Optimization is a method to search for the best solution of the given problem. It can be found in all areas of human activity. One of the great importance it is also in the field of automation.
In the context of the present work we examined some software-based options, that are prepared with two MATLAB tools. These are so-called Optimization toolbox and Global optimization toolbox. Among many options, that are available among many mentioned toolboxes, we examined and tested two functions for global optimization, two for local optimization and two for hybrid realizations.
In the second chapter, we described main features and forms of individual call functions call. Presented are two functions that allow us global optimization. These are a method called genetic algorithm (ga) and method called simulated annealing (simulannealbnd). We also described local functions fminsearch (it is available in basic MATLAB) and fmincon. Function fminsearch allows unlimited optimization, while function fmincon realizes limited optimization. This means that we can limit the scope of investigation according to the knowledge of the problem. Optimization toolboxes allow also some combination calls of individual functions. We tested two options in present work.
In the third chapter, we presented results of the optimization of three groups of problems through mathematical functions, problems of modelling and control design. To gain orderliness and transparency of obtained results we have built a graphical interface and connected it with the toolbox LABI (Laboratory of mathematical models and multivariable systems). Number of functions for analyzing dynamic systems are also available inside LABI. User can observe course of individual optimization problems, final results and carry out their analysis.
Chapter four (Conclusion) summarizes major findings, among which we have to mention the following:
- local optimization methods are effective in cases where we can do relatively good estimation of optimum proximity and the number of optimization parameters is small.
- in case of complex optimization problems it is better to start with one of the global methods, which generally do not find a real optimum,
- if simulation is integrated in optimization, we have to pay attention to the stability of numerical solution and stability of the system,
- there is extraordinary potential for hybrid or combined methods, where we start optimization with one of the global methods followed by one of local methods,
- results of the combined solution are not unique.
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