In this paper, gene sets, instead of individual genes, have been used in the genetic
process to speed up the convergence. A gene-set mutation operator has been proposed,
which can make several neighboring genes to simultaneously mutate. A gene-set
crossover operator has also been designed to choose the crossover points at the
boundary of gene sets. The proposed gene-set mutation and crossover operators will
cause a larger diversity than the conventional ones.
A hierarchical gene-set genetic algorithm has been proposed, which uses
adjustable gene-set lengths to find final solutions. The gene-set length is shortened in
half in each phase until the length is 1. In this way, the proposed genetic algorithm can
search more flexibly in a solution space.
Effectively avoiding local optimal trapping has always been an import research
topic in GA. In this paper, another escape operation, as well as the mutation operation,
has been designed for gene-set genetic algorithms to increase the probability of
finding global optima. Gene sets, instead of individual genes, have been used in the
genetic process to speed up the convergence. The operation length can be logically
thought of as the number of gene sets, which is much shorter than the total
chromosome length. The convergence speed can thus be improved and the execution
time can be reduced.
The property that a longer gene set will cause a larger diversity has been
formally proven. An escape operation based on the property has also been designed
and a modified gene-set genetic algorithm with the escape operation has been
proposed. Using the escape operation, the proposed algorithm can help the escape of
local optima through the change of gene-set sizes to a large value. Even when the
population has (δ, k)-converged, the proposed algorithm can also help the search of
global optima since the gene-set operations with the original gene-set length will still
be done as long as the predefined number of termination generations is not achieved.
The modified gene-set genetic algorithm can thus consider both the escape from local
optima and the search for global optima.
We have proposed another gene-set genetic algorithm, which simultaneously
considers the escape operation and dynamic mutation rates to improve the escape
effects from local optimums. Using dynamic mutation rates, the proposed algorithm
can enlarge the searching region to amend the shortcoming of the offspring due to
large gene-set sizes. The latter can also cause the escape operator to escape from local
optimums more effectively.
Different mutation rates have thus been used for different lengths of gene sets.
The property that using longer gene sets will cause the population to produce less
offspring has formally been shown. Longer gene sets will be allowed larger mutation
rates.
Three problems have been used for experiments, respectively with one-peak,
two-peak, and multi-peak solution spaces. From the experimental results, the
proposed hierarchical gene-set GA (HGSGA) spends less computational time and gets
better fitness values than simple GA. HGSGA can reduce the number of fitness
evaluation since the offspring chromosomes generated for gene-sets is smaller than
those by the conventional one. HGSGA(m) can reduce the number of fitness
evaluation due to both the escape operation and the adjustable gene-length since a
longer gene-set size will generate fewer offspring to be evaluated. HGSGA(m2) spent
a little more computational time than HGSGA(m) since the former might generate
more offspring to process. The proposed modified gene-set GA (HGSGA(m2)) with
dynamic mutation rates can thus achieve a good trade-off between improving
convergence speed and reducing execution time. In the future, we will attempt to
further improve the performance of the proposed approach.
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