Fuzzy optimization
Document Actions
The results obtained from classical methods of optimization
involving deterministic variables exhibit various shortcomings. In
particular, the effects of the uncertainty attached to input
information is often ignored altogether or only taken into account to a
limited degree. The classical deterministic optimization problem
according to
is considered under the aspect of uncertainty, and extended.
For the objective function z(x, e) the optimum solution xOPT from the set of design variables X (design space) is determined under compliance with the equality constraints hj(x, e) and the inequality constraints gi(x, e).
Input parameters such as geometrical parameters, material parameters,
external load parameters, reliability parameters and economic
parameters are lumped together in the vector e.
Considering
the uncertain parameters to be fuzzy variables, the deterministic
optimization problem is extended to a fuzzy optimization problem
The numerical solution of the fuzzy optimization problem is based on α-level optimization.
References
- Möller, B, Graf, W, and Stransky, W (2004) Fuzzy-Optimization of Structures, In: Proceedings of ICCES04, edited by S.N. Atluri and S.J.N. Tadeu. Tech Science Press, Madeira, pages 1765–1770.
- Möller, B, Beer, M, Graf, W, and Stransky, W (2000) Dynamic Structural Analysis Considering Fuzziness, In: 4th Euromech Solid Mechanics Conference, edited by M. Potier-Ferry and L. S. Toth. Euromech, Metz, pages 616.
