Evolution and Optimum Seeking

246 Summary and Outlook
2. Optimal allocation of investments to various health-service programs in Columbia
(Schwefel, 1972)
3. Solving curve- tting problems by combining a least-squares method with the evolution
strategy (Plaschko and Wagner, 1973)
4. Minimum-weight designing of truss constructions partly in combination with linear
programming (Ley ner, 1974 and Ho er, 1976)
5. Optimal shaping of vaulted reinforced concrete shells (Hartmann, 1974)
6. Optimal dimensioning of quadruple-joint drives (Anders, 1977)
7. Approximating the solution of a set of non-linear di erential equations (Rodlo ,
1976)
8. Optimal design of arm prostheses (Brudermann, 1977)
9. Optimization of urban and regional water supply systems (Cembrowicz and Krauter,
1977)
10. Combining the evolution strategy with factorial design techniques (Kobelt and
Schneider, 1977)
11. Optimization within a dynamic simulation model of a socioeconomic system (Krallmann,
1978)
12. Optimization of a thermal water jet propulsion system (Markwich, 1978)
13. Optimization of a regional system for the removal of refuse (von Falkenhausen, 1980)
14. Estimation of parameters within a model of oods (North, 1980)
15. Interactive superimposing of di erent direct search techniques onto dynamic simulation
models, especially models of the energy system of the Federal Republic of
Germany (Heckler, 1979 Drepper, Heckler, and Schwefel, 1979).
Much longer lists of references concerning applications as well as theoretical work in
the eld of evolutionary computation have been compiled meanwhile by Alander (1992,
1994) and Back, Ho meister, and Schwefel (1993).
Among the many di erent elds of applications only one will be addressed here, i.e.,
non-linear regression and correlation analysis. In general this leads to a multimodal
optimization problem when the parameters searched for enter the hypotheses non-linearly,
e.g., as exponents. Very helpful under such circumstances is a tool with which one can
switch from one to the other minimization method. Beginning with a multimembered
evolution strategy and re ning the intermediate results by means of a variable metric
method has often led to practically useful results (e.g., Frankhauser and Schwefel, 1992).
In some cases of practical applications of evolution strategies it turns out that the
number of variables describing the objective function has to vary itself. An example was