Summary and Conclusion - Self-Adaptive Heuristics for Evolutionary Computation - page 134

Self-adaptation controls the estimated distribution of the optimum's location.
But it also suffers from shortcomings. One example for the latter is the premature
step size reduction of ES in the vicinity of infeasible parts of the search space.
When self-adaptation fails, adaptive parameter control heuristics can help as the
proposed constraint handling methods of this topic show.
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Constraint handling heuristics for optima with active constraints.
We proved step size reduction for a (1+1)-EA leading to premature conver-
gence under simplified conditions, i.e. linear fitness function and constraints.
Our proof is based on a success rate analysis considering a simplified EA model.
The situation at the constraint boundary can be modeled by two different
states. From the success rates and the possible state transitions, the expected
step size changes can be derived for each step. Experiments showed the pre-
mature fitness stagnation for two traditional constraint-handling techniques,
death penalty and a dynamic penalty function on constrained problems. In this
work we introduced three constraint-handling techniques aiming at the prema-
ture fitness stagnation of ES. The DSES makes use of a least mutation strength
. But it also prevents the convergence of the optimum. Hence, we introduced
an adaptation technique to reduce and allow the unlimited convergence. The
parameters and ϑ define the speed of the -reduction process. The second
heuristic is the TSES, inspired by the concepts of sex and pairing. Each in-
dividual is assigned with a feature called sex, which determines its selection
objective. Some modifications are necessary to prevent a step size explosion.
Last, the NAES evolves the covariance matrix with a nested EA and conse-
quently shows a poor performance. Hence, we cannot recommend the NAES
for practical constraint handling, but the approach shows that the rotation of
the mutation ellipsoid improves the success rate. Extensive experimental anal-
ysis showed the behavior and properties of the proposed methods.

8.2 Conclusion

Self-adaptation is an ecient way of improving evolutionary search. But a nec-
essary condition for its success is a tight link between strategy parameters and
fitness. This link is not existing for every type of parameter. The crossover points
are an example for a weak link. Mutation strongly controls the protagonist ex-
ploration and antagonist exploitation and therefore offers a direct link between
its strategy parameters and the corresponding fitness. The bias control of the
BMO and the number of successive edge swaps of SA-INV are examples for the
success of self-adaptation of mutation parameters. But self-adaptation can also
be misleading: due to local optima in the strategy parameter space, it may result
in premature fitness stagnation. Hence, it has to be used with care and sense
for search domain characteristics. Furthermore, adaptive heuristic extensions
like the proposed constraint handling techniques offer useful means to overcome
premature stagnation. To summarize all results, well-designed self-adaptive and
adaptive heuristics are ecient techniques to improve evolutionary search and
convergence properties.