortest expected length efficiently, despite the fact that we do not have convergence in the classic sense. To prove our results, we introduce a stronger drift theorem that can also deal with the situation that the progress is faster when one is closer to the goal.

Optimizing expected path lengths with ant colony optimization using fitness proportional update

“…This gives a qualitative difference to [14] and [4], where the algorithms did not favor paths that are good in expectation, but instead paths either have low weights with reasonable probability (in [14]) or paths which come out better than others in direct comparison with probability higher than 0.5 (in [4]). As an illustration, consider the following (multi-) graph with random variables A, B and C as edge weights.…”

“…In [4], the MMAS-el algorithm was modified by reevaluating the best-so-far solution every iteration to avoid permanently being mislead by a single exceptionally good evaluation of a non-optimal solution. The paper shows that, in this case, the pheromones converge to the solution which has a better evaluation against any other solution in a direct comparison more than half of the time; however, such a solution need not exist, and even if it exists, it is not necessarily the solution optimal in expectation.…”

On the Effectiveness of Sampling for Evolutionary Optimization in Noisy Environments

“…For example, for (1+1)-EA without noise, N 1 = 1 and N 2 = 1. Note that, for EAs under noise, we assume that the reevaluation strategy [13,14,18] is used, i.e., when accessing the fitness of a solution, it is always reevaluated. For example, for (1+1)-EA with sampling, both f…”

On the Effectiveness of Sampling for Evolutionary Optimization in Noisy Environments

“…For example, for (1+1)-EA without noise, N 1 = 1 and N 2 = 1. Note that, for EAs under noise, we assume that the reevaluation strategy [13,14,18] is used, i.e., when accessing the fitness of a solution, it is always reevaluated. For example, for (1+1)-EA with sampling, both f N k (x ′ ) and f N k (x) will be calculated and recalculated in each iteration; thus, N 1 = k and N 2 = 2k.…”