ON THE CONCEPT OF VECTOR OPTIMIZATION IN THE TASKS OF MULTICRITERIAL CHOICE
DOI:
https://doi.org/10.20998/2079-0023.2022.01.07Keywords:
criteria, vectors, multi criteria optimization, local criteria, reference target vector, decision subsystemsAbstract
Problems of multi-criteria choice with estimates of applicants by a number of local criteria are considered. Known approaches to the solution of such problems use their peculiarities with the allocation of the corresponding classes of problems and a number of assumptions that significantly limit the possibilities of their practical application. This is the use of fixed scales to compare values that do not correspond to real ranges of values, the assumption of linear relationships between quality assessments and decision attributes, the absence of nonlinear relationships between estimates of local criteria and parameter values of solutions from different ranges. The given circumstances can lead to the loss of adequacy of the taken decisions and cause unacceptable consequences. An approach to procedures of multi-criteria optimization based on the content of optimization as a choice of a solution applicant with the best values of the chosen vector criterion within the elements of the admissible solution set is outlined. To find a solution, it is suggested to use a generalized criterion in the form of a scalar product of vectors, one of which contains components of the values of local criteria for the solution pretender, and the other is a virtual vector of the target reference in a given space with the best or predicted values. To compare the applicants, we propose approaches to forming a subset of Pareto optimal solutions as a set of solutions by consistent local criteria, using a series of concessions on the local criteria represented by mathematical models with the allocation of alternatives to change the values of local criterion estimates, allowing the formation of consistent solutions. The results of the analysis allow us to use the proposed approaches to form a subset of effective solutions in the decision support subsystems, providing operational management of dynamic processes of service and production.
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