Introduction - Self-Adaptive Heuristics for Evolutionary Computation - page 5

we try to find the building blocks or common features self-adaptively. We intro-
duce various self-adaptive crossover operators for numerical and for string rep-
resentations. For ES self-adaptive recombination conducts a morphing between
dominant and intermediate recombination. For genetic algorithms in string rep-
resentation self-adaptive crossover means the automatic adaptation of crossover
points. Our experimental analysis shows the behavior on unimodal, multimodal
and constrained search spaces. All experiments will show that neither a sig-
nificant improvement nor a deterioration can be achieved. We conclude, that
the postulated building blocks can hardly be found by means of self-adaptive
crossover point control. But in order to show that the optimization of the struc-
ture of crossover can lead to an improvement, we propose a one-step crossover
optimization scheme.
Chapter VII: Constraint Handling Heuristics for Evolution Strategies
EAs with a self-adaptive step control mechanism like ES often suffer from prema-
ture fitness stagnation on constrained numerical optimization problems. When
the optimum lies on the constraint boundary or even in a vertex of the feasible
search space, a disadvantageous success probability results in premature step size
reduction. A proof of step size reduction leading to premature convergence for
a (1+1)-EA under simplified conditions gives insight into success rate situation.
We introduce three new constraint-handling methods for ES on constrained con-
tinuous search spaces. The death penalty step control evolution strategy (DSES)
is based on the controlled reduction of a minimum step size depending on the
distance to the infeasible search space. The two sexes evolution strategy (TSES)
is inspired by the biological concept of sexual selection and pairing. At last, the
nested angle evolution strategy (NAES) is an approach in which the angles of
the correlated mutation of the inner ES are adapted by the outer ES. All meth-
ods are experimentally evaluated on common test problems and compared with
existing penalty-based constraint-handling methods.
Chapter VIII: Summary and Discussion
In the last chapter we summarize the main results of this work and discuss
its research contributions. Attention is drawn to the benefits and limitations of
self-adaptation. Many parameters can be controlled self-adaptively with great
success. The mutation step size for ES or the bias of the BMO are examples for
successful self-adaptive parameter control. But there are also limitations. When-
ever the link between strategy parameter change and fitness is not tight enough,
e.g. in the case of self-adaptive crossover, self-adaptation may fail. Strategy pa-
rameter drift like premature step size reduction is another negative effect that
might occur. At the end, we come to the conclusion that self-adaptation is an
advanced feature of EC, which offers great potential, but has to be applied with
care and sense for the search space augmentation.