A Software System for Multicriteria Analysis and Optimization*

The multicriteria analysis (MA) and multicriteria optimization (MO) problems are multicriteria decision making problems. In MA and MO problems several criteria are simultaneously optimized. In the general case there does not exist one alternative(solution), which optimizes all the criteria. The solution of MA or MO problem is a set of alternatives, called a set of the non-dominating or of the Pareto optimal alternatives. Each alternative in this set could be a solution of the multicriteria problem. In order to select one alternative, it is necessary to have additional information set by the so-called decision maker (DM). The information that the DM provides reflects his/ her global preferences with respect to the quality of the alternative sought. The methods developed to solve MA problems, can be grouped in three separate classes: weighting methods, outranking methods and interactive methods. The main element in the weighting methods is the way of determining the criteria weights, which reflect DM’s preferences to the highest degree. Many methods for criteria weighting have been developed. A value tradeoff method is proposed in [10]. The analytic hierarchy process (AHP weighting method) is developed in [30], using pair-wise criteria comparison. This method is generalized to reflect DM’s uncertainty about the estimates in the reciprocal matrix. A direct ranking and rating method is proposed in [40]. A mathematical programming model with sensitivity analysis is used in [15] to determine the intervals of weights, within which the same ranking result is produced. The weighting methods use a DM’s preference model, which does not allow the existence of incomparable alternatives and the preference information obtained by the DM (different types of criteria comparison) is sufficient to determine whether one of the alternatives must be preferred or whether the two alternatives are equal for the DM.