
Genetic Algorithms Digest   Thursday, September 5 1991   Volume 5 : Issue 27

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Today's Topics:

	- order operators
	- re: order operators
	- newspaper article of interest
	- archive of publications

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

 First European Conference on Artificial Life (v5n10)         Dec 11-13, 1991
 Canadian AI Conference, Vancouver, (CFP 1/7)                 May 11-15, 1992
 10th National Conference on AI, San Jose, (CFP 1/15)         Jul 12-17, 1992
 ECAI 92, 10th European Conference on AI (v5n13)              Aug  3-7,  1992
 Parallel Problem Solving from Nature, Brussels, (CFP 4/15)   Sep 28-30, 1992

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

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From: jrv@sdimax2.mitre.org
Date: Fri, 30 Aug 91 08:59:51 EDT
Subject: order operators

   I was not able to attend ICGA91, but I'm now working my way through the
   proceedings.  Starkweather et al.  describe two sequencing operators in
   [1], both credited to Syswerda [2], which appear to me to be
   equivalent.

   Order Crossover #2: "...key positions are chosen randomly and the order
   in which these elements appear in one parent is imposed on the other
   parent to produce two offspring..."

   P1:              a b c d e f g h i j 
   P2:              c f a j h d i g b e
   cross pts:           * *     *   *
   offspring:       a j c d e f g h i b

   Position Based Crossover: "Several random locations in the sequence are
   selected along with one parent; the elements in those positions are
   inherited from that parent.  The remaining elements are inherited in
   the order in which they appear in the alternate parent, skipping over
   all elements which have already been included in the offspring."

   P1:              a b c d e f g h i j 
   cross pts:         * *     *     *
   P2:              c f a j h d i g b e
   offspring:       a b c j h f d g i e

   In each case, one group of elements inherit their absolute positions
   from one parent and the rest inherit their relative positions from the
   other parent.  In Order Crossover #2, the cross points indicate the
   elements inheriting relative positions.  In Position Based Crossover,
   the cross points indicate the elements inheriting absolute positions.

   For each set of cross points for one operator, there is an equivalent
   set of cross points for the other operator giving the same result.  In
   the first example above,

   P1:              a b c d e f g h i j 
   OX2 cross pts:       * * * * * *       <--- inheriting absolute positions

   P2:              c f a j h d i g b e
   PBX cross pts:       * *     *   *     <--- inheriting relative positions

   offspring:       a j c d e f g h i b

   In the experiments reported in [1], the two operators gave different
   results.  The only explanation I can think of is that the fraction of
   elements inheriting absolute positions was different.  The descriptions
   quoted above don't give any guidance on this point ("positions are
   chosen randomly" vs.  "several random locations")

   I don't have [2] conveniently available.  Have Starkweather et al.
   accurately described Syswerda's operators?  How many cross points were
   used for each operator in [1]?


   [1] T. Starkweather, S. McDaniel, K. Mathias, D. Whitley, and C. Whitley,
   "A Comparison of Genetic Sequencing Operators,", ICGA91, pp. 69-76

   [2] G.  Syswerda, "Schedule Optimization Using Genetic Algorithms," in
   Handbook of Genetic Algorithms, L.  Davis, ed., 1990.  


				      - Jim Van Zandt (jrv@mbunix.mitre.org)

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From: starkwea@CS.ColoState.EDU (tim starkweather)
Date: Tue, 3 Sep 91 12:51:13 MDT
Subject: re: order operators

   In reply to comments made in:

   > From: jrv@sdimax2.mitre.org

   > I was not able to attend ICGA91, but I'm now working my way through the
   > proceedings.  Starkweather et al.  describe two sequencing operators in
   > [1], both credited to Syswerda [2], which appear to me to be
   > equivalent.

   > In each case, one group of elements inherit their absolute positions
   > from one parent and the rest inherit their relative positions from the
   > other parent.  In Order Crossover #2, the cross points indicate the
   > elements inheriting relative positions.  In Position Based Crossover,
   > the cross points indicate the elements inheriting absolute positions.

     After carefully reviewing the operators (along with D. Whitley
   and K. Mathias), we agree that what is 
   presented as Order Crossover #2 and Position-based Crossover in [1]
   are basically equivalent, if the number of crossover points averages
   half the length of the string.  Furthermore,  we found there is a 
   simple transformation which shows both of these operators will 
   yield identical results (assuming complementary crossover points are used).
   The following example transforms the "order crossover #2" 
   to the "position-based" operator. 
   Consider the following strings:

	 P1:   a b c d e f g h i j
	 P2:   e i b d f a j g c h
   X-points:     * *   *     *

   Assume that P1 is selected.  The order "b c e h" is imposed on P2.

   Thus,       e i b d f a j g c h   (Phase 1)
	       -   -           - -
   becomes    
	       b _ c _ _ _ _ _ e h

   and the remaining elements are copied directly from P2:  
	       b i c d f a j g e h

   To effect the transformation with the "position-based" operator, 
   compliment the positions in (Phase 1) above for the crossover sites:
	 P1:   a b c d e f g h i j
	 P2:   e i b d f a j g c h
   X-points:     *   * * * * *

   Crossover sites are directly copied from P2:
	       _ i _ d f a j g _ _
   Relative order of remaining elements are taken from P1:
	       b i c d f a j g e h

   This yields the same offspring as above since the elements are directly
   copied from these positions in both cases and the remaining elements
   are ordered accordings to the relative order or the other parent in
   both cases.   The operators are identical--not because they produce the
   same results given the same crossover points, but because given
   sets of crossover points that are complementary in (Phase 1), they
   are identical.   Therefore, if 50% of the points are selected for
   recombination, the operators are the same in expectation. 

   > In the experiments reported in [1], the two operators gave different
   > results.  The only explanation I can think of is that the fraction of
   > elements inheriting absolute positions was different.  The descriptions
   > quoted above don't give any guidance on this point ("positions are
   > chosen randomly" vs.  "several random locations")

   This is indeed the reason why the 2 operators produced different results
   on the problems in [1].  The number of crossover points used for each
   operator was on average less than half the length of the string.
   Thus, the "position-based" operator was really emphasizing relative
   order, since the number of positions inheriting relative order information
   from one parent was greater than the number of points which were directly
   copied from the other parent.  The reverse is true for the operator
   described as "order crossover #2".  In the scheduling application
   described in our paper, where order information was deemed the crucial
   information, this explains why the "position-based" operator actually
   performed a little better.

   > I don't have [2] conveniently available.  Have Starkweather et al.
   > accurately described Syswerda's operators?  How many cross points were
   > used for each operator in [1]?

   We have reviewed the description of these operators in [2], and our
   descriptions appear to be consistent.  One would have to assume that the
   number of crossover points used did not have a mean of half the string
   length, since the operators behaved differently in [2] also.
   In [1], we did make the observation that the "position-based"
   operator was really an order type operator. The comments made 
   by Jim Van Zandt about these "two" operators is very astute.

   > [1] T. Starkweather, S. McDaniel, K. Mathias, D. Whitley, and C. Whitley,
   > "A Comparison of Genetic Sequencing Operators,", ICGA91, pp. 69-76

   > [2] G.  Syswerda, "Schedule Optimization Using Genetic Algorithms," in
   > Handbook of Genetic Algorithms, L.  Davis, ed., 1990.  

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

From: ramsey@AIC.NRL.Navy.Mil
Date: Thu, 5 Sep 91 09:52:58 EDT
Subject: newspaper article of interest

   I recently saw the following article in the Science section of
   the Washington Post and I thought the GA community might find it
   interesting.

   -- Connie

   Entomology: Low-Risk Strategy for Survival

      Mutual funds or junk bonds?  Blind date or the girl next door?

      Risk-taking strategies determine the short-term well-being of
   individuals and the long-term evolutionary success of species.
   Bumblebees, Leslie Real reports in Science, appear to be a dramatic
   case of survival of the very cautious.

      The University of North Carolina biologist constructed an
   enclosure in which bees had their choice of two kinds of artificial
   flowers: blue ones, containing 2 ml of nectar each; and yellow
   ones, one-third of which contained 6 ml of nectar and the rest
   nothing.  Each flower type promised the same average amount of
   reward, but only the yellow was risky.  Bees chose the no-risk
   blue 84 percent of the time, and made that decision after trying
   only a few individual flowers instead of waiting for a larger
   and, perhaps, more accurate sample.

     What evolutionary advantage is there to this hasty and conservative
   strategy for "short-term energy maximization"?  Limited bee-brain
   computing power may be a factor.  But the system is also neatly
   adapted to the way food sources turn up in the highly competitive
   wild: Once a bee finds a promising flower patch, "it generally
   restricts its foraging to neighboring plants, ultimately exhausting
   the resources in that local patch," Real noted.  So bees capable
   of making a fast decision will eat better.  And since the best
   plants tend to occur in clumps, averaging over a large number of
   flowers would be counterproductive as well as harder to recall.

					   -- Curt Suplee

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From: Bernd Rosauer <rosauer%fzi.uka.de@RELAY.CS.NET>
Date:     Tue, 20 Aug 91 17:01:21 GMT
Subject:  archive of publications

   I wonder if there is anybody maintaining an archive of
   publications on GA like the neuroprose archive?

   Bernd

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End of Genetic Algorithms Digest
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