
Genetic Algorithms Digest   Wednesday, May 29 1991   Volume 5 : Issue 11

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

Today's Topics:
	- Ga-List is back!
	- Re: Error in Handbook of Genetic Algorithms
 	- Announcement: ICGA-91 Workshop on Classifier Systems
	- Grey Code
	- Results using GA to solve TSP problem (3 messages)
	- Reporting population average fitness on Simple GAs
	- Genetic Algorithm Course, July 22-26, 1991

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

4th Intl. Conference on Genetic Algorithms (v5n9)            Jul 13-16, 1991
AAAI 91, National Conference on AI, Anaheim, CA              Jul 14-19, 1991
EUROPEAN SUMMER SCHOOL on MACHINE LEARNING (v5n7)            Jul 22-31, 1991
Genetic Algorithm Course, Stanford (v5n11)                   Jul 22-26, 1991
IJCAI 91, International Joint Conference on AI, Sydney, AU   Aug 25-30, 1991
First European Conference on Artificial Life (v5n8)          Dec 11-13, 1991

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

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Date: Wednesday, May 29 1991
From: Alan C. Schultz (GA-LIST Moderator)
Subject: GA-List is back!

	Well, I am back from a two week+ vacation, and GA-List
	is back on line.  We have a small back up of submissions
	here, but we should have them all out with in a week
	or so.

	--Alan

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Date: 11 Apr 91 13:07:01 EDT
From: David Davis <70461.1552@CompuServe.COM>
Subject: Re: Error in Handbook of Genetic Algorithms

    The error Wayne noted in a prior GA-list has been pointed out by a number
    of people.  As Wayne said, it is pernicious and quite unfortunate.  I
    believe Aaron Konstam was the first reader to call it to my attention.
    The error affects the equations on pages 8 and 31.  In each case, add .5
    to the initial constants (yielding 1.0 on p. 8 and 1000.0 on p. 31).  In
    addition, the entire denominator of each fraction is squared.  Thus, the
    denominators should be
      (1.0 + 0.001 * (x**2 + y**2))**2

    I deeply regret the mistake.  It will be fixed in future printings of the
    book.

    David Davis

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From: booker@starbase.MITRE.ORG (Lashon Booker)
Date: Tue, 7 May 91 09:11:39 EDT
Subject: Announcement: ICGA-91 Workshop on Classifier Systems

	Classifier Systems have always been a promising approach
     for investigating fundamental issues in induction and complex
     adaptive systems. What are the prospects for realizing this
     potential? What has been accomplished so far, and what are the
     important issues that should guide future research? This
     workshop will examine these questions and others related to
     the classifier system paradigm. If you are interested in
     participating, please let me know as soon as possible.

     Lashon
     booker@ai.mitre.org

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Date: Tue, 26 Mar 91 14:25:22 -0500
From: vose@cs.utk.edu
Subject: gray code

   The following is an interesting fact about a Grey code which is easily
   proved by induction on n = string length:

   Let A be the n by n matrix with 1's down the diagonal and the
   sub-diagonal.  For example, if n = 4 then

		| 1 0 0 0 |
	A  =    | 1 1 0 0 |
		| 0 1 1 0 |
		! 0 0 1 1 |

   Let v be a column vector representing a binary integer with most
   significant bit first.  For example, the integer 12 has corresponding
   vector

		| 1 |
	v  = 	| 1 |
		| 0 |
		| 0 |
		
   The Grey code vector corresponding to v is then given by the matrix
   product

	Av

   where all operations are done modulo 2.  One can take this result and
   optimize it into a reasonable conversion algorithm for Grey coding
   (multiplication modulo 2 is the same as logical-and, and addition modulo 2
   is the same as exclusive-or).  Naturally, it follows that decoding
   corresponds to multiplication by the inverse matrix.

   By the way, the inverse of A (again, modulo 2) is the matrix with 1's
   everywhere except above the diagonal.  For our example,

	 -1	| 1 0 0 0 |
	A   =   | 1 1 0 0 |
		| 1 1 1 0 |
		! 1 1 1 1 |

--------------------------------

[ Ed's Note:  The following three messages are from Mark Lidd
  concerning his results on various published TSP problems.  I heard
  him give a talk where he described his technique, and it is interesting.
  Hopefully he will write something up soon, or describe it in
  GA-List ;-)
]

Date: Wednesday, 27 Mar 1991 14:26:28 EST
From: m22389@mwvm.mitre.org (Mark Lidd)
Subject: Oliver's Traveling Salesman Problem Solution

   The solution as published by Whitley, etc. in Proceedings of the Third
   International Conference on Genetic Algorithms page 140 is not the best
   solution anymore. The new best solution is:

   replace his city sub-tour sequence.
   (71,44) (64,60) (68,58) 83,69)
   with
   (71,44) (68,58) (64,60) (83,69)

   The resulting tour, as computed by his metric (page 140) is length 420 and
   was computed by a GA.

   *
   *        Mark

--------------------------------

From: m22389@mwvm.mitre.org (Mark Lidd)
Subject: more optimal (optimun (?) tours)

   A few tours have been found: Another (Oliver's 30 city problem) tour of
   integer length 420 but shorter in floating is: same tour as previous but
   change sequence (69 58) (67 54) (62 54) (84 37) to (69 58) (62 54) (67 54)
   (84 37).  For Eilon's 50 city problem a tour of 425 has been found, the
   shortest previously reported in the literature (Whitley, et. al. 89) being
   428.  Change sequence from (21 51) (27 58) (28 48) (33 52) (41 52) (37 56)
   (33 61) (41 62) to (21 51) (28 48 ) (33 52) (27 58) (33 61) (37 56) (41
   52) (42 62). (Note: I use the mirror image. My (x y) are others (y x)).
   If you know of shorter tours in floating point or integer, please send
   them to me.  My tours were computed i n integer arithmetic using
   "classical GAs".

   *
   *        Mark

--------------------------------

From: m22389@mwvm.mitre.org (Mark Lidd)
Date: Monday, 8 Apr 1991 09:20:29 EDT
Subject: Better & Better

   Best tours so far found for Eilon's 75 cities problem are: tour length =
   442, population: 150, trials 35K tour length = 439, population: 150,
   trials 200K These tours are shorter than previously published tours

   *
   *        Mark


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From: pl160988@mtecv2.mty.itesm.mx (Ing. Ivan Ordonez)
Date: Fri, 5 Apr 91 17:12:06 CST
Subject: Reporting population average fitness on Simple GAs

	    I have noticed that a common practice when reporting results in
    simple genetic algorithms is showing the evaluation of the best
    individual and/or the average individual per generation. After plotting
    these results, the best individuals make a somewhat noisy plot, while
    the average individuals make a smooth variation, representing in some
    way the fitness of the entire population.

	    However, how representative can the average individual be? I
    claim that it depends on the selection operator. When using roulette
    wheel selection the survival chance of every individual strictly depends
    on the fitness/average ratio, as stated in Holland's schemata
    theorem. Thus, the average fitness is a good measure of the behavior of
    an entire population.

	    On the other hand, when the survival chance of an individual
    does not depend on its absolute fitness but on its relative ranking to the
    other individuals, as happens when using tournament selection or ranking,
    the average fitness of the population has little meaning. This is very
    apparent when the fitness function has a wide range of variation (for
    example, an exponential function), and when trying to find the minimal.
    This makes the average a representant of the worse individual of the
    population, more than a representant of the entire population.
    Therefore, the best way to represent a population is not by reporting
    the average, but by reporting the median of a ranked population. This
    way the noise from the worse individuals is eliminated, and a
    representative individual is reported in a way that matches the idea
    of ranking or tournament selection.

	    Ivan Ordonez-Reinoso. pl160988@mtecv2.mty.itesm.mx

--------------------------------

From: "David E. Goldberg" <GOLDBERG@VMD.CSO.UIUC.EDU>
Date: Tue, 23 Apr 91 07:31:08 CDT
Subject: Genetic Algorithm Course, July 22-26, 1991

    A five-day short course entitled "Genetic Algorithms in Search,
    Optimization, and Machine Learning" will be presented at Stanford
    University's Western Institute in Computer Science on July 22-26
    by David E. Goldberg (Illinois) and John R. Koza (Stanford).
    The course presents in-depth coverage of GA mechanics, theory, and
    application in search, optimization, and machine learning.  Students
    will be encouraged to solve their own problems in hands-on computer
    workshops monitored by the course instructors.  For further information
    regarding this course contact Joleen Barnhill, Western Institute in
    Computer Science, PO Box 1238, Magalia, CA 95954, (916) 873-0575,
    email: barnhill@hudson.stanford.edu.

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End of Genetic Algorithms Digest
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