Reduction of a Multi Criteria Optimization Problem to a Single Criterion Task

This paper is devoted to a problem of a multi criteria optimization of systems. A variant of the linear weighted sum scalarization is described for the reduction of discrete multi criteria optimization problems to a single criterion task. This variant uses the utility concept to transform each of multiple criteria to a uniform numeric form. The reduction is done by defining a generalized criterion as a linear sum of weighted utility values associated with original individual criteria of given optimization problem. The use of utility values instead of actual values of criteria considerably simplifies the aggregation of multiple criteria that in general can be of different types and ranges of values. Created single generalized criterion can be used to determine the best alternative among the given set of alternatives by a single criterion optimization. The detailed algorithm is given that implements all operations to calculate such a criterion and to determine the optimal solution of the problem.