Evolutionary Algorithms (EAs), popular population-based stochastic
search-methods, have the tendency to lose diversity within their population of
feasible solutions and to converge into a single solution. Niching methods,
the extension of EAs to multi-modal optimization, address this issue by
maintaining the diversity of certain properties within the population - and this
way they allow parallel convergence into multiple good solutions in multimodal
domains. To this end, niching methods have been studied mainly within the field
of Genetic Algorithms (GAs). The research in this direction has yielded various
successful methods which have been shown to find multiple solutions efficiently,
but naturally were limited to low-dimensional real-valued problems. Evolution
Strategies (ES) are a canonical EA for real-valued function optimization,
due to their straightforward encoding, their specific variation operators, the
self-adaptation of their mutation distribution as well as to their high
performance in this domain in comparison with other methods on benchmark
problems. The higher the dimensionality of the search space, the more suitable a
task becomes for an ES.
The study of niching is challenging both from the theoretical point of view
and from the practical point of view. The theoretical challenge is two-fold -
maintaining the diversity within a population-based stochastic algorithm from
the computational perspective, but also having an insight into speciation
theory from the biological perspective. The practical aspect provides a
real-world motivation for this problem - there is an increasing interest of the
applications' community in providing the decision maker with multiple solutions
with different conceptual designs, for single- or multi-objective
[LEFT] An analogy: find the best runners with the highest genetic diversity among
each other. [CENTER]
Natural speciation: illustration. [RIGHT] Speciation table: butterflies.
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Ofer M. Shir, PhD Dissertation: Niching in
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Illustration: Niching in Action
Tracking 4 minima on the Fletcher-Powell n=2 landscape with the Mahalanobis-CMA+ routine: avi.