Linear Scalarization in Multi-Criterion Optimization

The well-known linear scalarization of criteria is considered from the point of the general model of multi-criterion choice, which includes a set of feasible alternatives and a vector criterion, as well as the preference relation of the decision maker. The focus of this paper is the correctness of the application of this method for solving multi-criterion problems. A class of problems is analyzed where the use of linear scalarization can be justified. Moreover, a combined approach is proposed for solving multi-criterion problems, which consists in prior reduction of the Pareto set based on information regarding the decision maker's preference relation with subsequent extremization of the linear combination of the initial criteria on the reduced set.