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Paper details
Number 2 - June 2025
Volume 35 - 2025
Choice of norm for evaluating trade-off solutions in multi-criteria optimisation problems in the control of complex objects
Bogdan Zak
Abstract
When formulating multi-criteria optimisation tasks, there are two important problems to consider. The first is the selection
of a number of sub-criteria such that their importance, number, and order correspond to the modelled decision-making
situation, while the second is the choice of the solution method to ensure its optimality with respect to individual subcriteria.
Therefore, the solution boils down to the search for a certain compromise that takes into account the influence of
individual sub-criteria on the obtained result. For these reasons, the article presents conditions for selecting the number of
sub-criteria, yielding conditions of completeness, consistency, and nonredundancy that the adopted vector criterion must
satisfy, as well as conditions for selecting a compromise solution to ensure the utility of all sub-criteria and a lower limit of
the maximum value of the individual loss. Using the formulated conditions, a vector quality criterion was selected and a
compromise solution was chosen for the task of controlling a ship in a collision situation. The method proposed in the paper
can be useful for modelling any decision situation, especially in systems where the task can be solved using the ideal-point method.
Keywords
decision making, vector criterion, polyoptimisation