PARETO ANALYSIS VIS-A-VIS BALANCE SPACE APPROACH IN MULTIOBJECTIVE GLOBAL OPTIMIZATION

There is much controversy about the balance space approach, introduced first in Ref. 1, pp. 138-140, with the consideration of the balance n umber and balance vectors, and then further developed in Ref. 2, with the consideration of balance points and balance sets. There were attem pts to identify the balance space approach with some other methods of multiobjective optimization, notably the method proposed in Ref. 3 and most recently Pareto analysis, as presented in Ref 4. In this paper, we compare Pareto analysis with the balance space approach on several examples to demonstrate the interrelation and the differences of the t wo methods. As a byproduct, it is shown that, in some cases, the entir e Pareto sets, proper and adjoint, can be determined very simply, with out any special investigation of the (nonscalarized, nonconvex) multio bjective global optimization problem. The method of parameter introduc tion is presented in application to determining the Pareto sets and ba lance set. The use of computer graphics software complemented with the Gauss-Jordan matrix reduction algorithm is proposed for a class of ot herwise intractable problems with nonconvex constraint sets.