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Genetic Optimizer
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 <chapter id="geqo">
  <docinfo>
   <author>
    <firstname>Martin</firstname>
    <surname>Utesch</surname>
    <affiliation>
     <orgname>
      University of Mining and Technology
     </orgname>
     <orgdiv>
      Institute of Automatic Control
     </orgdiv>
     <address>
      <city>
       Freiberg
      </city>
      <country>
       Germany
      </country>
     </address>
    </affiliation>
   </author>
   <date>1997-10-02</date>
  </docinfo>

  <title>Genetic Query Optimization in Database Systems</title>

  <para>
   <note>
    <title>Author</title>
    <para>
     Written by <ulink url="mailto:utesch@aut.tu-freiberg.de">Martin Utesch</ulink>
     for the Institute of Automatic Control at the University of Mining and Technology in Freiberg, Germany.
    </para>
   </note>
  </para>

  <sect1>
   <title>Query Handling as a Complex Optimization Problem</title>

   <para>
    Among all relational operators the most difficult one to process and
    optimize is the <firstterm>join</firstterm>. The number of alternative plans to answer a query
    grows exponentially with the number of <command>join</command>s included in it. Further
    optimization effort is caused by the support of a variety of
    <firstterm>join methods</firstterm>
    (e.g., nested loop, index scan, merge join in <productname>Postgres</productname>) to
    process individual <command>join</command>s and a diversity of
    <firstterm>indices</firstterm> (e.g., r-tree,
    b-tree, hash in <productname>Postgres</productname>) as access paths for relations.
   </para>

   <para>
    The current <productname>Postgres</productname> optimizer
    implementation performs a <firstterm>near-
     exhaustive search</firstterm> over the space of alternative strategies. This query
    optimization technique is inadequate to support database application
    domains that involve the need for extensive queries, such as artificial
    intelligence.
   </para>

   <para>
    The Institute of Automatic Control at the University of Mining and
    Technology, in Freiberg, Germany, encountered the described problems as its
    folks wanted to take the <productname>Postgres</productname> DBMS as the backend for a decision
    support knowledge based system for the maintenance of an electrical
    power grid. The DBMS needed to handle large <command>join</command> queries for the
    inference machine of the knowledge based system.
   </para>

   <para>
    Performance difficulties within exploring the space of possible query
    plans arose the demand for a new optimization technique being developed.
   </para>

   <para>
    In the following we propose the implementation of a <firstterm>Genetic Algorithm</firstterm>
    as an option for the database query optimization problem.
   </para>
  </sect1>

  <sect1>
   <title>Genetic Algorithms (<acronym>GA</acronym>)</title>

   <para>
    The <acronym>GA</acronym> is a heuristic optimization method which operates through 
    determined, randomized search. The set of possible solutions for the
    optimization problem is considered as a
    <firstterm>erm>popula</firstterm>erm> of <firstterm>individuals</firstterm>.
    The degree of adaption of an individual to its environment is specified
    by its <firstterm>fitness</firstterm>.
   </para>

   <para>
    The coordinates of an individual in the search space are represented
    by <firstterm>chromosomes</firstterm>, in essence a set of character
    strings. A <firstterm>gene</firstterm> is a
    subsection of a chromosome which encodes the value of a single parameter
    being optimized. Typical encodings for a gene could be <firstterm>binary</firstterm> or
    <firstterm>integer</firstterm>.
   </para>

   <para>
    Through simulation of the evolutionary operations <firstterm>recombination</firstterm>,
    <firstterm>mutation</firstterm>, and
    <firstterm>selection</firstterm> new generations of search points are found
    that show a higher average fitness than their ancestors.
   </para>

   <para>
    According to the "comp.ai.genetic" <acronym>FAQ</acronym> it cannot be stressed too
    strongly that a <acronym>GA</acronym> is not a pure random search for a solution to a
    problem. A <acronym>GA</acronym> uses stochastic processes, but the result is distinctly
    non-random (better than random). 

    <programlisting>
Structured Diagram of a <acronym>GA</acronym>:
---------------------------

P(t)    generation of ancestors at a time t
P''(t)  generation of descendants at a time t

+=========================================+
|>>>>>>>>>>>  Algorithm GA  <<<<<<<<<<<<<<|
+=========================================+
| INITIALIZE t := 0                       |
+=========================================+
| INITIALIZE P(t)                         |
+=========================================+
| evalute FITNESS of P(t)                 |
+=========================================+
| while not STOPPING CRITERION do         |
|   +-------------------------------------+
|   | P'(t)  := RECOMBINATION{P(t)}       |
|   +-------------------------------------+
|   | P''(t) := MUTATION{P'(t)}           |
|   +-------------------------------------+
|   | P(t+1) := SELECTION{P''(t) + P(t)}  |
|   +-------------------------------------+
|   | evalute FITNESS of P''(t)           |
|   +-------------------------------------+
|   | t := t + 1                          |
+===+=====================================+
    </programlisting>
   </para>
  </sect1>

  <sect1>
   <title>Genetic Query Optimization (<acronym>GEQO</acronym>) in Postgres</title>

   <para>
    The <acronym>GEQO</acronym> module is intended for the solution of the query
    optimization problem similar to a traveling salesman problem (<acronym>TSP</acronym>).
    Possible query plans are encoded as integer strings. Each string
    represents the <command>join</command> order from one relation of the query to the next.
    E. g., the query tree
    <programlisting>
   /\
  /\ 2
 /\ 3
4  1
    </programlisting>
    is encoded by the integer string '4-1-3-2',
    which means, first join relation '4' and '1', then '3', and
    then '2', where 1, 2, 3, 4 are relids in <productname>Postgres</productname>.
   </para>

   <para>
    Parts of the <acronym>GEQO</acronym> module are adapted from D. Whitley's Genitor
    algorithm.
   </para>

   <para>
    Specific characteristics of the <acronym>GEQO</acronym>
    implementation in <productname>Postgres</productname>
    are:

    <itemizedlist spacing="compact" mark="bullet">
     <listitem>
      <para>
       Usage of a <firstterm>steady state</firstterm> <acronym>GA</acronym> (replacement of the least fit
       individuals in a population, not whole-generational replacement)
       allows fast convergence towards improved query plans. This is
       essential for query handling with reasonable time;
      </para>
     </listitem>

     <listitem>
      <para>
       Usage of <firstterm>edge recombination crossover</firstterm> which is especially suited
       to keep edge losses low for the solution of the
       <acronym>cro</acronym>cronym> by means of a <acronym>GA</acronym>;
      </para>
     </listitem>

     <listitem>
      <para>
       Mutation as genetic operator is deprecated so that no repair
       mechanisms are needed to generate legal <acronym>TSP</acronym> tours.
      </para>
     </listitem>
    </itemizedlist>
   </para>

   <para>
    The <acronym>GEQO</acronym> module gives the following benefits to
    the <productname>Postgres</productname> DBMS
    compared to the <productname>Postgres</productname> query optimizer implementation:

    <itemizedlist spacing="compact" mark="bullet">
     <listitem>
      <para>
       Handling of large <command>join</command> queries through non-exhaustive search;
      </para>
     </listitem>

     <listitem>
      <para>
       Improved cost size approximation of query plans since no longer
       plan merging is needed (the <acronym>GEQO</acronym> module evaluates the cost for a
       query plan as an individual).
      </para>
     </listitem>
    </itemizedlist>
   </para>

  </sect1>

  <sect1>
   <title>Future Implementation Tasks for
    <productname>PostgreSQL</> <acronym>GEQO</acronym></title>

   <sect2>
    <title>Basic Improvements</title>

    <sect3>
     <title>Improve genetic algorithm parameter settings</title>

     <para>
      In file <filename>backend/optimizer/geqo/geqo_params.c</filename>, routines
      <function>gimme_pool_size</function> and <function>gimme_number_generations</function>,
      we have to find a compromise for the parameter settings
      to satisfy two competing demands:
      <itemizedlist spacing="compact">
       <listitem>
	<para>
	 Optimality of the query plan
	</para>
       </listitem>
       <listitem>
	<para>
	 Computing time
	</para>
       </listitem>
      </itemizedlist>
     </para>
    </sect3>

    <sect3>
     <title>Find better solution for integer overflow</title>

     <para>
      In file <filename>backend/optimizer/geqo/geqo_eval.c</filename>, routine
      <function>geqo_joinrel_size</function>,
      the present hack for MAXINT overflow is to set the <productname>Postgres</productname> integer
      value of <structfield>rel->size</structfield> to its logarithm.
      Modifications of <structname>Rel</structname> in <filename>backend/nodes/relation.h</filename> will
      surely have severe impacts on the whole <productname>Postgres</productname> implementation.
     </para>
    </sect3>

    <sect3>
     <title>Find solution for exhausted memory</title>

     <para>
      Memory exhaustion may occur with more than 10 relations involved in a query.
      In file <filename>backend/optimizer/geqo/geqo_eval.c</filename>, routine
      <function>gimme_tree</function> is recursively called.
      Maybe I forgot something to be freed correctly, but I dunno what.
      Of course the <structname>rel</structname> data structure of the
      <command>join</command> keeps growing and
      growing the more relations are packed into it.
      Suggestions are welcome :-(
     </para>
    </sect3>
   </sect2>


   <bibliography id="geqo-biblio">
    <title>
     References
    </title>
    <para>Reference information for <acronym>GEQ</acronym> algorithms.
    </para>
    <biblioentry>

     <bookbiblio>
      <title>
       The Hitch-Hiker's Guide to Evolutionary Computation
      </title>
      <authorgroup>
       <author>
	<firstname>J&ouml;rg</firstname>
	<surname>Heitk&ouml;tter</surname>
       </author>
       <author>
	<firstname>David</firstname>
	<surname>Beasley</surname>
       </author>
      </authorgroup>
      <publisher>
       <publishername>
	InterNet resource
       </publishername>
      </publisher>
      <abstract>
       <para>
	FAQ in <ulink url="news://comp.ai.genetic">comp.ai.genetic</ulink>
	is available at <ulink
	 url="ftp://ftp.Germany.EU.net/pub/research/softcomp/EC/Welcome.html">Encore</ulink>.
       </para>
      </abstract>
     </bookbiblio>

     <bookbiblio>
      <title>
       The Design and Implementation of the Postgres Query Optimizer
      </title>
      <authorgroup>
       <author>
	<firstname>Z.</firstname>
	<surname>Fong</surname>
       </author>
      </authorgroup>
      <publisher>
       <publishername>
	University of California, Berkeley Computer Science Department
       </publishername>
      </publisher>
      <abstract>
       <para>
	File <filename>planner/Report.ps</filename> in the 'postgres-papers' distribution.
       </para>
      </abstract>
     </bookbiblio>

     <bookbiblio>
      <title>
       Fundamentals of Database Systems
      </title>
      <authorgroup>
       <author>
	<firstname>R.</firstname>
	<surname>Elmasri</surname>
       </author>
       <author>
	<firstname>S.</firstname>
	<surname>Navathe</surname>
       </author>
      </authorgroup>
      <publisher>
       <publishername>
	The Benjamin/Cummings Pub., Inc.
       </publishername>
      </publisher>
     </bookbiblio>

    </biblioentry>
   </bibliography>

  </sect1>
 </chapter>

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