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Genetic Optimizer
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 <chapter id="geqo">
  <chapterinfo>
   <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>
  </chapterinfo>

  <title id="geqo-title">Genetic Query Optimizer</title>

  <para>
   <note>
    <title>Author</title>
    <para>
     Written by Martin Utesch (<email>utesch@aut.tu-freiberg.de</email>)
     for the Institute of Automatic Control at the University of Mining and Technology in Freiberg, Germany.
    </para>
   </note>
  </para>

  <sect1 id="geqo-intro">
   <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 joins included in it. Further optimization effort is
    caused by the support of a variety of <firstterm>join
    methods</firstterm> (e.g., nested loop, hash join, merge join in
    <productname>PostgreSQL</productname>) to process individual joins
    and a diversity of <firstterm>indexes</firstterm> (e.g., R-tree,
    B-tree, hash in <productname>PostgreSQL</productname>) as access
    paths for relations.
   </para>

   <para>
    The current <productname>PostgreSQL</productname> optimizer
    implementation performs a <firstterm>near-exhaustive
    search</firstterm> over the space of alternative strategies. This
    algorithm, first introduced in the <quote>System R</quote>
    database, produces a near-optimal join order, but can take an
    enormous amount of time and memory space when the number of joins
    in the query grows large. This makes the ordinary
    <productname>PostgreSQL</productname> query optimizer
    inappropriate for queries that join a large number of tables.
   </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>PostgreSQL</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 join queries for the
    inference machine of the knowledge based system.
   </para>

   <para>
    Performance difficulties in exploring the space of possible query
    plans created the demand for a new optimization technique to be developed.
   </para>

   <para>
    In the following we describe the implementation of a
    <firstterm>Genetic Algorithm</firstterm> to solve the join
    ordering problem in a manner that is efficient for queries
    involving large numbers of joins.
   </para>
  </sect1>

  <sect1 id="geqo-intro2">
   <title>Genetic Algorithms</title>

   <para>
    The genetic algorithm (<acronym>GA</acronym>) is a heuristic optimization method which
    operates through
    nondeterministic, randomized search. The set of possible solutions for the
    optimization problem is considered as a
    <firstterm>population</firstterm> of <firstterm>individuals</firstterm>.
    The degree of adaptation 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 <systemitem class="resource">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). 
   </para>

   <figure id="geqo-diagram">
    <title>Structured Diagram of a Genetic Algorithm</title>

    <informaltable frame="none">
     <tgroup cols="2">
      <tbody>
       <row>
        <entry>P(t)</entry>
        <entry>generation of ancestors at a time t</entry>
       </row>

       <row>
        <entry>P''(t)</entry>
        <entry>generation of descendants at a time t</entry>
       </row>
      </tbody>
     </tgroup>
    </informaltable>

<literallayout class="monospaced">
+=========================================+
|&gt;&gt;&gt;&gt;&gt;&gt;&gt;&gt;&gt;&gt;&gt;  Algorithm GA  &lt;&lt;&lt;&lt;&lt;&lt;&lt;&lt;&lt;&lt;&lt;&lt;&lt;&lt;|
+=========================================+
| INITIALIZE t := 0                       |
+=========================================+
| INITIALIZE P(t)                         |
+=========================================+
| evaluate 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)}  |
|   +-------------------------------------+
|   | evaluate FITNESS of P''(t)          |
|   +-------------------------------------+
|   | t := t + 1                          |
+===+=====================================+
</literallayout>
   </figure>
  </sect1>

  <sect1 id="geqo-pg-intro">
   <title>Genetic Query Optimization (<acronym>GEQO</acronym>) in PostgreSQL</title>

   <para>
    The <acronym>GEQO</acronym> module approaches the query
    optimization problem as though it were the well-known traveling salesman
    problem (<acronym>TSP</acronym>).
    Possible query plans are encoded as integer strings. Each string
    represents the join order from one relation of the query to the next.
    For example, the join tree
<literallayout class="monospaced">
   /\
  /\ 2
 /\ 3
4  1
</literallayout>
    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 relation IDs within the
    <productname>PostgreSQL</productname> optimizer.
   </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>PostgreSQL</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>TSP</acronym> 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 allows
    the <productname>PostgreSQL</productname> query optimizer to
    support large join queries effectively through
    non-exhaustive search.
   </para>

  <sect2 id="geqo-future">
   <title>Future Implementation Tasks for
    <productname>PostgreSQL</> <acronym>GEQO</acronym></title>

     <para>
      Work is still needed to improve the genetic algorithm parameter
      settings.
      In file <filename>src/backend/optimizer/geqo/geqo_main.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>

     <para>
      At a more basic level, it is not clear that solving query optimization
      with a GA algorithm designed for TSP is appropriate.  In the TSP case,
      the cost associated with any substring (partial tour) is independent
      of the rest of the tour, but this is certainly not true for query
      optimization.  Thus it is questionable whether edge recombination
      crossover is the most effective mutation procedure.
     </para>

   </sect2>
  </sect1>

 <sect1 id="geqo-biblio">
  <title>Further Reading</title>

  <para>
   The following resources contain additional information about
   genetic algorithms:

   <itemizedlist>
    <listitem>
     <para>
      <ulink url="http://surf.de.uu.net/encore/www/">The Hitch-Hiker's
      Guide to Evolutionary Computation</ulink> (FAQ for <ulink
      url="news://comp.ai.genetic">comp.ai.genetic</ulink>)
     </para>
    </listitem>
   
    <listitem>
     <para>
      <ulink url="http://www.red3d.com/cwr/evolve.html">Evolutionary
       Computation and its application to art and design</ulink> by
      Craig Reynolds
     </para>
    </listitem>

    <listitem>
     <para>
      <xref linkend="ELMA99">
     </para>
    </listitem>

    <listitem>
     <para>
      <xref linkend="FONG">
     </para>
    </listitem>
   </itemizedlist>
  </para>

 </sect1>
</chapter>

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