Polioptymalizacja rozmyta w MATLABie

Skutecznym sposobem wdrożenia optymalizacji do praktyki może być wykorzystanie logiki rozmytej do tworzenia modeli matematycznych zadania optymalizacji, jeśli jest dostępna wiedza ekspercka dotycząca obiektu optymalizacji. Dzięki temu: a) unika się żmudnego procesu budowania modelu analitycznego i b) umożliwia się uwzględnienie w modelu rozmytych kryteriów i ograniczeń. W pracy pokazano procedurę wspomagania optymalizacji za pomocą pakietu MATLAB na przykładzie z dwoma i z trzema kryteriami optymalizacji, w ujęciu polioptymalizacyjnym. Wyciągnięto wnioski metodologiczne.

As for now, optimization techniques are not very popular in real engineering, though they are taught at universities and are recognized as very useful in design and management. Probably the main reason is that mathematical models of objects are difficult to device and, what more criteria may not be precisely defined. A way to enhance an effective implementation of optimisation and MADM techniques to a real practice is a fuzzy logic approach to modelling an optimisation problem, if only the expert knowledge is at hand. It yields: a) avoiding the laborious and often not possible process of building an analytical model, b) makes it possible to use fuzzy and imprecise notions and aspects. In the paper there is proposed a procedure how to device and handle such models in the MATLAB environment to get a Pareto set solutions, in poly-optimisation. The methodology is illustrated on an example of a chemical reactor. The poly-optimal control is to be found. First, having stated criteria, as fuzzy and/or non-fuzzy notions (product quality and effectiveness, in the example), an expert arbitrarily defines decision variables (process temperature, time and mixing velocity), and their membership functions, then a mathematical model is established as a set of rules if - then (Fig. 1). This model may be intuitively verified and corrected by graphical presentations, as in Fig. 2. Then, a poly-optimisation is completed: either by survey of all possible solutions (Fig. 3) and reducing the set to the Pareto solutions (Figs. 4 - 6), or by mathematical optimization algorithms. In the example a first approach is adopted. The example is extended: a third non-fuzzy criterion is introduced (cost). (Figs. 7 - 9).Methodological conclusions are formulated, too.