Modelling and Control Design of Vibration Reduction Systems by Tomasz Krzyzynski & Igor Maciejewski & Lutz Meyer & Henning Meyer

Author:Tomasz Krzyzynski & Igor Maciejewski & Lutz Meyer & Henning Meyer
Language: eng
Format: epub
ISBN: 9783030030476
Publisher: Springer International Publishing

(5.1)

where are the particular optimisation criteria and are the decision variables. Multi-criteria optimisation is concerned with the minimisation of a vector of criteria that can be the subject of a number of constraints or bounds as follows:

(5.2)

subject to the following constraints:inequality constraints

(5.3)

equality constraints

(5.4)

and the following ranges of decision variables:

(5.5)

where and are the vectors of the minimal and maximal values of selected decision variables.

In order to solve this problem, the concept of Pareto optimality should be used. Non-dominated solutions (synonyms are: Pareto-optimal solutions, non-inferior solutions) have to be found in the feasible region of solutions. These non-dominated solutions are characterised by the fact that any attempt to improve the selected criterion must be associated with the deterioration of other optimisation criteria [3]. In Fig. 5.1, the method of searching non-dominated solutions by means of multi-criteria optimisation is graphically illustrated for a two-dimensional problem.

Fig. 5.1Graphical illustration of the multi-criteria optimisation procedure: criterion space (a) and decision variable space (b)

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