17,089 research outputs found
Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs
In this paper, we present Batch Informed Trees (BIT*), a planning algorithm
based on unifying graph- and sampling-based planning techniques. By recognizing
that a set of samples describes an implicit random geometric graph (RGG), we
are able to combine the efficient ordered nature of graph-based techniques,
such as A*, with the anytime scalability of sampling-based algorithms, such as
Rapidly-exploring Random Trees (RRT).
BIT* uses a heuristic to efficiently search a series of increasingly dense
implicit RGGs while reusing previous information. It can be viewed as an
extension of incremental graph-search techniques, such as Lifelong Planning A*
(LPA*), to continuous problem domains as well as a generalization of existing
sampling-based optimal planners. It is shown that it is probabilistically
complete and asymptotically optimal.
We demonstrate the utility of BIT* on simulated random worlds in
and and manipulation problems on CMU's HERB, a
14-DOF two-armed robot. On these problems, BIT* finds better solutions faster
than RRT, RRT*, Informed RRT*, and Fast Marching Trees (FMT*) with faster
anytime convergence towards the optimum, especially in high dimensions.Comment: 8 Pages. 6 Figures. Video available at
http://www.youtube.com/watch?v=TQIoCC48gp
Batch Informed Trees (BIT*): Informed Asymptotically Optimal Anytime Search
Path planning in robotics often requires finding high-quality solutions to
continuously valued and/or high-dimensional problems. These problems are
challenging and most planning algorithms instead solve simplified
approximations. Popular approximations include graphs and random samples, as
respectively used by informed graph-based searches and anytime sampling-based
planners. Informed graph-based searches, such as A*, traditionally use
heuristics to search a priori graphs in order of potential solution quality.
This makes their search efficient but leaves their performance dependent on the
chosen approximation. If its resolution is too low then they may not find a
(suitable) solution but if it is too high then they may take a prohibitively
long time to do so. Anytime sampling-based planners, such as RRT*,
traditionally use random sampling to approximate the problem domain
incrementally. This allows them to increase resolution until a suitable
solution is found but makes their search dependent on the order of
approximation. Arbitrary sequences of random samples approximate the problem
domain in every direction simultaneously and but may be prohibitively
inefficient at containing a solution. This paper unifies and extends these two
approaches to develop Batch Informed Trees (BIT*), an informed, anytime
sampling-based planner. BIT* solves continuous path planning problems
efficiently by using sampling and heuristics to alternately approximate and
search the problem domain. Its search is ordered by potential solution quality,
as in A*, and its approximation improves indefinitely with additional
computational time, as in RRT*. It is shown analytically to be almost-surely
asymptotically optimal and experimentally to outperform existing sampling-based
planners, especially on high-dimensional planning problems.Comment: International Journal of Robotics Research (IJRR). 32 Pages. 16
Figure
An Atypical Survey of Typical-Case Heuristic Algorithms
Heuristic approaches often do so well that they seem to pretty much always
give the right answer. How close can heuristic algorithms get to always giving
the right answer, without inducing seismic complexity-theoretic consequences?
This article first discusses how a series of results by Berman, Buhrman,
Hartmanis, Homer, Longpr\'{e}, Ogiwara, Sch\"{o}ening, and Watanabe, from the
early 1970s through the early 1990s, explicitly or implicitly limited how well
heuristic algorithms can do on NP-hard problems. In particular, many desirable
levels of heuristic success cannot be obtained unless severe, highly unlikely
complexity class collapses occur. Second, we survey work initiated by Goldreich
and Wigderson, who showed how under plausible assumptions deterministic
heuristics for randomized computation can achieve a very high frequency of
correctness. Finally, we consider formal ways in which theory can help explain
the effectiveness of heuristics that solve NP-hard problems in practice.Comment: This article is currently scheduled to appear in the December 2012
issue of SIGACT New
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
Towards a Theory-Guided Benchmarking Suite for Discrete Black-Box Optimization Heuristics: Profiling EA Variants on OneMax and LeadingOnes
Theoretical and empirical research on evolutionary computation methods
complement each other by providing two fundamentally different approaches
towards a better understanding of black-box optimization heuristics. In
discrete optimization, both streams developed rather independently of each
other, but we observe today an increasing interest in reconciling these two
sub-branches. In continuous optimization, the COCO (COmparing Continuous
Optimisers) benchmarking suite has established itself as an important platform
that theoreticians and practitioners use to exchange research ideas and
questions. No widely accepted equivalent exists in the research domain of
discrete black-box optimization.
Marking an important step towards filling this gap, we adjust the COCO
software to pseudo-Boolean optimization problems, and obtain from this a
benchmarking environment that allows a fine-grained empirical analysis of
discrete black-box heuristics. In this documentation we demonstrate how this
test bed can be used to profile the performance of evolutionary algorithms.
More concretely, we study the optimization behavior of several EA
variants on the two benchmark problems OneMax and LeadingOnes. This comparison
motivates a refined analysis for the optimization time of the EA
on LeadingOnes
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