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Parallelization of the genetic algorithms for solving
some NP - complete problems
Abstract
The genetic algorithm (GA) method for solving several complexes
combinatorial optimization problems: simple plant location problem,
uncapacitated network design problem and index selection problem is
described. These NP-complete problems have various applications, not only in
practical areas such as manufacturing, traffic, distribution planning or trading,
but also in specific areas associated with computers and programming such as
database design, telecommunications, local area networks, global area
networks and Internet.
Sequential GA implementation contains various genetic operators of
selection crossover and mutation realized on flexible way. Many variations of
fitness function, GA finishing criteria and several generation replacement
schemes are given too. All common GA variables are grouped into one
structure, and adding the problem's depended functions is relatively easy. On
this manner a fast way for solving new problems is provided.
This implementation is parallelized, and implemented on multiprocessor
system, using the MPI standard (Message Passing Interface). MPI is fast and
flexible practical interface for many multiprocessor architectures. For the
program developing and performance testing the network of PC workstations is
used. Distributed model for parallelizing GA is implemented. In this model every
process executes GA on its own subpopulation with occasional exchange of
good individuals between neighbor processes.
For further performance improvement of the sequential and parallel
implementation a new technique, called caching GA is developed. Caching has
not influence to the quality of solution, but only improve GA running time.
Caching GA is a general technique, (applicable for solving many problems by
genetic algorithms) giving, relatively, good results applying on NP-complete
problems.
The computational results for given problems are presented to indicate that
the sequential GA implementation is capable to produce high-quality solutions.
In some cases this technique is superior to all known heuristic and other
methods in the literature. Parallelization and implementation by MPI standard
provides further improving performances. The compatible program code is
obtained and could be executed on more powerful parallel platform.
Key words: Genetic Algorithms, Parallel Algorithms, NP-complete problems,
Simple Plant Location Problem, Uncapacitated Network Design Problem, Index
Selection Problem, Caching GA.