Martin
Utesch
University of Mining and Technology
Institute of Automatic Control
Freiberg
Germany
1997-10-02
Genetic Query Optimization in Database Systems
Author
Written by Martin Utesch
for the Institute of Automatic Control at the University of Mining and Technology in Freiberg, Germany.
Query Handling as a Complex Optimization Problem
Among all relational operators the most difficult one to process and
optimize is the join. 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 join methods
(e.g., nested loop, index scan, merge join in Postgres) to
process individual joins and a diversity of indices (e.g., r-tree,
b-tree, hash in Postgres) as access paths for relations.
The current Postgres optimizer implementation performs a near-
exhaustive search 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.
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 Postgres 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.
Performance difficulties within exploring the space of possible query
plans arose the demand for a new optimization technique being developed.
In the following we propose the implementation of a Genetic Algorithm
as an option for the database query optimization problem.
Genetic Algorithms (GA)
The GA is a heuristic optimization method which operates through
determined, randomized search. The set of possible solutions for the
optimization problem is considered as a population of individuals.
The degree of adaption of an individual to its environment is specified
by its fitness.
The coordinates of an individual in the search space are represented
by chromosomes, in essence a set of character strings. A gene is a
subsection of a chromosome which encodes the value of a single parameter
being optimized. Typical encodings for a gene could be binary or
integer.
Through simulation of the evolutionary operations recombination,
mutation, and selection new generations of search points are found
that show a higher average fitness than their ancestors.
According to the "comp.ai.genetic" FAQ it cannot be stressed too
strongly that a GA is not a pure random search for a solution to a
problem. A GA uses stochastic processes, but the result is distinctly
non-random (better than random).
Structured Diagram of a GA:
---------------------------
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 |
+===+=====================================+
Genetic Query Optimization (GEQO) in Postgres
The GEQO module is intended for the solution of the query
optimization problem similar to a traveling salesman problem (TSP).
Possible query plans are encoded as integer strings. Each string
represents the join order from one relation of the query to the next.
E. g., the query tree
/\
/\ 2
/\ 3
4 1
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 Postgres.
Parts of the GEQO module are adapted from D. Whitley's Genitor
algorithm.
Specific characteristics of the GEQO implementation in Postgres
are:
Usage of a steady state GA (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;
Usage of edge recombination crossover which is especially suited
to keep edge losses low for the solution of the TSP by means of a GA;
Mutation as genetic operator is deprecated so that no repair
mechanisms are needed to generate legal TSP tours.
The GEQO module gives the following benefits to the Postgres DBMS
compared to the Postgres query optimizer implementation:
Handling of large join queries through non-exhaustive search;
Improved cost size approximation of query plans since no longer
plan merging is needed (the GEQO module evaluates the cost for a
query plan as an individual).
Future Implementation Tasks for Postgres GEQO
Basic Improvements
Improve freeing of memory when query is already processed
With large join queries the computing time spent for the genetic query
optimization seems to be a mere fraction of the time
Postgres
needs for freeing memory via routine MemoryContextFree,
file backend/utils/mmgr/mcxt.c.
Debugging showed that it get stucked in a loop of routine
OrderedElemPop, file backend/utils/mmgr/oset.c.
The same problems arise with long queries when using the normal
Postgres query optimization algorithm.
Improve genetic algorithm parameter settings
In file backend/optimizer/geqo/geqo_params.c, routines
gimme_pool_size and gimme_number_generations,
we have to find a compromise for the parameter settings
to satisfy two competing demands:
Optimality of the query plan
Computing time
Find better solution for integer overflow
In file backend/optimizer/geqo/geqo_eval.c, routine
geqo_joinrel_size,
the present hack for MAXINT overflow is to set the Postgres integer
value of rel->size to its logarithm.
Modifications of Rel in backend/nodes/relation.h will
surely have severe impacts on the whole Postgres implementation.
Find solution for exhausted memory
Memory exhaustion may occur with more than 10 relations involved in a query.
In file backend/optimizer/geqo/geqo_eval.c, routine
gimme_tree is recursively called.
Maybe I forgot something to be freed correctly, but I dunno what.
Of course the rel data structure of the join keeps growing and
growing the more relations are packed into it.
Suggestions are welcome :-(
Further Improvements
Enable bushy query tree processing within Postgres;
that may improve the quality of query plans.
References
Reference information for GEQ algorithms.
The Hitch-Hiker's Guide to Evolutionary Computation
Jörg
Heitkötter
David
Beasley
InterNet resource
FAQ in comp.ai.genetic
is available at Encore.
The Design and Implementation of the Postgres Query Optimizer
Z.
Fong
University of California, Berkeley Computer Science Department
File planner/Report.ps in the 'postgres-papers' distribution.
Fundamentals of Database Systems
R.
Elmasri
S.
Navathe
The Benjamin/Cummings Pub., Inc.