Multi-objective Optimization with Discrete Alternatives on the Basis of Ratio Analysis

Willem Karel M. Brauers, Edmundas Kazimieras Zavadskas


On the basis of ratio analysis, two methods are developed for multi-objective optimization with discrete alternatives. The first method is MOORA (Multi-objective Optimization on the basis of Ratio Analysis), which serves as a matrix of responses to the alternatives to the objectives to which ratios are applied. The set of ratios has the square roots of the sum of the squared responses as denominators. These ratios are considered to be the best choice among different examples of ratios. The final results varying between zero and one are added up or subtracted to minimize the objective. Finally, all alternatives are ranked according to the size of their obtained dimensionless numbers. Eventually, the most refined way to give more importance to an objective is to replace an objective by different sub-objectives. As a second method, based on the same reasoning as the MOORA method, the Reference Point Method is applied. Ultimately, it is concluded that the second method only serves as a control instrument or as the second best method.


multi-objective optimization; alternative measurement; discrete alternatives; ratio analysis; sub-objectives; MOORA; reference point method; TOPSIS

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"Intellectual Economics" ISSN online 1822-8038 / ISSN print 1822-8011