
Genetic Algorithms Digest   Monday, 28 January 1991   Volume 5 : Issue 2

 - Send submissions to GA-List@AIC.NRL.NAVY.MIL
 - Send administrative requests to GA-List-Request@AIC.NRL.NAVY.MIL

Today's Topics:
	- From moderator
	- Dave Davis' new book ordering info...
	- How Short is a Building Block?
	- Call for papers: Special Issue of MLJ on Reinforcement Learning

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CALENDAR OF GA-RELATED ACTIVITIES: (with GA-List issue reference)

4th Intl. Conference on Genetic Algorithms (v4n17)          Jul 14-17, 1991
          (Deadline for submissions is Feb 1)
AAAI91 - Deadline for submissions is Jan 30, 1991
Machine Learning Workshop - Deadline for submissions is March 1, 1991
Special Issue of MLJ on Reinforcement Learning - (v5n2)
	   Deadline for submissions is  March 1, 1991

(Send announcements of other activities to GA-List@aic.nrl.navy.mil)

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Date: Monday, 28 January 1991
From: Alan C. Schultz (GA-List moderator)
Subject: Information...

	I now have very complete information from Dave Davis on his
	new book.  See the first article...

	Alan C. Schultz

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Date: Sat, 26 Jan 91 0:31:18 EST
From: Dan Cerys <cerys@BBN.COM>
Subject: Dave's book info

    Here's the long-awaited message from Dave Davis regarding his new book
    and associated software.

    Dan

    === From Dave Davis: =============

    I would like to announce two new, related genetic algorithm
    publications.  The first is the Handbook of Genetic Algorithms,
    currently available from Van Nostrand Reinhold.  The Handbook is
    a 385-page volume on the topic of optimization with genetic
    algorithms.  It has two parts.  Part I is a tutorial on genetic
    algorithm optimization written by me (Lawrence Davis).  Part II
    contains twelve chapters by authors who have applied genetic
    algorithms to real-world problems.  Included in
    Part II are chapters on design, scheduling, message routing,
    parameterization, strategy acquisition, molecular analysis,
    neural network design and training, and chaotic model parameter 
    optimization.  The book should be useful to anybody interested
    in the topic of genetic algorithm optimization.  It should be a
    tremendous aid to people who intend to apply cutting-edge
    genetic algorithms to real-world problems of their own.  

    Orders for the book may be placed by telephone at 1-800-926-2665
    if you are in the USA and have a credit card.  (This is the Van
    Nostrand Reinhold order number.)  Customers outside the USA can
    write to Thomson International Publishing, 10 Davis Drive,
    Belmont, California 94002 USA.  The book will also be available at
    technical bookstores.


    The second publication is a software package called GENESIS and OOGA:
    Two Genetic Algorithms.  This package contains a revised and improved
    version of John J. Grefenstette's GENESIS system, a C-based system for
    genetic algorithm optimization.  It also contains OOGA, the
    Object-Oriented Genetic Algorithm, a CLOS-based system written by me and
    made usable for CLOS systems by Daniel Cerys.  OOGA accompanies the
    tutorial in the Handbook of Genetic Algorithms and that is easy to
    modify for application to one's own optimization problems.  You will
    need a C compiler to use GENESIS.  You will need a Common Lisp
    implementation with CLOS support to use OOGA.  The software is available
    in the form of either IBM PC or Macintosh disks, and can be run a
    variety of hardware implementations.

    These two systems and their documentation are sold together.
    Information about ordering this package appears in the Handbook of
    Genetic Algorithms.  The cost of the software and documentation is
    $52.50 ($60 for international destinations).  For additional
    information, or to order, write: TSP P.O. Box 991 Melrose, MA 02176

    David Davis
    Tica Associates
    36 Hampshire St.
    Cambridge, MA 02139

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Date: Mon, 21 Jan 91 08:42 GMT
From: BARRY MCMULLIN <75008378%dcu.ie@pucc.PRINCETON.EDU>
Subject: How Short is a Building Block?

    % (NOTE: This involves some abstruse mathematical notation, impossible
    % to convey in raw ASCII. So I've done it in LaTeX format.  To make
    % sense of it, you need to cut this message out, run it through LaTeX,
    % and then either print it or use a previewer...
    %
    % ---CUT HERE----
    \documentstyle[11pt]{article}
    \begin{document}
    \title{How Short is a Building Block?}
    \author{Barry McMullin,\\ Dublin City University,\\ McMullinB@DCU.IE}
    \date{21st January 1991}
    \maketitle

    Goldberg, in his book ``Genetic Alogorithms'', introduces the term {\em
    building block\/} for schemata which have high fitness and {\em short
    defining length\/}; but, as far as I can see, he is somewhat coy about
    how short is short.  However, Holland provided an analysis of this
    issue in ``Adaptation in Natural and Artificial Systems'', p.103.  His
    conclusion is, roughly, that there is a tradeoff between the length and
    the required fitness---a longer schema needs to be relatively more fit
    than a shorter one, if it is to increase under a GA.  With this informal
    result, I completely agree.

    But: I claim that there is an error in Holland's detailed analysis of
    the relation between schema size and the selection pressure required for
    it to increase.

    This is probably well known to the GA gurus out there, but it took me by
    surprise, and I expended quite a while puzzling over it, so, for anyone
    else who may be interested, here is an explanation.

    Holland concludes, as a corollary to his Theorem 6.2.3, that, in order
    to increase, ``\ldots the longest schemata (if they occur in small
    proportion) may have to exhibit a performance twice the population
    average.''

    I claim the correct conclusion is, rather, that, in order to increase,
    ``\ldots the longest schemata (if they occur in small proportion) may
    have to exhibit a performance which exceeds the population average by an
    {\em arbitrarily large\/} factor.''

    This is derived as follows:

    Define:

    \[
      c \equiv P_C \frac{l(\xi)}{(l-1)} (1 - P(\xi,t))
    \]

    Then, from Theorem 6.2.3, a schema will definitely increase if:

    \[
      \frac{ \hat{\mu}_\xi(t) } { \hat{\mu}(t) } \geq \frac{1}{1-c}
    \]

    This factor will be {\em unlimited\/} as $c \rightarrow 1$. From the
    definition of $c$, this is precisely what will happen if $P_C
    \rightarrow 1$ (i.e.\ unconditional crossover), and $l(\xi) = (l-1)$
    (i.e.\ a maximum length schema), and, finally, $P(\xi,t) \rightarrow 0$
    (i.e.\ the schema occurs in arbitrarily small proportion---implicitly
    requiring an arbitrarily large population).  Now these are precisely the
    conditions mentioned by Holland, and so we get the conclusion, given
    above, that the schema may need to exceed the population average
    performance by an arbitrarily large factor ($1/(1-c) \rightarrow
    \infty$) in order to increase. QED.

    For completeness,  Holland's erroneous conclusion arises as follows:

    Holland notes that $1/(1-c) \geq (1+c)$ for $c \leq 1$.  Therefore,
    if the schema increases, we must have:

    \[
      \frac{ \hat{\mu}_\xi(t) } { \hat{\mu}(t) } \geq 1+c \rightarrow 2
    \]

    Now this is all true, as far as it goes---but the implication goes only
    one way.  The converse does not hold.  That is, the condition above is
    necessary {\em but not sufficient\/} for the schema to increase (the
    earlier quoted condition is the sufficient one); whereas Holland
    interprets it as sufficient in coming to his conclusion.  In effect, the
    logic is somewhat like saying that 10 is greater than 2, so any number
    greater than 2 must be greater than 10\ldots

    Finally: nothing critical hangs on this in the rest of Holland's book,
    so from that point of view its an insignificant slip; however, for
    curiosity's sake, I'd be interested in any comments anybody may have on
    this issue---in particular, whether anyone has noticed this aspect of
    the behavior of long schemata in {\em empirical\/} GA studies.

    \end{document}
    % ---CUT HERE---

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Date: Wed, 12 Sep 90 11:32:21 -0400
From: rich@gte.com (Rich Sutton)
Subject: Call for papers: Special Issue of MLJ on Reinforcement Learning


			       CALL FOR PAPERS

    The journal Machine Learning will be publishing a special issue on
    REINFORCEMENT LEARNING in 1991.  By "reinforcement learning" I mean
    trial-and-error learning from performance feedback without an explicit
    teacher other than the external environment.  Of particular interest is
    the learning of mappings from situation to action in this way.
    Reinforcement learning has most often been studied within connectionist
    or classifier-system (genetic) paradigms, but it need not be.

    Manuscripts must be received by March 1, 1991, to assure full
    consideration.  One copy should be mailed to the editor:

	    Richard S. Sutton
	    GTE Laboratories, MS-44
	    40 Sylvan Road
	    Waltham, MA  02254
	    USA

    In addition, four copies should be mailed to:

	    Karen Cullen
	    MACH Editorial Office
	    Kluwer Academic Publishers
	    101 Philip Drive
	    Assinippi Park
	    Norwell, MA 02061
	    USA

    Papers will be subject to the standard review process.

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End of Genetic Algorithms Digest
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