System Analysis of Multi-Criteria Optimization Methods on a Finite Set of Alternatives

The functions used by different optimization methods are interpreted with expected utility viewpoint. It makes possible to distinguish two groups of methods - criterion and functional choice ones. The first group of methods sets preferences on the values of the criteria, and the second - on the values of the functions presenting the preferences of decision maker on the scales of attributes. Such an interpretation of functions that does not depend on how they are created, allowed considering methods of multi-criteria optimization and multi-dimensional utility from unified positions. The analytic hierarchy process uses the priority function calculated based on the matrix of pairwise comparisons. So, it is related to the group of methods of functional choice too. The resulting system allows one to compare their methods for quality and evaluate the effectiveness of tasks solving.