1,123 research outputs found
Faster Black-Box Algorithms Through Higher Arity Operators
We extend the work of Lehre and Witt (GECCO 2010) on the unbiased black-box
model by considering higher arity variation operators. In particular, we show
that already for binary operators the black-box complexity of \leadingones
drops from for unary operators to . For \onemax, the
unary black-box complexity drops to O(n) in the binary case.
For -ary operators, , the \onemax-complexity further decreases to
.Comment: To appear at FOGA 201
Reducing the Arity in Unbiased Black-Box Complexity
We show that for all the -ary unbiased black-box
complexity of the -dimensional \onemax function class is . This
indicates that the power of higher arity operators is much stronger than what
the previous bound by Doerr et al. (Faster black-box algorithms
through higher arity operators, Proc. of FOGA 2011, pp. 163--172, ACM, 2011)
suggests.
The key to this result is an encoding strategy, which might be of independent
interest. We show that, using -ary unbiased variation operators only, we may
simulate an unrestricted memory of size bits.Comment: An extended abstract of this paper has been accepted for inclusion in
the proceedings of the Genetic and Evolutionary Computation Conference (GECCO
2012
Black-Box Complexity of the Binary Value Function
The binary value function, or BinVal, has appeared in several studies in
theory of evolutionary computation as one of the extreme examples of linear
pseudo-Boolean functions. Its unbiased black-box complexity was previously
shown to be at most , where is the problem
size. We augment it with an upper bound of ,
which is more precise for many values of . We also present a lower bound of
. Additionally, we prove that BinVal is an easiest
function among all unimodal pseudo-Boolean functions at least for unbiased
algorithms.Comment: 24 pages, one figure. An extended two-page abstract of this work will
appear in proceedings of the Genetic and Evolutionary Computation Conference,
GECCO'1
Black-Box Complexity: Breaking the Barrier of LeadingOnes
We show that the unrestricted black-box complexity of the -dimensional
XOR- and permutation-invariant LeadingOnes function class is . This shows that the recent natural looking bound is
not tight.
The black-box optimization algorithm leading to this bound can be implemented
in a way that only 3-ary unbiased variation operators are used. Hence our bound
is also valid for the unbiased black-box complexity recently introduced by
Lehre and Witt (GECCO 2010). The bound also remains valid if we impose the
additional restriction that the black-box algorithm does not have access to the
objective values but only to their relative order (ranking-based black-box
complexity).Comment: 12 pages, to appear in the Proc. of Artificial Evolution 2011, LNCS
7401, Springer, 2012. For the unrestricted black-box complexity of
LeadingOnes there is now a tight bound, cf.
http://eccc.hpi-web.de/report/2012/087
Better Fixed-Arity Unbiased Black-Box Algorithms
In their GECCO'12 paper, Doerr and Doerr proved that the -ary unbiased
black-box complexity of OneMax on bits is for . We propose an alternative strategy for achieving this unbiased black-box
complexity when . While it is based on the same idea of
block-wise optimization, it uses -ary unbiased operators in a different way.
For each block of size we set up, in queries, a virtual
coordinate system, which enables us to use an arbitrary unrestricted algorithm
to optimize this block. This is possible because this coordinate system
introduces a bijection between unrestricted queries and a subset of -ary
unbiased operators. We note that this technique does not depend on OneMax being
solved and can be used in more general contexts.
This together constitutes an algorithm which is conceptually simpler than the
one by Doerr and Doerr, and at the same time achieves better constant factors
in the asymptotic notation. Our algorithm works in ,
where relates to . Our experimental evaluation of this algorithm
shows its efficiency already for .Comment: An extended abstract will appear at GECCO'1
Better Fixed-Arity Unbiased Black-Box Algorithms
In their GECCO'12 paper, Doerr and Doerr proved that the -ary unbiased
black-box complexity of OneMax on bits is for . We propose an alternative strategy for achieving this unbiased black-box
complexity when . While it is based on the same idea of
block-wise optimization, it uses -ary unbiased operators in a different way.
For each block of size we set up, in queries, a virtual
coordinate system, which enables us to use an arbitrary unrestricted algorithm
to optimize this block. This is possible because this coordinate system
introduces a bijection between unrestricted queries and a subset of -ary
unbiased operators. We note that this technique does not depend on OneMax being
solved and can be used in more general contexts.
This together constitutes an algorithm which is conceptually simpler than the
one by Doerr and Doerr, and at the same time achieves better constant factors
in the asymptotic notation. Our algorithm works in ,
where relates to . Our experimental evaluation of this algorithm
shows its efficiency already for .Comment: An extended abstract will appear at GECCO'1
Unbiased Black-Box Complexities of Jump Functions
We analyze the unbiased black-box complexity of jump functions with small,
medium, and large sizes of the fitness plateau surrounding the optimal
solution.
Among other results, we show that when the jump size is , that is, only a small constant fraction of the fitness values
is visible, then the unbiased black-box complexities for arities and higher
are of the same order as those for the simple \textsc{OneMax} function. Even
for the extreme jump function, in which all but the two fitness values
and are blanked out, polynomial-time mutation-based (i.e., unary unbiased)
black-box optimization algorithms exist. This is quite surprising given that
for the extreme jump function almost the whole search space (all but a
fraction) is a plateau of constant fitness.
To prove these results, we introduce new tools for the analysis of unbiased
black-box complexities, for example, selecting the new parent individual not by
comparing the fitnesses of the competing search points, but also by taking into
account the (empirical) expected fitnesses of their offspring.Comment: This paper is based on results presented in the conference versions
[GECCO 2011] and [GECCO 2014
OneMax in Black-Box Models with Several Restrictions
Black-box complexity studies lower bounds for the efficiency of
general-purpose black-box optimization algorithms such as evolutionary
algorithms and other search heuristics. Different models exist, each one being
designed to analyze a different aspect of typical heuristics such as the memory
size or the variation operators in use. While most of the previous works focus
on one particular such aspect, we consider in this work how the combination of
several algorithmic restrictions influence the black-box complexity. Our
testbed are so-called OneMax functions, a classical set of test functions that
is intimately related to classic coin-weighing problems and to the board game
Mastermind.
We analyze in particular the combined memory-restricted ranking-based
black-box complexity of OneMax for different memory sizes. While its isolated
memory-restricted as well as its ranking-based black-box complexity for bit
strings of length is only of order , the combined model does not
allow for algorithms being faster than linear in , as can be seen by
standard information-theoretic considerations. We show that this linear bound
is indeed asymptotically tight. Similar results are obtained for other memory-
and offspring-sizes. Our results also apply to the (Monte Carlo) complexity of
OneMax in the recently introduced elitist model, in which only the best-so-far
solution can be kept in the memory. Finally, we also provide improved lower
bounds for the complexity of OneMax in the regarded models.
Our result enlivens the quest for natural evolutionary algorithms optimizing
OneMax in iterations.Comment: This is the full version of a paper accepted to GECCO 201
Toward an architecture for quantum programming
It is becoming increasingly clear that, if a useful device for quantum
computation will ever be built, it will be embodied by a classical computing
machine with control over a truly quantum subsystem, this apparatus performing
a mixture of classical and quantum computation.
This paper investigates a possible approach to the problem of programming
such machines: a template high level quantum language is presented which
complements a generic general purpose classical language with a set of quantum
primitives. The underlying scheme involves a run-time environment which
calculates the byte-code for the quantum operations and pipes it to a quantum
device controller or to a simulator.
This language can compactly express existing quantum algorithms and reduce
them to sequences of elementary operations; it also easily lends itself to
automatic, hardware independent, circuit simplification. A publicly available
preliminary implementation of the proposed ideas has been realized using the
C++ language.Comment: 23 pages, 5 figures, A4paper. Final version accepted by EJPD ("swap"
replaced by "invert" for Qops). Preliminary implementation available at:
http://sra.itc.it/people/serafini/quantum-computing/qlang.htm
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