Evolution and Optimum Seeking

Summary and Outlook 245
tition between several populations that alter the concept of the optimum seeking strategy
itself. The simplest possibility, for example, would be to vary the number of parents and
of descendants two or more groups would be set up each with its own values of these
parameters, each group would be given a xed time to seek the optimum then the group
that has advanced the most would be allowed to \survive." In this way these strategy
variables would be determined to best suit the particular problem and computer, with the
objective of minimizing the required computation time. One might call such an approach
meta- or hierarchical evolution strategy (see Back, 1994a,b).
The solution of problems with multiple objectives could also be approached with the
multimembered evolution strategy. This is really the most common type of problem
in nature. The selection step, the reduction to the best of the descendants, could be
subdivided into several partial steps, in each ofwhich only one of the criteria for selection
is applied. In this way noweighting of the partial objectives would be required. First
attempts with only two variables and two partial objectives showed that a point onthe
Pareto line is always approached as the optimum. By unequal distribution of the partial
selections the solution point could be displaced towards one of the partial objectives. At
this stage subjective information would have to be applied because all the Pareto-optimal
solutions are initially equally good (see Kursawe, 1991, 1992).
Contrary to many statements or conjectures that organic evolution is a particularly
wasteful optimization process, it proves again and again to be precisely suited to advancing
with maximum speed without losing reliability ofconvergence, even to better and
better local optima. This is just what is required in numerical optimization. In both
cases the available resources limit what can be achieved. In one case these are the limitations
of food and the nite area of the earth for accommodating life, in the other they
are the nite number of satellite processors of a parallel-organized mainframe computer
and its limited (core) storage space. If the evolution strategy can be considered as the
sought-after universal optimization method, then this is not in the sense that it solves
a particular problem (e.g., a linear or quadratic function) exactly, with the least iterations
or generations, but rather refers to its being the most readily extended concept,
able to solve very di cult problems, problems with particularly many variables, under
unfavorable conditions such as stochastic perturbations, discrete variables, time-varying
optima, and multimodal objective functions (see Hammel and Back, 1994). Accordingly,
the results and assessments introduced in the present work can at best be considered as
a rst step in the development towards a universal evolution strategy.
Finally, some early applications of the evolution strategy will be cited. Experimental
tasks were the starting point for the realization of the rst ideas for an optimization
strategy based on the example of biological evolution. It was also rst applied here to
the solution of practical problems (see Schwefel, 1968 Klockgether and Schwefel, 1970
Rechenberg, 1973). Meanwhile it is being applied just as widely to optimization problems
that can be expressed in computational or algorithmic form, e.g., in the form of simulation
models. The following is a list of some of the successful applications, with references to
the relevant publications.
1. Optimal dimensioning of the core of a fast sodium-type breeder reactor (Heusener,
1970)