Martin Utesch University of Mining and Technology Institute of Automatic Control

Freiberg Germany

1997-10-02 Written by Martin Utesch for the Institute of Automatic Control at the University of Mining and Technology in Freiberg, Germany. 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. 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 | +===+=====================================+ 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). 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. 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 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. 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 :-( Reference information for GEQ algorithms. Jörg Heitkötter David Beasley InterNet resource FAQ in comp.ai.genetic is available at Encore. Z. Fong University of California, Berkeley Computer Science Department File planner/Report.ps in the 'postgres-papers' distribution. R. Elmasri S. Navathe The Benjamin/Cummings Pub., Inc.