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An analysis of population diversity and multi-chromosome GAs on deceptive
problems
Menglin Li Colm O'Riordan Seamus Hill
Information Technology, NUI Galway
M.Li1@nuigalway.ie colm.oriordan@nuigalway.ie seamus.hill@nuigalway.ie
Abstract
This research examined new representations for
evolutionary computation and illustrates their
performance on a range of problems. The role diversity
plays is also examined.
1. Introduction
Much research has shown that population diversity
plays a significant role in GAs avoiding being trapped
in local optima in deceptive problems [1] and in dealing
with dynamic environments [2]. Previous research on
how to solve deceptive or dynamic environmental
problems has focused on maintaining diversity [3]. This
research discusses a new direction in using GAs to
solve deceptive fitness landscape by controlling the
convergence direction instead of simply increasing the
population diversity. Supported by experiments, the
deceptive problem's solution space has been analysed.
Based on this analysis, the diversity and convergence of
genetic algorithms are discussed. The reasons why a
GA can or cannot solve different kinds of deceptive
problems is then explained. Experiments show that the
canonical genetic algorithms with elitism can solve
most deceptive problems, if given enough generations.
Two new multi-chromosome genetic algorithms have
been designed to accelerate the GA's searching speed in
more complicated deceptive problems by looking for a
new balance between diversity and convergence. Five
different problems have been used in the testing. The
results show that the lack of diversity is not the only
reason that normal GAs have difficulty in solving
deceptive problems but that convergence direction is
also important.
2. Analysis
2.1 Diversity Measurement
Following an analysis of the potential problems
associated with the pair-wise diversity measures in
binary chromosomes representation, we proposed two
new diversity measurements which have the ability to
quantitatively measure and analyse, diversity within the
population together with the difference between
populations. Define: (α) is the number of the gene
which has the value $\alpha$ in position k.
where
2.2 New Representations
Through a set of experiments, we analysed the
solution space of a range of selected deceptive problems.
154
Two new genetic algorithms (DGA, TGA) have been
introduced to solve deceptive and dynamic environment
problems based on multi-chromosome representations.
Both DGA and TGA do not have dominance system as
they use a fixed dominant chromosome. The recessive
chromosome will help the GAs to maintain diversity
after the dominant chromosome has converged. A third
chromosome has been added in TGA, which is used to
search for local minima around the current optima, to
check if the current best fitness individual is a local
optimum, and reduce the time spent on searching
around the local optima.
3. Experiments and Results
Different problems have been used in the testing.
The results show that the lack of diversity is not the
only reason that normal genetic algorithms have
difficulty in solving deceptive problems but that
convergence direction is also important. Simulations
and empirical analysis demonstrated that the new
proposed algorithms are superior to the canonical GA
on a range of problems.
CGA DGA TGA
Order 3 99.5% 99.5% 100%
Mixed Order 27.5% 37.5% 100%
Rastrigin’s Func. 65.5% 60.5% 90%
Multi-Level Func. 37.5% 66.5% 88%
Completely deceptive NA% NA% 100%
4. Conclusions and Further work
The analysis of population diversity and deceptive
problems shows that the diversity is not the only
parameter that may affect the GAs' performance in
solving these kinds of problems. The experiment results
show that increasing the diversity can increase the
probability that GAs solve deceptive problems, and that
the ability to maintain convergence directions affects
the efficiency. Maintaining diversity while controlling
the convergence direction is much more efficient than
only maintaining the diversity.
Future work may include more analysis in the
relationships of GAs' convergence and diversity.
5. References
[1] T. Friedrich, P. S. Oliveto, D. Sudholt, and C. Witt.
Theoretical analysis of diversity mechanisms for global
exploration. In GECCO '08, pages 945{952. ACM, 2008.
[2] L. T. Bui, J. Branke, and H. A. Abbass. Diversity as a
selection pressure in dynamic environments. In GECCO'05,
pages 1557{1558. ACM, 2005.
[3] S. Hill and C. O'Riordan. Solving fully deceptive
problems in changing environments. In AICS 21st, July
2010.