Choice of Norm for Evaluating Trade–Off Solutions in Multi–Criteria Optimisation Problems in the Control of Complex Objects

• Published in: International journal of applied mathematics and computer science Vol. 35; no. 2; pp. 225 - 234
• Main Author: Zak, Bogdan
• Format: Journal Article
• Language: English
• Published: Zielona Góra Sciendo 01.06.2025; De Gruyter Poland
• Subjects: Decision making; Design; Methods; Multiple criterion; Optimization; polyoptimisation; Task complexity; vector criterion
• ISSN: 1641-876X; 2083-8492
• DOI: 10.61822/amcs-2025-0016

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.