517 research outputs found
Upper Bounds on the Runtime of the Univariate Marginal Distribution Algorithm on OneMax
A runtime analysis of the Univariate Marginal Distribution Algorithm (UMDA)
is presented on the OneMax function for wide ranges of its parameters and
. If for some constant and
, a general bound on the expected runtime
is obtained. This bound crucially assumes that all marginal probabilities of
the algorithm are confined to the interval . If for a constant and , the
behavior of the algorithm changes and the bound on the expected runtime becomes
, which typically even holds if the borders on the marginal
probabilities are omitted.
The results supplement the recently derived lower bound
by Krejca and Witt (FOGA 2017) and turn out as
tight for the two very different values and . They also improve the previously best known upper bound by Dang and Lehre (GECCO 2015).Comment: Version 4: added illustrations and experiments; improved presentation
in Section 2.2; to appear in Algorithmica; the final publication is available
at Springer via http://dx.doi.org/10.1007/s00453-018-0463-
On the Runtime of Randomized Local Search and Simple Evolutionary Algorithms for Dynamic Makespan Scheduling
Evolutionary algorithms have been frequently used for dynamic optimization
problems. With this paper, we contribute to the theoretical understanding of
this research area. We present the first computational complexity analysis of
evolutionary algorithms for a dynamic variant of a classical combinatorial
optimization problem, namely makespan scheduling. We study the model of a
strong adversary which is allowed to change one job at regular intervals.
Furthermore, we investigate the setting of random changes. Our results show
that randomized local search and a simple evolutionary algorithm are very
effective in dynamically tracking changes made to the problem instance.Comment: Conference version appears at IJCAI 201
Runtime Analysis for Self-adaptive Mutation Rates
We propose and analyze a self-adaptive version of the
evolutionary algorithm in which the current mutation rate is part of the
individual and thus also subject to mutation. A rigorous runtime analysis on
the OneMax benchmark function reveals that a simple local mutation scheme for
the rate leads to an expected optimization time (number of fitness evaluations)
of when is at least for
some constant . For all values of , this
performance is asymptotically best possible among all -parallel
mutation-based unbiased black-box algorithms.
Our result shows that self-adaptation in evolutionary computation can find
complex optimal parameter settings on the fly. At the same time, it proves that
a relatively complicated self-adjusting scheme for the mutation rate proposed
by Doerr, Gie{\ss}en, Witt, and Yang~(GECCO~2017) can be replaced by our simple
endogenous scheme.
On the technical side, the paper contributes new tools for the analysis of
two-dimensional drift processes arising in the analysis of dynamic parameter
choices in EAs, including bounds on occupation probabilities in processes with
non-constant drift
Optimizing Linear Functions with Randomized Search Heuristics - The Robustness of Mutation
The analysis of randomized search heuristics on classes of functions
is fundamental for the understanding of the underlying stochastic
process and the development of suitable proof techniques. Recently,
remarkable progress has been made in bounding the expected
optimization time of the simple (1+1) EA on the class of linear
functions. We improve the best known bound in this setting from
(1.39+o(1))(en ln n) to (en ln n)+O(n) in expectation and with high
probability, which is tight up to lower-order terms. Moreover, upper
and lower bounds for arbitrary mutations probabilities p are derived,
which imply expected polynomial optimization time as long as
p=O((ln n)/n) and which are tight if p=c/n for a constant c. As a
consequence, the standard mutation probability p=1/n is optimal for
all linear functions, and the (1+1) EA is found to be an optimal
mutation-based algorithm. Furthermore, the algorithm turns out to be
surprisingly robust since large neighborhood explored by the mutation
operator does not disrupt the search
Tight Bounds on the Optimization Time of a Randomized Search Heuristic on Linear Functions
The analysis of randomized search heuristics on classes of functions is fundamental to the understanding of the underlying stochastic process and the development of suitable proof techniques. Recently, remarkable progress has been made in bounding the expected optimization time of a simple evolutionary algorithm, called (1+1) EA, on the class of linear functions. We improve the previously best known bound in this setting from (1.39+o(1))en ln n to en ln n+O(n) in expectation and with high probability, which is tight up to lower-order terms. Moreover, upper and lower bounds for arbitrary mutation probabilities p are derived, which imply expected polynomial optimization time as long as p = O((ln n)/n) and p = Ω(n−C) for a constant C > 0, and which are tight if p = c/n for a constant c > 0. As a consequence, the standard mutation probability p = 1/n is optimal for all linear functions, and the (1+1) EA is found to be an optimal mutation-based algorithm. Furthermore, the algorithm turns out to be surprisingly robust since the large neighbourhood explored by the mutation operator does not disrupt the search.</jats:p
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