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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
    possible query plans grows exponentially with the
    number of joins in the query. 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.,
    B-tree, hash, GiST and GIN in <productname>PostgreSQL</productname>) as 
    access paths for relations.
   </para>

   <para>
    The normal <productname>PostgreSQL</productname> query optimizer
    performs a <firstterm>near-exhaustive search</firstterm> over the
    space of alternative strategies. This algorithm, first introduced
    in IBM's System R 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 some problems when
    it wanted to use <productname>PostgreSQL</productname> 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. The number of joins in these queries made using the
    normal query optimizer infeasible.
   </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>
    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>
    Parts of the <acronym>GEQO</acronym> module are adapted from D. Whitley's
    Genitor algorithm.
   </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>
   <title>Generating Possible Plans with <acronym>GEQO</acronym></title>

   <para>
    The <acronym>GEQO</acronym> planning process uses the standard planner
    code to generate plans for scans of individual relations.  Then join
    plans are developed using the genetic approach.  As shown above, each
    candidate join plan is represented by a sequence in which to join
    the base relations.  In the initial stage, the <acronym>GEQO</acronym>
    code simply generates some possible join sequences at random.  For each
    join sequence considered, the standard planner code is invoked to
    estimate the cost of performing the query using that join sequence.
    (For each step of the join sequence, all three possible join strategies
    are considered; and all the initially-determined relation scan plans
    are available.  The estimated cost is the cheapest of these
    possibilities.)  Join sequences with lower estimated cost are considered
    <quote>more fit</> than those with higher cost.  The genetic algorithm
    discards the least fit candidates.  Then new candidates are generated
    by combining genes of more-fit candidates &mdash; that is, by using
    randomly-chosen portions of known low-cost join sequences to create
    new sequences for consideration.  This process is repeated until a
    preset number of join sequences have been considered; then the best
    one found at any time during the search is used to generate the finished
    plan.
   </para>

   <para>
    This process is inherently nondeterministic, because of the randomized
    choices made during both the initial population selection and subsequent
    <quote>mutation</> of the best candidates.  Hence different plans may
    be selected from one run to the next, resulting in varying run time
    and varying output row order.
   </para>

  </sect2>

  <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>
      In the current implementation, the fitness of each candidate join
      sequence is estimated by running the standard planner's join selection
      and cost estimation code from scratch.  To the extent that different
      candidates use similar sub-sequences of joins, a great deal of work
      will be repeated.  This could be made significantly faster by retaining
      cost estimates for sub-joins.  The problem is to avoid expending
      unreasonable amounts of memory on retaining that state.
     </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://www.aip.de/~ast/EvolCompFAQ/">
      The Hitch-Hiker's Guide to Evolutionary Computation</ulink>, (FAQ for <ulink
      url="news://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="ELMA04">
     </para>
    </listitem>

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

 </sect1>
</chapter>
