Abstract: |
Various optimisation problems are solved during the technological processes design. In the thesis optimal design problems with mentioned properties are analysed, and it is shown that standard optimisation methods are ineffective to solve such problems.
In the thesis the optimisation problems are analysed, where objective function may be multi-extremal and discontinuous, and local minimum points can be near the points of discontinuity. The efficiency of various optimisation methods in optimal design problems with such properties have been experimentally evaluated.
We consider also optimisation problems with implicitly defined and small feasible region. A two-stage method has been developed, suitable for such. The first stage uses continuation to identify feasible region. The feasible region is enlarged by softening constraints of the feasible region. Algorithm generating a set of points in the feasible region is a sequential procedure, which starts with generating points in the largest enclosure and finishes with the feasible region. There were developed and experimentally evaluated three algorithms based on this approach. The second stage is an evolutionary algorithm, which leads a search of the best solution. There were implemented three algorithms of optimisation in the feasible region, which effectiveness has been compared experimentally.
Multi-criteria optimisation problem whose criteria have more than one local minimum and may be discontinues is considered. In the thesis there is described a new iterative multi-criteria global optimisation method. The method is developed using visualization and data analysis techniques and a dimensionality reduction idea is applied to solve such problems.
Developed and experimentally evaluated methods were applied to optimization problems of chemical engineering. |
