Abstract: A new method is proposed for multi-objective optimization with discrete alternatives: MOORA (Multi-Objective Optimization on the basis of Ratio Analysis). This method refers to a matrix of responses of alternatives to objectives, to which ratios are applied. A well established other method for multi-objective optimization is used for comparison, namely the reference point method. Later on, it is demonstrated that this is the best choice among the different competing methods. In MOORA the set of ratios has the square roots of the sum of squared responses as denominators. These ratios, as dimensionless, seem to be the best choice among different ratios. These dimensionless ratios, situated between zero and one, are added in the case of maximization or subtracted in case of minimization. Finally, all alternatives are ranked, according to the obtained ratios. Eventually, to give more importance to an objective, an objective can be replaced by different sub-objectives or a coefficient of importance can be specified. An example on privatization in a transition economy illustrates the application of the method. If application is situated originally in a “welfare” economy, centered on production, MOORA becomes even more significant in a “wellbeing economy”, where consumer sovereignty is assumed.

The MOORA method and its application to privatization in a transition economy

In a nonparametric (distribution-free) approach to the correlation between two sets of measurements made on the same individuals, each set may be ranked in order of magnitude. The standard (Pearson) product-moment correlation coefficient is calculated on the two sets of ranks. Simple formulae are available, and adjustments are made for tied ranks. Test and estimation procedures are described. The relationship with the Kendall rank correlation coefficient is discussed.


Keywords:

nonparametric;
distribution-free;
Pearson correlation coefficient;
tied ranks;
Kendall rank correlation;
Fisher's z

Spearman Rank Correlation

Part I: Fundamental Concepts.- 1 Introduction.- 2 Persistence Models.- 3 Bootstrap Confidence Intervals.- Part II: Univariate Time Series.- 4 Regression I.- 5 Spectral Analysis.- 6. Extreme Value Time Series.- Part III: Bivariate Time Series.- 7 Correlation.- 8 Regression II.- Part IV: Outlook.- 9 Future Directions.

Climate Time Series Analysis: Classical Statistical and Bootstrap Methods

Multi-Objective Optimization takes care of different objectives with the objectives keeping their own units. The internal mechanical solution of a Ratio System, producing dimensionless numbers, is preferred. The ratio system creates the opportunity to use a second approach: a Reference Point Theory, which uses the ratios of the ratio system. This overall theory is called MOORA (Multi-Objective Optimization by Ratio Analysis). The results are still more convincing if a Full Multiplicative Form is added forming MULTIMOORA. The control by three different approaches forms a guaranty for a solution being as non-subjective as possible. MULTIMOORA, tested after robustness, showed positive results.

http://www.usfx.bo/nueva/vicerrectorado/citas/TECNOLOGICAS_20/Informatica/33.pdf

Robustness of MULTIMOORA: A Method for Multi-Objective Optimization

Multi‐objective analysis is a popular tool to solve many economic, managerial and construction problems. The objective of this research is to develop and implement a methodology for multi‐objective optimization of multi‐alternative decisions in road construction. After a rough overview of the articles dealing with the multi‐objective decision and assessment of road design alternatives described by discrete values, Multi‐Objective Optimization on the basis of the Ratio Analysis (MOORA) method was selected. This method focuses on a matrix of alternative responses on the objectives. A case study demonstrates the concept of multi‐objective optimization of road design alternatives and the best road design alternative is determined.

Multi‐objective decision‐making for road design

‘footrule’ for measuring correlation

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‘footrule’ for measuring correlation