
Genetic Algorithms Digest    Tuesday, 28 August 1990    Volume 4 : Issue 19

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

Today's Topics:

	**** SPECIAL ISSUE OF WORKSHOP ABSTRACTS (PART 2) ****

	- Message from moderator
	- Variable Default Hierarchy Separation in a Classifier System 
		Robert E. Smith and David E. Goldberg 
	- A Grammar-Based Genetic Algorithm
		H. James Antonisse
	- Epistasis Variance - Suitability of a Representation to a GA
		Yuval Davidor
	- A Comparative Analysis of Selection Schemes Used in GAs
		David E. Goldberg and Kalyanmoy Deb


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

Conference on Simulation of Adaptive Behavior, Paris (v4n17)  Sep 24-28, 1990
Workshop Parallel Prob Solving from Nature, W Germany (v4n18) Oct 1-3,   1990
2nd Intl Conf on Tools for AI, Washington, DC (v4n6)          Nov 6-9,   1990
4th Intl. Conference on Genetic Algorithms (v4n17)            Jul 14-17, 1991

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

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Date: Tue, 28 Aug 1990
From: Alan C. Schultz (GA-List Moderator)
Subject: Another Special issue

	This is the second issue comprised of abstracts from talks
	presented at the Foundations of Genetic Algorithms Workshop
	held July 15-18, 1990, at Indiana University.  The workshop
	was organized by Gregory Rawlins.

	Last call for those who have not submitted their abstracts!

	--Alan

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

Date: Fri, 17 Aug 90 09:23:32 CDT
From: Robert Elliott Smith <rob@galab2.mh.ua.edu>
Subject: Variable Default Hierarchy Separation in a Classifier System 


   Variable Default Hierarchy Separation in a Classifier System 
	    Robert E. Smith and David E. Goldberg 
		 The University of Alabama 
	     Department of Engineering Mechanics 
		    Tuscaloosa, Alabama

			 Abstract

  Traditionally, some form of auction-based, specificity-biased
  allocation of credit(AOC) and conflict resolution (CR) scheme has been used
  to encourage default hierarchy formation in the LCS.  These AOC/CR
  schemes have two major limitations.  The first is that they lead to a
  fixed steady-state difference between the bids of rules. This fixed
  separation is dictated by pre-specified LCS parameters and the given
  specificity difference between rules.  Since unknown environmental
  factors (e.g. noise, the repeated application of taxes, and reward
  delays) dictate what amount of separation is adequate for a given
  environment, these parameters cannot be specified for general utility.  The
  second limitation is that specificity may not reflect  the correct
  priority of a rule in a default hierarchy.  Classifiers can be
  placed into working default hierarchies in priority positions that are
  not related to their specificity. It is true that default
  hierarchies can be formed for any given environment such that
  specificity-based prioritization is possible. However, if the system is
  only able to exploit this restricted class of default hierarchies, the
  rule discovery burden on the GA is increased. Under this restriction, a
  system can only thoroughly evaluate rules in the context of sets that
  can be prioritized based on specificity, thus limiting the GA's
  effectiveness. Additionally, the class of effective rule sets that can
  be discovered by the GA is narrowed.

  To allow for more robust default hierarchy formation in the LCS, this
  study suggests a modified CR scheme that associates two separate
  measures with each classifier.  The first measure is a reward estimate
  that is updated in the same manner as strength in the traditional LCS
  scheme.  The second  measure is a priority factor that biases CR.  
  The priority factor is updated using a necessity auction.  A
  necessity auction is a more realistic simulation of a real auction where
  the winning classifier need only pay out the bid of its nearest
  competitor. Under the modified scheme, bids are based on reward
  estimates, but conflicts are resolved based on the product of the
  reward estimate and the priority factor. In terms of economic analogy,
  the priority factor can be thought of as a cash reserve, or as some
  other net-profit-based influence on the auction procedure.  Note that
  this scheme has the benefit of yielding a more clear-cut
  classifier fitness measure for the GA.  Since the reward estimate in
  this scheme is not used to measure a classifier's priority
  (as happens with strength in the traditional scheme), it can more
  adequately reflect a classifier's fitness in the current rule set.

  Analysis and experimentation show that separate priority factors and
  the necessity auction induce variable bid separation for multi-level
  default hierarchies.  This separation adapts to fit the characteristics
  of the environment and leads to consistent preference of the exception
  over the default.

  Robert Elliott Smith
      Department of Engineering of Mechanics
      The University of Alabama
      P. O. Box 870278
      Tuscaloosa, Alabama 35487
  <<email>> rob@galab2.mh.ua.edu 
  <<phone>> (205) 348-4661

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

Date: Wed, 22 Aug 90 15:37:32 EDT
From: jima@starbase.MITRE.ORG (Jim Antonisse)
Subject: A Grammar-Based Genetic Algorithm


   A Grammar-Based Genetic Algorithm

   H. James Antonisse
   antonisse@ai.mitre.org

   The MITRE Corporation W418
   7525 Colshire Drive, McLean, VA 22102
   (703) 883-7887

   One major obstacle to a widened role for the genetic algorithm 
   (GA) has been its foundation on unstructured problem 
   representations.  Although unstructured representations form 
   the basis of the theory underlying the GA, such representations 
   contrast sharply with most work in the artificial intelligence 
   community.  The presentation proposed a general reformulation of 
   the genetic algorithm that makes it appropriate to any 
   representation that can be cast in a formal grammar.  First a 
   reconstruction of the basis of the source of the GA's power was 
   presented.  The reconstruction clarified the three biases,
   the statistical bias, inductive bias, and proximity  bias, inherent
   in the GA approach.  The problem that confronts the GA in structured
   domains was illustrated and a solution presented that is appropriate
   for any domain defined by a grammar.  The approach results in a new
   crossover operator that folds the grammar into the operator in a
   completely general way.  Fragments of legal expressions that are
   crossed using this operator are guaranteed to lead to new expressions
   that are legal in the grammar. 

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

Date: Wed, 22 Aug 90 18:15:06 -0300
From: yuval@wisdom.weizmann.ac.il (Yuval Davidor)
Subject: Epistasis Variance

 Epistasis Variance - Suitability of a Representation to a Genetic Algorithm

  Yuval Davidor
  Department of Applied Mathematics and Computer Science,
  Weizmann Institute of Science, Rehovot 76100, Israel.
  yuval@wisdom.weizmann.ac.il

  The choice of a representation is the most important constraint
  imposed on a GA.  The discussion on epistasis variance attempts to
  suggest a new viewpoint on the interaction between a representation
  and a GA, and a criterion with which the suitability of a particular
  representation for a GA can be assessed.  The paper promotes the
  following dogma:

  1) GAs only 'see' the representation and therefore, all nonlinearities
     embedded in the application (objective function, population, and
     representation structure) are folded into the representation.
  2) GAs will work well if one can estimate fairly well the value of a
     complete genotype by knowing the value of its alleles.

	  The second point suggests nonlinear interactions among the
  representation parameters, and that if these nonlinearities are
  moderate, then the given representation is suitable for a GA (no
  statements are offered at present to the optimum amount of
  nonlinearity).  Biologists call these interactions, Epistasis,
  which means in Greek "masking ".  Either too much or too little
  epistasis (nonlinear interactions) detracts from the relative
  efficiency of a GA.
	  It is suggested that measures to qualify the suitability of a
  representation to a GA search can be developed with the concept of
  epistasis by attempting to decompose genotypes' fitness into allelic
  values.  Measuring the variance of the discrepancy between the
  original and re-constructed fitnesses indicates the amount of epistasis
  and hence, the suitability of the representation to a GA.  Furthermore,
  thus quantifying epistasis offers a powerful mechanism to `spy' on the
  on other central issues such as premature convergence and optimal
  population size).

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

Date: Sat, 25 Aug 90 18:21:42 CDT
From: Deb <KDEB3@UA1VM.ua.edu>
Subject: Comparative Analysis of Selection Schemes Used in GAs

  A Comparative Analysis of Selection Schemes Used in Genetic Algorithms

             David E. Goldberg   and   Kalyanmoy Deb

  This paper considers a number of selection schemes commonly used in modern
  genetic algorithms.  Specifically, proportionate reproduction,
  ranking selection, tournament selection, and Genitor (or `steady state')
  selection are compared on the basis of solutions to
  deterministic difference or differential equations, which are verified
  through computer simulations.  The analysis
  provides convenient approximate or exact solutions as well as
  useful convergence time and growth ratio estimates.
  The paper recommends practical application of the analyses and suggests
  a number of paths for more detailed analytical investigation of
  selection techniques.

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End of Genetic Algorithms Digest
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