Download Survey of Methods to Prevent Premature Convergence in

Survey of Methods to Prevent Premature
Convergence in Evolutionary Algorithms
Matthew Bardeen
Dept. de Ciencias de Computación
Universidad de Talca
Curicó, Chile
Email: [email protected]
I.
E XTENDED A BSTRACT
Evolutionary algorithms (EA) are general metaheuristic
algorithms which have very good characteristics. They are
relatively robust and usually generate very good solutions
to hard problems [15], [16], [23], [29]. However, they also
have many problems with the population converging to a suboptimal solution instead of an optimal one [27], [28]. This
occurrence is called premature convergence, and it is of great
importance to develop EAs that consistently avoid it.
Premature convergence is closely related to the diversity
of the population. The mutation rate, crossover rate, and
selection method of a particular EA reflect the trade-off the
algorithm has made between exploration of the search space
of the problem and exploitation of the current knowledge
[6], [9], [23]. However, the need for diversity within the
population is not always constant – in the beginning stages
of an EA search, diversity is helpful for finding promising
areas of the search space, but in later stages it is essential to
exploit the information already known. Each new study using
an EA seems to have a new method to prevent premature
convergence and it is not clear which works best under what
conditions [1], [10], [12], [19], [21], [22], [32]. Therefore,
this work will summarize and organize the current methods
to prevent premature convergence and the ways to measure
their effectiveness.
The methods can be broken down into three main categories – structured populations to lower the transfer rate of
genetic material between individuals, selection operators that
lower selection pressure or help to retain diversity, and the
storage and reintroduction of genetic material [27].
The structured population methods work to avoid premature convergence by separating populations and limiting the
rate of genetic transfer between them. This generates diversity
through design, as genes do not spread as quickly throughout
the population. Some actually separate the populations into
large “islands” and periodically migrate an individual between
islands [3], [30]. Another popular structured method is to
introduce spatial structure to the population, so that individuals
may only reproduce with neighbors [14], [18].
One example of selection operators is fitness sharing,
which works by emulating niches in normal evolution [8], [15].
In this method, solutions are penalized during the assignation
of fitness for occupying closely related portions of the fitness
landscape. This encourages further exploration of the solution
space of a given problem, however increases the complexity
of the calculations for fitness, costing computation time. Other
methods such as adapting the probabilities of crossover and
mutation, either based on population characteristics or individual fitness, have been used to help prevent convergence [7],
[24], [26], [27].
The retention of genetic material for later re-injection into
the population is another popular means of retaining diversity
[13], [32]. Elitist genetic algorithms that save good solutions
from past populations for future re-injection are popular and
effective [4], [16]. These methods inject whole individuals into
the population to retain genetic diversity. Genetic algorithms
which inject random individuals have also been used with good
effect in dynamic optimization problems [25]. An interesting
alternative is the virus evolutionary genetic algorithm, which
uses the analogy of a virus to inject substrings from one
member of a population to another [11].
Each of these methods aim to solve the problem of
premature convergence by encouraging exploration and less
exploitation in the population, though particular methods are
often tailored to specific problems. For example, dynamic
optimization problems require more exploration to shift the
population in response to the the environment – the insertion of
random individuals acts as to insert new material for crossover
in order to permit those shifts [25].
There are few empirical studies of just how well these
methods work in their goal, even though many researchers have
previously proposed diversity measurements of a population
[2], [5], [17], [31]. When looking at the genotypic diversity, entropy and Hamming distance are commonly used [17]. Another
alternative is to look at the diversity of the fitness scores [2],
[20]. However, it is well known that many diversity measuring
methods are inherently linked to either the representation of
the problem or to problem space itself [6].
Thus, the problem of premature convergence is a challenging one. As a start, more work needs to be done to clarify the
concept and provide a link between diversity and convergence.
Once an appropriate measure has been developed (if possible),
the different techniques discussed above should be tested
empirically for their effectiveness. Perhaps the techniques may
only be able to be tested for a small subset of problems, but
the field of evolutionary computation can only benefit from the
effort.
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