6 research outputs found
Sorting by Swaps with Noisy Comparisons
We study sorting of permutations by random swaps if each comparison gives the
wrong result with some fixed probability . We use this process as
prototype for the behaviour of randomized, comparison-based optimization
heuristics in the presence of noisy comparisons. As quality measure, we compute
the expected fitness of the stationary distribution. To measure the runtime, we
compute the minimal number of steps after which the average fitness
approximates the expected fitness of the stationary distribution.
We study the process where in each round a random pair of elements at
distance at most are compared. We give theoretical results for the extreme
cases and , and experimental results for the intermediate cases. We
find a trade-off between faster convergence (for large ) and better quality
of the solution after convergence (for small ).Comment: An extended abstract of this paper has been presented at Genetic and
Evolutionary Computation Conference (GECCO 2017
The Genetic Algorithm for Permutations
The genetic algorithm is a bright example of an
evolutionary algorithm which was developed based on the insights from
theoretical findings. This algorithm uses crossover, and it was shown to
asymptotically outperform all mutation-based evolutionary algorithms even on
simple problems like OneMax. Subsequently it was studied on a number of other
problems, but all of these were pseudo-Boolean.
We aim at improving this situation by proposing an adaptation of the
genetic algorithm to permutation-based problems. Such
an adaptation is required, because permutations are noticeably different from
bit strings in some key aspects, such as the number of possible mutations and
their mutual dependence. We also present the first runtime analysis of this
algorithm on a permutation-based problem called Ham whose properties resemble
those of OneMax. On this problem, where the simple mutation-based algorithms
have the running time of for problem size , the
genetic algorithm finds the optimum in fitness
queries. We augment this analysis with experiments, which show that this
algorithm is also fast in practice.Comment: This contribution is a slightly extended version of the paper
accepted to the GECCO 2020 workshop on permutation-based problem