It is worth noting that, the performance of most approaches in MCOPs is more or less dependent on the NDF geometry.
In this paper, an efficient numerical method for solving MCOPs based on PS scalarization has been presented.
An MCOP with more than one conflicting criteria is given by
MCOP: min f(x), p [greater than or equal to] 2 s.t.
A feasible point [??] [member of] X is called A weakly efficient solution (WES) of MCOP (1) if there is no other x [member of] X in which f (x) < f (x).
An efficient solution (ES) of MCOP (1), if there is no other x [member of] X in which f(x) [less than or equal to] f(x).
The collection of all ES and WES of MCOP (1) is represented by [X.sub.E] and [X.sub.wE], respectively.
The point [y.sup.I] = ([y.sup.I.sub.1],..., [y.sup.I.sub.p]) is called the MCOP ideal point (1) where I min [y.sup.I.sub.i] = [min.sub.x[member of]X] [f.sub.i](x), i = 1,..., p.
The following model based on the ordering cone [mathematical expression not reproducible] can be solved in order to determine the ES of MCOP (1):
Assume [bar.x] be an ES of MCOP (1), then (0,[bar.x]) is an optimal solution (OS) of (3) with a = f ([bar.x]) and arbitrary r [not equal to] [0.sub.p].
Assume ([bar.t],[bar.x]) be an OS of (3), then [bar.x] is a WES of MCOP (1) and a + [bar.t] r [??] f ([bar.x]).